Subgroups — #30652113

Order 16256.

1040 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550496	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550494	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550492	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550490	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550485	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550483	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550478	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550476	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550474	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550472	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550469	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550467	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550465	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550462	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550460	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550458	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550430	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550423	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550413	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550410	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550408	C₂	1	1	yes	maximal, characteristic, complemented
22	#22550406	C₂	1	1	yes	maximal, characteristic, complemented
23	#22550406	C₂	1	1	yes	maximal, characteristic, complemented
24	#22550404	C₂	1	1	yes	maximal, characteristic, complemented
25	#22550404	C₂	1	1	yes	maximal, characteristic, complemented
26	#22550385	C₂	1	1	yes	maximal, characteristic, complemented
27	#22550385	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#14523248	C₂	1	1	yes	maximal, characteristic, complemented
29	#22550344	C₂	1	1	yes	maximal, characteristic, complemented
30	#117×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#529×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523248	C₂²	1	1	yes	characteristic
33	C₂×#14523248	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
35	#16861208	C₂²	1	1	yes	characteristic, complemented
36	#16861208	C₂²	1	1	yes	characteristic, complemented
37	#16861207	C₂²	1	1	yes	characteristic, complemented
38	#16861205	C₂²	1	1	yes	characteristic, complemented
39	#16861204	C₂²	1	1	yes	characteristic
40	#16861204	C₂²	1	1	yes	characteristic
41	#16861204	C₂²	1	1	yes	characteristic
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	#16861203	C₂²	1	1	yes	characteristic
46	#16861203	C₂²	1	1	yes	characteristic, complemented
47	#16861202	C₂²	1	1	yes	characteristic
48	#16861202	C₂²	1	1	yes	characteristic
49	#16861202	C₂²	1	1	yes	characteristic
50	#16861202	C₂²	1	1	yes	characteristic, complemented
51	#16861202	C₂²	1	1	yes	characteristic, complemented
52	#16861202	C₂²	1	1	yes	characteristic, complemented
53	#16861201	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	#16861199	C₂²	1	1	yes	characteristic, complemented
59	#16861199	C₂²	1	1	yes	characteristic, complemented
60	#16861199	C₂²	1	1	yes	characteristic, complemented
61	#16861199	C₂²	1	1	yes	characteristic, complemented
62	#16861198	C₂²	1	1	yes	characteristic
63	#16861197	C₂²	1	1	yes	characteristic
64	#16861196	C₂²	1	1	yes	characteristic
65	#16861195	C₂²	1	1	yes	characteristic
66	#16861195	C₂²	1	1	yes	characteristic
67	#16861195	C₂²	1	1	yes	characteristic
68	#16861195	C₂²	1	1	yes	characteristic
69	#16861195	C₂²	1	1	yes	characteristic, complemented
70	#16861195	C₂²	1	1	yes	characteristic, complemented
71	#16861194	C₂²	1	1	yes	characteristic
72	#16861194	C₂²	1	1	yes	characteristic
73	#16861194	C₂²	1	1	yes	characteristic
74	#16861194	C₂²	1	1	yes	characteristic
75	#16861194	C₂²	1	1	yes	characteristic, complemented
76	#16861194	C₂²	1	1	yes	characteristic, complemented
77	#16861193	C₂²	1	1	yes	characteristic
78	#16861193	C₂²	1	1	yes	characteristic, complemented
79	#16861192	C₂²	1	1	yes	characteristic
80	#16861192	C₂²	1	1	yes	characteristic, complemented
81	#16861191	C₂²	1	1	yes	characteristic
82	#16861191	C₂²	1	1	yes	characteristic
83	#16861191	C₂²	1	1	yes	characteristic
84	#16861191	C₂²	1	1	yes	characteristic
85	#16861191	C₂²	1	1	yes	characteristic, complemented
86	#16861191	C₂²	1	1	yes	characteristic, complemented
87	#16861190	C₂²	1	1	yes	characteristic
88	#16861190	C₂²	1	1	yes	characteristic, complemented
89	#16861189	C₂²	1	1	yes	characteristic
90	#16861189	C₂²	1	1	yes	characteristic, complemented
91	#16861188	C₂²	1	1	yes	characteristic, complemented
92	#16861187	C₂²	1	1	yes	characteristic
93	#16861187	C₂²	1	1	yes	characteristic
94	#16861187	C₂²	1	1	yes	characteristic
95	#16861187	C₂²	1	1	yes	characteristic
96	#16861187	C₂²	1	1	yes	characteristic, complemented
97	#16861187	C₂²	1	1	yes	characteristic, complemented
98	#16861186	C₂²	1	1	yes	characteristic
99	#16861186	C₂²	1	1	yes	characteristic
100	#16861186	C₂²	1	1	yes	characteristic, complemented
101	#16861186	C₂²	1	1	yes	characteristic, complemented
102	#16861185	C₂²	1	1	yes	characteristic
103	#16861185	C₂²	1	1	yes	characteristic, complemented
104	#16861184	C₂²	1	1	yes	characteristic
105	#16861184	C₂²	1	1	yes	characteristic
106	#16861183	C₂²	1	1	yes	characteristic
107	#16861182	C₂²	1	1	yes	characteristic
108	#16861182	C₂²	1	1	yes	characteristic
109	#16861182	C₂²	1	1	yes	characteristic
110	#16861182	C₂²	1	1	yes	characteristic
111	#16861182	C₂²	1	1	yes	characteristic
112	#16861182	C₂²	1	1	yes	characteristic
113	#16861181	C₂²	1	1	yes	characteristic
114	#16861181	C₂²	1	1	yes	characteristic
115	#16861181	C₂²	1	1	yes	characteristic
116	#16861181	C₂²	1	1	yes	characteristic
117	#16861180	C₂²	1	1	yes	characteristic
118	#16861180	C₂²	1	1	yes	characteristic
119	#16861179	C₂²	1	1	yes	characteristic
120	#16861179	C₂²	1	1	yes	characteristic
121	#16861177	C₂²	1	1	yes	characteristic
122	#16861177	C₂²	1	1	yes	characteristic
123	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
124	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
125	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
126	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
127	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
128	#16861174	C₂²	1	1	yes	characteristic, complemented
129	#16861174	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
131	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
132	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
133	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
134	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
135	#16861171	C₂²	1	1	yes	characteristic
136	#16861171	C₂²	1	1	yes	characteristic
137	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
138	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
139	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
140	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
141	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
142	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
143	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
144	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
146	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
147	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
148	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	#16861168	C₂²	1	1	yes	characteristic
152	#16861168	C₂²	1	1	yes	characteristic, complemented
153	#16861167	C₂²	1	1	yes	characteristic
154	#16861167	C₂²	1	1	yes	characteristic
155	#16861166	C₂²	1	1	yes	characteristic
156	#16861166	C₂²	1	1	yes	characteristic
157	#16861166	C₂²	1	1	yes	characteristic
158	#16861166	C₂²	1	1	yes	characteristic
159	#16861166	C₂²	1	1	yes	characteristic, complemented
160	#16861166	C₂²	1	1	yes	characteristic, complemented
161	#16861165	C₂²	1	1	yes	characteristic
162	#16861165	C₂²	1	1	yes	characteristic
163	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
164	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
167	C₂×C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
168	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
169	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
170	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₂₇	C₂²	1	1	yes	characteristic
173	#126×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
174	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
175	#124×C₁₂₇	C₂²	1	1	yes	characteristic
176	#123×C₁₂₇	C₂²	1	1	yes	characteristic
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	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
183	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
184	#117×C₁₂₇	C₂²	1	1	yes	characteristic
185	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
188	#14523248	—	2	4	no	—
189	#14523248	—	2	4	no	—
190	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
191	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
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×D₅₀₈	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	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
211	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
212	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₁₂₇	—	2	4	no	—
214	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
238	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₁₂₇⋊C₄	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	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₁₂₇	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	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₁₂₇)⋊C₄	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	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
297	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
298	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
299	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
300	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
301	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
302	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
303	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
304	C₄×Dic₁₂₇	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	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
311	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
312	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
313	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
314	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
315	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
316	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
325	C₄⋊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	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×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	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
339	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
340	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
341	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
342	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
343	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
344	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
345	C₂²×D₁₂₇	—	2	2	no	—
346	C₂²×D₁₂₇	—	4	1	no	—
347	C₂²×D₁₂₇	—	4	1	no	—
348	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
349	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
350	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
351	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
352	Dic₂₅₄	—	2	2	no	—
353	Dic₂₅₄	—	2	2	no	—
354	Dic₂₅₄	—	4	1	no	—
355	Dic₂₅₄	—	4	1	no	—
356	Dic₂₅₄	—	4	1	no	—
357	D₅₀₈	—	2	2	no	—
358	D₅₀₈	—	2	2	no	—
359	D₅₀₈	—	4	1	no	—
360	D₅₀₈	—	4	1	no	—
361	D₅₀₈	—	4	1	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	—	4	1	no	—
367	C₂²⋊D₁₂₇	—	4	1	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	C₂×Dic₁₂₇	—	2	2	no	—
373	C₂×Dic₁₂₇	—	4	1	no	—
374	C₂×Dic₁₂₇	—	4	1	no	—
375	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
387	C₄×D₁₂₇	—	2	2	no	—
388	C₄×D₁₂₇	—	2	2	no	—
389	C₄×D₁₂₇	—	2	2	no	—
390	C₄×D₁₂₇	—	2	2	no	—
391	C₄×D₁₂₇	—	2	2	no	—
392	C₄×D₁₂₇	—	4	1	no	—
393	C₄×D₁₂₇	—	4	1	no	—
394	C₄×D₁₂₇	—	4	1	no	—
395	C₄×D₁₂₇	—	4	1	no	—
396	C₄×D₁₂₇	—	4	1	no	—
397	C₄×D₁₂₇	—	4	1	no	—
398	C₄×D₁₂₇	—	4	1	no	—
399	C₄×D₁₂₇	—	4	1	no	—
400	C₄×D₁₂₇	#41	1	4	yes	—
401	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
402	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
403	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
404	Q₈×C₁₂₇	—	4	1	no	—
405	D₄×C₁₂₇	—	4	1	no	—
406	D₄×C₁₂₇	—	4	1	no	—
407	D₄×C₁₂₇	—	4	1	no	—
408	C₂×C₄×C₁₂₇	—	2	2	no	—
409	C₂×C₄×C₁₂₇	—	2	2	no	—
410	C₂×C₄×C₁₂₇	—	2	2	no	—
411	C₂×C₄×C₁₂₇	—	4	1	no	—
412	C₂×C₄×C₁₂₇	—	4	1	no	—
413	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
425	C₂²×C₁₂₇	—	2	1	no	—
426	C₂²×C₁₂₇	—	2	1	no	—
427	C₂²×C₁₂₇	—	2	1	no	—
428	C₂²×C₁₂₇	—	2	1	no	—
429	C₂²×C₁₂₇	—	2	1	no	—
430	C₂²×C₁₂₇	—	2	1	no	—
431	C₂²×C₁₂₇	—	2	1	no	—
432	C₂²×C₁₂₇	—	2	1	no	—
433	C₂²×C₁₂₇	—	2	1	no	—
434	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
435	C₂×D₁₂₇	—	2	1	no	—
436	C₂×D₁₂₇	—	2	1	no	—
437	C₂×D₁₂₇	—	2	1	no	—
438	C₂×D₁₂₇	—	2	1	no	—
439	C₂×D₁₂₇	—	2	1	no	—
440	C₂×D₁₂₇	—	2	1	no	—
441	C₂×D₁₂₇	—	2	1	no	—
442	C₂×D₁₂₇	—	2	1	no	—
443	C₂×D₁₂₇	—	2	1	no	—
444	C₂×D₁₂₇	—	2	1	no	—
445	C₂×D₁₂₇	—	2	1	no	—
446	C₂×D₁₂₇	—	4	4	no	—
447	C₂×D₁₂₇	C₂×#41	1	2	yes	—
448	C₄×C₁₂₇	—	2	1	no	—
449	C₄×C₁₂₇	—	2	1	no	—
450	C₄×C₁₂₇	—	2	1	no	—
451	C₄×C₁₂₇	—	2	1	no	—
452	C₄×C₁₂₇	—	2	1	no	—
453	C₄×C₁₂₇	—	2	1	no	—
454	C₄×C₁₂₇	—	2	1	no	—
455	C₄×C₁₂₇	—	2	1	no	—
456	C₄×C₁₂₇	—	2	1	no	—
457	C₄×C₁₂₇	—	2	1	no	—
458	C₄×C₁₂₇	—	2	1	no	—
459	C₄×C₁₂₇	C₂×#41	1	2	yes	—
460	Dic₁₂₇	—	2	1	no	—
461	Dic₁₂₇	—	2	1	no	—
462	Dic₁₂₇	—	2	1	no	—
463	Dic₁₂₇	—	2	1	no	—
464	Dic₁₂₇	—	2	1	no	—
465	Dic₁₂₇	—	2	1	no	—
466	Dic₁₂₇	—	2	1	no	—
467	Dic₁₂₇	—	2	1	no	—
468	Dic₁₂₇	—	2	1	no	—
469	Dic₁₂₇	—	2	1	no	—
470	Dic₁₂₇	—	2	1	no	—
471	Dic₁₂₇	C₂×#41	1	2	yes	—
472	C₂×C₁₂₇	—	4	1	no	—
473	C₂×C₁₂₇	—	4	1	no	—
474	C₂×C₁₂₇	—	4	1	no	—
475	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
476	C₂×C₁₂₇	#585	1	1	yes	characteristic
477	C₂×C₁₂₇	#585	1	1	yes	characteristic
478	D₁₂₇	—	2	2	no	—
479	D₁₂₇	—	4	1	no	—
480	D₁₂₇	—	4	1	no	—
481	D₁₂₇	—	4	1	no	—
482	#3455	—	127	1	no	maximal, Sylow
483	C₁₂₇	#3455	1	1	yes	characteristic, complemented, Sylow
484	#542	—	127	1	no	—
485	#542	—	127	1	no	—
486	#542	—	127	1	no	—
487	#542	—	127	1	no	—
488	#541	—	127	1	no	—
489	#541	—	127	1	no	—
490	#540	—	127	1	no	—
491	#540	—	127	1	no	—
492	#539	—	127	1	no	—
493	#539	—	127	1	no	—
494	#539	—	127	1	no	—
495	#539	—	127	1	no	—
496	#538	—	127	1	no	—
497	#538	—	127	1	no	—
498	#538	—	127	1	no	—
499	#538	—	127	1	no	—
500	#533	—	127	1	no	—
501	#532	—	127	1	no	—
502	#529	—	127	1	no	—
503	#529	—	127	1	no	—
504	#529	—	127	1	no	—
505	#529	—	127	1	no	—
506	#529	—	127	1	no	—
507	#529	—	127	1	no	—
508	#529	—	127	1	no	—
509	#529	D₁₂₇	1	1	yes	characteristic, complemented
510	#525	—	127	1	no	—
511	#525	—	127	1	no	—
512	C₄×#41	—	127	1	no	—
513	C₄×#41	—	127	1	no	—
514	C₂×#117	—	127	1	no	—
515	C₂×#41	—	127	1	no	—
516	C₂×#41	—	127	1	no	—
517	C₂³×C₄	—	127	1	no	—
518	C₄⋊Q₈	—	127	1	no	—
519	C₄⋊Q₈	—	127	1	no	—
520	C₄⋊Q₈	—	127	1	no	—
521	#127	—	127	1	no	—
522	#126	—	127	1	no	—
523	#126	—	127	1	no	—
524	#126	—	127	1	no	—
525	#126	—	127	1	no	—
526	#126	—	127	1	no	—
527	#126	—	127	1	no	—
528	#126	—	127	1	no	—
529	#126	—	127	1	no	—
530	#126	—	127	1	no	—
531	#126	—	127	1	no	—
532	#126	—	127	1	no	—
533	#126	—	127	1	no	—
534	#126	—	127	1	no	—
535	#126	—	127	1	no	—
536	#126	C₂×D₁₂₇	1	1	yes	characteristic
537	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
538	#125	—	127	1	no	—
539	#125	—	127	1	no	—
540	#125	—	127	1	no	—
541	#125	—	127	1	no	—
542	#125	—	127	1	no	—
543	#125	—	127	1	no	—
544	#125	—	127	1	no	—
545	#125	—	127	1	no	—
546	#125	—	127	1	no	—
547	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
548	#124	—	127	1	no	—
549	#124	—	127	1	no	—
550	#124	—	127	1	no	—
551	#124	—	127	1	no	—
552	#124	—	127	1	no	—
553	#124	—	127	1	no	—
554	#124	—	127	1	no	—
555	#124	—	127	1	no	—
556	#124	—	127	1	no	—
557	#124	C₂×D₁₂₇	1	1	yes	characteristic
558	#123	—	127	1	no	—
559	#123	—	127	1	no	—
560	#123	—	127	1	no	—
561	#123	—	127	1	no	—
562	#123	—	127	1	no	—
563	#123	—	127	1	no	—
564	#123	—	127	1	no	—
565	#123	—	127	1	no	—
566	#123	—	127	1	no	—
567	#123	—	127	1	no	—
568	#123	—	127	1	no	—
569	#123	—	127	1	no	—
570	#123	—	127	1	no	—
571	#123	—	127	1	no	—
572	#123	—	127	1	no	—
573	#123	—	127	1	no	—
574	#123	—	127	1	no	—
575	#123	—	127	1	no	—
576	#123	C₂×D₁₂₇	1	1	yes	characteristic
577	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
578	C₂²⋊Q₈	—	127	1	no	—
579	C₂²⋊Q₈	—	127	1	no	—
580	C₂²⋊Q₈	—	127	1	no	—
581	C₂²⋊Q₈	—	127	1	no	—
582	C₂²⋊Q₈	—	127	1	no	—
583	C₂²⋊Q₈	—	127	1	no	—
584	C₂²⋊Q₈	—	127	1	no	—
585	C₂²⋊Q₈	—	127	1	no	—
586	C₂²⋊Q₈	—	127	1	no	—
587	C₂²⋊Q₈	—	127	1	no	—
588	C₂²⋊Q₈	—	127	1	no	—
589	C₂²⋊Q₈	—	127	1	no	—
590	C₂²⋊Q₈	—	127	1	no	—
591	C₂²⋊Q₈	—	127	1	no	—
592	C₂²⋊Q₈	—	127	1	no	—
593	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
594	#121	—	127	1	no	—
595	#121	—	127	1	no	—
596	#121	—	127	1	no	—
597	#121	—	127	1	no	—
598	#121	—	127	1	no	—
599	#121	—	127	1	no	—
600	#121	—	127	1	no	—
601	#121	—	127	1	no	—
602	#121	—	127	1	no	—
603	#121	—	127	1	no	—
604	#121	—	127	1	no	—
605	#121	—	127	1	no	—
606	#121	—	127	1	no	—
607	#121	—	127	1	no	—
608	#121	—	127	1	no	—
609	#121	C₂×D₁₂₇	1	1	yes	characteristic
610	#120	—	127	1	no	—
611	#120	—	127	1	no	—
612	#120	—	127	1	no	—
613	#120	—	127	1	no	—
614	C₄×Q₈	—	127	1	no	—
615	C₄×Q₈	—	127	1	no	—
616	C₄×Q₈	—	127	1	no	—
617	C₄×Q₈	—	127	1	no	—
618	C₄×Q₈	—	127	1	no	—
619	C₄×Q₈	—	127	1	no	—
620	C₄×Q₈	—	127	1	no	—
621	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
622	C₄×D₄	—	127	1	no	—
623	C₄×D₄	—	127	1	no	—
624	C₄×D₄	—	127	1	no	—
625	C₄×D₄	—	127	1	no	—
626	C₄×D₄	—	127	1	no	—
627	C₄×D₄	—	127	1	no	—
628	C₄×D₄	—	127	1	no	—
629	C₄×D₄	—	127	1	no	—
630	C₄×D₄	—	127	1	no	—
631	C₄×D₄	—	127	1	no	—
632	C₄×D₄	—	127	1	no	—
633	C₄×D₄	—	127	1	no	—
634	C₄×D₄	—	127	1	no	—
635	C₄×D₄	—	127	1	no	—
636	C₄×D₄	—	127	1	no	—
637	C₄×D₄	—	127	1	no	—
638	C₄×D₄	—	127	1	no	—
639	C₄×D₄	—	127	1	no	—
640	C₄×D₄	—	127	1	no	—
641	C₄×D₄	—	127	1	no	—
642	C₄×D₄	—	127	1	no	—
643	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
644	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
645	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
646	#117	—	127	1	no	—
647	#117	—	127	1	no	—
648	#117	—	127	1	no	—
649	#117	—	127	1	no	—
650	#117	—	127	1	no	—
651	#117	—	127	1	no	—
652	#117	—	127	1	no	—
653	#117	—	127	1	no	—
654	#117	—	127	1	no	—
655	#117	—	127	1	no	—
656	#117	—	127	1	no	—
657	#117	—	127	1	no	—
658	#117	C₂×D₁₂₇	1	1	yes	characteristic
659	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
660	C₂×C₄⋊C₄	—	127	1	no	—
661	C₂×C₄⋊C₄	—	127	1	no	—
662	C₂×C₂²⋊C₄	—	127	1	no	—
663	C₂×C₂²⋊C₄	—	127	1	no	—
664	C₂×C₄²	—	127	1	no	—
665	C₂×C₄²	—	127	1	no	—
666	C₂×C₄²	—	127	1	no	—
667	C₂×C₄²	—	127	1	no	—
668	C₂×C₄²	—	127	1	no	—
669	C₂×C₄²	C₂×D₁₂₇	1	1	yes	characteristic, complemented
670	C₂⁴	—	127	1	no	—
671	#41	—	254	4	no	—
672	#41	—	254	4	no	—
673	C₂×Q₈	—	127	1	no	—
674	C₂×Q₈	—	127	1	no	—
675	C₂×Q₈	—	127	1	no	—
676	C₂×Q₈	—	127	1	no	—
677	C₂×Q₈	—	127	1	no	—
678	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
679	C₂×D₄	—	127	1	no	—
680	C₂×D₄	—	127	1	no	—
681	C₂×D₄	—	127	1	no	—
682	C₂×D₄	—	127	1	no	—
683	C₂×D₄	—	127	1	no	—
684	C₂×D₄	—	127	1	no	—
685	C₂×D₄	—	127	1	no	—
686	C₂×D₄	—	127	1	no	—
687	C₂×D₄	—	127	1	no	—
688	C₂×D₄	—	127	1	no	—
689	C₂×D₄	—	127	1	no	—
690	C₂×D₄	—	127	1	no	—
691	C₂×D₄	—	127	1	no	—
692	C₂×D₄	—	127	1	no	—
693	C₂×D₄	—	127	1	no	—
694	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
695	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
696	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
697	C₂²×C₄	—	127	1	no	—
698	C₂²×C₄	—	127	1	no	—
699	C₂²×C₄	—	127	1	no	—
700	C₂²×C₄	—	127	1	no	—
701	C₂²×C₄	—	127	1	no	—
702	C₂²×C₄	—	127	1	no	—
703	C₂²×C₄	—	127	1	no	—
704	C₂²×C₄	—	127	1	no	—
705	C₂²×C₄	—	127	1	no	—
706	C₂²×C₄	—	127	1	no	—
707	C₂²×C₄	—	127	1	no	—
708	C₂²×C₄	—	127	1	no	—
709	C₂²×C₄	—	127	1	no	—
710	C₂²×C₄	—	127	1	no	—
711	C₂²×C₄	—	127	1	no	—
712	C₂²×C₄	—	127	1	no	—
713	C₂²×C₄	—	127	1	no	—
714	C₂²×C₄	—	254	4	no	—
715	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
720	C₄⋊C₄	—	127	1	no	—
721	C₄⋊C₄	—	127	1	no	—
722	C₄⋊C₄	—	127	1	no	—
723	C₄⋊C₄	—	127	1	no	—
724	C₄⋊C₄	—	127	1	no	—
725	C₄⋊C₄	—	127	1	no	—
726	C₄⋊C₄	—	127	1	no	—
727	C₄⋊C₄	—	127	1	no	—
728	C₄⋊C₄	—	127	1	no	—
729	C₄⋊C₄	—	127	1	no	—
730	C₄⋊C₄	—	127	1	no	—
731	C₄⋊C₄	—	127	1	no	—
732	C₄⋊C₄	—	127	1	no	—
733	C₄⋊C₄	—	127	1	no	—
734	C₄⋊C₄	—	127	1	no	—
735	C₄⋊C₄	—	127	1	no	—
736	C₄⋊C₄	—	127	1	no	—
737	C₄⋊C₄	—	127	1	no	—
738	C₄⋊C₄	—	127	1	no	—
739	C₄⋊C₄	—	127	1	no	—
740	C₄⋊C₄	—	127	1	no	—
741	C₄⋊C₄	—	127	1	no	—
742	C₄⋊C₄	—	127	1	no	—
743	C₄⋊C₄	—	127	1	no	—
744	C₄⋊C₄	—	127	1	no	—
745	C₄⋊C₄	—	127	1	no	—
746	C₄⋊C₄	—	127	1	no	—
747	C₄⋊C₄	—	127	1	no	—
748	C₄⋊C₄	—	127	1	no	—
749	C₄⋊C₄	—	127	1	no	—
750	C₄⋊C₄	—	127	1	no	—
751	C₄⋊C₄	—	127	1	no	—
752	C₄⋊C₄	—	127	1	no	—
753	C₄⋊C₄	—	127	1	no	—
754	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	—	127	1	no	—
780	C₂²⋊C₄	—	127	1	no	—
781	C₂²⋊C₄	—	127	1	no	—
782	C₂²⋊C₄	—	127	1	no	—
783	C₂²⋊C₄	—	127	1	no	—
784	C₂²⋊C₄	—	127	1	no	—
785	C₂²⋊C₄	—	127	1	no	—
786	C₂²⋊C₄	—	127	1	no	—
787	C₂²⋊C₄	—	127	1	no	—
788	C₂²⋊C₄	—	127	1	no	—
789	C₂²⋊C₄	—	127	1	no	—
790	C₂²⋊C₄	—	127	1	no	—
791	C₂²⋊C₄	—	127	1	no	—
792	C₂²⋊C₄	—	127	1	no	—
793	C₂²⋊C₄	—	127	1	no	—
794	C₂²⋊C₄	—	127	1	no	—
795	C₂²⋊C₄	—	127	1	no	—
796	C₂²⋊C₄	—	127	1	no	—
797	C₂²⋊C₄	—	127	1	no	—
798	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
808	C₄²	—	127	1	no	—
809	C₄²	—	127	1	no	—
810	C₄²	—	127	1	no	—
811	C₄²	—	127	1	no	—
812	C₄²	—	127	1	no	—
813	C₄²	—	127	1	no	—
814	C₄²	—	127	1	no	—
815	C₄²	—	127	1	no	—
816	C₄²	—	127	1	no	—
817	C₄²	—	127	1	no	—
818	C₄²	—	127	1	no	—
819	C₄²	—	127	1	no	—
820	C₄²	—	127	1	no	—
821	C₄²	—	127	1	no	—
822	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
823	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
824	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
825	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
826	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
827	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
828	C₂³	—	127	1	no	—
829	C₂³	—	127	1	no	—
830	C₂³	—	127	1	no	—
831	C₂³	—	127	1	no	—
832	C₂³	—	508	1	no	—
833	C₂³	—	508	1	no	—
834	C₂³	—	254	2	no	—
835	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
836	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
837	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
838	Q₈	—	4	1	no	—
839	Q₈	—	508	1	no	—
840	Q₈	—	508	1	no	—
841	Q₈	—	508	1	no	—
842	Q₈	—	254	2	no	—
843	Q₈	—	254	2	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	508	1	no	—
848	D₄	—	508	1	no	—
849	D₄	—	508	1	no	—
850	D₄	—	508	1	no	—
851	D₄	—	508	1	no	—
852	D₄	—	508	1	no	—
853	D₄	—	508	1	no	—
854	D₄	—	508	1	no	—
855	D₄	—	508	1	no	—
856	D₄	—	254	2	no	—
857	D₄	—	254	2	no	—
858	D₄	—	254	2	no	—
859	D₄	—	254	2	no	—
860	D₄	—	254	2	no	—
861	D₄	—	254	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	127	1	no	—
868	C₂×C₄	—	127	4	no	—
869	C₂×C₄	—	127	1	no	—
870	C₂×C₄	—	127	1	no	—
871	C₂×C₄	—	127	1	no	—
872	C₂×C₄	—	127	1	no	—
873	C₂×C₄	—	127	1	no	—
874	C₂×C₄	—	127	1	no	—
875	C₂×C₄	—	127	1	no	—
876	C₂×C₄	—	127	1	no	—
877	C₂×C₄	—	127	1	no	—
878	C₂×C₄	—	127	1	no	—
879	C₂×C₄	—	127	1	no	—
880	C₂×C₄	—	508	1	no	—
881	C₂×C₄	—	508	1	no	—
882	C₂×C₄	—	508	1	no	—
883	C₂×C₄	—	508	1	no	—
884	C₂×C₄	—	508	1	no	—
885	C₂×C₄	—	508	1	no	—
886	C₂×C₄	—	508	1	no	—
887	C₂×C₄	—	508	1	no	—
888	C₂×C₄	—	508	1	no	—
889	C₂×C₄	—	508	1	no	—
890	C₂×C₄	—	254	2	no	—
891	C₂×C₄	—	254	2	no	—
892	C₂×C₄	—	254	2	no	—
893	C₂×C₄	—	254	2	no	—
894	C₂×C₄	—	254	2	no	—
895	C₂×C₄	—	254	2	no	—
896	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
897	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
898	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	127	2	no	—
918	C₂²	—	508	4	no	—
919	C₂²	—	254	1	no	—
920	C₂²	—	254	1	no	—
921	C₂²	—	254	1	no	—
922	C₂²	—	254	1	no	—
923	C₂²	—	254	1	no	—
924	C₂²	—	254	1	no	—
925	C₂²	—	254	1	no	—
926	C₂²	—	254	1	no	—
927	C₂²	—	254	1	no	—
928	C₂²	—	254	1	no	—
929	C₂²	—	254	1	no	—
930	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	127	2	no	—
943	C₄	—	254	1	no	—
944	C₄	—	254	1	no	—
945	C₄	—	254	1	no	—
946	C₄	—	254	1	no	—
947	C₄	—	254	1	no	—
948	C₄	—	254	1	no	—
949	C₄	—	254	1	no	—
950	C₄	—	254	1	no	—
951	C₄	—	254	1	no	—
952	C₄	—	254	1	no	—
953	C₄	—	254	1	no	—
954	C₄	#41×D₁₂₇	1	2	yes	—
955	C₂	—	4	1	no	—
956	C₂	—	4	1	no	—
957	C₂	—	4	1	no	—
958	C₂	—	508	1	no	—
959	C₂	—	508	1	no	—
960	C₂	—	508	1	no	—
961	C₂	—	254	2	no	—
962	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
963	C₂	#22550712	1	1	yes	characteristic
964	C₂	#22550712	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₂₇
Fitting	#529×C₁₂₇	C₂
hypercenter	#529	D₁₂₇
hypocenter	C₁₂₇	#3455
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #22550496	C₂	semidirect
2. #22550494	C₂	semidirect
3. #22550492	C₂	semidirect
4. #22550490	C₂	semidirect
5. #22550485	C₂	semidirect
6. #22550483	C₂	semidirect
7. #22550478	C₂	semidirect
8. #22550476	C₂	semidirect
9. #22550474	C₂	semidirect
10. #22550472	C₂	semidirect
11. #22550469	C₂	semidirect
12. #22550467	C₂	semidirect
13. #22550465	C₂	semidirect
14. #22550462	C₂	semidirect
15. #22550460	C₂	semidirect
16. #22550458	C₂	semidirect
17. #22550430	C₂	semidirect
18. #22550423	C₂	semidirect
19. #22550413	C₂	semidirect
20. #22550410	C₂	semidirect
21. #22550408	C₂	semidirect
22. #22550406	C₂	semidirect
23. #22550406	C₂	semidirect
24. #22550404	C₂	semidirect
25. #22550404	C₂	semidirect
26. #22550385	C₂	semidirect
27. #22550385	C₂	semidirect
28. C₄×#14523248	C₂	semidirect
29. #22550344	C₂	semidirect
30. #117×D₁₂₇	C₂	semidirect
31. #529×C₁₂₇	C₂	semidirect
35. #16861208	C₂²	semidirect
36. #16861208	C₂²	semidirect
37. #16861207	C₂²	semidirect
38. #16861205	C₂²	semidirect
42. #16861204	C₂²	semidirect
43. #16861204	C₂²	semidirect
44. #16861204	C₂²	semidirect
46. #16861203	C₂²	semidirect
50. #16861202	C₂²	semidirect
51. #16861202	C₂²	semidirect
52. #16861202	C₂²	semidirect
53. #16861201	C₂²	semidirect
54. #16861200	C₂²	semidirect
55. #16861200	C₂²	semidirect
56. #16861199	C₂²	semidirect
57. #16861199	C₂²	semidirect
58. #16861199	C₂²	semidirect
59. #16861199	C₂²	semidirect
60. #16861199	C₂²	semidirect
61. #16861199	C₂²	semidirect
69. #16861195	C₂²	semidirect
70. #16861195	C₂²	semidirect
75. #16861194	C₂²	semidirect
76. #16861194	C₂²	semidirect
78. #16861193	C₂²	semidirect
80. #16861192	C₂²	semidirect
85. #16861191	C₂²	semidirect
86. #16861191	C₂²	semidirect
88. #16861190	C₂²	semidirect
90. #16861189	C₂²	semidirect
91. #16861188	C₂²	semidirect
96. #16861187	C₂²	semidirect
97. #16861187	C₂²	semidirect
100. #16861186	C₂²	semidirect
101. #16861186	C₂²	semidirect
103. #16861185	C₂²	semidirect
123. C₄×Dic₂₅₄	C₂²	semidirect
124. C₄×Dic₂₅₄	C₂²	semidirect
125. C₄×Dic₂₅₄	C₂²	semidirect
126. C₄×Dic₂₅₄	C₂²	semidirect
127. C₄×Dic₂₅₄	C₂²	semidirect
128. #16861174	C₂²	semidirect
129. #16861174	C₂²	semidirect
134. C₄×D₅₀₈	C₂²	semidirect
143. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
144. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
145. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
146. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
149. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
150. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
152. #16861168	C₂²	semidirect
159. #16861166	C₂²	semidirect
160. #16861166	C₂²	semidirect
167. C₂×C₄×Dic₁₂₇	C₂²	semidirect
170. C₄²×D₁₂₇	C₂²	semidirect
171. C₄²×D₁₂₇	C₂²	semidirect
173. #126×C₁₂₇	C₂²	semidirect
174. #125×C₁₂₇	C₂²	semidirect
177. #123×C₁₂₇	C₂²	semidirect
178. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
180. C₄×Q₈×C₁₂₇	C₂²	semidirect
183. C₄×D₄×C₁₂₇	C₂²	semidirect
185. #117×C₁₂₇	C₂²	semidirect
186. C₂×C₄²×C₁₂₇	C₂²	semidirect
483. C₁₂₇	#3455	semidirect
509. #529	D₁₂₇	semidirect
537. #126	C₂×D₁₂₇	semidirect
547. #125	C₂×D₁₂₇	semidirect
577. #123	C₂×D₁₂₇	semidirect
593. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
621. C₄×Q₈	C₂×D₁₂₇	semidirect
645. C₄×D₄	C₂×D₁₂₇	semidirect
659. #117	C₂×D₁₂₇	semidirect
669. C₂×C₄²	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550496	2
#22550494	2
#22550492	2
#22550490	2
#22550485	2
#22550483	2
#22550478	2
#22550476	2
#22550474	2
#22550472	2
#22550469	2
#22550467	2
#22550465	2
#22550462	2
#22550460	2
#22550458	2
#22550430	2
#22550423	2
#22550413	2
#22550410	2
#22550408	2
#22550406	2
#22550404	2
#22550385	2
C₄×#14523248	2
#22550344	2
#117×D₁₂₇	2
#529×C₁₂₇	2
#3455	127