Subgroups — #30652910

Order 16256.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 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	#22550615	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550614	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550573	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550571	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550557	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550552	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550523	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550520	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550516	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550513	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550513	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550513	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₂²⋊D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550508	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550479	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550476	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550470	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550470	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550469	C₂	1	1	yes	maximal, characteristic, complemented
22	#22550462	C₂	1	1	yes	maximal, characteristic, complemented
23	#22550461	C₂	1	1	yes	maximal, characteristic, complemented
24	#22550458	C₂	1	1	yes	maximal, characteristic, complemented
25	#22550455	C₂	1	1	yes	maximal, characteristic, complemented
26	#22550436	C₂	1	1	yes	maximal, characteristic, complemented
27	#22550435	C₂	1	1	yes	maximal, characteristic, complemented
28	#22550384	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16861180	C₂	1	1	yes	maximal, characteristic, complemented
31	#534×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
40	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
42	#16861205	C₂²	1	1	yes	characteristic, complemented
43	#16861205	C₂²	1	1	yes	characteristic, complemented
44	#16861204	C₂²	1	1	yes	characteristic, complemented
45	#16861204	C₂²	1	1	yes	characteristic, complemented
46	#16861202	C₂²	1	1	yes	characteristic, complemented
47	#16861202	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	#16861200	C₂²	1	1	yes	characteristic, complemented
53	#16861200	C₂²	1	1	yes	characteristic, complemented
54	#16861199	C₂²	1	1	yes	characteristic, complemented
55	#16861199	C₂²	1	1	yes	characteristic, complemented
56	#16861196	C₂²	1	1	yes	characteristic, complemented
57	#16861196	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	#16861195	C₂²	1	1	yes	characteristic, complemented
62	#16861194	C₂²	1	1	yes	characteristic, complemented
63	#16861194	C₂²	1	1	yes	characteristic, complemented
64	#16861193	C₂²	1	1	yes	characteristic, complemented
65	#16861193	C₂²	1	1	yes	characteristic, complemented
66	#16861193	C₂²	1	1	yes	characteristic, complemented
67	#16861193	C₂²	1	1	yes	characteristic, complemented
68	#16861192	C₂²	1	1	yes	characteristic, complemented
69	#16861192	C₂²	1	1	yes	characteristic, complemented
70	#16861192	C₂²	1	1	yes	characteristic, complemented
71	#16861192	C₂²	1	1	yes	characteristic, complemented
72	#16861191	C₂²	1	1	yes	characteristic, complemented
73	#16861191	C₂²	1	1	yes	characteristic, complemented
74	#16861191	C₂²	1	1	yes	characteristic, complemented
75	#16861191	C₂²	1	1	yes	characteristic, complemented
76	#16861191	C₂²	1	1	yes	characteristic, complemented
77	#16861191	C₂²	1	1	yes	characteristic, complemented
78	#16861191	C₂²	1	1	yes	characteristic, complemented
79	#16861191	C₂²	1	1	yes	characteristic, complemented
80	#16861190	C₂²	1	1	yes	characteristic, complemented
81	#16861190	C₂²	1	1	yes	characteristic, complemented
82	#16861190	C₂²	1	1	yes	characteristic, complemented
83	#16861190	C₂²	1	1	yes	characteristic, complemented
84	#16861190	C₂²	1	1	yes	characteristic, complemented
85	#16861190	C₂²	1	1	yes	characteristic, complemented
86	#16861189	C₂²	1	1	yes	characteristic, complemented
87	#16861189	C₂²	1	1	yes	characteristic, complemented
88	#16861188	C₂²	1	1	yes	characteristic, complemented
89	#16861188	C₂²	1	1	yes	characteristic, complemented
90	#16861187	C₂²	1	1	yes	characteristic, complemented
91	#16861187	C₂²	1	1	yes	characteristic, complemented
92	#16861186	C₂²	1	1	yes	characteristic, complemented
93	#16861186	C₂²	1	1	yes	characteristic, complemented
94	#16861186	C₂²	1	1	yes	characteristic, complemented
95	#16861186	C₂²	1	1	yes	characteristic, complemented
96	#16861186	C₂²	1	1	yes	characteristic, complemented
97	#16861186	C₂²	1	1	yes	characteristic, complemented
98	#16861183	C₂²	1	1	yes	characteristic, complemented
99	#16861183	C₂²	1	1	yes	characteristic, complemented
100	#16861182	C₂²	1	1	yes	characteristic, complemented
101	#16861182	C₂²	1	1	yes	characteristic, complemented
102	#16861182	C₂²	1	1	yes	characteristic, complemented
103	#16861182	C₂²	1	1	yes	characteristic, complemented
104	#16861182	C₂²	1	1	yes	characteristic, complemented
105	#16861182	C₂²	1	1	yes	characteristic, complemented
106	#16861181	C₂²	1	1	yes	characteristic
107	#16861181	C₂²	1	1	yes	characteristic
108	#16861181	C₂²	1	1	yes	characteristic, complemented
109	#16861181	C₂²	1	1	yes	characteristic, complemented
110	#16861181	C₂²	1	1	yes	characteristic, complemented
111	#16861181	C₂²	1	1	yes	characteristic, complemented
112	#16861181	C₂²	1	1	yes	characteristic, complemented
113	#16861181	C₂²	1	1	yes	characteristic, complemented
114	#16861181	C₂²	1	1	yes	characteristic, complemented
115	#16861181	C₂²	1	1	yes	characteristic, complemented
116	#16861181	C₂²	1	1	yes	characteristic, complemented
117	#16861181	C₂²	1	1	yes	characteristic, complemented
118	#16861180	C₂²	1	1	yes	characteristic
119	#16861180	C₂²	1	1	yes	characteristic, complemented
120	#16861180	C₂²	1	1	yes	characteristic, complemented
121	#16861180	C₂²	1	1	yes	characteristic, complemented
122	#16861180	C₂²	1	1	yes	characteristic, complemented
123	#16861180	C₂²	1	1	yes	characteristic, complemented
124	#16861180	C₂²	1	1	yes	characteristic, complemented
125	#16861180	C₂²	1	1	yes	characteristic, complemented
126	#16861180	C₂²	1	1	yes	characteristic, complemented
127	#16861180	C₂²	1	1	yes	characteristic, complemented
128	#16861180	C₂²	1	1	yes	characteristic, complemented
129	#16861180	C₂²	1	1	yes	characteristic, complemented
130	#16861179	C₂²	1	1	yes	characteristic, complemented
131	#16861179	C₂²	1	1	yes	characteristic, complemented
132	#16861178	C₂²	1	1	yes	characteristic
133	#16861178	C₂²	1	1	yes	characteristic, complemented
134	#16861178	C₂²	1	1	yes	characteristic, complemented
135	#16861178	C₂²	1	1	yes	characteristic, complemented
136	#16861177	C₂²	1	1	yes	characteristic, complemented
137	#16861177	C₂²	1	1	yes	characteristic, complemented
138	#16861177	C₂²	1	1	yes	characteristic, complemented
139	#16861177	C₂²	1	1	yes	characteristic, complemented
140	#16861177	C₂²	1	1	yes	characteristic, complemented
141	#16861177	C₂²	1	1	yes	characteristic, complemented
142	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	#16861171	C₂²	1	1	yes	characteristic, complemented
147	#16861171	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₁₂₇	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	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	#16861168	C₂²	1	1	yes	characteristic, complemented
159	#16861165	C₂²	1	1	yes	characteristic, complemented
160	#16861165	C₂²	1	1	yes	characteristic, complemented
161	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
164	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
165	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
166	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
172	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
173	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
174	#123×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	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
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	#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	#120×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
185	#120×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	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
190	#14523248	—	4	2	no	—
191	#14523247	—	4	2	no	—
192	#14523247	—	4	2	no	—
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×C₂²⋊D₁₂₇	—	4	2	no	—
200	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
201	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
202	C₂×C₂²⋊D₁₂₇	—	4	2	no	—
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	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	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
225	D₄×D₁₂₇	—	4	2	no	—
226	D₄×D₁₂₇	—	4	2	no	—
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	C₂×C₄×D₁₂₇	—	4	2	no	—
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	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₁₂₇	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	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
255	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
256	C₄⋊Dic₁₂₇	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	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	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	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₂₇	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	C₂⁴×C₁₂₇	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₁₂₇	—	4	2	no	—
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	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
332	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
333	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
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	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	C₄⋊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	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
354	C₂²×D₁₂₇	—	2	2	no	—
355	C₂²×D₁₂₇	—	2	2	no	—
356	C₂²×D₁₂₇	—	2	2	no	—
357	C₂²×D₁₂₇	—	4	1	no	—
358	C₂²×D₁₂₇	—	4	1	no	—
359	C₂²×D₁₂₇	—	4	1	no	—
360	C₂²×D₁₂₇	—	4	1	no	—
361	C₂²×D₁₂₇	—	4	1	no	—
362	C₂²×D₁₂₇	—	4	1	no	—
363	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
364	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
365	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
366	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
367	Dic₂₅₄	—	4	1	no	—
368	Dic₂₅₄	—	4	1	no	—
369	Dic₂₅₄	—	4	1	no	—
370	D₅₀₈	—	2	2	no	—
371	D₅₀₈	—	4	1	no	—
372	D₅₀₈	—	4	1	no	—
373	C₂²⋊D₁₂₇	—	2	2	no	—
374	C₂²⋊D₁₂₇	—	2	2	no	—
375	C₂²⋊D₁₂₇	—	2	2	no	—
376	C₂²⋊D₁₂₇	—	2	2	no	—
377	C₂²⋊D₁₂₇	—	2	2	no	—
378	C₂²⋊D₁₂₇	—	2	2	no	—
379	C₂²⋊D₁₂₇	—	2	2	no	—
380	C₂²⋊D₁₂₇	—	4	1	no	—
381	C₂²⋊D₁₂₇	—	4	1	no	—
382	C₂²⋊D₁₂₇	—	4	1	no	—
383	C₂²⋊D₁₂₇	—	4	1	no	—
384	C₂²⋊D₁₂₇	—	4	1	no	—
385	C₂²⋊D₁₂₇	—	4	1	no	—
386	C₂²⋊D₁₂₇	—	4	1	no	—
387	C₂²⋊D₁₂₇	—	4	1	no	—
388	C₂²⋊D₁₂₇	—	4	1	no	—
389	C₂²⋊D₁₂₇	—	4	1	no	—
390	C₂²⋊D₁₂₇	—	4	1	no	—
391	C₂²⋊D₁₂₇	—	4	1	no	—
392	C₂²⋊D₁₂₇	—	4	1	no	—
393	C₂²⋊D₁₂₇	—	4	1	no	—
394	C₂²⋊D₁₂₇	—	4	1	no	—
395	C₂×Dic₁₂₇	—	2	2	no	—
396	C₂×Dic₁₂₇	—	4	1	no	—
397	C₂×Dic₁₂₇	—	4	1	no	—
398	C₂×Dic₁₂₇	—	4	1	no	—
399	C₂×Dic₁₂₇	—	4	1	no	—
400	C₂×Dic₁₂₇	—	4	1	no	—
401	C₂×Dic₁₂₇	—	4	1	no	—
402	C₂×Dic₁₂₇	—	4	1	no	—
403	C₂×Dic₁₂₇	—	4	1	no	—
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	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
416	C₄×D₁₂₇	—	2	2	no	—
417	C₄×D₁₂₇	—	4	1	no	—
418	C₄×D₁₂₇	—	4	1	no	—
419	C₄×D₁₂₇	—	4	1	no	—
420	C₄×D₁₂₇	—	4	1	no	—
421	C₄×D₁₂₇	—	4	1	no	—
422	C₄×D₁₂₇	—	4	1	no	—
423	C₄×D₁₂₇	—	4	1	no	—
424	C₄×D₁₂₇	—	4	1	no	—
425	C₄×D₁₂₇	—	4	1	no	—
426	C₂³×C₁₂₇	—	2	2	no	—
427	C₂³×C₁₂₇	—	2	2	no	—
428	C₂³×C₁₂₇	—	4	1	no	—
429	C₂³×C₁₂₇	—	4	1	no	—
430	C₂³×C₁₂₇	—	4	1	no	—
431	C₂³×C₁₂₇	—	4	1	no	—
432	C₂³×C₁₂₇	—	4	1	no	—
433	C₂³×C₁₂₇	—	4	1	no	—
434	C₂³×C₁₂₇	—	4	1	no	—
435	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
436	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
437	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
438	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
439	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
440	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
441	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
442	D₄×C₁₂₇	—	2	2	no	—
443	D₄×C₁₂₇	—	2	2	no	—
444	D₄×C₁₂₇	—	4	1	no	—
445	D₄×C₁₂₇	—	4	1	no	—
446	D₄×C₁₂₇	—	4	1	no	—
447	D₄×C₁₂₇	—	4	1	no	—
448	D₄×C₁₂₇	—	4	1	no	—
449	D₄×C₁₂₇	—	4	1	no	—
450	D₄×C₁₂₇	—	4	1	no	—
451	D₄×C₁₂₇	—	4	1	no	—
452	D₄×C₁₂₇	—	4	1	no	—
453	D₄×C₁₂₇	—	4	1	no	—
454	C₂×C₄×C₁₂₇	—	2	2	no	—
455	C₂×C₄×C₁₂₇	—	4	1	no	—
456	C₂×C₄×C₁₂₇	—	4	1	no	—
457	C₂×C₄×C₁₂₇	—	4	1	no	—
458	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
459	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
460	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
461	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
462	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
463	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
464	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
465	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
473	C₂²×C₁₂₇	—	2	1	no	—
474	C₂²×C₁₂₇	—	2	1	no	—
475	C₂²×C₁₂₇	—	2	1	no	—
476	C₂²×C₁₂₇	—	2	1	no	—
477	C₂²×C₁₂₇	—	2	1	no	—
478	C₂²×C₁₂₇	—	2	1	no	—
479	C₂²×C₁₂₇	—	2	1	no	—
480	C₂²×C₁₂₇	—	2	1	no	—
481	C₂²×C₁₂₇	—	2	1	no	—
482	C₂²×C₁₂₇	—	2	1	no	—
483	C₂²×C₁₂₇	—	2	1	no	—
484	C₂²×C₁₂₇	—	2	1	no	—
485	C₂²×C₁₂₇	—	2	1	no	—
486	C₂²×C₁₂₇	—	8	2	no	—
487	C₂²×C₁₂₇	—	8	2	no	—
488	C₂²×C₁₂₇	—	8	2	no	—
489	C₂²×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
490	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
491	C₂×D₁₂₇	—	2	1	no	—
492	C₂×D₁₂₇	—	2	1	no	—
493	C₂×D₁₂₇	—	2	1	no	—
494	C₂×D₁₂₇	—	2	1	no	—
495	C₂×D₁₂₇	—	2	1	no	—
496	C₂×D₁₂₇	—	2	1	no	—
497	C₂×D₁₂₇	—	2	1	no	—
498	C₂×D₁₂₇	—	2	1	no	—
499	C₂×D₁₂₇	—	2	1	no	—
500	C₂×D₁₂₇	—	2	1	no	—
501	C₂×D₁₂₇	—	2	1	no	—
502	C₂×D₁₂₇	—	4	4	no	—
503	C₂×D₁₂₇	—	8	2	no	—
504	C₂×D₁₂₇	—	8	2	no	—
505	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
506	C₄×C₁₂₇	—	2	1	no	—
507	C₄×C₁₂₇	—	2	1	no	—
508	C₄×C₁₂₇	—	2	1	no	—
509	C₄×C₁₂₇	—	2	1	no	—
510	C₄×C₁₂₇	—	2	1	no	—
511	C₄×C₁₂₇	—	2	1	no	—
512	C₄×C₁₂₇	—	2	1	no	—
513	C₄×C₁₂₇	—	2	1	no	—
514	Dic₁₂₇	—	2	1	no	—
515	Dic₁₂₇	—	2	1	no	—
516	Dic₁₂₇	—	2	1	no	—
517	Dic₁₂₇	—	2	1	no	—
518	Dic₁₂₇	—	2	1	no	—
519	Dic₁₂₇	—	2	1	no	—
520	Dic₁₂₇	—	2	1	no	—
521	Dic₁₂₇	—	2	1	no	—
522	Dic₁₂₇	—	2	1	no	—
523	Dic₁₂₇	—	2	1	no	—
524	Dic₁₂₇	—	2	1	no	—
525	Dic₁₂₇	—	2	1	no	—
526	C₂×C₁₂₇	—	2	2	no	—
527	C₂×C₁₂₇	—	4	1	no	—
528	C₂×C₁₂₇	—	4	1	no	—
529	C₂×C₁₂₇	—	4	1	no	—
530	C₂×C₁₂₇	—	4	1	no	—
531	C₂×C₁₂₇	—	4	1	no	—
532	C₂×C₁₂₇	—	4	1	no	—
533	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂×C₁₂₇	#585	1	1	yes	characteristic
536	D₁₂₇	—	2	2	no	—
537	D₁₂₇	—	4	1	no	—
538	D₁₂₇	—	4	1	no	—
539	D₁₂₇	—	4	1	no	—
540	#3534	—	127	1	no	maximal, Sylow
541	C₁₂₇	#3534	1	1	yes	characteristic, complemented, Sylow
542	#562	—	127	1	no	—
543	#562	—	127	1	no	—
544	#560	—	127	1	no	—
545	#560	—	127	1	no	—
546	#553	—	127	1	no	—
547	#553	—	127	1	no	—
548	#551	—	127	1	no	—
549	#551	—	127	1	no	—
550	#546	—	127	1	no	—
551	#546	—	127	1	no	—
552	#546	—	127	1	no	—
553	#546	—	127	1	no	—
554	#546	—	127	1	no	—
555	#546	—	127	1	no	—
556	D₄²	—	127	1	no	—
557	D₄²	—	127	1	no	—
558	#540	—	127	1	no	—
559	#540	—	127	1	no	—
560	#539	—	127	1	no	—
561	#539	—	127	1	no	—
562	#539	—	127	1	no	—
563	#538	—	127	1	no	—
564	#538	—	127	1	no	—
565	#538	—	127	1	no	—
566	#537	—	127	1	no	—
567	#534	—	127	1	no	—
568	#534	—	127	1	no	—
569	#534	D₁₂₇	1	1	yes	characteristic, complemented
570	#525	—	127	1	no	—
571	C₂×#123	—	127	1	no	—
572	C₂×#121	—	127	1	no	—
573	C₂×#41	—	127	1	no	—
574	C₂×#41	—	127	1	no	—
575	C₂×#41	—	127	1	no	—
576	C₂²×D₄	—	127	1	no	—
577	C₂²×D₄	—	127	1	no	—
578	C₂²×D₄	—	127	1	no	—
579	C₂²×D₄	—	127	1	no	—
580	C₂²×D₄	—	127	1	no	—
581	C₂²×D₄	—	127	1	no	—
582	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
583	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
584	C₂³×C₄	—	127	1	no	—
585	#127	—	127	1	no	—
586	#127	—	127	1	no	—
587	#126	—	127	1	no	—
588	#126	—	127	1	no	—
589	#126	—	127	1	no	—
590	#126	—	127	1	no	—
591	#126	—	127	1	no	—
592	#126	—	127	1	no	—
593	#126	—	127	1	no	—
594	#126	—	127	1	no	—
595	#125	—	127	1	no	—
596	#125	—	127	1	no	—
597	#125	—	127	1	no	—
598	#125	—	127	1	no	—
599	#124	—	127	1	no	—
600	#124	—	127	1	no	—
601	#124	—	127	1	no	—
602	#124	—	127	1	no	—
603	#124	—	127	1	no	—
604	#124	—	127	1	no	—
605	#123	—	127	1	no	—
606	#123	—	127	1	no	—
607	#123	—	127	1	no	—
608	#123	—	127	1	no	—
609	#123	—	127	1	no	—
610	#123	—	127	1	no	—
611	#123	—	127	1	no	—
612	#123	—	127	1	no	—
613	#123	—	127	1	no	—
614	#123	—	127	1	no	—
615	#123	—	127	1	no	—
616	#123	—	127	1	no	—
617	#123	—	127	1	no	—
618	#123	—	127	1	no	—
619	#123	—	127	1	no	—
620	#123	—	127	1	no	—
621	#123	—	127	1	no	—
622	#123	—	127	1	no	—
623	#123	—	127	1	no	—
624	#123	—	127	1	no	—
625	#123	—	127	1	no	—
626	#123	—	127	1	no	—
627	#123	—	127	1	no	—
628	#123	—	127	1	no	—
629	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
630	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
631	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
632	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
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	—	127	1	no	—
640	C₂²⋊Q₈	—	127	1	no	—
641	C₂²⋊Q₈	—	127	1	no	—
642	C₂²⋊Q₈	—	127	1	no	—
643	C₂²⋊Q₈	—	127	1	no	—
644	C₂²⋊Q₈	—	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	—	127	1	no	—
670	#121	—	127	1	no	—
671	#121	—	127	1	no	—
672	#121	—	127	1	no	—
673	#121	—	127	1	no	—
674	#121	—	127	1	no	—
675	#121	—	127	1	no	—
676	#121	—	127	1	no	—
677	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
678	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
679	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
680	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
681	#120	—	127	1	no	—
682	#120	—	127	1	no	—
683	#120	—	127	1	no	—
684	#120	—	127	1	no	—
685	#120	—	127	1	no	—
686	#120	—	127	1	no	—
687	#120	—	127	1	no	—
688	#120	—	127	1	no	—
689	#120	—	127	1	no	—
690	#120	—	127	1	no	—
691	#120	—	127	1	no	—
692	#120	—	127	1	no	—
693	#120	C₂×D₁₂₇	1	1	yes	characteristic
694	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
695	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
696	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
697	C₄×D₄	—	127	1	no	—
698	C₄×D₄	—	127	1	no	—
699	C₄×D₄	—	127	1	no	—
700	C₄×D₄	—	127	1	no	—
701	C₄×D₄	—	127	1	no	—
702	C₄×D₄	—	127	1	no	—
703	C₄×D₄	—	127	1	no	—
704	C₄×D₄	—	127	1	no	—
705	C₄×D₄	—	127	1	no	—
706	C₄×D₄	—	127	1	no	—
707	C₄×D₄	—	127	1	no	—
708	C₄×D₄	—	127	1	no	—
709	C₄×D₄	—	127	1	no	—
710	C₄×D₄	—	127	1	no	—
711	C₄×D₄	—	127	1	no	—
712	C₄×D₄	—	127	1	no	—
713	#117	—	127	1	no	—
714	#117	—	127	1	no	—
715	#117	—	127	1	no	—
716	C₂×C₄⋊C₄	—	127	1	no	—
717	C₂×C₄⋊C₄	—	127	1	no	—
718	C₂×C₄⋊C₄	—	127	1	no	—
719	C₂×C₂²⋊C₄	—	127	1	no	—
720	C₂×C₂²⋊C₄	—	127	1	no	—
721	C₂×C₂²⋊C₄	—	127	1	no	—
722	C₂×C₂²⋊C₄	—	127	1	no	—
723	C₂×C₂²⋊C₄	—	127	1	no	—
724	C₂×C₂²⋊C₄	—	127	1	no	—
725	C₂×C₂²⋊C₄	—	127	1	no	—
726	C₂×C₂²⋊C₄	—	127	1	no	—
727	C₂×C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
728	C₂⁴	—	127	1	no	—
729	C₂⁴	—	127	1	no	—
730	C₂⁴	—	127	1	no	—
731	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
732	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
733	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
734	#41	—	508	2	no	—
735	#41	—	508	2	no	—
736	#41	—	508	2	no	—
737	C₂×Q₈	—	127	1	no	—
738	C₂×Q₈	—	127	1	no	—
739	C₂×Q₈	—	127	1	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	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	—	127	1	no	—
749	C₂×D₄	—	127	1	no	—
750	C₂×D₄	—	127	1	no	—
751	C₂×D₄	—	127	1	no	—
752	C₂×D₄	—	127	1	no	—
753	C₂×D₄	—	127	1	no	—
754	C₂×D₄	—	127	1	no	—
755	C₂×D₄	—	127	1	no	—
756	C₂×D₄	—	127	1	no	—
757	C₂×D₄	—	127	1	no	—
758	C₂×D₄	—	127	1	no	—
759	C₂×D₄	—	127	1	no	—
760	C₂×D₄	—	127	1	no	—
761	C₂×D₄	—	127	1	no	—
762	C₂×D₄	—	127	1	no	—
763	C₂×D₄	—	127	1	no	—
764	C₂×D₄	—	127	1	no	—
765	C₂×D₄	—	127	1	no	—
766	C₂×D₄	—	127	1	no	—
767	C₂×D₄	—	508	2	no	—
768	C₂×D₄	—	508	2	no	—
769	C₂×D₄	—	508	2	no	—
770	C₂×D₄	—	508	2	no	—
771	C₂×D₄	—	508	2	no	—
772	C₂×D₄	—	508	2	no	—
773	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
774	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
775	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
776	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
777	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
778	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
779	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
780	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
781	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
782	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
784	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	—	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	—	508	2	no	—
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	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	—	127	1	no	—
821	C₄⋊C₄	—	127	1	no	—
822	C₄⋊C₄	—	127	1	no	—
823	C₄⋊C₄	—	127	1	no	—
824	C₄⋊C₄	—	127	1	no	—
825	C₄⋊C₄	—	127	1	no	—
826	C₄⋊C₄	—	127	1	no	—
827	C₄⋊C₄	—	127	1	no	—
828	C₄⋊C₄	—	127	1	no	—
829	C₄⋊C₄	—	127	1	no	—
830	C₄⋊C₄	—	127	1	no	—
831	C₄⋊C₄	—	127	1	no	—
832	C₄⋊C₄	—	127	1	no	—
833	C₄⋊C₄	—	127	1	no	—
834	C₄⋊C₄	—	127	1	no	—
835	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
838	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
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	—	127	1	no	—
859	C₂²⋊C₄	—	127	1	no	—
860	C₂²⋊C₄	—	127	1	no	—
861	C₂²⋊C₄	—	127	1	no	—
862	C₂²⋊C₄	—	127	1	no	—
863	C₂²⋊C₄	—	127	1	no	—
864	C₂²⋊C₄	—	127	1	no	—
865	C₂²⋊C₄	—	127	1	no	—
866	C₂²⋊C₄	—	127	1	no	—
867	C₂²⋊C₄	—	127	1	no	—
868	C₂²⋊C₄	—	127	1	no	—
869	C₂²⋊C₄	—	127	1	no	—
870	C₂²⋊C₄	—	127	1	no	—
871	C₂²⋊C₄	—	127	1	no	—
872	C₂²⋊C₄	—	127	1	no	—
873	C₂²⋊C₄	—	127	1	no	—
874	C₂²⋊C₄	—	127	1	no	—
875	C₂²⋊C₄	—	127	1	no	—
876	C₂²⋊C₄	—	127	1	no	—
877	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
886	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
889	C₄²	—	127	1	no	—
890	C₄²	—	127	1	no	—
891	C₄²	—	127	1	no	—
892	C₄²	—	127	1	no	—
893	C₄²	—	127	1	no	—
894	C₄²	—	127	1	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	4	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	4	1	no	—
902	C₂³	—	4	1	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	127	1	no	—
905	C₂³	—	127	1	no	—
906	C₂³	—	127	1	no	—
907	C₂³	—	127	1	no	—
908	C₂³	—	508	1	no	—
909	C₂³	—	508	1	no	—
910	C₂³	—	508	1	no	—
911	C₂³	—	508	1	no	—
912	C₂³	—	508	1	no	—
913	C₂³	—	508	1	no	—
914	C₂³	—	254	2	no	—
915	C₂³	—	254	2	no	—
916	C₂³	—	254	2	no	—
917	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
918	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
919	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
920	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
921	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
922	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
923	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
924	Q₈	—	508	1	no	—
925	Q₈	—	508	1	no	—
926	Q₈	—	508	1	no	—
927	D₄	—	2	2	no	—
928	D₄	—	2	2	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	1	no	—
939	D₄	—	508	1	no	—
940	D₄	—	508	1	no	—
941	D₄	—	508	1	no	—
942	D₄	—	508	1	no	—
943	D₄	—	508	1	no	—
944	D₄	—	508	1	no	—
945	D₄	—	508	1	no	—
946	D₄	—	508	1	no	—
947	D₄	—	508	1	no	—
948	D₄	—	508	1	no	—
949	D₄	—	508	1	no	—
950	D₄	—	508	1	no	—
951	D₄	—	508	1	no	—
952	D₄	—	508	1	no	—
953	D₄	—	508	1	no	—
954	D₄	—	508	1	no	—
955	D₄	—	508	1	no	—
956	D₄	—	254	2	no	—
957	D₄	—	254	2	no	—
958	D₄	—	254	2	no	—
959	D₄	—	254	2	no	—
960	D₄	—	254	2	no	—
961	D₄	—	254	2	no	—
962	D₄	—	254	2	no	—
963	D₄	—	254	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	127	1	no	—
969	C₂×C₄	—	127	1	no	—
970	C₂×C₄	—	127	1	no	—
971	C₂×C₄	—	127	1	no	—
972	C₂×C₄	—	127	1	no	—
973	C₂×C₄	—	127	1	no	—
974	C₂×C₄	—	127	1	no	—
975	C₂×C₄	—	127	1	no	—
976	C₂×C₄	—	127	1	no	—
977	C₂×C₄	—	127	1	no	—
978	C₂×C₄	—	127	1	no	—
979	C₂×C₄	—	127	1	no	—
980	C₂×C₄	—	508	1	no	—
981	C₂×C₄	—	508	1	no	—
982	C₂×C₄	—	508	1	no	—
983	C₂×C₄	—	508	1	no	—
984	C₂×C₄	—	508	1	no	—
985	C₂×C₄	—	508	1	no	—
986	C₂×C₄	—	508	1	no	—
987	C₂×C₄	—	508	1	no	—
988	C₂×C₄	—	508	1	no	—
989	C₂×C₄	—	508	1	no	—
990	C₂×C₄	—	508	1	no	—
991	C₂×C₄	—	508	1	no	—
992	C₂×C₄	—	508	1	no	—
993	C₂×C₄	—	508	1	no	—
994	C₂×C₄	—	508	1	no	—
995	C₂×C₄	—	508	1	no	—
996	C₂×C₄	—	508	1	no	—
997	C₂×C₄	—	254	2	no	—
998	C₂×C₄	—	254	2	no	—
999	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1006	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	8	2	no	—
1028	C₂²	—	8	2	no	—
1029	C₂²	—	8	2	no	—
1030	C₂²	—	127	2	no	—
1031	C₂²	—	1016	2	no	—
1032	C₂²	—	1016	2	no	—
1033	C₂²	—	508	4	no	—
1034	C₂²	—	254	1	no	—
1035	C₂²	—	254	1	no	—
1036	C₂²	—	254	1	no	—
1037	C₂²	—	254	1	no	—
1038	C₂²	—	254	1	no	—
1039	C₂²	—	254	1	no	—
1040	C₂²	—	254	1	no	—
1041	C₂²	—	254	1	no	—
1042	C₂²	—	254	1	no	—
1043	C₂²	—	254	1	no	—
1044	C₂²	—	254	1	no	—
1045	C₂²	#16861254	1	2	yes	—
1046	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	254	1	no	—
1056	C₄	—	254	1	no	—
1057	C₄	—	254	1	no	—
1058	C₄	—	254	1	no	—
1059	C₄	—	254	1	no	—
1060	C₄	—	254	1	no	—
1061	C₄	—	254	1	no	—
1062	C₄	—	254	1	no	—
1063	C₄	—	254	1	no	—
1064	C₄	—	254	1	no	—
1065	C₄	—	254	1	no	—
1066	C₄	—	254	1	no	—
1067	C₂	—	2	2	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	508	1	no	—
1075	C₂	—	508	1	no	—
1076	C₂	—	508	1	no	—
1077	C₂	—	254	2	no	—
1078	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
1079	C₂	C₂×#16861254	1	1	yes	characteristic
1080	C₂	#22550711	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#534×C₁₂₇	C₂
hypercenter	#534	D₁₂₇
hypocenter	C₁₂₇	#3534
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #534

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. #22550615	C₂	semidirect
4. #22550614	C₂	semidirect
5. #22550573	C₂	semidirect
6. #22550571	C₂	semidirect
7. #22550557	C₂	semidirect
8. #22550552	C₂	semidirect
9. #22550523	C₂	semidirect
10. #22550520	C₂	semidirect
11. #22550516	C₂	semidirect
12. #22550513	C₂	semidirect
13. #22550513	C₂	semidirect
14. #22550513	C₂	semidirect
15. D₄×C₂²⋊D₁₂₇	C₂	semidirect
16. #22550508	C₂	semidirect
17. #22550479	C₂	semidirect
18. #22550476	C₂	semidirect
19. #22550470	C₂	semidirect
20. #22550470	C₂	semidirect
21. #22550469	C₂	semidirect
22. #22550462	C₂	semidirect
23. #22550461	C₂	semidirect
24. #22550458	C₂	semidirect
25. #22550455	C₂	semidirect
26. #22550436	C₂	semidirect
27. #22550435	C₂	semidirect
28. #22550384	C₂	semidirect
29. #123×D₁₂₇	C₂	semidirect
30. C₂×#16861180	C₂	semidirect
31. #534×C₁₂₇	C₂	semidirect
32. C₂×#14523248	C₂²	semidirect
33. C₂×#14523247	C₂²	semidirect
34. C₂×#14523247	C₂²	semidirect
35. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
36. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
37. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
38. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
40. C₂×D₄×D₁₂₇	C₂²	semidirect
41. C₂²×C₄×D₁₂₇	C₂²	semidirect
42. #16861205	C₂²	semidirect
43. #16861205	C₂²	semidirect
44. #16861204	C₂²	semidirect
45. #16861204	C₂²	semidirect
46. #16861202	C₂²	semidirect
47. #16861202	C₂²	semidirect
48. #16861202	C₂²	semidirect
49. #16861202	C₂²	semidirect
50. #16861202	C₂²	semidirect
51. #16861202	C₂²	semidirect
52. #16861200	C₂²	semidirect
53. #16861200	C₂²	semidirect
54. #16861199	C₂²	semidirect
55. #16861199	C₂²	semidirect
56. #16861196	C₂²	semidirect
57. #16861196	C₂²	semidirect
58. #16861195	C₂²	semidirect
59. #16861195	C₂²	semidirect
60. #16861195	C₂²	semidirect
61. #16861195	C₂²	semidirect
62. #16861194	C₂²	semidirect
63. #16861194	C₂²	semidirect
64. #16861193	C₂²	semidirect
65. #16861193	C₂²	semidirect
66. #16861193	C₂²	semidirect
67. #16861193	C₂²	semidirect
68. #16861192	C₂²	semidirect
69. #16861192	C₂²	semidirect
70. #16861192	C₂²	semidirect
71. #16861192	C₂²	semidirect
72. #16861191	C₂²	semidirect
73. #16861191	C₂²	semidirect
74. #16861191	C₂²	semidirect
75. #16861191	C₂²	semidirect
76. #16861191	C₂²	semidirect
77. #16861191	C₂²	semidirect
78. #16861191	C₂²	semidirect
79. #16861191	C₂²	semidirect
80. #16861190	C₂²	semidirect
81. #16861190	C₂²	semidirect
82. #16861190	C₂²	semidirect
83. #16861190	C₂²	semidirect
84. #16861190	C₂²	semidirect
85. #16861190	C₂²	semidirect
86. #16861189	C₂²	semidirect
87. #16861189	C₂²	semidirect
88. #16861188	C₂²	semidirect
89. #16861188	C₂²	semidirect
90. #16861187	C₂²	semidirect
91. #16861187	C₂²	semidirect
92. #16861186	C₂²	semidirect
93. #16861186	C₂²	semidirect
94. #16861186	C₂²	semidirect
95. #16861186	C₂²	semidirect
96. #16861186	C₂²	semidirect
97. #16861186	C₂²	semidirect
98. #16861183	C₂²	semidirect
99. #16861183	C₂²	semidirect
100. #16861182	C₂²	semidirect
101. #16861182	C₂²	semidirect
102. #16861182	C₂²	semidirect
103. #16861182	C₂²	semidirect
104. #16861182	C₂²	semidirect
105. #16861182	C₂²	semidirect
108. #16861181	C₂²	semidirect
109. #16861181	C₂²	semidirect
110. #16861181	C₂²	semidirect
111. #16861181	C₂²	semidirect
112. #16861181	C₂²	semidirect
113. #16861181	C₂²	semidirect
114. #16861181	C₂²	semidirect
115. #16861181	C₂²	semidirect
116. #16861181	C₂²	semidirect
117. #16861181	C₂²	semidirect
119. #16861180	C₂²	semidirect
120. #16861180	C₂²	semidirect
121. #16861180	C₂²	semidirect
122. #16861180	C₂²	semidirect
123. #16861180	C₂²	semidirect
124. #16861180	C₂²	semidirect
125. #16861180	C₂²	semidirect
126. #16861180	C₂²	semidirect
127. #16861180	C₂²	semidirect
128. #16861180	C₂²	semidirect
129. #16861180	C₂²	semidirect
130. #16861179	C₂²	semidirect
131. #16861179	C₂²	semidirect
133. #16861178	C₂²	semidirect
134. #16861178	C₂²	semidirect
135. #16861178	C₂²	semidirect
136. #16861177	C₂²	semidirect
137. #16861177	C₂²	semidirect
138. #16861177	C₂²	semidirect
139. #16861177	C₂²	semidirect
140. #16861177	C₂²	semidirect
141. #16861177	C₂²	semidirect
142. D₄×Dic₁₂₇	C₂²	semidirect
143. D₄×Dic₁₂₇	C₂²	semidirect
144. D₄×Dic₁₂₇	C₂²	semidirect
145. D₄×Dic₁₂₇	C₂²	semidirect
146. #16861171	C₂²	semidirect
147. #16861171	C₂²	semidirect
148. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
149. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
150. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
151. C₄×C₂²⋊D₁₂₇	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. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
158. #16861168	C₂²	semidirect
159. #16861165	C₂²	semidirect
160. #16861165	C₂²	semidirect
161. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
162. C₄⋊C₄×D₁₂₇	C₂²	semidirect
163. C₄⋊C₄×D₁₂₇	C₂²	semidirect
164. C₂×C₂²⋊Dic₁₂₇	C₂²	semidirect
165. C₂×C₂²⋊Dic₁₂₇	C₂²	semidirect
166. C₂×C₂²⋊Dic₁₂₇	C₂²	semidirect
167. C₂×C₂²⋊Dic₁₂₇	C₂²	semidirect
168. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
169. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
170. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
171. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
172. C₂²×D₄×C₁₂₇	C₂²	semidirect
173. C₂²×D₄×C₁₂₇	C₂²	semidirect
174. #123×C₁₂₇	C₂²	semidirect
175. #123×C₁₂₇	C₂²	semidirect
176. #123×C₁₂₇	C₂²	semidirect
177. #123×C₁₂₇	C₂²	semidirect
178. #121×C₁₂₇	C₂²	semidirect
179. #121×C₁₂₇	C₂²	semidirect
180. #121×C₁₂₇	C₂²	semidirect
181. #121×C₁₂₇	C₂²	semidirect
183. #120×C₁₂₇	C₂²	semidirect
184. #120×C₁₂₇	C₂²	semidirect
185. #120×C₁₂₇	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₁₂₇	C₂²	semidirect
541. C₁₂₇	#3534	semidirect
569. #534	D₁₂₇	semidirect
582. C₂²×D₄	C₂×D₁₂₇	semidirect
583. C₂²×D₄	C₂×D₁₂₇	semidirect
629. #123	C₂×D₁₂₇	semidirect
630. #123	C₂×D₁₂₇	semidirect
631. #123	C₂×D₁₂₇	semidirect
632. #123	C₂×D₁₂₇	semidirect
677. #121	C₂×D₁₂₇	semidirect
678. #121	C₂×D₁₂₇	semidirect
679. #121	C₂×D₁₂₇	semidirect
680. #121	C₂×D₁₂₇	semidirect
694. #120	C₂×D₁₂₇	semidirect
695. #120	C₂×D₁₂₇	semidirect
696. #120	C₂×D₁₂₇	semidirect
727. 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
#22550623	2
#22550621	2
#22550615	2
#22550614	2
#22550573	2
#22550571	2
#22550557	2
#22550552	2
#22550523	2
#22550520	2
#22550516	2
#22550513	2
D₄×C₂²⋊D₁₂₇	2
#22550508	2
#22550479	2
#22550476	2
#22550470	2
#22550469	2
#22550462	2
#22550461	2
#22550458	2
#22550455	2
#22550436	2
#22550435	2
#22550384	2
#123×D₁₂₇	2
C₂×#16861180	2
#534×C₁₂₇	2
#3534	127