Subgroups — #30652945

Order 16256.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550623	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550621	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550621	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550620	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550585	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550580	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550535	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550532	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550525	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550524	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550520	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550516	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550516	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550513	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550513	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550502	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550501	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550494	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550490	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550470	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550468	C₂	1	1	yes	maximal, characteristic, complemented
22	#22550461	C₂	1	1	yes	maximal, characteristic, complemented
23	#22550459	C₂	1	1	yes	maximal, characteristic, complemented
24	#22550455	C₂	1	1	yes	maximal, characteristic, complemented
25	#22550454	C₂	1	1	yes	maximal, characteristic, complemented
26	#22550453	C₂	1	1	yes	maximal, characteristic, complemented
27	#22550453	C₂	1	1	yes	maximal, characteristic, complemented
28	#22550382	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#16861186	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16861181	C₂	1	1	yes	maximal, characteristic, complemented
31	#546×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
36	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
38	C₂²×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
41	C₂³×Dic₁₂₇	C₂²	1	1	yes	characteristic
42	#16861208	C₂²	1	1	yes	characteristic, complemented
43	#16861207	C₂²	1	1	yes	characteristic, complemented
44	#16861204	C₂²	1	1	yes	characteristic, complemented
45	#16861203	C₂²	1	1	yes	characteristic, complemented
46	#16861202	C₂²	1	1	yes	characteristic, complemented
47	#16861202	C₂²	1	1	yes	characteristic, complemented
48	#16861201	C₂²	1	1	yes	characteristic, complemented
49	#16861200	C₂²	1	1	yes	characteristic, complemented
50	#16861199	C₂²	1	1	yes	characteristic, complemented
51	#16861199	C₂²	1	1	yes	characteristic, complemented
52	#16861197	C₂²	1	1	yes	characteristic, complemented
53	#16861196	C₂²	1	1	yes	characteristic, complemented
54	#16861196	C₂²	1	1	yes	characteristic, complemented
55	#16861195	C₂²	1	1	yes	characteristic, complemented
56	#16861195	C₂²	1	1	yes	characteristic, complemented
57	#16861195	C₂²	1	1	yes	characteristic, complemented
58	#16861195	C₂²	1	1	yes	characteristic, complemented
59	#16861195	C₂²	1	1	yes	characteristic, complemented
60	#16861195	C₂²	1	1	yes	characteristic, complemented
61	#16861194	C₂²	1	1	yes	characteristic, complemented
62	#16861193	C₂²	1	1	yes	characteristic, complemented
63	#16861193	C₂²	1	1	yes	characteristic, complemented
64	#16861193	C₂²	1	1	yes	characteristic, complemented
65	#16861192	C₂²	1	1	yes	characteristic, complemented
66	#16861192	C₂²	1	1	yes	characteristic, complemented
67	#16861192	C₂²	1	1	yes	characteristic, complemented
68	#16861191	C₂²	1	1	yes	characteristic, complemented
69	#16861191	C₂²	1	1	yes	characteristic, complemented
70	#16861191	C₂²	1	1	yes	characteristic, complemented
71	#16861191	C₂²	1	1	yes	characteristic, complemented
72	#16861191	C₂²	1	1	yes	characteristic, complemented
73	#16861190	C₂²	1	1	yes	characteristic, complemented
74	#16861190	C₂²	1	1	yes	characteristic, complemented
75	#16861190	C₂²	1	1	yes	characteristic, complemented
76	#16861190	C₂²	1	1	yes	characteristic, complemented
77	#16861189	C₂²	1	1	yes	characteristic, complemented
78	#16861189	C₂²	1	1	yes	characteristic, complemented
79	#16861188	C₂²	1	1	yes	characteristic
80	#16861188	C₂²	1	1	yes	characteristic, complemented
81	#16861188	C₂²	1	1	yes	characteristic, complemented
82	#16861188	C₂²	1	1	yes	characteristic, complemented
83	#16861188	C₂²	1	1	yes	characteristic, complemented
84	#16861188	C₂²	1	1	yes	characteristic, complemented
85	#16861187	C₂²	1	1	yes	characteristic, complemented
86	#16861187	C₂²	1	1	yes	characteristic, complemented
87	#16861187	C₂²	1	1	yes	characteristic, complemented
88	#16861187	C₂²	1	1	yes	characteristic, complemented
89	#16861187	C₂²	1	1	yes	characteristic, complemented
90	#16861187	C₂²	1	1	yes	characteristic, complemented
91	#16861186	C₂²	1	1	yes	characteristic
92	#16861186	C₂²	1	1	yes	characteristic
93	#16861186	C₂²	1	1	yes	characteristic
94	#16861186	C₂²	1	1	yes	characteristic
95	#16861186	C₂²	1	1	yes	characteristic
96	#16861186	C₂²	1	1	yes	characteristic
97	#16861186	C₂²	1	1	yes	characteristic
98	#16861186	C₂²	1	1	yes	characteristic, complemented
99	#16861186	C₂²	1	1	yes	characteristic, complemented
100	#16861186	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	#16861186	C₂²	1	1	yes	characteristic, complemented
108	#16861186	C₂²	1	1	yes	characteristic, complemented
109	#16861185	C₂²	1	1	yes	characteristic, complemented
110	#16861185	C₂²	1	1	yes	characteristic, complemented
111	#16861185	C₂²	1	1	yes	characteristic, complemented
112	#16861183	C₂²	1	1	yes	characteristic, complemented
113	#16861183	C₂²	1	1	yes	characteristic, complemented
114	#16861183	C₂²	1	1	yes	characteristic, complemented
115	#16861182	C₂²	1	1	yes	characteristic, complemented
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
122	#16861181	C₂²	1	1	yes	characteristic
123	#16861181	C₂²	1	1	yes	characteristic
124	#16861181	C₂²	1	1	yes	characteristic
125	#16861181	C₂²	1	1	yes	characteristic
126	#16861181	C₂²	1	1	yes	characteristic
127	#16861181	C₂²	1	1	yes	characteristic
128	#16861181	C₂²	1	1	yes	characteristic
129	#16861181	C₂²	1	1	yes	characteristic, complemented
130	#16861181	C₂²	1	1	yes	characteristic, complemented
131	#16861181	C₂²	1	1	yes	characteristic, complemented
132	#16861181	C₂²	1	1	yes	characteristic, complemented
133	#16861181	C₂²	1	1	yes	characteristic, complemented
134	#16861181	C₂²	1	1	yes	characteristic, complemented
135	#16861181	C₂²	1	1	yes	characteristic, complemented
136	#16861181	C₂²	1	1	yes	characteristic, complemented
137	#16861180	C₂²	1	1	yes	characteristic, complemented
138	#16861180	C₂²	1	1	yes	characteristic, complemented
139	#16861180	C₂²	1	1	yes	characteristic, complemented
140	#16861180	C₂²	1	1	yes	characteristic, complemented
141	#16861179	C₂²	1	1	yes	characteristic
142	#16861178	C₂²	1	1	yes	characteristic
143	#16861178	C₂²	1	1	yes	characteristic
144	#16861177	C₂²	1	1	yes	characteristic
145	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
146	#16861174	C₂²	1	1	yes	characteristic, complemented
147	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
148	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
149	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
150	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
152	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
153	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
155	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
156	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	#16861165	C₂²	1	1	yes	characteristic, complemented
160	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
161	C₂×Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
162	C₂×Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	C₂×Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	C₂×Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
166	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
167	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
168	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
169	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
172	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
173	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
174	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
175	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
177	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
178	#121×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	#120×C₁₂₇	C₂²	1	1	yes	characteristic
182	#120×C₁₂₇	C₂²	1	1	yes	characteristic
183	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
187	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
188	#14523248	—	4	2	no	—
189	#14523248	—	4	2	no	—
190	#14523247	—	4	2	no	—
191	#14523247	—	4	2	no	—
192	#14523247	—	4	2	no	—
193	#14523247	—	4	2	no	—
194	C₂×Dic₂₅₄	—	4	2	no	—
195	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
196	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
197	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
198	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
199	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
200	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
201	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
202	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
203	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
204	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
206	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
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	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₂₇	—	4	2	no	—
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	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
230	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
231	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
232	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
233	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
234	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
235	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
236	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₂₇	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	C₄⋊Dic₁₂₇	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	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
270	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
271	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
272	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
273	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
274	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
275	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
276	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
277	Dic₁₂₇⋊C₄	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	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
288	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₁₂₇	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
310	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
313	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
314	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
315	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
316	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
317	C₂⁴×C₁₂₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₁₂₇	C₂³	1	1	yes	characteristic
319	#41×C₁₂₇	—	4	2	no	—
320	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₁₂₇	—	4	2	no	—
322	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
323	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
324	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
325	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
326	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
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	C₂²×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	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
338	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
339	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
340	C₄⋊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	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	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
354	C₂²×D₁₂₇	—	2	2	no	—
355	C₂²×D₁₂₇	—	4	1	no	—
356	C₂²×D₁₂₇	—	4	1	no	—
357	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
358	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
360	Dic₂₅₄	—	2	2	no	—
361	Dic₂₅₄	—	2	2	no	—
362	Dic₂₅₄	—	4	1	no	—
363	Dic₂₅₄	—	4	1	no	—
364	Dic₂₅₄	—	4	1	no	—
365	Dic₂₅₄	—	4	1	no	—
366	Dic₂₅₄	—	4	1	no	—
367	Dic₂₅₄	—	4	1	no	—
368	D₅₀₈	—	4	1	no	—
369	D₅₀₈	—	4	1	no	—
370	C₂²⋊D₁₂₇	—	2	2	no	—
371	C₂²⋊D₁₂₇	—	2	2	no	—
372	C₂²⋊D₁₂₇	—	2	2	no	—
373	C₂²⋊D₁₂₇	—	2	2	no	—
374	C₂²⋊D₁₂₇	—	2	2	no	—
375	C₂²⋊D₁₂₇	—	2	2	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	C₂×Dic₁₂₇	—	2	2	no	—
387	C₂×Dic₁₂₇	—	2	2	no	—
388	C₂×Dic₁₂₇	—	2	2	no	—
389	C₂×Dic₁₂₇	—	2	2	no	—
390	C₂×Dic₁₂₇	—	2	2	no	—
391	C₂×Dic₁₂₇	—	4	1	no	—
392	C₂×Dic₁₂₇	—	4	1	no	—
393	C₂×Dic₁₂₇	—	4	1	no	—
394	C₂×Dic₁₂₇	—	4	1	no	—
395	C₂×Dic₁₂₇	—	4	1	no	—
396	C₂×Dic₁₂₇	—	4	1	no	—
397	C₂×Dic₁₂₇	—	4	1	no	—
398	C₂×Dic₁₂₇	—	4	1	no	—
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	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
412	C₄×D₁₂₇	—	2	2	no	—
413	C₄×D₁₂₇	—	4	1	no	—
414	C₄×D₁₂₇	—	4	1	no	—
415	C₄×D₁₂₇	—	4	1	no	—
416	C₄×D₁₂₇	—	4	1	no	—
417	C₄×D₁₂₇	—	4	1	no	—
418	C₄×D₁₂₇	—	4	1	no	—
419	C₂³×C₁₂₇	—	2	2	no	—
420	C₂³×C₁₂₇	—	2	2	no	—
421	C₂³×C₁₂₇	—	2	2	no	—
422	C₂³×C₁₂₇	—	4	1	no	—
423	C₂³×C₁₂₇	—	4	1	no	—
424	C₂³×C₁₂₇	—	4	1	no	—
425	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
426	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
427	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
428	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
429	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
430	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
431	Q₈×C₁₂₇	—	4	1	no	—
432	D₄×C₁₂₇	—	2	2	no	—
433	D₄×C₁₂₇	—	2	2	no	—
434	D₄×C₁₂₇	—	2	2	no	—
435	D₄×C₁₂₇	—	2	2	no	—
436	D₄×C₁₂₇	—	4	1	no	—
437	D₄×C₁₂₇	—	4	1	no	—
438	D₄×C₁₂₇	—	4	1	no	—
439	D₄×C₁₂₇	—	4	1	no	—
440	D₄×C₁₂₇	—	4	1	no	—
441	C₂×C₄×C₁₂₇	—	2	2	no	—
442	C₂×C₄×C₁₂₇	—	4	1	no	—
443	C₂×C₄×C₁₂₇	—	4	1	no	—
444	C₂×C₄×C₁₂₇	—	4	1	no	—
445	C₂×C₄×C₁₂₇	—	4	1	no	—
446	C₂×C₄×C₁₂₇	—	4	1	no	—
447	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
448	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
449	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
450	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
451	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
452	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
453	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
454	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
455	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
456	C₂²×C₁₂₇	—	2	1	no	—
457	C₂²×C₁₂₇	—	2	1	no	—
458	C₂²×C₁₂₇	—	2	1	no	—
459	C₂²×C₁₂₇	—	2	1	no	—
460	C₂²×C₁₂₇	—	2	1	no	—
461	C₂²×C₁₂₇	—	2	1	no	—
462	C₂²×C₁₂₇	—	2	1	no	—
463	C₂²×C₁₂₇	—	2	1	no	—
464	C₂²×C₁₂₇	—	2	1	no	—
465	C₂²×C₁₂₇	—	2	1	no	—
466	C₂²×C₁₂₇	—	2	1	no	—
467	C₂²×C₁₂₇	—	2	1	no	—
468	C₂²×C₁₂₇	—	2	1	no	—
469	C₂²×C₁₂₇	—	2	1	no	—
470	C₂²×C₁₂₇	—	2	1	no	—
471	C₂²×C₁₂₇	—	2	1	no	—
472	C₂²×C₁₂₇	—	4	4	no	—
473	C₂²×C₁₂₇	—	8	2	no	—
474	C₂²×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
475	C₂²×C₁₂₇	2₋¹⁺⁴	1	2	yes	—
476	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
477	C₂×D₁₂₇	—	2	1	no	—
478	C₂×D₁₂₇	—	2	1	no	—
479	C₂×D₁₂₇	—	2	1	no	—
480	C₂×D₁₂₇	—	2	1	no	—
481	C₂×D₁₂₇	—	2	1	no	—
482	C₂×D₁₂₇	—	2	1	no	—
483	C₂×D₁₂₇	—	2	1	no	—
484	C₂×D₁₂₇	—	2	1	no	—
485	C₂×D₁₂₇	—	2	1	no	—
486	C₂×D₁₂₇	—	8	2	no	—
487	C₄×C₁₂₇	—	2	1	no	—
488	C₄×C₁₂₇	—	2	1	no	—
489	C₄×C₁₂₇	—	2	1	no	—
490	C₄×C₁₂₇	—	2	1	no	—
491	C₄×C₁₂₇	—	2	1	no	—
492	C₄×C₁₂₇	—	2	1	no	—
493	C₄×C₁₂₇	—	2	1	no	—
494	C₄×C₁₂₇	—	2	1	no	—
495	C₄×C₁₂₇	—	2	1	no	—
496	Dic₁₂₇	—	2	1	no	—
497	Dic₁₂₇	—	2	1	no	—
498	Dic₁₂₇	—	2	1	no	—
499	Dic₁₂₇	—	2	1	no	—
500	Dic₁₂₇	—	2	1	no	—
501	Dic₁₂₇	—	2	1	no	—
502	Dic₁₂₇	—	2	1	no	—
503	Dic₁₂₇	—	2	1	no	—
504	Dic₁₂₇	—	2	1	no	—
505	Dic₁₂₇	—	2	1	no	—
506	Dic₁₂₇	—	2	1	no	—
507	Dic₁₂₇	—	2	1	no	—
508	Dic₁₂₇	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₁₂₇	—	2	2	no	—
510	C₂×C₁₂₇	—	2	2	no	—
511	C₂×C₁₂₇	—	4	1	no	—
512	C₂×C₁₂₇	—	4	1	no	—
513	C₂×C₁₂₇	—	4	1	no	—
514	C₂×C₁₂₇	—	4	1	no	—
515	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₁₂₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
518	D₁₂₇	—	4	1	no	—
519	D₁₂₇	—	4	1	no	—
520	D₁₂₇	—	4	1	no	—
521	#3536	—	127	1	no	maximal, Sylow
522	C₁₂₇	#3536	1	1	yes	characteristic, complemented, Sylow
523	#562	—	127	1	no	—
524	#562	—	127	1	no	—
525	#562	—	127	1	no	—
526	#562	—	127	1	no	—
527	#554	—	127	1	no	—
528	#554	—	127	1	no	—
529	#548	—	127	1	no	—
530	#548	—	127	1	no	—
531	#547	—	127	1	no	—
532	#547	—	127	1	no	—
533	#546	—	127	1	no	—
534	#546	—	127	1	no	—
535	#546	—	127	1	no	—
536	#546	—	127	1	no	—
537	#546	—	127	1	no	—
538	#546	D₁₂₇	1	1	yes	characteristic, complemented
539	#543	—	127	1	no	—
540	#543	—	127	1	no	—
541	#542	—	127	1	no	—
542	#542	—	127	1	no	—
543	#539	—	127	1	no	—
544	#539	—	127	1	no	—
545	#538	—	127	1	no	—
546	#538	—	127	1	no	—
547	#537	—	127	1	no	—
548	#537	—	127	1	no	—
549	#537	—	127	1	no	—
550	#537	—	127	1	no	—
551	#525	—	127	1	no	—
552	C₂×C₂²⋊Q₈	—	127	1	no	—
553	C₂×#121	—	127	1	no	—
554	C₂×#41	—	127	1	no	—
555	C₂×#41	—	127	1	no	—
556	C₂×#41	—	127	1	no	—
557	C₂×#41	—	127	1	no	—
558	C₂×#41	—	127	1	no	—
559	C₂×#41	—	127	1	no	—
560	C₂×#41	C₂×D₁₂₇	1	1	yes	characteristic, complemented
561	C₂²×Q₈	—	127	1	no	—
562	C₂²×D₄	—	127	1	no	—
563	C₂²×D₄	—	127	1	no	—
564	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic
565	C₂³×C₄	—	127	1	no	—
566	C₄⋊Q₈	—	127	1	no	—
567	C₄⋊Q₈	—	127	1	no	—
568	#126	—	127	1	no	—
569	#126	—	127	1	no	—
570	#126	—	127	1	no	—
571	#126	—	127	1	no	—
572	#125	—	127	1	no	—
573	#125	—	127	1	no	—
574	#125	—	127	1	no	—
575	#125	—	127	1	no	—
576	#124	—	127	1	no	—
577	#124	—	127	1	no	—
578	#124	—	127	1	no	—
579	#124	—	127	1	no	—
580	#124	—	127	1	no	—
581	#124	—	127	1	no	—
582	#124	—	127	1	no	—
583	#124	—	127	1	no	—
584	#124	—	127	1	no	—
585	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
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	C₂×D₁₂₇	1	1	yes	characteristic, complemented
603	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
604	C₂²⋊Q₈	—	127	1	no	—
605	C₂²⋊Q₈	—	127	1	no	—
606	C₂²⋊Q₈	—	127	1	no	—
607	C₂²⋊Q₈	—	127	1	no	—
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	—	127	1	no	—
624	C₂²⋊Q₈	—	127	1	no	—
625	C₂²⋊Q₈	—	127	1	no	—
626	C₂²⋊Q₈	—	127	1	no	—
627	C₂²⋊Q₈	—	127	1	no	—
628	C₂²⋊Q₈	—	127	1	no	—
629	C₂²⋊Q₈	—	127	1	no	—
630	C₂²⋊Q₈	—	127	1	no	—
631	C₂²⋊Q₈	—	127	1	no	—
632	C₂²⋊Q₈	—	127	1	no	—
633	C₂²⋊Q₈	—	127	1	no	—
634	C₂²⋊Q₈	—	127	1	no	—
635	C₂²⋊Q₈	—	127	1	no	—
636	C₂²⋊Q₈	—	127	1	no	—
637	C₂²⋊Q₈	—	127	1	no	—
638	C₂²⋊Q₈	—	127	1	no	—
639	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic
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	—	127	1	no	—
646	#121	—	127	1	no	—
647	#121	—	127	1	no	—
648	#121	—	127	1	no	—
649	#121	—	127	1	no	—
650	#121	—	127	1	no	—
651	#121	—	127	1	no	—
652	#121	—	127	1	no	—
653	#121	—	127	1	no	—
654	#121	—	127	1	no	—
655	#121	—	127	1	no	—
656	#121	—	127	1	no	—
657	#121	—	127	1	no	—
658	#121	—	127	1	no	—
659	#121	—	127	1	no	—
660	#121	—	127	1	no	—
661	#121	—	127	1	no	—
662	#121	—	127	1	no	—
663	#121	—	127	1	no	—
664	#121	—	127	1	no	—
665	#121	—	127	1	no	—
666	#121	—	127	1	no	—
667	#121	—	127	1	no	—
668	#121	—	127	1	no	—
669	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
670	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
671	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
672	#120	—	127	1	no	—
673	#120	—	127	1	no	—
674	#120	—	127	1	no	—
675	#120	—	127	1	no	—
676	#120	C₂×D₁₂₇	1	1	yes	characteristic
677	#120	C₂×D₁₂₇	1	1	yes	characteristic
678	C₄×Q₈	—	127	1	no	—
679	C₄×Q₈	—	127	1	no	—
680	C₄×D₄	—	127	1	no	—
681	C₄×D₄	—	127	1	no	—
682	C₄×D₄	—	127	1	no	—
683	C₄×D₄	—	127	1	no	—
684	C₄×D₄	—	127	1	no	—
685	C₄×D₄	—	127	1	no	—
686	C₄×D₄	—	127	1	no	—
687	C₄×D₄	—	127	1	no	—
688	C₄×D₄	—	127	1	no	—
689	C₄×D₄	—	127	1	no	—
690	C₄×D₄	—	127	1	no	—
691	C₄×D₄	—	127	1	no	—
692	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
693	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
694	#117	—	127	1	no	—
695	C₂×C₄⋊C₄	—	127	1	no	—
696	C₂×C₄⋊C₄	—	127	1	no	—
697	C₂×C₄⋊C₄	—	127	1	no	—
698	C₂×C₄⋊C₄	—	127	1	no	—
699	C₂×C₄⋊C₄	—	127	1	no	—
700	C₂×C₄⋊C₄	—	127	1	no	—
701	C₂×C₂²⋊C₄	—	127	1	no	—
702	C₂×C₂²⋊C₄	—	127	1	no	—
703	C₂×C₂²⋊C₄	—	127	1	no	—
704	C₂×C₂²⋊C₄	—	127	1	no	—
705	C₂×C₂²⋊C₄	—	127	1	no	—
706	C₂×C₂²⋊C₄	—	127	1	no	—
707	C₂×C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
709	C₂⁴	—	127	1	no	—
710	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
711	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
712	#41	—	4	2	no	—
713	#41	—	508	2	no	—
714	#41	—	508	2	no	—
715	#41	—	508	2	no	—
716	#41	—	508	2	no	—
717	#41	—	508	2	no	—
718	#41	—	508	2	no	—
719	C₂×Q₈	—	127	1	no	—
720	C₂×Q₈	—	127	1	no	—
721	C₂×Q₈	—	127	1	no	—
722	C₂×Q₈	—	127	1	no	—
723	C₂×Q₈	—	127	1	no	—
724	C₂×Q₈	—	127	1	no	—
725	C₂×Q₈	—	127	1	no	—
726	C₂×Q₈	—	127	1	no	—
727	C₂×Q₈	—	508	2	no	—
728	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	127	1	no	—
731	C₂×D₄	—	127	1	no	—
732	C₂×D₄	—	127	1	no	—
733	C₂×D₄	—	127	1	no	—
734	C₂×D₄	—	127	1	no	—
735	C₂×D₄	—	127	1	no	—
736	C₂×D₄	—	127	1	no	—
737	C₂×D₄	—	127	1	no	—
738	C₂×D₄	—	127	1	no	—
739	C₂×D₄	—	127	1	no	—
740	C₂×D₄	—	127	1	no	—
741	C₂×D₄	—	127	1	no	—
742	C₂×D₄	—	127	1	no	—
743	C₂×D₄	—	127	1	no	—
744	C₂×D₄	—	127	1	no	—
745	C₂×D₄	—	127	1	no	—
746	C₂×D₄	—	127	1	no	—
747	C₂×D₄	—	127	1	no	—
748	C₂×D₄	—	508	2	no	—
749	C₂×D₄	—	508	2	no	—
750	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
751	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
752	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
753	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
754	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
755	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
756	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
757	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
758	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
759	C₂²×C₄	—	127	1	no	—
760	C₂²×C₄	—	127	1	no	—
761	C₂²×C₄	—	127	1	no	—
762	C₂²×C₄	—	127	1	no	—
763	C₂²×C₄	—	127	1	no	—
764	C₂²×C₄	—	127	1	no	—
765	C₂²×C₄	—	127	1	no	—
766	C₂²×C₄	—	127	1	no	—
767	C₂²×C₄	—	127	1	no	—
768	C₂²×C₄	—	127	1	no	—
769	C₂²×C₄	—	127	1	no	—
770	C₂²×C₄	—	127	1	no	—
771	C₂²×C₄	—	127	1	no	—
772	C₂²×C₄	—	127	1	no	—
773	C₂²×C₄	—	127	1	no	—
774	C₂²×C₄	—	127	1	no	—
775	C₂²×C₄	—	127	1	no	—
776	C₂²×C₄	—	127	1	no	—
777	C₂²×C₄	—	127	1	no	—
778	C₂²×C₄	—	127	1	no	—
779	C₂²×C₄	—	508	2	no	—
780	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
781	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
782	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
783	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
784	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
785	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	—	127	1	no	—
791	C₄⋊C₄	—	127	1	no	—
792	C₄⋊C₄	—	127	1	no	—
793	C₄⋊C₄	—	127	1	no	—
794	C₄⋊C₄	—	127	1	no	—
795	C₄⋊C₄	—	127	1	no	—
796	C₄⋊C₄	—	127	1	no	—
797	C₄⋊C₄	—	127	1	no	—
798	C₄⋊C₄	—	127	1	no	—
799	C₄⋊C₄	—	127	1	no	—
800	C₄⋊C₄	—	127	1	no	—
801	C₄⋊C₄	—	127	1	no	—
802	C₄⋊C₄	—	127	1	no	—
803	C₄⋊C₄	—	127	1	no	—
804	C₄⋊C₄	—	127	1	no	—
805	C₄⋊C₄	—	127	1	no	—
806	C₄⋊C₄	—	127	1	no	—
807	C₄⋊C₄	—	127	1	no	—
808	C₄⋊C₄	—	127	1	no	—
809	C₄⋊C₄	—	127	1	no	—
810	C₄⋊C₄	—	127	1	no	—
811	C₄⋊C₄	—	127	1	no	—
812	C₄⋊C₄	—	127	1	no	—
813	C₄⋊C₄	—	127	1	no	—
814	C₄⋊C₄	—	127	1	no	—
815	C₄⋊C₄	—	127	1	no	—
816	C₄⋊C₄	—	127	1	no	—
817	C₄⋊C₄	—	127	1	no	—
818	C₄⋊C₄	—	127	1	no	—
819	C₄⋊C₄	—	127	1	no	—
820	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
822	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
823	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	—	127	1	no	—
833	C₂²⋊C₄	—	127	1	no	—
834	C₂²⋊C₄	—	127	1	no	—
835	C₂²⋊C₄	—	127	1	no	—
836	C₂²⋊C₄	—	127	1	no	—
837	C₂²⋊C₄	—	127	1	no	—
838	C₂²⋊C₄	—	127	1	no	—
839	C₂²⋊C₄	—	127	1	no	—
840	C₂²⋊C₄	—	127	1	no	—
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	—	127	1	no	—
856	C₂²⋊C₄	—	127	1	no	—
857	C₂²⋊C₄	—	127	1	no	—
858	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
859	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
860	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
869	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
870	C₄²	—	127	1	no	—
871	C₄²	—	127	1	no	—
872	C₄²	—	127	1	no	—
873	C₄²	—	127	1	no	—
874	C₄²	—	127	1	no	—
875	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	4	1	no	—
880	C₂³	—	4	1	no	—
881	C₂³	—	4	1	no	—
882	C₂³	—	127	1	no	—
883	C₂³	—	127	1	no	—
884	C₂³	—	127	1	no	—
885	C₂³	—	508	1	no	—
886	C₂³	—	508	1	no	—
887	C₂³	—	254	2	no	—
888	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
889	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
890	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
891	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
892	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
893	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
894	Q₈	—	4	1	no	—
895	Q₈	—	508	1	no	—
896	Q₈	—	508	1	no	—
897	Q₈	—	508	1	no	—
898	Q₈	—	508	1	no	—
899	Q₈	—	508	1	no	—
900	Q₈	—	508	1	no	—
901	Q₈	—	254	2	no	—
902	Q₈	—	254	2	no	—
903	D₄	—	2	2	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	1	no	—
910	D₄	—	4	1	no	—
911	D₄	—	4	1	no	—
912	D₄	—	508	1	no	—
913	D₄	—	508	1	no	—
914	D₄	—	508	1	no	—
915	D₄	—	508	1	no	—
916	D₄	—	508	1	no	—
917	D₄	—	508	1	no	—
918	D₄	—	508	1	no	—
919	D₄	—	508	1	no	—
920	D₄	—	508	1	no	—
921	D₄	—	508	1	no	—
922	D₄	—	508	1	no	—
923	D₄	—	508	1	no	—
924	D₄	—	254	2	no	—
925	D₄	—	254	2	no	—
926	D₄	—	254	2	no	—
927	D₄	—	254	2	no	—
928	D₄	—	254	2	no	—
929	D₄	—	254	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	127	1	no	—
937	C₂×C₄	—	127	1	no	—
938	C₂×C₄	—	127	1	no	—
939	C₂×C₄	—	127	1	no	—
940	C₂×C₄	—	127	1	no	—
941	C₂×C₄	—	127	1	no	—
942	C₂×C₄	—	127	1	no	—
943	C₂×C₄	—	127	1	no	—
944	C₂×C₄	—	127	1	no	—
945	C₂×C₄	—	127	1	no	—
946	C₂×C₄	—	127	1	no	—
947	C₂×C₄	—	127	1	no	—
948	C₂×C₄	—	127	1	no	—
949	C₂×C₄	—	508	1	no	—
950	C₂×C₄	—	508	1	no	—
951	C₂×C₄	—	508	1	no	—
952	C₂×C₄	—	508	1	no	—
953	C₂×C₄	—	508	1	no	—
954	C₂×C₄	—	508	1	no	—
955	C₂×C₄	—	508	1	no	—
956	C₂×C₄	—	508	1	no	—
957	C₂×C₄	—	508	1	no	—
958	C₂×C₄	—	508	1	no	—
959	C₂×C₄	—	508	1	no	—
960	C₂×C₄	—	508	1	no	—
961	C₂×C₄	—	508	1	no	—
962	C₂×C₄	—	508	1	no	—
963	C₂×C₄	—	254	2	no	—
964	C₂×C₄	—	254	2	no	—
965	C₂×C₄	—	254	2	no	—
966	C₂×C₄	—	254	2	no	—
967	C₂×C₄	—	254	2	no	—
968	C₂×C₄	—	254	2	no	—
969	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
970	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
971	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
972	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
973	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
974	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
975	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
976	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
977	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	4	4	no	—
995	C₂²	—	8	2	no	—
996	C₂²	—	1016	2	no	—
997	C₂²	—	254	1	no	—
998	C₂²	—	254	1	no	—
999	C₂²	—	254	1	no	—
1000	C₂²	—	254	1	no	—
1001	C₂²	—	254	1	no	—
1002	C₂²	—	254	1	no	—
1003	C₂²	—	254	1	no	—
1004	C₂²	—	254	1	no	—
1005	C₂²	—	254	1	no	—
1006	C₂²	#16861254	1	2	yes	—
1007	C₂²	#16861256	1	2	yes	—
1008	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	127	2	no	—
1019	C₄	—	254	1	no	—
1020	C₄	—	254	1	no	—
1021	C₄	—	254	1	no	—
1022	C₄	—	254	1	no	—
1023	C₄	—	254	1	no	—
1024	C₄	—	254	1	no	—
1025	C₄	—	254	1	no	—
1026	C₄	—	254	1	no	—
1027	C₄	—	254	1	no	—
1028	C₄	—	254	1	no	—
1029	C₄	—	254	1	no	—
1030	C₄	—	254	1	no	—
1031	C₂	—	2	2	no	—
1032	C₂	—	2	2	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	4	1	no	—
1036	C₂	—	4	1	no	—
1037	C₂	—	508	1	no	—
1038	C₂	—	508	1	no	—
1039	C₂	—	508	1	no	—
1040	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
1041	C₂	C₂×#16861254	1	1	yes	characteristic
1042	C₂	C₂×#16861256	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#546×C₁₂₇	C₂
hypercenter	#546	D₁₂₇
hypocenter	C₁₂₇	#3536
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #22550623	C₂	semidirect
2. #22550621	C₂	semidirect
3. #22550621	C₂	semidirect
4. #22550620	C₂	semidirect
5. #22550585	C₂	semidirect
6. #22550580	C₂	semidirect
7. #22550535	C₂	semidirect
8. #22550532	C₂	semidirect
9. #22550525	C₂	semidirect
10. #22550524	C₂	semidirect
11. #22550520	C₂	semidirect
12. #22550516	C₂	semidirect
13. #22550516	C₂	semidirect
14. #22550513	C₂	semidirect
15. #22550513	C₂	semidirect
16. #22550502	C₂	semidirect
17. #22550501	C₂	semidirect
18. #22550494	C₂	semidirect
19. #22550490	C₂	semidirect
20. #22550470	C₂	semidirect
21. #22550468	C₂	semidirect
22. #22550461	C₂	semidirect
23. #22550459	C₂	semidirect
24. #22550455	C₂	semidirect
25. #22550454	C₂	semidirect
26. #22550453	C₂	semidirect
27. #22550453	C₂	semidirect
28. #22550382	C₂	semidirect
29. C₂×#16861186	C₂	semidirect
30. C₂×#16861181	C₂	semidirect
31. #546×C₁₂₇	C₂	semidirect
32. C₂×#14523248	C₂²	semidirect
33. C₂×#14523248	C₂²	semidirect
34. C₂×#14523247	C₂²	semidirect
35. C₂×#14523247	C₂²	semidirect
36. C₂×#14523247	C₂²	semidirect
37. C₂×#14523247	C₂²	semidirect
38. C₂²×Dic₂₅₄	C₂²	semidirect
42. #16861208	C₂²	semidirect
43. #16861207	C₂²	semidirect
44. #16861204	C₂²	semidirect
45. #16861203	C₂²	semidirect
46. #16861202	C₂²	semidirect
47. #16861202	C₂²	semidirect
48. #16861201	C₂²	semidirect
49. #16861200	C₂²	semidirect
50. #16861199	C₂²	semidirect
51. #16861199	C₂²	semidirect
52. #16861197	C₂²	semidirect
53. #16861196	C₂²	semidirect
54. #16861196	C₂²	semidirect
55. #16861195	C₂²	semidirect
56. #16861195	C₂²	semidirect
57. #16861195	C₂²	semidirect
58. #16861195	C₂²	semidirect
59. #16861195	C₂²	semidirect
60. #16861195	C₂²	semidirect
61. #16861194	C₂²	semidirect
62. #16861193	C₂²	semidirect
63. #16861193	C₂²	semidirect
64. #16861193	C₂²	semidirect
65. #16861192	C₂²	semidirect
66. #16861192	C₂²	semidirect
67. #16861192	C₂²	semidirect
68. #16861191	C₂²	semidirect
69. #16861191	C₂²	semidirect
70. #16861191	C₂²	semidirect
71. #16861191	C₂²	semidirect
72. #16861191	C₂²	semidirect
73. #16861190	C₂²	semidirect
74. #16861190	C₂²	semidirect
75. #16861190	C₂²	semidirect
76. #16861190	C₂²	semidirect
77. #16861189	C₂²	semidirect
78. #16861189	C₂²	semidirect
80. #16861188	C₂²	semidirect
81. #16861188	C₂²	semidirect
82. #16861188	C₂²	semidirect
83. #16861188	C₂²	semidirect
84. #16861188	C₂²	semidirect
85. #16861187	C₂²	semidirect
86. #16861187	C₂²	semidirect
87. #16861187	C₂²	semidirect
88. #16861187	C₂²	semidirect
89. #16861187	C₂²	semidirect
90. #16861187	C₂²	semidirect
98. #16861186	C₂²	semidirect
99. #16861186	C₂²	semidirect
100. #16861186	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. #16861186	C₂²	semidirect
108. #16861186	C₂²	semidirect
109. #16861185	C₂²	semidirect
110. #16861185	C₂²	semidirect
111. #16861185	C₂²	semidirect
112. #16861183	C₂²	semidirect
113. #16861183	C₂²	semidirect
114. #16861183	C₂²	semidirect
115. #16861182	C₂²	semidirect
116. #16861182	C₂²	semidirect
117. #16861182	C₂²	semidirect
118. #16861182	C₂²	semidirect
119. #16861182	C₂²	semidirect
129. #16861181	C₂²	semidirect
130. #16861181	C₂²	semidirect
131. #16861181	C₂²	semidirect
132. #16861181	C₂²	semidirect
133. #16861181	C₂²	semidirect
134. #16861181	C₂²	semidirect
135. #16861181	C₂²	semidirect
136. #16861181	C₂²	semidirect
137. #16861180	C₂²	semidirect
138. #16861180	C₂²	semidirect
139. #16861180	C₂²	semidirect
140. #16861180	C₂²	semidirect
145. C₄×Dic₂₅₄	C₂²	semidirect
146. #16861174	C₂²	semidirect
149. D₄×Dic₁₂₇	C₂²	semidirect
150. D₄×Dic₁₂₇	C₂²	semidirect
152. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
153. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
156. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
158. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
159. #16861165	C₂²	semidirect
160. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
162. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
163. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
164. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
165. C₄⋊C₄×D₁₂₇	C₂²	semidirect
172. C₂×#41×C₁₂₇	C₂²	semidirect
174. #124×C₁₂₇	C₂²	semidirect
175. #123×C₁₂₇	C₂²	semidirect
176. #123×C₁₂₇	C₂²	semidirect
178. #121×C₁₂₇	C₂²	semidirect
179. #121×C₁₂₇	C₂²	semidirect
180. #121×C₁₂₇	C₂²	semidirect
184. C₄×D₄×C₁₂₇	C₂²	semidirect
522. C₁₂₇	#3536	semidirect
538. #546	D₁₂₇	semidirect
560. C₂×#41	C₂×D₁₂₇	semidirect
585. #124	C₂×D₁₂₇	semidirect
602. #123	C₂×D₁₂₇	semidirect
603. #123	C₂×D₁₂₇	semidirect
669. #121	C₂×D₁₂₇	semidirect
670. #121	C₂×D₁₂₇	semidirect
671. #121	C₂×D₁₂₇	semidirect
693. C₄×D₄	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550623	2
#22550621	2
#22550620	2
#22550585	2
#22550580	2
#22550535	2
#22550532	2
#22550525	2
#22550524	2
#22550520	2
#22550516	2
#22550513	2
#22550502	2
#22550501	2
#22550494	2
#22550490	2
#22550470	2
#22550468	2
#22550461	2
#22550459	2
#22550455	2
#22550454	2
#22550453	2
#22550382	2
C₂×#16861186	2
C₂×#16861181	2
#546×C₁₂₇	2
#3536	127