Subgroups — #30652898

Order 16256.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550628	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550623	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550620	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550614	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550608	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550578	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550577	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550568	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550566	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550555	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550553	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550549	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550530	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550526	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550521	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550515	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550495	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550492	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550479	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550478	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550470	C₂	1	1	yes	maximal, characteristic, complemented
22	#22550467	C₂	1	1	yes	maximal, characteristic, complemented
23	#22550464	C₂	1	1	yes	maximal, characteristic, complemented
24	#22550463	C₂	1	1	yes	maximal, characteristic, complemented
25	#22550460	C₂	1	1	yes	maximal, characteristic, complemented
26	#22550441	C₂	1	1	yes	maximal, characteristic, complemented
27	#22550436	C₂	1	1	yes	maximal, characteristic, complemented
28	#22550382	C₂	1	1	yes	maximal, characteristic, complemented
29	#22550382	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16861193	C₂	1	1	yes	maximal, characteristic, complemented
31	#538×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523247	C₂²	1	1	yes	characteristic
33	C₂×#14523247	C₂²	1	1	yes	characteristic
34	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
37	C₂³×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
38	#16861209	C₂²	1	1	yes	characteristic, complemented
39	#16861208	C₂²	1	1	yes	characteristic, complemented
40	#16861205	C₂²	1	1	yes	characteristic
41	#16861205	C₂²	1	1	yes	characteristic, complemented
42	#16861204	C₂²	1	1	yes	characteristic, complemented
43	#16861204	C₂²	1	1	yes	characteristic, complemented
44	#16861204	C₂²	1	1	yes	characteristic, complemented
45	#16861204	C₂²	1	1	yes	characteristic, complemented
46	#16861204	C₂²	1	1	yes	characteristic, complemented
47	#16861203	C₂²	1	1	yes	characteristic, complemented
48	#16861202	C₂²	1	1	yes	characteristic, complemented
49	#16861202	C₂²	1	1	yes	characteristic, complemented
50	#16861202	C₂²	1	1	yes	characteristic, complemented
51	#16861202	C₂²	1	1	yes	characteristic, complemented
52	#16861201	C₂²	1	1	yes	characteristic, complemented
53	#16861200	C₂²	1	1	yes	characteristic, complemented
54	#16861200	C₂²	1	1	yes	characteristic, complemented
55	#16861200	C₂²	1	1	yes	characteristic, complemented
56	#16861199	C₂²	1	1	yes	characteristic, complemented
57	#16861199	C₂²	1	1	yes	characteristic, complemented
58	#16861198	C₂²	1	1	yes	characteristic, complemented
59	#16861197	C₂²	1	1	yes	characteristic, complemented
60	#16861195	C₂²	1	1	yes	characteristic
61	#16861195	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	#16861194	C₂²	1	1	yes	characteristic, complemented
67	#16861194	C₂²	1	1	yes	characteristic, complemented
68	#16861194	C₂²	1	1	yes	characteristic, complemented
69	#16861193	C₂²	1	1	yes	characteristic
70	#16861193	C₂²	1	1	yes	characteristic
71	#16861193	C₂²	1	1	yes	characteristic
72	#16861193	C₂²	1	1	yes	characteristic
73	#16861193	C₂²	1	1	yes	characteristic
74	#16861193	C₂²	1	1	yes	characteristic
75	#16861193	C₂²	1	1	yes	characteristic, complemented
76	#16861193	C₂²	1	1	yes	characteristic, complemented
77	#16861193	C₂²	1	1	yes	characteristic, complemented
78	#16861193	C₂²	1	1	yes	characteristic, complemented
79	#16861193	C₂²	1	1	yes	characteristic, complemented
80	#16861193	C₂²	1	1	yes	characteristic, complemented
81	#16861193	C₂²	1	1	yes	characteristic, complemented
82	#16861193	C₂²	1	1	yes	characteristic, complemented
83	#16861192	C₂²	1	1	yes	characteristic, complemented
84	#16861191	C₂²	1	1	yes	characteristic
85	#16861191	C₂²	1	1	yes	characteristic
86	#16861191	C₂²	1	1	yes	characteristic, complemented
87	#16861191	C₂²	1	1	yes	characteristic, complemented
88	#16861191	C₂²	1	1	yes	characteristic, complemented
89	#16861191	C₂²	1	1	yes	characteristic, complemented
90	#16861191	C₂²	1	1	yes	characteristic, complemented
91	#16861190	C₂²	1	1	yes	characteristic
92	#16861190	C₂²	1	1	yes	characteristic
93	#16861190	C₂²	1	1	yes	characteristic, complemented
94	#16861189	C₂²	1	1	yes	characteristic, complemented
95	#16861189	C₂²	1	1	yes	characteristic, complemented
96	#16861189	C₂²	1	1	yes	characteristic, complemented
97	#16861188	C₂²	1	1	yes	characteristic, complemented
98	#16861188	C₂²	1	1	yes	characteristic, complemented
99	#16861187	C₂²	1	1	yes	characteristic, complemented
100	#16861187	C₂²	1	1	yes	characteristic, complemented
101	#16861186	C₂²	1	1	yes	characteristic, complemented
102	#16861186	C₂²	1	1	yes	characteristic, complemented
103	#16861186	C₂²	1	1	yes	characteristic, complemented
104	#16861186	C₂²	1	1	yes	characteristic, complemented
105	#16861186	C₂²	1	1	yes	characteristic, complemented
106	#16861186	C₂²	1	1	yes	characteristic, complemented
107	#16861185	C₂²	1	1	yes	characteristic, complemented
108	#16861185	C₂²	1	1	yes	characteristic, complemented
109	#16861184	C₂²	1	1	yes	characteristic, complemented
110	#16861183	C₂²	1	1	yes	characteristic
111	#16861183	C₂²	1	1	yes	characteristic, complemented
112	#16861183	C₂²	1	1	yes	characteristic, complemented
113	#16861182	C₂²	1	1	yes	characteristic
114	#16861182	C₂²	1	1	yes	characteristic
115	#16861182	C₂²	1	1	yes	characteristic
116	#16861182	C₂²	1	1	yes	characteristic, complemented
117	#16861182	C₂²	1	1	yes	characteristic, complemented
118	#16861182	C₂²	1	1	yes	characteristic, complemented
119	#16861182	C₂²	1	1	yes	characteristic, complemented
120	#16861181	C₂²	1	1	yes	characteristic
121	#16861181	C₂²	1	1	yes	characteristic, complemented
122	#16861181	C₂²	1	1	yes	characteristic, complemented
123	#16861181	C₂²	1	1	yes	characteristic, complemented
124	#16861181	C₂²	1	1	yes	characteristic, complemented
125	#16861181	C₂²	1	1	yes	characteristic, complemented
126	#16861181	C₂²	1	1	yes	characteristic, complemented
127	#16861180	C₂²	1	1	yes	characteristic
128	#16861180	C₂²	1	1	yes	characteristic
129	#16861180	C₂²	1	1	yes	characteristic, complemented
130	#16861179	C₂²	1	1	yes	characteristic
131	#16861179	C₂²	1	1	yes	characteristic, complemented
132	#16861178	C₂²	1	1	yes	characteristic
133	#16861178	C₂²	1	1	yes	characteristic, complemented
134	#16861177	C₂²	1	1	yes	characteristic
135	#16861177	C₂²	1	1	yes	characteristic
136	#16861177	C₂²	1	1	yes	characteristic
137	#16861177	C₂²	1	1	yes	characteristic, complemented
138	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
139	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
141	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
142	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
143	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
145	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
146	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
147	#16861171	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	#16861168	C₂²	1	1	yes	characteristic, complemented
157	#16861167	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	#16861165	C₂²	1	1	yes	characteristic, complemented
162	#16861165	C₂²	1	1	yes	characteristic, complemented
163	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
164	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
165	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
166	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
167	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
168	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
169	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
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
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
183	#120×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
185	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
188	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
189	#14523247	—	4	2	no	—
190	#14523247	—	4	2	no	—
191	#14523247	—	4	2	no	—
192	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
193	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
195	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
196	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
197	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
198	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
199	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
201	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
217	D₄×D₁₂₇	—	4	2	no	—
218	C₂²×Dic₁₂₇	—	4	2	no	—
219	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
221	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
224	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
225	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
226	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
227	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
228	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
249	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
250	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
251	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
252	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
253	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
281	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
307	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
313	C₂⁴×C₁₂₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
325	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
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
337	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
346	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
347	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
348	C₂²×D₁₂₇	—	2	2	no	—
349	C₂²×D₁₂₇	—	4	1	no	—
350	C₂²×D₁₂₇	—	4	1	no	—
351	C₂²×D₁₂₇	—	4	1	no	—
352	C₂²×D₁₂₇	—	4	1	no	—
353	C₂²×D₁₂₇	—	4	1	no	—
354	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
356	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
357	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
358	Dic₂₅₄	—	4	1	no	—
359	Dic₂₅₄	—	4	1	no	—
360	Dic₂₅₄	—	4	1	no	—
361	Dic₂₅₄	—	4	1	no	—
362	D₅₀₈	—	4	1	no	—
363	D₅₀₈	—	4	1	no	—
364	D₅₀₈	—	4	1	no	—
365	D₅₀₈	—	4	1	no	—
366	C₂²⋊D₁₂₇	—	2	2	no	—
367	C₂²⋊D₁₂₇	—	2	2	no	—
368	C₂²⋊D₁₂₇	—	4	1	no	—
369	C₂²⋊D₁₂₇	—	4	1	no	—
370	C₂²⋊D₁₂₇	—	4	1	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	C₂×Dic₁₂₇	—	2	2	no	—
383	C₂×Dic₁₂₇	—	2	2	no	—
384	C₂×Dic₁₂₇	—	2	2	no	—
385	C₂×Dic₁₂₇	—	4	1	no	—
386	C₂×Dic₁₂₇	—	4	1	no	—
387	C₂×Dic₁₂₇	—	4	1	no	—
388	C₂×Dic₁₂₇	—	4	1	no	—
389	C₂×Dic₁₂₇	—	4	1	no	—
390	C₂×Dic₁₂₇	—	4	1	no	—
391	C₂×Dic₁₂₇	—	4	1	no	—
392	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
404	C₄×D₁₂₇	—	4	1	no	—
405	C₄×D₁₂₇	—	4	1	no	—
406	C₄×D₁₂₇	—	4	1	no	—
407	C₄×D₁₂₇	—	4	1	no	—
408	C₄×D₁₂₇	—	4	1	no	—
409	C₄×D₁₂₇	—	4	1	no	—
410	C₄×D₁₂₇	—	4	1	no	—
411	C₄×D₁₂₇	—	4	1	no	—
412	C₂³×C₁₂₇	—	2	2	no	—
413	C₂³×C₁₂₇	—	4	1	no	—
414	C₂³×C₁₂₇	—	4	1	no	—
415	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
416	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
417	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
418	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
419	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
420	Q₈×C₁₂₇	—	4	1	no	—
421	D₄×C₁₂₇	—	2	2	no	—
422	D₄×C₁₂₇	—	2	2	no	—
423	D₄×C₁₂₇	—	4	1	no	—
424	D₄×C₁₂₇	—	4	1	no	—
425	D₄×C₁₂₇	—	4	1	no	—
426	D₄×C₁₂₇	—	4	1	no	—
427	D₄×C₁₂₇	—	4	1	no	—
428	C₂×C₄×C₁₂₇	—	4	1	no	—
429	C₂×C₄×C₁₂₇	—	4	1	no	—
430	C₂×C₄×C₁₂₇	—	4	1	no	—
431	C₂×C₄×C₁₂₇	—	4	1	no	—
432	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
434	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
435	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
436	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
437	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
438	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
439	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
440	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
441	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
442	C₂²×C₁₂₇	—	2	1	no	—
443	C₂²×C₁₂₇	—	2	1	no	—
444	C₂²×C₁₂₇	—	2	1	no	—
445	C₂²×C₁₂₇	—	2	1	no	—
446	C₂²×C₁₂₇	—	2	1	no	—
447	C₂²×C₁₂₇	—	2	1	no	—
448	C₂²×C₁₂₇	—	2	1	no	—
449	C₂²×C₁₂₇	—	2	1	no	—
450	C₂²×C₁₂₇	—	2	1	no	—
451	C₂²×C₁₂₇	—	2	1	no	—
452	C₂²×C₁₂₇	—	2	1	no	—
453	C₂²×C₁₂₇	—	2	1	no	—
454	C₂²×C₁₂₇	—	2	1	no	—
455	C₂²×C₁₂₇	—	2	1	no	—
456	C₂²×C₁₂₇	—	4	4	no	—
457	C₂²×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
458	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
459	C₂×D₁₂₇	—	2	1	no	—
460	C₂×D₁₂₇	—	2	1	no	—
461	C₂×D₁₂₇	—	2	1	no	—
462	C₂×D₁₂₇	—	2	1	no	—
463	C₂×D₁₂₇	—	2	1	no	—
464	C₂×D₁₂₇	—	2	1	no	—
465	C₂×D₁₂₇	—	2	1	no	—
466	C₂×D₁₂₇	—	2	1	no	—
467	C₂×D₁₂₇	—	2	1	no	—
468	C₂×D₁₂₇	—	2	1	no	—
469	C₂×D₁₂₇	—	2	1	no	—
470	C₂×D₁₂₇	—	2	1	no	—
471	C₂×D₁₂₇	—	8	2	no	—
472	C₂×D₁₂₇	—	8	2	no	—
473	C₄×C₁₂₇	—	2	1	no	—
474	C₄×C₁₂₇	—	2	1	no	—
475	C₄×C₁₂₇	—	2	1	no	—
476	C₄×C₁₂₇	—	2	1	no	—
477	C₄×C₁₂₇	—	2	1	no	—
478	C₄×C₁₂₇	—	2	1	no	—
479	C₄×C₁₂₇	—	2	1	no	—
480	C₄×C₁₂₇	—	2	1	no	—
481	C₄×C₁₂₇	—	2	1	no	—
482	C₄×C₁₂₇	—	2	1	no	—
483	Dic₁₂₇	—	2	1	no	—
484	Dic₁₂₇	—	2	1	no	—
485	Dic₁₂₇	—	2	1	no	—
486	Dic₁₂₇	—	2	1	no	—
487	Dic₁₂₇	—	2	1	no	—
488	Dic₁₂₇	—	2	1	no	—
489	Dic₁₂₇	—	2	1	no	—
490	Dic₁₂₇	—	2	1	no	—
491	Dic₁₂₇	—	2	1	no	—
492	Dic₁₂₇	—	2	1	no	—
493	Dic₁₂₇	—	2	1	no	—
494	Dic₁₂₇	—	2	1	no	—
495	C₂×C₁₂₇	—	2	2	no	—
496	C₂×C₁₂₇	—	4	1	no	—
497	C₂×C₁₂₇	—	4	1	no	—
498	C₂×C₁₂₇	—	4	1	no	—
499	C₂×C₁₂₇	—	4	1	no	—
500	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂×C₁₂₇	#585	1	1	yes	characteristic
502	C₂×C₁₂₇	#585	1	1	yes	characteristic
503	D₁₂₇	—	4	1	no	—
504	D₁₂₇	—	4	1	no	—
505	D₁₂₇	—	4	1	no	—
506	D₁₂₇	—	4	1	no	—
507	#3533	—	127	1	no	maximal, Sylow
508	C₁₂₇	#3533	1	1	yes	characteristic, complemented, Sylow
509	#563	—	127	1	no	—
510	#562	—	127	1	no	—
511	#562	—	127	1	no	—
512	#560	—	127	1	no	—
513	#559	—	127	1	no	—
514	#553	—	127	1	no	—
515	#553	—	127	1	no	—
516	#552	—	127	1	no	—
517	#552	—	127	1	no	—
518	#551	—	127	1	no	—
519	#551	—	127	1	no	—
520	#551	—	127	1	no	—
521	#547	—	127	1	no	—
522	#547	—	127	1	no	—
523	#546	—	127	1	no	—
524	#546	—	127	1	no	—
525	#542	—	127	1	no	—
526	#542	—	127	1	no	—
527	#540	—	127	1	no	—
528	#540	—	127	1	no	—
529	#539	—	127	1	no	—
530	#539	—	127	1	no	—
531	#538	—	127	1	no	—
532	#538	—	127	1	no	—
533	#538	—	127	1	no	—
534	#538	D₁₂₇	1	1	yes	characteristic, complemented
535	#535	—	127	1	no	—
536	#534	—	127	1	no	—
537	#525	—	127	1	no	—
538	#525	—	127	1	no	—
539	C₂×#123	—	127	1	no	—
540	C₂×#41	—	127	1	no	—
541	C₂×#41	—	127	1	no	—
542	C₂×#41	—	127	1	no	—
543	C₂²×D₄	—	127	1	no	—
544	C₂²×D₄	—	127	1	no	—
545	C₂³×C₄	—	127	1	no	—
546	C₄⋊Q₈	—	127	1	no	—
547	C₄⋊Q₈	—	127	1	no	—
548	#127	—	127	1	no	—
549	#127	—	127	1	no	—
550	#126	—	127	1	no	—
551	#126	—	127	1	no	—
552	#126	—	127	1	no	—
553	#126	—	127	1	no	—
554	#126	—	127	1	no	—
555	#126	—	127	1	no	—
556	#126	—	127	1	no	—
557	#126	—	127	1	no	—
558	#126	—	127	1	no	—
559	#126	—	127	1	no	—
560	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
561	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
562	#125	—	127	1	no	—
563	#125	—	127	1	no	—
564	#125	—	127	1	no	—
565	#125	—	127	1	no	—
566	#125	—	127	1	no	—
567	#125	—	127	1	no	—
568	#124	—	127	1	no	—
569	#124	—	127	1	no	—
570	#124	—	127	1	no	—
571	#124	—	127	1	no	—
572	#124	—	127	1	no	—
573	#124	—	127	1	no	—
574	#124	—	127	1	no	—
575	#124	—	127	1	no	—
576	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
577	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
578	#123	—	127	1	no	—
579	#123	—	127	1	no	—
580	#123	—	127	1	no	—
581	#123	—	127	1	no	—
582	#123	—	127	1	no	—
583	#123	—	127	1	no	—
584	#123	—	127	1	no	—
585	#123	—	127	1	no	—
586	#123	—	127	1	no	—
587	#123	—	127	1	no	—
588	#123	—	127	1	no	—
589	#123	—	127	1	no	—
590	#123	—	127	1	no	—
591	#123	—	127	1	no	—
592	#123	—	127	1	no	—
593	#123	—	127	1	no	—
594	#123	—	127	1	no	—
595	#123	—	127	1	no	—
596	#123	—	127	1	no	—
597	#123	—	127	1	no	—
598	#123	—	127	1	no	—
599	#123	—	127	1	no	—
600	#123	—	127	1	no	—
601	#123	—	127	1	no	—
602	#123	—	127	1	no	—
603	#123	—	127	1	no	—
604	#123	—	127	1	no	—
605	#123	—	127	1	no	—
606	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
607	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
608	C₂²⋊Q₈	—	127	1	no	—
609	C₂²⋊Q₈	—	127	1	no	—
610	C₂²⋊Q₈	—	127	1	no	—
611	C₂²⋊Q₈	—	127	1	no	—
612	C₂²⋊Q₈	—	127	1	no	—
613	C₂²⋊Q₈	—	127	1	no	—
614	C₂²⋊Q₈	—	127	1	no	—
615	C₂²⋊Q₈	—	127	1	no	—
616	C₂²⋊Q₈	—	127	1	no	—
617	C₂²⋊Q₈	—	127	1	no	—
618	C₂²⋊Q₈	—	127	1	no	—
619	C₂²⋊Q₈	—	127	1	no	—
620	C₂²⋊Q₈	—	127	1	no	—
621	C₂²⋊Q₈	—	127	1	no	—
622	C₂²⋊Q₈	—	127	1	no	—
623	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
624	#121	—	127	1	no	—
625	#121	—	127	1	no	—
626	#121	—	127	1	no	—
627	#121	—	127	1	no	—
628	#121	—	127	1	no	—
629	#121	—	127	1	no	—
630	#121	—	127	1	no	—
631	#121	—	127	1	no	—
632	#121	—	127	1	no	—
633	#121	—	127	1	no	—
634	#121	—	127	1	no	—
635	#121	—	127	1	no	—
636	#121	—	127	1	no	—
637	#121	—	127	1	no	—
638	#121	—	127	1	no	—
639	#121	—	127	1	no	—
640	#121	—	127	1	no	—
641	#121	—	127	1	no	—
642	#121	—	127	1	no	—
643	#121	—	127	1	no	—
644	#121	—	127	1	no	—
645	#121	C₂×D₁₂₇	1	1	yes	characteristic
646	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
647	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
648	#120	—	127	1	no	—
649	#120	—	127	1	no	—
650	#120	—	127	1	no	—
651	#120	—	127	1	no	—
652	#120	—	127	1	no	—
653	#120	—	127	1	no	—
654	#120	—	127	1	no	—
655	#120	—	127	1	no	—
656	#120	C₂×D₁₂₇	1	1	yes	characteristic
657	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
658	C₄×Q₈	—	127	1	no	—
659	C₄×Q₈	—	127	1	no	—
660	C₄×D₄	—	127	1	no	—
661	C₄×D₄	—	127	1	no	—
662	C₄×D₄	—	127	1	no	—
663	C₄×D₄	—	127	1	no	—
664	C₄×D₄	—	127	1	no	—
665	C₄×D₄	—	127	1	no	—
666	C₄×D₄	—	127	1	no	—
667	C₄×D₄	—	127	1	no	—
668	C₄×D₄	—	127	1	no	—
669	C₄×D₄	—	127	1	no	—
670	C₄×D₄	—	127	1	no	—
671	C₄×D₄	—	127	1	no	—
672	C₄×D₄	—	127	1	no	—
673	C₄×D₄	—	127	1	no	—
674	C₄×D₄	—	127	1	no	—
675	C₄×D₄	—	127	1	no	—
676	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
677	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
678	#117	—	127	1	no	—
679	#117	—	127	1	no	—
680	#117	—	127	1	no	—
681	#117	—	127	1	no	—
682	#117	—	127	1	no	—
683	#117	—	127	1	no	—
684	#117	—	127	1	no	—
685	C₂×C₄⋊C₄	—	127	1	no	—
686	C₂×C₄⋊C₄	—	127	1	no	—
687	C₂×C₄⋊C₄	—	127	1	no	—
688	C₂×C₄⋊C₄	—	127	1	no	—
689	C₂×C₂²⋊C₄	—	127	1	no	—
690	C₂×C₂²⋊C₄	—	127	1	no	—
691	C₂×C₂²⋊C₄	—	127	1	no	—
692	C₂×C₂²⋊C₄	—	127	1	no	—
693	C₂×C₂²⋊C₄	—	127	1	no	—
694	C₂×C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
695	C₂⁴	—	127	1	no	—
696	C₂⁴	—	127	1	no	—
697	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
698	#41	—	508	2	no	—
699	#41	—	508	2	no	—
700	#41	—	508	2	no	—
701	C₂×Q₈	—	127	1	no	—
702	C₂×Q₈	—	127	1	no	—
703	C₂×Q₈	—	127	1	no	—
704	C₂×Q₈	—	127	1	no	—
705	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
706	C₂×D₄	—	127	1	no	—
707	C₂×D₄	—	127	1	no	—
708	C₂×D₄	—	127	1	no	—
709	C₂×D₄	—	127	1	no	—
710	C₂×D₄	—	127	1	no	—
711	C₂×D₄	—	127	1	no	—
712	C₂×D₄	—	127	1	no	—
713	C₂×D₄	—	127	1	no	—
714	C₂×D₄	—	127	1	no	—
715	C₂×D₄	—	127	1	no	—
716	C₂×D₄	—	127	1	no	—
717	C₂×D₄	—	127	1	no	—
718	C₂×D₄	—	127	1	no	—
719	C₂×D₄	—	127	1	no	—
720	C₂×D₄	—	127	1	no	—
721	C₂×D₄	—	127	1	no	—
722	C₂×D₄	—	127	1	no	—
723	C₂×D₄	—	127	1	no	—
724	C₂×D₄	—	127	1	no	—
725	C₂×D₄	—	127	1	no	—
726	C₂×D₄	—	508	2	no	—
727	C₂×D₄	—	508	2	no	—
728	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
729	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
730	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
731	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
735	C₂²×C₄	—	127	1	no	—
736	C₂²×C₄	—	127	1	no	—
737	C₂²×C₄	—	127	1	no	—
738	C₂²×C₄	—	127	1	no	—
739	C₂²×C₄	—	127	1	no	—
740	C₂²×C₄	—	127	1	no	—
741	C₂²×C₄	—	127	1	no	—
742	C₂²×C₄	—	127	1	no	—
743	C₂²×C₄	—	127	1	no	—
744	C₂²×C₄	—	127	1	no	—
745	C₂²×C₄	—	127	1	no	—
746	C₂²×C₄	—	127	1	no	—
747	C₂²×C₄	—	127	1	no	—
748	C₂²×C₄	—	127	1	no	—
749	C₂²×C₄	—	127	1	no	—
750	C₂²×C₄	—	127	1	no	—
751	C₂²×C₄	—	127	1	no	—
752	C₂²×C₄	—	127	1	no	—
753	C₂²×C₄	—	508	2	no	—
754	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
758	C₄⋊C₄	—	127	1	no	—
759	C₄⋊C₄	—	127	1	no	—
760	C₄⋊C₄	—	127	1	no	—
761	C₄⋊C₄	—	127	1	no	—
762	C₄⋊C₄	—	127	1	no	—
763	C₄⋊C₄	—	127	1	no	—
764	C₄⋊C₄	—	127	1	no	—
765	C₄⋊C₄	—	127	1	no	—
766	C₄⋊C₄	—	127	1	no	—
767	C₄⋊C₄	—	127	1	no	—
768	C₄⋊C₄	—	127	1	no	—
769	C₄⋊C₄	—	127	1	no	—
770	C₄⋊C₄	—	127	1	no	—
771	C₄⋊C₄	—	127	1	no	—
772	C₄⋊C₄	—	127	1	no	—
773	C₄⋊C₄	—	127	1	no	—
774	C₄⋊C₄	—	127	1	no	—
775	C₄⋊C₄	—	127	1	no	—
776	C₄⋊C₄	—	127	1	no	—
777	C₄⋊C₄	—	127	1	no	—
778	C₄⋊C₄	—	127	1	no	—
779	C₄⋊C₄	—	127	1	no	—
780	C₄⋊C₄	—	127	1	no	—
781	C₄⋊C₄	—	127	1	no	—
782	C₄⋊C₄	—	127	1	no	—
783	C₄⋊C₄	—	127	1	no	—
784	C₄⋊C₄	—	127	1	no	—
785	C₄⋊C₄	—	127	1	no	—
786	C₄⋊C₄	—	127	1	no	—
787	C₄⋊C₄	—	127	1	no	—
788	C₄⋊C₄	—	127	1	no	—
789	C₄⋊C₄	—	127	1	no	—
790	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
796	C₂²⋊C₄	—	127	1	no	—
797	C₂²⋊C₄	—	127	1	no	—
798	C₂²⋊C₄	—	127	1	no	—
799	C₂²⋊C₄	—	127	1	no	—
800	C₂²⋊C₄	—	127	1	no	—
801	C₂²⋊C₄	—	127	1	no	—
802	C₂²⋊C₄	—	127	1	no	—
803	C₂²⋊C₄	—	127	1	no	—
804	C₂²⋊C₄	—	127	1	no	—
805	C₂²⋊C₄	—	127	1	no	—
806	C₂²⋊C₄	—	127	1	no	—
807	C₂²⋊C₄	—	127	1	no	—
808	C₂²⋊C₄	—	127	1	no	—
809	C₂²⋊C₄	—	127	1	no	—
810	C₂²⋊C₄	—	127	1	no	—
811	C₂²⋊C₄	—	127	1	no	—
812	C₂²⋊C₄	—	127	1	no	—
813	C₂²⋊C₄	—	127	1	no	—
814	C₂²⋊C₄	—	127	1	no	—
815	C₂²⋊C₄	—	127	1	no	—
816	C₂²⋊C₄	—	127	1	no	—
817	C₂²⋊C₄	—	127	1	no	—
818	C₂²⋊C₄	—	127	1	no	—
819	C₂²⋊C₄	—	127	1	no	—
820	C₂²⋊C₄	—	127	1	no	—
821	C₂²⋊C₄	—	127	1	no	—
822	C₂²⋊C₄	—	127	1	no	—
823	C₂²⋊C₄	—	127	1	no	—
824	C₂²⋊C₄	—	127	1	no	—
825	C₂²⋊C₄	—	127	1	no	—
826	C₂²⋊C₄	—	127	1	no	—
827	C₂²⋊C₄	—	127	1	no	—
828	C₂²⋊C₄	—	127	1	no	—
829	C₂²⋊C₄	—	127	1	no	—
830	C₂²⋊C₄	—	127	1	no	—
831	C₂²⋊C₄	—	127	1	no	—
832	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
846	C₄²	—	127	1	no	—
847	C₄²	—	127	1	no	—
848	C₄²	—	127	1	no	—
849	C₄²	—	127	1	no	—
850	C₄²	—	127	1	no	—
851	C₄²	—	127	1	no	—
852	C₄²	—	127	1	no	—
853	C₄²	—	127	1	no	—
854	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
855	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
856	C₂³	—	2	2	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	127	1	no	—
860	C₂³	—	127	1	no	—
861	C₂³	—	127	1	no	—
862	C₂³	—	127	1	no	—
863	C₂³	—	508	1	no	—
864	C₂³	—	508	1	no	—
865	C₂³	—	508	1	no	—
866	C₂³	—	508	1	no	—
867	C₂³	—	508	1	no	—
868	C₂³	—	254	2	no	—
869	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
870	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
871	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
872	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
873	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	508	1	no	—
876	Q₈	—	508	1	no	—
877	Q₈	—	508	1	no	—
878	Q₈	—	508	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	2	no	—
881	D₄	—	4	1	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	4	1	no	—
886	D₄	—	508	1	no	—
887	D₄	—	508	1	no	—
888	D₄	—	508	1	no	—
889	D₄	—	508	1	no	—
890	D₄	—	508	1	no	—
891	D₄	—	508	1	no	—
892	D₄	—	508	1	no	—
893	D₄	—	508	1	no	—
894	D₄	—	508	1	no	—
895	D₄	—	508	1	no	—
896	D₄	—	508	1	no	—
897	D₄	—	508	1	no	—
898	D₄	—	508	1	no	—
899	D₄	—	508	1	no	—
900	D₄	—	508	1	no	—
901	D₄	—	508	1	no	—
902	D₄	—	508	1	no	—
903	D₄	—	508	1	no	—
904	D₄	—	254	2	no	—
905	D₄	—	254	2	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	127	1	no	—
911	C₂×C₄	—	127	1	no	—
912	C₂×C₄	—	127	1	no	—
913	C₂×C₄	—	127	1	no	—
914	C₂×C₄	—	127	1	no	—
915	C₂×C₄	—	127	1	no	—
916	C₂×C₄	—	127	1	no	—
917	C₂×C₄	—	127	1	no	—
918	C₂×C₄	—	127	1	no	—
919	C₂×C₄	—	127	1	no	—
920	C₂×C₄	—	127	1	no	—
921	C₂×C₄	—	127	1	no	—
922	C₂×C₄	—	508	1	no	—
923	C₂×C₄	—	508	1	no	—
924	C₂×C₄	—	508	1	no	—
925	C₂×C₄	—	508	1	no	—
926	C₂×C₄	—	508	1	no	—
927	C₂×C₄	—	508	1	no	—
928	C₂×C₄	—	508	1	no	—
929	C₂×C₄	—	508	1	no	—
930	C₂×C₄	—	508	1	no	—
931	C₂×C₄	—	508	1	no	—
932	C₂×C₄	—	508	1	no	—
933	C₂×C₄	—	508	1	no	—
934	C₂×C₄	—	508	1	no	—
935	C₂×C₄	—	508	1	no	—
936	C₂×C₄	—	508	1	no	—
937	C₂×C₄	—	254	2	no	—
938	C₂×C₄	—	254	2	no	—
939	C₂×C₄	—	254	2	no	—
940	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	4	4	no	—
965	C₂²	—	1016	2	no	—
966	C₂²	—	1016	2	no	—
967	C₂²	—	254	1	no	—
968	C₂²	—	254	1	no	—
969	C₂²	—	254	1	no	—
970	C₂²	—	254	1	no	—
971	C₂²	—	254	1	no	—
972	C₂²	—	254	1	no	—
973	C₂²	—	254	1	no	—
974	C₂²	—	254	1	no	—
975	C₂²	—	254	1	no	—
976	C₂²	—	254	1	no	—
977	C₂²	—	254	1	no	—
978	C₂²	—	254	1	no	—
979	C₂²	#16861255	1	2	yes	—
980	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	254	1	no	—
992	C₄	—	254	1	no	—
993	C₄	—	254	1	no	—
994	C₄	—	254	1	no	—
995	C₄	—	254	1	no	—
996	C₄	—	254	1	no	—
997	C₄	—	254	1	no	—
998	C₄	—	254	1	no	—
999	C₄	—	254	1	no	—
1000	C₄	—	254	1	no	—
1001	C₄	—	254	1	no	—
1002	C₄	—	254	1	no	—
1003	C₂	—	2	2	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	508	1	no	—
1009	C₂	—	508	1	no	—
1010	C₂	—	508	1	no	—
1011	C₂	—	508	1	no	—
1012	C₂	C₂×#16861255	1	1	yes	characteristic
1013	C₂	#22550711	1	1	yes	characteristic
1014	C₂	#22550711	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	#3533
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. #22550628	C₂	semidirect
2. #22550623	C₂	semidirect
3. #22550620	C₂	semidirect
4. #22550614	C₂	semidirect
5. #22550608	C₂	semidirect
6. #22550578	C₂	semidirect
7. #22550577	C₂	semidirect
8. #22550568	C₂	semidirect
9. #22550566	C₂	semidirect
10. #22550555	C₂	semidirect
11. #22550553	C₂	semidirect
12. #22550549	C₂	semidirect
13. #22550530	C₂	semidirect
14. #22550526	C₂	semidirect
15. #22550521	C₂	semidirect
16. #22550515	C₂	semidirect
17. #22550495	C₂	semidirect
18. #22550492	C₂	semidirect
19. #22550479	C₂	semidirect
20. #22550478	C₂	semidirect
21. #22550470	C₂	semidirect
22. #22550467	C₂	semidirect
23. #22550464	C₂	semidirect
24. #22550463	C₂	semidirect
25. #22550460	C₂	semidirect
26. #22550441	C₂	semidirect
27. #22550436	C₂	semidirect
28. #22550382	C₂	semidirect
29. #22550382	C₂	semidirect
30. C₂×#16861193	C₂	semidirect
31. #538×C₁₂₇	C₂	semidirect
34. C₂×#14523247	C₂²	semidirect
37. C₂³×Dic₁₂₇	C₂²	semidirect
38. #16861209	C₂²	semidirect
39. #16861208	C₂²	semidirect
41. #16861205	C₂²	semidirect
42. #16861204	C₂²	semidirect
43. #16861204	C₂²	semidirect
44. #16861204	C₂²	semidirect
45. #16861204	C₂²	semidirect
46. #16861204	C₂²	semidirect
47. #16861203	C₂²	semidirect
48. #16861202	C₂²	semidirect
49. #16861202	C₂²	semidirect
50. #16861202	C₂²	semidirect
51. #16861202	C₂²	semidirect
52. #16861201	C₂²	semidirect
53. #16861200	C₂²	semidirect
54. #16861200	C₂²	semidirect
55. #16861200	C₂²	semidirect
56. #16861199	C₂²	semidirect
57. #16861199	C₂²	semidirect
58. #16861198	C₂²	semidirect
59. #16861197	C₂²	semidirect
61. #16861195	C₂²	semidirect
62. #16861195	C₂²	semidirect
63. #16861195	C₂²	semidirect
64. #16861195	C₂²	semidirect
65. #16861195	C₂²	semidirect
66. #16861194	C₂²	semidirect
67. #16861194	C₂²	semidirect
68. #16861194	C₂²	semidirect
75. #16861193	C₂²	semidirect
76. #16861193	C₂²	semidirect
77. #16861193	C₂²	semidirect
78. #16861193	C₂²	semidirect
79. #16861193	C₂²	semidirect
80. #16861193	C₂²	semidirect
81. #16861193	C₂²	semidirect
82. #16861193	C₂²	semidirect
83. #16861192	C₂²	semidirect
86. #16861191	C₂²	semidirect
87. #16861191	C₂²	semidirect
88. #16861191	C₂²	semidirect
89. #16861191	C₂²	semidirect
90. #16861191	C₂²	semidirect
93. #16861190	C₂²	semidirect
94. #16861189	C₂²	semidirect
95. #16861189	C₂²	semidirect
96. #16861189	C₂²	semidirect
97. #16861188	C₂²	semidirect
98. #16861188	C₂²	semidirect
99. #16861187	C₂²	semidirect
100. #16861187	C₂²	semidirect
101. #16861186	C₂²	semidirect
102. #16861186	C₂²	semidirect
103. #16861186	C₂²	semidirect
104. #16861186	C₂²	semidirect
105. #16861186	C₂²	semidirect
106. #16861186	C₂²	semidirect
107. #16861185	C₂²	semidirect
108. #16861185	C₂²	semidirect
109. #16861184	C₂²	semidirect
111. #16861183	C₂²	semidirect
112. #16861183	C₂²	semidirect
116. #16861182	C₂²	semidirect
117. #16861182	C₂²	semidirect
118. #16861182	C₂²	semidirect
119. #16861182	C₂²	semidirect
121. #16861181	C₂²	semidirect
122. #16861181	C₂²	semidirect
123. #16861181	C₂²	semidirect
124. #16861181	C₂²	semidirect
125. #16861181	C₂²	semidirect
126. #16861181	C₂²	semidirect
129. #16861180	C₂²	semidirect
131. #16861179	C₂²	semidirect
133. #16861178	C₂²	semidirect
137. #16861177	C₂²	semidirect
138. Q₈×Dic₁₂₇	C₂²	semidirect
139. C₄×Dic₂₅₄	C₂²	semidirect
140. C₄×D₅₀₈	C₂²	semidirect
141. C₄×D₅₀₈	C₂²	semidirect
142. D₄×Dic₁₂₇	C₂²	semidirect
143. D₄×Dic₁₂₇	C₂²	semidirect
144. D₄×Dic₁₂₇	C₂²	semidirect
145. D₄×Dic₁₂₇	C₂²	semidirect
146. D₄×Dic₁₂₇	C₂²	semidirect
147. #16861171	C₂²	semidirect
149. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
150. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
151. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
152. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
153. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
154. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
155. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
156. #16861168	C₂²	semidirect
157. #16861167	C₂²	semidirect
158. #16861167	C₂²	semidirect
159. #16861166	C₂²	semidirect
160. #16861165	C₂²	semidirect
161. #16861165	C₂²	semidirect
162. #16861165	C₂²	semidirect
163. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
164. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
165. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
166. C₄⋊C₄×D₁₂₇	C₂²	semidirect
169. C₂×(C₂×D₁₂₇)⋊C₄	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
180. #121×C₁₂₇	C₂²	semidirect
181. #121×C₁₂₇	C₂²	semidirect
183. #120×C₁₂₇	C₂²	semidirect
185. C₄×D₄×C₁₂₇	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₁₂₇	C₂²	semidirect
508. C₁₂₇	#3533	semidirect
534. #538	D₁₂₇	semidirect
560. #126	C₂×D₁₂₇	semidirect
561. #126	C₂×D₁₂₇	semidirect
576. #124	C₂×D₁₂₇	semidirect
577. #124	C₂×D₁₂₇	semidirect
606. #123	C₂×D₁₂₇	semidirect
607. #123	C₂×D₁₂₇	semidirect
623. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
646. #121	C₂×D₁₂₇	semidirect
647. #121	C₂×D₁₂₇	semidirect
657. #120	C₂×D₁₂₇	semidirect
677. C₄×D₄	C₂×D₁₂₇	semidirect
694. C₂×C₂²⋊C₄	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550628	2
#22550623	2
#22550620	2
#22550614	2
#22550608	2
#22550578	2
#22550577	2
#22550568	2
#22550566	2
#22550555	2
#22550553	2
#22550549	2
#22550530	2
#22550526	2
#22550521	2
#22550515	2
#22550495	2
#22550492	2
#22550479	2
#22550478	2
#22550470	2
#22550467	2
#22550464	2
#22550463	2
#22550460	2
#22550441	2
#22550436	2
#22550382	2
C₂×#16861193	2
#538×C₁₂₇	2
#3533	127