Subgroups — #30652881

Order 16256.

1336 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550618	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550617	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550616	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550614	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550555	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550553	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550551	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550522	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550521	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550519	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550518	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550517	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550515	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×D₅₀₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550510	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550510	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550465	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550465	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550464	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550462	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550460	C₂	1	1	yes	maximal, characteristic, complemented
22	#22550444	C₂	1	1	yes	maximal, characteristic, complemented
23	#22550442	C₂	1	1	yes	maximal, characteristic, complemented
24	#22550441	C₂	1	1	yes	maximal, characteristic, complemented
25	#22550437	C₂	1	1	yes	maximal, characteristic, complemented
26	#22550436	C₂	1	1	yes	maximal, characteristic, complemented
27	#22550434	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×#16861179	C₂	1	1	yes	maximal, characteristic, complemented
29	#120×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
30	#120×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#538×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14523249	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
48	#16861206	C₂²	1	1	yes	characteristic, complemented
49	#16861205	C₂²	1	1	yes	characteristic, complemented
50	#16861205	C₂²	1	1	yes	characteristic, complemented
51	#16861205	C₂²	1	1	yes	characteristic, complemented
52	#16861204	C₂²	1	1	yes	characteristic, complemented
53	#16861204	C₂²	1	1	yes	characteristic, complemented
54	#16861204	C₂²	1	1	yes	characteristic, complemented
55	#16861203	C₂²	1	1	yes	characteristic, complemented
56	#16861202	C₂²	1	1	yes	characteristic, complemented
57	#16861202	C₂²	1	1	yes	characteristic, complemented
58	#16861198	C₂²	1	1	yes	characteristic, complemented
59	#16861198	C₂²	1	1	yes	characteristic, complemented
60	#16861197	C₂²	1	1	yes	characteristic, complemented
61	#16861197	C₂²	1	1	yes	characteristic, complemented
62	#16861195	C₂²	1	1	yes	characteristic, complemented
63	#16861195	C₂²	1	1	yes	characteristic, complemented
64	#16861195	C₂²	1	1	yes	characteristic, complemented
65	#16861195	C₂²	1	1	yes	characteristic, complemented
66	#16861195	C₂²	1	1	yes	characteristic, complemented
67	#16861195	C₂²	1	1	yes	characteristic, complemented
68	#16861194	C₂²	1	1	yes	characteristic, complemented
69	#16861194	C₂²	1	1	yes	characteristic, complemented
70	#16861194	C₂²	1	1	yes	characteristic, complemented
71	#16861194	C₂²	1	1	yes	characteristic, complemented
72	#16861194	C₂²	1	1	yes	characteristic, complemented
73	#16861194	C₂²	1	1	yes	characteristic, complemented
74	#16861194	C₂²	1	1	yes	characteristic, complemented
75	#16861193	C₂²	1	1	yes	characteristic, complemented
76	#16861193	C₂²	1	1	yes	characteristic, complemented
77	#16861192	C₂²	1	1	yes	characteristic, complemented
78	#16861191	C₂²	1	1	yes	characteristic, complemented
79	#16861191	C₂²	1	1	yes	characteristic, complemented
80	#16861191	C₂²	1	1	yes	characteristic, complemented
81	#16861191	C₂²	1	1	yes	characteristic, complemented
82	#16861191	C₂²	1	1	yes	characteristic, complemented
83	#16861190	C₂²	1	1	yes	characteristic, complemented
84	#16861189	C₂²	1	1	yes	characteristic, complemented
85	#16861188	C₂²	1	1	yes	characteristic, complemented
86	#16861187	C₂²	1	1	yes	characteristic, complemented
87	#16861187	C₂²	1	1	yes	characteristic, complemented
88	#16861185	C₂²	1	1	yes	characteristic, complemented
89	#16861184	C₂²	1	1	yes	characteristic, complemented
90	#16861184	C₂²	1	1	yes	characteristic, complemented
91	#16861184	C₂²	1	1	yes	characteristic, complemented
92	#16861184	C₂²	1	1	yes	characteristic, complemented
93	#16861184	C₂²	1	1	yes	characteristic, complemented
94	#16861184	C₂²	1	1	yes	characteristic, complemented
95	#16861184	C₂²	1	1	yes	characteristic, complemented
96	#16861183	C₂²	1	1	yes	characteristic, complemented
97	#16861183	C₂²	1	1	yes	characteristic, complemented
98	#16861183	C₂²	1	1	yes	characteristic, complemented
99	#16861183	C₂²	1	1	yes	characteristic, complemented
100	#16861182	C₂²	1	1	yes	characteristic, complemented
101	#16861182	C₂²	1	1	yes	characteristic, complemented
102	#16861182	C₂²	1	1	yes	characteristic, complemented
103	#16861182	C₂²	1	1	yes	characteristic, complemented
104	#16861182	C₂²	1	1	yes	characteristic, complemented
105	#16861182	C₂²	1	1	yes	characteristic, complemented
106	#16861182	C₂²	1	1	yes	characteristic, complemented
107	#16861182	C₂²	1	1	yes	characteristic, complemented
108	#16861182	C₂²	1	1	yes	characteristic, complemented
109	#16861182	C₂²	1	1	yes	characteristic, complemented
110	#16861182	C₂²	1	1	yes	characteristic, complemented
111	#16861181	C₂²	1	1	yes	characteristic, complemented
112	#16861181	C₂²	1	1	yes	characteristic, complemented
113	#16861181	C₂²	1	1	yes	characteristic, complemented
114	#16861180	C₂²	1	1	yes	characteristic, complemented
115	#16861180	C₂²	1	1	yes	characteristic, complemented
116	#16861179	C₂²	1	1	yes	characteristic
117	#16861179	C₂²	1	1	yes	characteristic
118	#16861179	C₂²	1	1	yes	characteristic, complemented
119	#16861179	C₂²	1	1	yes	characteristic, complemented
120	#16861179	C₂²	1	1	yes	characteristic, complemented
121	#16861179	C₂²	1	1	yes	characteristic, complemented
122	#16861179	C₂²	1	1	yes	characteristic, complemented
123	#16861179	C₂²	1	1	yes	characteristic, complemented
124	#16861179	C₂²	1	1	yes	characteristic, complemented
125	#16861179	C₂²	1	1	yes	characteristic, complemented
126	#16861179	C₂²	1	1	yes	characteristic, complemented
127	#16861179	C₂²	1	1	yes	characteristic, complemented
128	#16861179	C₂²	1	1	yes	characteristic, complemented
129	#16861179	C₂²	1	1	yes	characteristic, complemented
130	#16861179	C₂²	1	1	yes	characteristic, complemented
131	#16861179	C₂²	1	1	yes	characteristic, complemented
132	#16861179	C₂²	1	1	yes	characteristic, complemented
133	#16861179	C₂²	1	1	yes	characteristic, complemented
134	#16861179	C₂²	1	1	yes	characteristic, complemented
135	#16861179	C₂²	1	1	yes	characteristic, complemented
136	#16861178	C₂²	1	1	yes	characteristic, complemented
137	#16861178	C₂²	1	1	yes	characteristic, complemented
138	#16861177	C₂²	1	1	yes	characteristic
139	#16861177	C₂²	1	1	yes	characteristic, complemented
140	#16861177	C₂²	1	1	yes	characteristic, complemented
141	#16861177	C₂²	1	1	yes	characteristic, complemented
142	#16861177	C₂²	1	1	yes	characteristic, complemented
143	#16861177	C₂²	1	1	yes	characteristic, complemented
144	#16861177	C₂²	1	1	yes	characteristic, complemented
145	#16861177	C₂²	1	1	yes	characteristic, complemented
146	#16861177	C₂²	1	1	yes	characteristic, complemented
147	#16861177	C₂²	1	1	yes	characteristic, complemented
148	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
149	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
150	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
151	#16861171	C₂²	1	1	yes	characteristic, complemented
152	#16861171	C₂²	1	1	yes	characteristic, complemented
153	#16861171	C₂²	1	1	yes	characteristic, complemented
154	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
155	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
156	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	#16861167	C₂²	1	1	yes	characteristic, complemented
159	#16861166	C₂²	1	1	yes	characteristic, complemented
160	#16861165	C₂²	1	1	yes	characteristic, complemented
161	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
173	#126×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
174	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
175	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
177	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
179	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
180	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
181	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
182	#120×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
183	#120×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₂₇	—	4	2	no	—
188	C₂³×D₁₂₇	—	4	2	no	—
189	C₂³×D₁₂₇	—	4	2	no	—
190	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
191	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
192	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
193	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
194	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
195	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
196	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
197	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
198	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
199	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
200	#14523249	—	4	2	no	—
201	#14523248	—	4	2	no	—
202	#14523247	—	4	2	no	—
203	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic, complemented
204	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic, complemented
205	C₂×D₅₀₈	—	4	2	no	—
206	C₂×D₅₀₈	—	4	2	no	—
207	C₂×D₅₀₈	—	4	2	no	—
208	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
209	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
210	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
211	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
212	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
213	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
214	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
215	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
216	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
217	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
218	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
219	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
220	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
221	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
222	C₂×D₅₀₈	C₂³	1	1	yes	characteristic, complemented
223	C₂×D₅₀₈	C₂³	1	1	yes	characteristic, complemented
224	C₂×D₅₀₈	C₂³	1	1	yes	characteristic, complemented
225	C₂×D₅₀₈	C₂³	1	1	yes	characteristic, complemented
226	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
227	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic, complemented
244	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic, complemented
245	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic, complemented
246	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic, complemented
247	D₄×D₁₂₇	—	4	2	no	—
248	D₄×D₁₂₇	—	4	2	no	—
249	D₄×D₁₂₇	—	4	2	no	—
250	D₄×D₁₂₇	—	4	2	no	—
251	D₄×D₁₂₇	—	4	2	no	—
252	D₄×D₁₂₇	—	4	2	no	—
253	D₄×D₁₂₇	—	4	2	no	—
254	D₄×D₁₂₇	—	4	2	no	—
255	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
256	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
257	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
264	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
265	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
266	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
267	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
268	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
269	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
270	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
271	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
272	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
273	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
274	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
275	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
276	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
277	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
278	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
279	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
280	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
281	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
288	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
289	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
310	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
311	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
312	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
313	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
314	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
315	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
316	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
317	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
318	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
319	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
320	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
321	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
322	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
323	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
324	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
325	C₂⁴×C₁₂₇	C₂³	1	1	yes	characteristic
326	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
327	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
328	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
329	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
330	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
331	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
332	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
333	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
334	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
335	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
336	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
337	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
338	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
339	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
340	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
341	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
342	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
343	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
344	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
349	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
350	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
351	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
352	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
353	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
354	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
355	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
356	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
357	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
358	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
359	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
360	C₂²×D₁₂₇	—	2	2	no	—
361	C₂²×D₁₂₇	—	2	2	no	—
362	C₂²×D₁₂₇	—	2	2	no	—
363	C₂²×D₁₂₇	—	2	2	no	—
364	C₂²×D₁₂₇	—	2	2	no	—
365	C₂²×D₁₂₇	—	2	2	no	—
366	C₂²×D₁₂₇	—	2	2	no	—
367	C₂²×D₁₂₇	—	2	2	no	—
368	C₂²×D₁₂₇	—	2	2	no	—
369	C₂²×D₁₂₇	—	2	2	no	—
370	C₂²×D₁₂₇	—	2	2	no	—
371	C₂²×D₁₂₇	—	4	1	no	—
372	C₂²×D₁₂₇	—	4	1	no	—
373	C₂²×D₁₂₇	—	4	1	no	—
374	C₂²×D₁₂₇	—	4	1	no	—
375	C₂²×D₁₂₇	—	4	1	no	—
376	C₂²×D₁₂₇	—	4	1	no	—
377	C₂²×D₁₂₇	—	4	1	no	—
378	C₂²×D₁₂₇	—	4	1	no	—
379	C₂²×D₁₂₇	—	4	1	no	—
380	C₂²×D₁₂₇	—	4	1	no	—
381	C₂²×D₁₂₇	—	4	1	no	—
382	C₂²×D₁₂₇	—	4	1	no	—
383	C₂²×D₁₂₇	—	4	1	no	—
384	C₂²×D₁₂₇	—	4	1	no	—
385	C₂²×D₁₂₇	—	4	1	no	—
386	C₂²×D₁₂₇	—	4	1	no	—
387	C₂²×D₁₂₇	—	4	1	no	—
388	C₂²×D₁₂₇	—	4	1	no	—
389	C₂²×D₁₂₇	—	4	1	no	—
390	C₂²×D₁₂₇	—	4	16	no	—
391	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
392	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
393	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
394	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
395	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
396	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
397	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
398	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
399	Dic₂₅₄	—	4	1	no	—
400	Dic₂₅₄	—	4	1	no	—
401	D₅₀₈	—	2	2	no	—
402	D₅₀₈	—	2	2	no	—
403	D₅₀₈	—	2	2	no	—
404	D₅₀₈	—	2	2	no	—
405	D₅₀₈	—	2	2	no	—
406	D₅₀₈	—	2	2	no	—
407	D₅₀₈	—	4	1	no	—
408	D₅₀₈	—	4	1	no	—
409	D₅₀₈	—	4	1	no	—
410	D₅₀₈	—	4	1	no	—
411	D₅₀₈	—	4	1	no	—
412	D₅₀₈	—	4	1	no	—
413	D₅₀₈	—	4	1	no	—
414	D₅₀₈	—	4	1	no	—
415	D₅₀₈	—	4	1	no	—
416	D₅₀₈	—	4	1	no	—
417	D₅₀₈	—	4	1	no	—
418	D₅₀₈	—	4	1	no	—
419	C₂²⋊D₁₂₇	—	2	2	no	—
420	C₂²⋊D₁₂₇	—	2	2	no	—
421	C₂²⋊D₁₂₇	—	2	2	no	—
422	C₂²⋊D₁₂₇	—	2	2	no	—
423	C₂²⋊D₁₂₇	—	4	1	no	—
424	C₂²⋊D₁₂₇	—	4	1	no	—
425	C₂²⋊D₁₂₇	—	4	1	no	—
426	C₂²⋊D₁₂₇	—	4	1	no	—
427	C₂²⋊D₁₂₇	—	4	1	no	—
428	C₂²⋊D₁₂₇	—	4	1	no	—
429	C₂²⋊D₁₂₇	—	4	1	no	—
430	C₂²⋊D₁₂₇	—	4	1	no	—
431	C₂²⋊D₁₂₇	—	4	1	no	—
432	C₂²⋊D₁₂₇	—	4	1	no	—
433	C₂²⋊D₁₂₇	—	4	1	no	—
434	C₂²⋊D₁₂₇	—	4	1	no	—
435	C₂²⋊D₁₂₇	—	4	1	no	—
436	C₂²⋊D₁₂₇	—	4	1	no	—
437	C₂²⋊D₁₂₇	—	4	1	no	—
438	C₂²⋊D₁₂₇	—	4	1	no	—
439	C₂×Dic₁₂₇	—	2	2	no	—
440	C₂×Dic₁₂₇	—	4	1	no	—
441	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
449	C₄×D₁₂₇	—	2	2	no	—
450	C₄×D₁₂₇	—	2	2	no	—
451	C₄×D₁₂₇	—	4	1	no	—
452	C₄×D₁₂₇	—	4	1	no	—
453	C₄×D₁₂₇	—	4	1	no	—
454	C₄×D₁₂₇	—	4	1	no	—
455	C₄×D₁₂₇	—	4	1	no	—
456	C₄×D₁₂₇	—	4	1	no	—
457	C₄×D₁₂₇	—	4	1	no	—
458	C₄×D₁₂₇	—	4	1	no	—
459	C₄×D₁₂₇	—	4	1	no	—
460	C₄×D₁₂₇	—	4	1	no	—
461	C₂³×C₁₂₇	—	2	2	no	—
462	C₂³×C₁₂₇	—	4	1	no	—
463	C₂³×C₁₂₇	—	4	1	no	—
464	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
465	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
466	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
467	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
468	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
469	Q₈×C₁₂₇	—	4	1	no	—
470	D₄×C₁₂₇	—	2	2	no	—
471	D₄×C₁₂₇	—	2	2	no	—
472	D₄×C₁₂₇	—	4	1	no	—
473	D₄×C₁₂₇	—	4	1	no	—
474	D₄×C₁₂₇	—	4	1	no	—
475	D₄×C₁₂₇	—	4	1	no	—
476	D₄×C₁₂₇	—	4	1	no	—
477	C₂×C₄×C₁₂₇	—	4	1	no	—
478	C₂×C₄×C₁₂₇	—	4	1	no	—
479	C₂×C₄×C₁₂₇	—	4	1	no	—
480	C₂×C₄×C₁₂₇	—	4	1	no	—
481	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
482	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
483	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
484	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
485	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
486	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
487	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
488	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
489	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
490	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
491	C₂²×C₁₂₇	—	2	1	no	—
492	C₂²×C₁₂₇	—	2	1	no	—
493	C₂²×C₁₂₇	—	2	1	no	—
494	C₂²×C₁₂₇	—	2	1	no	—
495	C₂²×C₁₂₇	—	2	1	no	—
496	C₂²×C₁₂₇	—	2	1	no	—
497	C₂²×C₁₂₇	—	2	1	no	—
498	C₂²×C₁₂₇	—	2	1	no	—
499	C₂²×C₁₂₇	—	2	1	no	—
500	C₂²×C₁₂₇	—	2	1	no	—
501	C₂²×C₁₂₇	—	2	1	no	—
502	C₂²×C₁₂₇	—	2	1	no	—
503	C₂²×C₁₂₇	—	2	1	no	—
504	C₂²×C₁₂₇	—	2	1	no	—
505	C₂²×C₁₂₇	—	4	4	no	—
506	C₂²×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
507	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
508	C₂×D₁₂₇	—	2	1	no	—
509	C₂×D₁₂₇	—	2	1	no	—
510	C₂×D₁₂₇	—	2	1	no	—
511	C₂×D₁₂₇	—	2	1	no	—
512	C₂×D₁₂₇	—	2	1	no	—
513	C₂×D₁₂₇	—	2	1	no	—
514	C₂×D₁₂₇	—	2	1	no	—
515	C₂×D₁₂₇	—	2	1	no	—
516	C₂×D₁₂₇	—	2	1	no	—
517	C₂×D₁₂₇	—	2	1	no	—
518	C₂×D₁₂₇	—	2	1	no	—
519	C₂×D₁₂₇	—	2	1	no	—
520	C₂×D₁₂₇	—	2	1	no	—
521	C₂×D₁₂₇	—	2	1	no	—
522	C₂×D₁₂₇	—	2	1	no	—
523	C₂×D₁₂₇	—	2	1	no	—
524	C₂×D₁₂₇	—	2	1	no	—
525	C₂×D₁₂₇	—	2	1	no	—
526	C₂×D₁₂₇	—	2	1	no	—
527	C₂×D₁₂₇	—	2	1	no	—
528	C₂×D₁₂₇	—	2	1	no	—
529	C₂×D₁₂₇	—	2	1	no	—
530	C₂×D₁₂₇	—	4	4	no	—
531	C₂×D₁₂₇	—	4	4	no	—
532	C₂×D₁₂₇	—	4	4	no	—
533	C₂×D₁₂₇	—	4	4	no	—
534	C₂×D₁₂₇	—	4	4	no	—
535	C₂×D₁₂₇	—	4	4	no	—
536	C₂×D₁₂₇	—	8	2	no	—
537	C₂×D₁₂₇	—	8	2	no	—
538	C₂×D₁₂₇	—	8	2	no	—
539	C₂×D₁₂₇	—	8	2	no	—
540	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
541	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
542	C₄×C₁₂₇	—	2	1	no	—
543	C₄×C₁₂₇	—	2	1	no	—
544	C₄×C₁₂₇	—	2	1	no	—
545	C₄×C₁₂₇	—	2	1	no	—
546	C₄×C₁₂₇	—	2	1	no	—
547	C₄×C₁₂₇	—	2	1	no	—
548	C₄×C₁₂₇	—	2	1	no	—
549	C₄×C₁₂₇	—	2	1	no	—
550	C₄×C₁₂₇	—	2	1	no	—
551	C₄×C₁₂₇	—	2	1	no	—
552	Dic₁₂₇	—	2	1	no	—
553	Dic₁₂₇	—	2	1	no	—
554	Dic₁₂₇	—	2	1	no	—
555	Dic₁₂₇	—	2	1	no	—
556	Dic₁₂₇	—	2	1	no	—
557	Dic₁₂₇	—	2	1	no	—
558	Dic₁₂₇	—	2	1	no	—
559	Dic₁₂₇	—	2	1	no	—
560	C₂×C₁₂₇	—	2	2	no	—
561	C₂×C₁₂₇	—	4	1	no	—
562	C₂×C₁₂₇	—	4	1	no	—
563	C₂×C₁₂₇	—	4	1	no	—
564	C₂×C₁₂₇	—	4	1	no	—
565	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	D₁₂₇	—	2	2	no	—
569	D₁₂₇	—	2	2	no	—
570	D₁₂₇	—	4	1	no	—
571	D₁₂₇	—	4	1	no	—
572	D₁₂₇	—	4	1	no	—
573	D₁₂₇	—	4	1	no	—
574	D₁₂₇	—	4	1	no	—
575	D₁₂₇	—	4	1	no	—
576	#3532	—	127	1	no	maximal, Sylow
577	C₁₂₇	#3532	1	1	yes	characteristic, complemented, Sylow
578	H(3,𝔽₄)	—	127	1	no	—
579	#560	—	127	1	no	—
580	#560	—	127	1	no	—
581	#560	—	127	1	no	—
582	#551	—	127	1	no	—
583	#551	—	127	1	no	—
584	#551	—	127	1	no	—
585	#546	—	127	1	no	—
586	#546	—	127	1	no	—
587	#546	—	127	1	no	—
588	#546	—	127	1	no	—
589	#546	—	127	1	no	—
590	#546	—	127	1	no	—
591	D₄²	—	127	1	no	—
592	D₄²	—	127	1	no	—
593	D₄²	—	127	1	no	—
594	#538	—	127	1	no	—
595	#538	—	127	1	no	—
596	#538	—	127	1	no	—
597	#538	—	127	1	no	—
598	#538	—	127	1	no	—
599	#538	D₁₂₇	1	1	yes	characteristic, complemented
600	#535	—	127	1	no	—
601	#535	—	127	1	no	—
602	#535	—	127	1	no	—
603	#534	—	127	1	no	—
604	#534	—	127	1	no	—
605	#534	—	127	1	no	—
606	C₂×#120	—	127	1	no	—
607	C₂×#120	—	127	1	no	—
608	C₂×#120	—	127	1	no	—
609	C₂⁵	—	127	1	no	—
610	C₂×#41	—	127	1	no	—
611	C₂×#41	—	127	1	no	—
612	C₂×#41	—	127	1	no	—
613	C₂²×D₄	—	127	1	no	—
614	C₂²×D₄	—	127	1	no	—
615	C₂²×D₄	—	127	1	no	—
616	C₂²×D₄	—	127	1	no	—
617	C₂²×D₄	—	127	1	no	—
618	C₂²×D₄	—	127	1	no	—
619	C₂²×D₄	—	127	1	no	—
620	C₂²×D₄	—	127	1	no	—
621	C₂²×D₄	—	127	1	no	—
622	C₂²×D₄	—	127	1	no	—
623	C₂²×D₄	—	127	1	no	—
624	C₂²×D₄	—	127	1	no	—
625	#127	—	127	1	no	—
626	#127	—	127	1	no	—
627	#127	—	127	1	no	—
628	#127	—	127	1	no	—
629	#126	—	127	1	no	—
630	#126	—	127	1	no	—
631	#126	—	127	1	no	—
632	#126	—	127	1	no	—
633	#126	—	127	1	no	—
634	#126	—	127	1	no	—
635	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
636	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
637	#124	—	127	1	no	—
638	#124	—	127	1	no	—
639	#124	—	127	1	no	—
640	#124	—	127	1	no	—
641	#124	—	127	1	no	—
642	#124	—	127	1	no	—
643	#124	—	127	1	no	—
644	#124	—	127	1	no	—
645	#124	—	127	1	no	—
646	#124	—	127	1	no	—
647	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
648	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
649	#123	—	127	1	no	—
650	#123	—	127	1	no	—
651	#123	—	127	1	no	—
652	#123	—	127	1	no	—
653	#123	—	127	1	no	—
654	#123	—	127	1	no	—
655	#123	—	127	1	no	—
656	#123	—	127	1	no	—
657	#123	—	127	1	no	—
658	#123	—	127	1	no	—
659	#123	—	127	1	no	—
660	#123	—	127	1	no	—
661	#123	—	127	1	no	—
662	#123	—	127	1	no	—
663	#123	—	127	1	no	—
664	#123	—	127	1	no	—
665	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
666	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
667	C₂²⋊Q₈	—	127	1	no	—
668	C₂²⋊Q₈	—	127	1	no	—
669	C₂²⋊Q₈	—	127	1	no	—
670	C₂²⋊Q₈	—	127	1	no	—
671	C₂²⋊Q₈	—	127	1	no	—
672	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
673	#121	—	127	1	no	—
674	#121	—	127	1	no	—
675	#121	—	127	1	no	—
676	#121	—	127	1	no	—
677	#121	—	127	1	no	—
678	#121	—	127	1	no	—
679	#121	—	127	1	no	—
680	#121	—	127	1	no	—
681	#121	—	127	1	no	—
682	#121	—	127	1	no	—
683	#121	—	127	1	no	—
684	#121	—	127	1	no	—
685	#121	—	127	1	no	—
686	#121	—	127	1	no	—
687	#121	—	127	1	no	—
688	#121	—	127	1	no	—
689	#121	—	127	1	no	—
690	#121	—	127	1	no	—
691	#121	—	127	1	no	—
692	#121	—	127	1	no	—
693	#121	—	127	1	no	—
694	#121	—	127	1	no	—
695	#121	—	127	1	no	—
696	#121	—	127	1	no	—
697	#121	—	127	1	no	—
698	#121	—	127	1	no	—
699	#121	—	127	1	no	—
700	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
701	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
702	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
703	#120	—	127	1	no	—
704	#120	—	127	1	no	—
705	#120	—	127	1	no	—
706	#120	—	127	1	no	—
707	#120	—	127	1	no	—
708	#120	—	127	1	no	—
709	#120	—	127	1	no	—
710	#120	—	127	1	no	—
711	#120	—	127	1	no	—
712	#120	—	127	1	no	—
713	#120	—	127	1	no	—
714	#120	—	127	1	no	—
715	#120	—	127	1	no	—
716	#120	—	127	1	no	—
717	#120	—	127	1	no	—
718	#120	—	127	1	no	—
719	#120	—	127	1	no	—
720	#120	—	127	1	no	—
721	#120	—	127	1	no	—
722	#120	—	127	1	no	—
723	#120	—	127	1	no	—
724	#120	—	127	1	no	—
725	#120	—	127	1	no	—
726	#120	—	127	1	no	—
727	#120	—	127	1	no	—
728	#120	—	127	1	no	—
729	#120	—	127	1	no	—
730	#120	—	127	1	no	—
731	#120	—	127	1	no	—
732	#120	—	127	1	no	—
733	#120	—	127	1	no	—
734	#120	—	127	1	no	—
735	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
736	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
737	C₄×D₄	—	127	1	no	—
738	C₄×D₄	—	127	1	no	—
739	C₄×D₄	—	127	1	no	—
740	C₄×D₄	—	127	1	no	—
741	C₄×D₄	—	127	1	no	—
742	C₄×D₄	—	127	1	no	—
743	C₄×D₄	—	127	1	no	—
744	C₄×D₄	—	127	1	no	—
745	C₄×D₄	—	127	1	no	—
746	C₄×D₄	—	127	1	no	—
747	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
748	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
749	#117	—	127	1	no	—
750	#117	—	127	1	no	—
751	#117	—	127	1	no	—
752	C₂×C₂²⋊C₄	—	127	1	no	—
753	C₂×C₂²⋊C₄	—	127	1	no	—
754	C₂×C₂²⋊C₄	—	127	1	no	—
755	C₂×C₂²⋊C₄	—	127	1	no	—
756	C₂×C₂²⋊C₄	—	127	1	no	—
757	C₂×C₂²⋊C₄	—	127	1	no	—
758	C₂×C₂²⋊C₄	—	127	1	no	—
759	C₂×C₂²⋊C₄	—	127	1	no	—
760	C₂×C₂²⋊C₄	—	127	1	no	—
761	C₂×C₂²⋊C₄	—	127	1	no	—
762	C₂×C₂²⋊C₄	—	127	1	no	—
763	C₂×C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
764	C₂⁴	—	127	1	no	—
765	C₂⁴	—	127	1	no	—
766	C₂⁴	—	127	1	no	—
767	C₂⁴	—	127	1	no	—
768	C₂⁴	—	127	1	no	—
769	C₂⁴	—	127	1	no	—
770	C₂⁴	—	127	1	no	—
771	C₂⁴	—	127	1	no	—
772	C₂⁴	—	127	1	no	—
773	C₂⁴	—	127	1	no	—
774	C₂⁴	—	508	2	no	—
775	C₂⁴	—	508	2	no	—
776	C₂⁴	—	508	2	no	—
777	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
778	#41	—	508	2	no	—
779	#41	—	508	2	no	—
780	#41	—	508	2	no	—
781	C₂×Q₈	—	127	1	no	—
782	C₂×Q₈	—	127	1	no	—
783	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
784	C₂×D₄	—	127	1	no	—
785	C₂×D₄	—	127	1	no	—
786	C₂×D₄	—	127	1	no	—
787	C₂×D₄	—	127	1	no	—
788	C₂×D₄	—	127	1	no	—
789	C₂×D₄	—	127	1	no	—
790	C₂×D₄	—	127	1	no	—
791	C₂×D₄	—	127	1	no	—
792	C₂×D₄	—	127	1	no	—
793	C₂×D₄	—	127	1	no	—
794	C₂×D₄	—	127	1	no	—
795	C₂×D₄	—	127	1	no	—
796	C₂×D₄	—	127	1	no	—
797	C₂×D₄	—	127	1	no	—
798	C₂×D₄	—	127	1	no	—
799	C₂×D₄	—	127	1	no	—
800	C₂×D₄	—	127	1	no	—
801	C₂×D₄	—	127	1	no	—
802	C₂×D₄	—	127	1	no	—
803	C₂×D₄	—	127	1	no	—
804	C₂×D₄	—	127	1	no	—
805	C₂×D₄	—	127	1	no	—
806	C₂×D₄	—	127	1	no	—
807	C₂×D₄	—	127	1	no	—
808	C₂×D₄	—	127	1	no	—
809	C₂×D₄	—	127	1	no	—
810	C₂×D₄	—	127	1	no	—
811	C₂×D₄	—	127	1	no	—
812	C₂×D₄	—	127	1	no	—
813	C₂×D₄	—	127	1	no	—
814	C₂×D₄	—	127	1	no	—
815	C₂×D₄	—	127	1	no	—
816	C₂×D₄	—	127	1	no	—
817	C₂×D₄	—	127	1	no	—
818	C₂×D₄	—	127	1	no	—
819	C₂×D₄	—	127	1	no	—
820	C₂×D₄	—	127	1	no	—
821	C₂×D₄	—	127	1	no	—
822	C₂×D₄	—	508	2	no	—
823	C₂×D₄	—	508	2	no	—
824	C₂×D₄	—	508	2	no	—
825	C₂×D₄	—	508	2	no	—
826	C₂×D₄	—	508	2	no	—
827	C₂×D₄	—	508	2	no	—
828	C₂×D₄	—	508	2	no	—
829	C₂×D₄	—	508	2	no	—
830	C₂×D₄	—	508	2	no	—
831	C₂×D₄	—	508	2	no	—
832	C₂×D₄	—	508	2	no	—
833	C₂×D₄	—	508	2	no	—
834	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
835	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
836	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
837	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
838	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
839	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
840	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
841	C₂²×C₄	—	127	1	no	—
842	C₂²×C₄	—	127	1	no	—
843	C₂²×C₄	—	127	1	no	—
844	C₂²×C₄	—	127	1	no	—
845	C₂²×C₄	—	127	1	no	—
846	C₂²×C₄	—	127	1	no	—
847	C₂²×C₄	—	127	1	no	—
848	C₂²×C₄	—	127	1	no	—
849	C₂²×C₄	—	127	1	no	—
850	C₂²×C₄	—	127	1	no	—
851	C₂²×C₄	—	127	1	no	—
852	C₂²×C₄	—	127	1	no	—
853	C₂²×C₄	—	127	1	no	—
854	C₂²×C₄	—	127	1	no	—
855	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
858	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
859	C₄⋊C₄	—	127	1	no	—
860	C₄⋊C₄	—	127	1	no	—
861	C₄⋊C₄	—	127	1	no	—
862	C₄⋊C₄	—	127	1	no	—
863	C₄⋊C₄	—	127	1	no	—
864	C₄⋊C₄	—	127	1	no	—
865	C₄⋊C₄	—	127	1	no	—
866	C₄⋊C₄	—	127	1	no	—
867	C₄⋊C₄	—	127	1	no	—
868	C₄⋊C₄	—	127	1	no	—
869	C₄⋊C₄	—	127	1	no	—
870	C₄⋊C₄	—	127	1	no	—
871	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
872	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
873	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
874	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
875	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
876	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
877	C₂²⋊C₄	—	127	1	no	—
878	C₂²⋊C₄	—	127	1	no	—
879	C₂²⋊C₄	—	127	1	no	—
880	C₂²⋊C₄	—	127	1	no	—
881	C₂²⋊C₄	—	127	1	no	—
882	C₂²⋊C₄	—	127	1	no	—
883	C₂²⋊C₄	—	127	1	no	—
884	C₂²⋊C₄	—	127	1	no	—
885	C₂²⋊C₄	—	127	1	no	—
886	C₂²⋊C₄	—	127	1	no	—
887	C₂²⋊C₄	—	127	1	no	—
888	C₂²⋊C₄	—	127	1	no	—
889	C₂²⋊C₄	—	127	1	no	—
890	C₂²⋊C₄	—	127	1	no	—
891	C₂²⋊C₄	—	127	1	no	—
892	C₂²⋊C₄	—	127	1	no	—
893	C₂²⋊C₄	—	127	1	no	—
894	C₂²⋊C₄	—	127	1	no	—
895	C₂²⋊C₄	—	127	1	no	—
896	C₂²⋊C₄	—	127	1	no	—
897	C₂²⋊C₄	—	127	1	no	—
898	C₂²⋊C₄	—	127	1	no	—
899	C₂²⋊C₄	—	127	1	no	—
900	C₂²⋊C₄	—	127	1	no	—
901	C₂²⋊C₄	—	127	1	no	—
902	C₂²⋊C₄	—	127	1	no	—
903	C₂²⋊C₄	—	127	1	no	—
904	C₂²⋊C₄	—	127	1	no	—
905	C₂²⋊C₄	—	127	1	no	—
906	C₂²⋊C₄	—	127	1	no	—
907	C₂²⋊C₄	—	127	1	no	—
908	C₂²⋊C₄	—	127	1	no	—
909	C₂²⋊C₄	—	127	1	no	—
910	C₂²⋊C₄	—	127	1	no	—
911	C₂²⋊C₄	—	127	1	no	—
912	C₂²⋊C₄	—	127	1	no	—
913	C₂²⋊C₄	—	127	1	no	—
914	C₂²⋊C₄	—	127	1	no	—
915	C₂²⋊C₄	—	127	1	no	—
916	C₂²⋊C₄	—	127	1	no	—
917	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
918	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
919	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
920	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
921	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
922	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
923	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
924	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
925	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
926	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
927	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
928	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
929	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
930	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
931	C₄²	—	127	1	no	—
932	C₄²	—	127	1	no	—
933	C₄²	—	127	1	no	—
934	C₄²	—	127	1	no	—
935	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
936	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
937	C₂³	—	2	2	no	—
938	C₂³	—	4	1	no	—
939	C₂³	—	4	1	no	—
940	C₂³	—	127	1	no	—
941	C₂³	—	127	1	no	—
942	C₂³	—	127	1	no	—
943	C₂³	—	127	1	no	—
944	C₂³	—	127	1	no	—
945	C₂³	—	127	1	no	—
946	C₂³	—	127	1	no	—
947	C₂³	—	127	1	no	—
948	C₂³	—	508	1	no	—
949	C₂³	—	508	1	no	—
950	C₂³	—	508	1	no	—
951	C₂³	—	508	1	no	—
952	C₂³	—	508	1	no	—
953	C₂³	—	508	1	no	—
954	C₂³	—	508	1	no	—
955	C₂³	—	508	1	no	—
956	C₂³	—	508	1	no	—
957	C₂³	—	508	1	no	—
958	C₂³	—	508	1	no	—
959	C₂³	—	508	1	no	—
960	C₂³	—	508	1	no	—
961	C₂³	—	508	1	no	—
962	C₂³	—	508	1	no	—
963	C₂³	—	508	1	no	—
964	C₂³	—	508	1	no	—
965	C₂³	—	508	1	no	—
966	C₂³	—	508	1	no	—
967	C₂³	—	508	16	no	—
968	C₂³	—	254	2	no	—
969	C₂³	—	254	2	no	—
970	C₂³	—	254	2	no	—
971	C₂³	—	254	2	no	—
972	C₂³	—	254	2	no	—
973	C₂³	—	254	2	no	—
974	C₂³	—	254	2	no	—
975	C₂³	—	254	2	no	—
976	C₂³	—	254	2	no	—
977	C₂³	—	254	2	no	—
978	C₂³	—	254	2	no	—
979	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
980	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
981	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
982	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
983	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
984	Q₈	—	4	1	no	—
985	Q₈	—	508	1	no	—
986	Q₈	—	508	1	no	—
987	D₄	—	2	2	no	—
988	D₄	—	2	2	no	—
989	D₄	—	4	1	no	—
990	D₄	—	4	1	no	—
991	D₄	—	4	1	no	—
992	D₄	—	4	1	no	—
993	D₄	—	4	1	no	—
994	D₄	—	508	1	no	—
995	D₄	—	508	1	no	—
996	D₄	—	508	1	no	—
997	D₄	—	508	1	no	—
998	D₄	—	508	1	no	—
999	D₄	—	508	1	no	—
1000	D₄	—	508	1	no	—
1001	D₄	—	508	1	no	—
1002	D₄	—	508	1	no	—
1003	D₄	—	508	1	no	—
1004	D₄	—	508	1	no	—
1005	D₄	—	508	1	no	—
1006	D₄	—	508	1	no	—
1007	D₄	—	508	1	no	—
1008	D₄	—	508	1	no	—
1009	D₄	—	508	1	no	—
1010	D₄	—	508	1	no	—
1011	D₄	—	508	1	no	—
1012	D₄	—	508	1	no	—
1013	D₄	—	508	1	no	—
1014	D₄	—	508	1	no	—
1015	D₄	—	508	1	no	—
1016	D₄	—	508	1	no	—
1017	D₄	—	508	1	no	—
1018	D₄	—	508	1	no	—
1019	D₄	—	508	1	no	—
1020	D₄	—	508	1	no	—
1021	D₄	—	508	1	no	—
1022	D₄	—	254	2	no	—
1023	D₄	—	254	2	no	—
1024	D₄	—	254	2	no	—
1025	D₄	—	254	2	no	—
1026	D₄	—	254	2	no	—
1027	D₄	—	254	2	no	—
1028	D₄	—	254	2	no	—
1029	D₄	—	254	2	no	—
1030	D₄	—	254	2	no	—
1031	D₄	—	254	2	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	127	1	no	—
1037	C₂×C₄	—	127	1	no	—
1038	C₂×C₄	—	127	1	no	—
1039	C₂×C₄	—	127	1	no	—
1040	C₂×C₄	—	127	1	no	—
1041	C₂×C₄	—	127	1	no	—
1042	C₂×C₄	—	127	1	no	—
1043	C₂×C₄	—	127	1	no	—
1044	C₂×C₄	—	508	1	no	—
1045	C₂×C₄	—	508	1	no	—
1046	C₂×C₄	—	508	1	no	—
1047	C₂×C₄	—	508	1	no	—
1048	C₂×C₄	—	508	1	no	—
1049	C₂×C₄	—	508	1	no	—
1050	C₂×C₄	—	508	1	no	—
1051	C₂×C₄	—	508	1	no	—
1052	C₂×C₄	—	508	1	no	—
1053	C₂×C₄	—	508	1	no	—
1054	C₂×C₄	—	508	1	no	—
1055	C₂×C₄	—	254	2	no	—
1056	C₂×C₄	—	254	2	no	—
1057	C₂×C₄	—	254	2	no	—
1058	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1059	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1060	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1061	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1062	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1063	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1064	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1065	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1066	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1067	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	1	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	4	4	no	—
1083	C₂²	—	127	2	no	—
1084	C₂²	—	127	2	no	—
1085	C₂²	—	1016	2	no	—
1086	C₂²	—	1016	2	no	—
1087	C₂²	—	1016	2	no	—
1088	C₂²	—	1016	2	no	—
1089	C₂²	—	508	4	no	—
1090	C₂²	—	508	4	no	—
1091	C₂²	—	508	4	no	—
1092	C₂²	—	508	4	no	—
1093	C₂²	—	508	4	no	—
1094	C₂²	—	508	4	no	—
1095	C₂²	—	254	1	no	—
1096	C₂²	—	254	1	no	—
1097	C₂²	—	254	1	no	—
1098	C₂²	—	254	1	no	—
1099	C₂²	—	254	1	no	—
1100	C₂²	—	254	1	no	—
1101	C₂²	—	254	1	no	—
1102	C₂²	—	254	1	no	—
1103	C₂²	—	254	1	no	—
1104	C₂²	—	254	1	no	—
1105	C₂²	—	254	1	no	—
1106	C₂²	—	254	1	no	—
1107	C₂²	—	254	1	no	—
1108	C₂²	—	254	1	no	—
1109	C₂²	—	254	1	no	—
1110	C₂²	—	254	1	no	—
1111	C₂²	—	254	1	no	—
1112	C₂²	—	254	1	no	—
1113	C₂²	—	254	1	no	—
1114	C₂²	—	254	1	no	—
1115	C₂²	—	254	1	no	—
1116	C₂²	—	254	1	no	—
1117	C₂²	#16861255	1	2	yes	—
1118	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
1119	C₄	—	2	1	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	254	1	no	—
1130	C₄	—	254	1	no	—
1131	C₄	—	254	1	no	—
1132	C₄	—	254	1	no	—
1133	C₄	—	254	1	no	—
1134	C₄	—	254	1	no	—
1135	C₄	—	254	1	no	—
1136	C₄	—	254	1	no	—
1137	C₂	—	2	2	no	—
1138	C₂	—	4	1	no	—
1139	C₂	—	4	1	no	—
1140	C₂	—	4	1	no	—
1141	C₂	—	4	1	no	—
1142	C₂	—	508	1	no	—
1143	C₂	—	508	1	no	—
1144	C₂	—	508	1	no	—
1145	C₂	—	508	1	no	—
1146	C₂	—	508	1	no	—
1147	C₂	—	508	1	no	—
1148	C₂	—	254	2	no	—
1149	C₂	—	254	2	no	—
1150	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
1151	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
1152	C₂	C₂×#16861255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#538×C₁₂₇	C₂
hypercenter	#538	D₁₂₇
hypocenter	C₁₂₇	#3532
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22550618	C₂	semidirect
2. #22550617	C₂	semidirect
3. #22550616	C₂	semidirect
4. #22550614	C₂	semidirect
5. #22550555	C₂	semidirect
6. #22550553	C₂	semidirect
7. #22550551	C₂	semidirect
8. #22550522	C₂	semidirect
9. #22550521	C₂	semidirect
10. #22550519	C₂	semidirect
11. #22550518	C₂	semidirect
12. #22550517	C₂	semidirect
13. #22550515	C₂	semidirect
14. D₄×D₅₀₈	C₂	semidirect
15. #22550510	C₂	semidirect
16. #22550510	C₂	semidirect
17. #22550465	C₂	semidirect
18. #22550465	C₂	semidirect
19. #22550464	C₂	semidirect
20. #22550462	C₂	semidirect
21. #22550460	C₂	semidirect
22. #22550444	C₂	semidirect
23. #22550442	C₂	semidirect
24. #22550441	C₂	semidirect
25. #22550437	C₂	semidirect
26. #22550436	C₂	semidirect
27. #22550434	C₂	semidirect
28. C₂×#16861179	C₂	semidirect
29. #120×D₁₂₇	C₂	semidirect
30. #120×D₁₂₇	C₂	semidirect
31. #538×C₁₂₇	C₂	semidirect
32. C₂⁴×D₁₂₇	C₂²	semidirect
33. C₂×#14523249	C₂²	semidirect
34. C₂×#14523248	C₂²	semidirect
35. C₂×#14523247	C₂²	semidirect
36. C₂²×D₅₀₈	C₂²	semidirect
37. C₂²×D₅₀₈	C₂²	semidirect
38. C₂²×D₅₀₈	C₂²	semidirect
39. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
40. C₂×D₄×D₁₂₇	C₂²	semidirect
41. C₂×D₄×D₁₂₇	C₂²	semidirect
42. C₂×D₄×D₁₂₇	C₂²	semidirect
43. C₂×D₄×D₁₂₇	C₂²	semidirect
44. C₂×D₄×D₁₂₇	C₂²	semidirect
45. C₂×D₄×D₁₂₇	C₂²	semidirect
46. C₂×D₄×D₁₂₇	C₂²	semidirect
47. C₂×D₄×D₁₂₇	C₂²	semidirect
48. #16861206	C₂²	semidirect
49. #16861205	C₂²	semidirect
50. #16861205	C₂²	semidirect
51. #16861205	C₂²	semidirect
52. #16861204	C₂²	semidirect
53. #16861204	C₂²	semidirect
54. #16861204	C₂²	semidirect
55. #16861203	C₂²	semidirect
56. #16861202	C₂²	semidirect
57. #16861202	C₂²	semidirect
58. #16861198	C₂²	semidirect
59. #16861198	C₂²	semidirect
60. #16861197	C₂²	semidirect
61. #16861197	C₂²	semidirect
62. #16861195	C₂²	semidirect
63. #16861195	C₂²	semidirect
64. #16861195	C₂²	semidirect
65. #16861195	C₂²	semidirect
66. #16861195	C₂²	semidirect
67. #16861195	C₂²	semidirect
68. #16861194	C₂²	semidirect
69. #16861194	C₂²	semidirect
70. #16861194	C₂²	semidirect
71. #16861194	C₂²	semidirect
72. #16861194	C₂²	semidirect
73. #16861194	C₂²	semidirect
74. #16861194	C₂²	semidirect
75. #16861193	C₂²	semidirect
76. #16861193	C₂²	semidirect
77. #16861192	C₂²	semidirect
78. #16861191	C₂²	semidirect
79. #16861191	C₂²	semidirect
80. #16861191	C₂²	semidirect
81. #16861191	C₂²	semidirect
82. #16861191	C₂²	semidirect
83. #16861190	C₂²	semidirect
84. #16861189	C₂²	semidirect
85. #16861188	C₂²	semidirect
86. #16861187	C₂²	semidirect
87. #16861187	C₂²	semidirect
88. #16861185	C₂²	semidirect
89. #16861184	C₂²	semidirect
90. #16861184	C₂²	semidirect
91. #16861184	C₂²	semidirect
92. #16861184	C₂²	semidirect
93. #16861184	C₂²	semidirect
94. #16861184	C₂²	semidirect
95. #16861184	C₂²	semidirect
96. #16861183	C₂²	semidirect
97. #16861183	C₂²	semidirect
98. #16861183	C₂²	semidirect
99. #16861183	C₂²	semidirect
100. #16861182	C₂²	semidirect
101. #16861182	C₂²	semidirect
102. #16861182	C₂²	semidirect
103. #16861182	C₂²	semidirect
104. #16861182	C₂²	semidirect
105. #16861182	C₂²	semidirect
106. #16861182	C₂²	semidirect
107. #16861182	C₂²	semidirect
108. #16861182	C₂²	semidirect
109. #16861182	C₂²	semidirect
110. #16861182	C₂²	semidirect
111. #16861181	C₂²	semidirect
112. #16861181	C₂²	semidirect
113. #16861181	C₂²	semidirect
114. #16861180	C₂²	semidirect
115. #16861180	C₂²	semidirect
118. #16861179	C₂²	semidirect
119. #16861179	C₂²	semidirect
120. #16861179	C₂²	semidirect
121. #16861179	C₂²	semidirect
122. #16861179	C₂²	semidirect
123. #16861179	C₂²	semidirect
124. #16861179	C₂²	semidirect
125. #16861179	C₂²	semidirect
126. #16861179	C₂²	semidirect
127. #16861179	C₂²	semidirect
128. #16861179	C₂²	semidirect
129. #16861179	C₂²	semidirect
130. #16861179	C₂²	semidirect
131. #16861179	C₂²	semidirect
132. #16861179	C₂²	semidirect
133. #16861179	C₂²	semidirect
134. #16861179	C₂²	semidirect
135. #16861179	C₂²	semidirect
136. #16861178	C₂²	semidirect
137. #16861178	C₂²	semidirect
139. #16861177	C₂²	semidirect
140. #16861177	C₂²	semidirect
141. #16861177	C₂²	semidirect
142. #16861177	C₂²	semidirect
143. #16861177	C₂²	semidirect
144. #16861177	C₂²	semidirect
145. #16861177	C₂²	semidirect
146. #16861177	C₂²	semidirect
147. #16861177	C₂²	semidirect
148. C₄×D₅₀₈	C₂²	semidirect
149. C₄×D₅₀₈	C₂²	semidirect
150. C₄×D₅₀₈	C₂²	semidirect
151. #16861171	C₂²	semidirect
152. #16861171	C₂²	semidirect
153. #16861171	C₂²	semidirect
154. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
155. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
156. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
157. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
158. #16861167	C₂²	semidirect
159. #16861166	C₂²	semidirect
160. #16861165	C₂²	semidirect
161. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
162. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
163. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
164. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
165. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
166. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
167. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
168. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
169. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
170. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
171. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
172. #126×C₁₂₇	C₂²	semidirect
173. #126×C₁₂₇	C₂²	semidirect
174. #124×C₁₂₇	C₂²	semidirect
175. #124×C₁₂₇	C₂²	semidirect
176. #123×C₁₂₇	C₂²	semidirect
177. #123×C₁₂₇	C₂²	semidirect
178. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
179. #121×C₁₂₇	C₂²	semidirect
180. #121×C₁₂₇	C₂²	semidirect
181. #121×C₁₂₇	C₂²	semidirect
182. #120×C₁₂₇	C₂²	semidirect
183. #120×C₁₂₇	C₂²	semidirect
184. C₄×D₄×C₁₂₇	C₂²	semidirect
185. C₄×D₄×C₁₂₇	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₁₂₇	C₂²	semidirect
199. C₂³×D₁₂₇	C₂³	semidirect
203. C₂×Dic₂₅₄	C₂³	semidirect
204. C₂×Dic₂₅₄	C₂³	semidirect
222. C₂×D₅₀₈	C₂³	semidirect
223. C₂×D₅₀₈	C₂³	semidirect
224. C₂×D₅₀₈	C₂³	semidirect
225. C₂×D₅₀₈	C₂³	semidirect
243. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
244. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
245. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
246. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
256. C₂²×Dic₁₂₇	C₂³	semidirect
263. C₂×C₄×D₁₂₇	C₂³	semidirect
264. C₂×C₄×D₁₂₇	C₂³	semidirect
265. C₂×C₄×D₁₂₇	C₂³	semidirect
266. C₂×C₄×D₁₂₇	C₂³	semidirect
267. C₂×C₄×D₁₂₇	C₂³	semidirect
268. C₂×C₄×D₁₂₇	C₂³	semidirect
269. C₄⋊Dic₁₂₇	C₂³	semidirect
270. C₄⋊Dic₁₂₇	C₂³	semidirect
271. C₄⋊Dic₁₂₇	C₂³	semidirect
272. C₄⋊Dic₁₂₇	C₂³	semidirect
273. Dic₁₂₇⋊C₄	C₂³	semidirect
274. Dic₁₂₇⋊C₄	C₂³	semidirect
275. Dic₁₂₇⋊C₄	C₂³	semidirect
276. Dic₁₂₇⋊C₄	C₂³	semidirect
277. Dic₁₂₇⋊C₄	C₂³	semidirect
278. Dic₁₂₇⋊C₄	C₂³	semidirect
279. Dic₁₂₇⋊C₄	C₂³	semidirect
280. Dic₁₂₇⋊C₄	C₂³	semidirect
287. C₂²⋊Dic₁₂₇	C₂³	semidirect
288. C₂²⋊Dic₁₂₇	C₂³	semidirect
309. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
310. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
311. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
312. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
313. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
314. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
315. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
316. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
317. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
318. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
319. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
320. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
321. C₄×Dic₁₂₇	C₂³	semidirect
322. C₄×Dic₁₂₇	C₂³	semidirect
323. C₄×Dic₁₂₇	C₂³	semidirect
324. C₄×Dic₁₂₇	C₂³	semidirect
326. C₂×Q₈×C₁₂₇	C₂³	semidirect
333. C₂×D₄×C₁₂₇	C₂³	semidirect
336. C₂²×C₄×C₁₂₇	C₂³	semidirect
337. C₂²×C₄×C₁₂₇	C₂³	semidirect
338. C₄⋊C₄×C₁₂₇	C₂³	semidirect
339. C₄⋊C₄×C₁₂₇	C₂³	semidirect
340. C₄⋊C₄×C₁₂₇	C₂³	semidirect
341. C₄⋊C₄×C₁₂₇	C₂³	semidirect
342. C₄⋊C₄×C₁₂₇	C₂³	semidirect
343. C₄⋊C₄×C₁₂₇	C₂³	semidirect
354. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
355. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
356. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
357. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
358. C₄²×C₁₂₇	C₂³	semidirect
359. C₄²×C₁₂₇	C₂³	semidirect
577. C₁₂₇	#3532	semidirect
599. #538	D₁₂₇	semidirect
635. #126	C₂×D₁₂₇	semidirect
636. #126	C₂×D₁₂₇	semidirect
647. #124	C₂×D₁₂₇	semidirect
648. #124	C₂×D₁₂₇	semidirect
665. #123	C₂×D₁₂₇	semidirect
666. #123	C₂×D₁₂₇	semidirect
672. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
700. #121	C₂×D₁₂₇	semidirect
701. #121	C₂×D₁₂₇	semidirect
702. #121	C₂×D₁₂₇	semidirect
735. #120	C₂×D₁₂₇	semidirect
736. #120	C₂×D₁₂₇	semidirect
747. C₄×D₄	C₂×D₁₂₇	semidirect
748. C₄×D₄	C₂×D₁₂₇	semidirect
763. C₂×C₂²⋊C₄	C₂×D₁₂₇	semidirect
783. C₂×Q₈	C₂²×D₁₂₇	semidirect
840. C₂×D₄	C₂²×D₁₂₇	semidirect
857. C₂²×C₄	C₂²×D₁₂₇	semidirect
858. C₂²×C₄	C₂²×D₁₂₇	semidirect
871. C₄⋊C₄	C₂²×D₁₂₇	semidirect
872. C₄⋊C₄	C₂²×D₁₂₇	semidirect
873. C₄⋊C₄	C₂²×D₁₂₇	semidirect
874. C₄⋊C₄	C₂²×D₁₂₇	semidirect
875. C₄⋊C₄	C₂²×D₁₂₇	semidirect
876. C₄⋊C₄	C₂²×D₁₂₇	semidirect
927. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
928. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
929. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
930. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
935. C₄²	C₂²×D₁₂₇	semidirect
936. C₄²	C₂²×D₁₂₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22550618	2
#22550617	2
#22550616	2
#22550614	2
#22550555	2
#22550553	2
#22550551	2
#22550522	2
#22550521	2
#22550519	2
#22550518	2
#22550517	2
#22550515	2
D₄×D₅₀₈	2
#22550510	2
#22550465	2
#22550464	2
#22550462	2
#22550460	2
#22550444	2
#22550442	2
#22550441	2
#22550437	2
#22550436	2
#22550434	2
C₂×#16861179	2
#120×D₁₂₇	2
#538×C₁₂₇	2
#3532	127