Subgroups — #30652145

Order 16256.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550506	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550497	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550494	C₂	1	2	yes	maximal, complemented
4	#22550491	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550477	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550476	C₂	1	2	yes	maximal, complemented
7	#22550462	C₂	1	2	yes	maximal, complemented
8	#22550458	C₂	1	2	yes	maximal, complemented
9	#22550455	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550442	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550439	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550424	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550421	C₂	1	2	yes	maximal, complemented
14	#22550421	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550411	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550407	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550403	C₂	1	2	yes	maximal, complemented
18	#22550386	C₂	1	2	yes	maximal, complemented
19	#22550384	C₂	1	2	yes	maximal, complemented
20	#22550344	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#14523247	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#540×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523248	C₂²	1	1	yes	characteristic
25	C₂×#14523247	C₂²	1	1	yes	characteristic
26	C₂×#14523247	C₂²	1	2	yes	complemented
27	C₂×#14523247	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	—
30	#16861209	C₂²	1	1	yes	characteristic, complemented
31	#16861208	C₂²	1	1	yes	characteristic, complemented
32	#16861208	C₂²	1	2	yes	complemented
33	#16861205	C₂²	1	1	yes	characteristic
34	#16861205	C₂²	1	2	yes	—
35	#16861204	C₂²	1	2	yes	complemented
36	#16861204	C₂²	1	2	yes	complemented
37	#16861202	C₂²	1	2	yes	complemented
38	#16861202	C₂²	1	2	yes	complemented
39	#16861200	C₂²	1	1	yes	characteristic, complemented
40	#16861199	C₂²	1	2	yes	complemented
41	#16861197	C₂²	1	1	yes	characteristic
42	#16861196	C₂²	1	1	yes	characteristic
43	#16861196	C₂²	1	2	yes	complemented
44	#16861195	C₂²	1	2	yes	—
45	#16861195	C₂²	1	2	yes	complemented
46	#16861195	C₂²	1	2	yes	complemented
47	#16861195	C₂²	1	2	yes	complemented
48	#16861194	C₂²	1	2	yes	complemented
49	#16861192	C₂²	1	2	yes	complemented
50	#16861192	C₂²	1	2	yes	complemented
51	#16861191	C₂²	1	2	yes	complemented
52	#16861191	C₂²	1	2	yes	complemented
53	#16861190	C₂²	1	2	yes	complemented
54	#16861189	C₂²	1	2	yes	—
55	#16861189	C₂²	1	1	yes	characteristic, complemented
56	#16861188	C₂²	1	2	yes	complemented
57	#16861188	C₂²	1	1	yes	characteristic, complemented
58	#16861187	C₂²	1	2	yes	—
59	#16861187	C₂²	1	2	yes	complemented
60	#16861186	C₂²	1	2	yes	complemented
61	#16861184	C₂²	1	1	yes	characteristic
62	#16861183	C₂²	1	1	yes	characteristic
63	#16861183	C₂²	1	2	yes	complemented
64	#16861182	C₂²	1	2	yes	—
65	#16861182	C₂²	1	2	yes	complemented
66	#16861181	C₂²	1	2	yes	—
67	#16861181	C₂²	1	2	yes	—
68	#16861181	C₂²	1	2	yes	complemented
69	#16861181	C₂²	1	2	yes	complemented
70	#16861180	C₂²	1	2	yes	—
71	#16861180	C₂²	1	1	yes	characteristic
72	#16861180	C₂²	1	1	yes	characteristic, complemented
73	#16861180	C₂²	1	2	yes	complemented
74	#16861179	C₂²	1	2	yes	—
75	#16861177	C₂²	1	2	yes	—
76	#16861177	C₂²	1	2	yes	—
77	#16861177	C₂²	1	2	yes	—
78	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
79	#16861174	C₂²	1	1	yes	characteristic, complemented
80	#16861174	C₂²	1	1	yes	characteristic, complemented
81	#16861174	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
84	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
86	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
87	#16861171	C₂²	1	1	yes	characteristic
88	#16861171	C₂²	1	1	yes	characteristic
89	#16861171	C₂²	1	1	yes	characteristic
90	#16861171	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
93	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
96	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
97	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
100	#16861167	C₂²	1	1	yes	characteristic
101	#16861167	C₂²	1	2	yes	complemented
102	#16861166	C₂²	1	1	yes	characteristic
103	#16861166	C₂²	1	1	yes	characteristic, complemented
104	#16861165	C₂²	1	2	yes	complemented
105	#16861165	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₂₇	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
110	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
112	#127×C₁₂₇	C₂²	1	1	yes	characteristic
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₂₇	C₂²	1	2	yes	complemented
115	#123×C₁₂₇	C₂²	1	2	yes	complemented
116	#121×C₁₂₇	C₂²	1	1	yes	characteristic
117	#121×C₁₂₇	C₂²	1	2	yes	complemented
118	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₂₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	2	yes	—
124	#14523248	—	2	4	no	—
125	#14523247	—	2	4	no	—
126	#14523247	—	4	4	no	—
127	#14523247	—	4	4	no	—
128	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₅₄	C₂³	1	2	yes	—
131	C₂×Dic₂₅₄	C₂³	1	2	yes	—
132	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
133	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
134	C₂×D₅₀₈	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
144	D₄×D₁₂₇	—	2	4	no	—
145	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
146	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
147	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
148	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₂₇	—	4	4	no	—
151	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
154	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
156	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
157	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
161	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
163	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
164	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
165	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
166	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
167	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
168	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
169	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
170	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
172	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
182	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₂₇	C₂³	1	2	yes	—
195	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₂₇	C₂³	1	2	yes	—
197	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₂₇	C₂³	1	2	yes	—
205	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
208	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
209	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
210	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
226	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
227	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
228	C₂²×D₁₂₇	—	2	4	no	—
229	C₂²×D₁₂₇	—	4	2	no	—
230	C₂²×D₁₂₇	—	4	2	no	—
231	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
232	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
234	Dic₂₅₄	—	2	2	no	—
235	Dic₂₅₄	—	2	2	no	—
236	Dic₂₅₄	—	4	2	no	—
237	Dic₂₅₄	—	4	2	no	—
238	D₅₀₈	—	2	2	no	—
239	D₅₀₈	—	2	2	no	—
240	D₅₀₈	—	4	2	no	—
241	C₂²⋊D₁₂₇	—	2	4	no	—
242	C₂²⋊D₁₂₇	—	2	2	no	—
243	C₂²⋊D₁₂₇	—	2	4	no	—
244	C₂²⋊D₁₂₇	—	2	2	no	—
245	C₂²⋊D₁₂₇	—	4	2	no	—
246	C₂²⋊D₁₂₇	—	4	2	no	—
247	C₂²⋊D₁₂₇	—	4	2	no	—
248	C₂²⋊D₁₂₇	—	4	2	no	—
249	C₂²⋊D₁₂₇	—	4	2	no	—
250	C₂×Dic₁₂₇	—	2	4	no	—
251	C₂×Dic₁₂₇	—	2	4	no	—
252	C₂×Dic₁₂₇	—	2	4	no	—
253	C₂×Dic₁₂₇	—	2	2	no	—
254	C₂×Dic₁₂₇	—	4	1	no	—
255	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
257	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
260	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
264	C₄×D₁₂₇	—	2	2	no	—
265	C₄×D₁₂₇	—	2	2	no	—
266	C₄×D₁₂₇	—	2	4	no	—
267	C₄×D₁₂₇	—	2	2	no	—
268	C₄×D₁₂₇	—	4	2	no	—
269	C₄×D₁₂₇	—	4	2	no	—
270	C₄×D₁₂₇	—	4	1	no	—
271	C₄×D₁₂₇	—	4	1	no	—
272	C₄×D₁₂₇	#41	1	4	yes	complemented
273	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
274	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
275	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
276	D₄×C₁₂₇	—	2	2	no	—
277	D₄×C₁₂₇	—	2	2	no	—
278	D₄×C₁₂₇	—	4	2	no	—
279	D₄×C₁₂₇	—	4	2	no	—
280	D₄×C₁₂₇	—	4	2	no	—
281	D₄×C₁₂₇	—	4	2	no	—
282	C₂×C₄×C₁₂₇	—	2	2	no	—
283	C₂×C₄×C₁₂₇	—	4	2	no	—
284	C₂×C₄×C₁₂₇	—	4	2	no	—
285	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
292	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₁₂₇	—	2	1	no	—
294	C₂²×C₁₂₇	—	2	2	no	—
295	C₂²×C₁₂₇	—	2	2	no	—
296	C₂²×C₁₂₇	—	2	2	no	—
297	C₂²×C₁₂₇	—	2	1	no	—
298	C₂²×C₁₂₇	—	2	2	no	—
299	C₂²×C₁₂₇	—	2	2	no	—
300	C₂²×C₁₂₇	—	2	1	no	—
301	C₂²×C₁₂₇	—	2	2	no	—
302	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₂₇	—	2	1	no	—
304	C₂×D₁₂₇	—	2	1	no	—
305	C₂×D₁₂₇	—	2	1	no	—
306	C₂×D₁₂₇	—	2	2	no	—
307	C₂×D₁₂₇	—	2	2	no	—
308	C₂×D₁₂₇	—	2	1	no	—
309	C₂×D₁₂₇	—	2	1	no	—
310	C₂×D₁₂₇	—	2	2	no	—
311	C₂×D₁₂₇	—	4	8	no	—
312	C₂×D₁₂₇	C₂×#41	1	2	yes	—
313	C₄×C₁₂₇	—	2	1	no	—
314	C₄×C₁₂₇	—	2	1	no	—
315	C₄×C₁₂₇	—	2	2	no	—
316	C₄×C₁₂₇	—	2	1	no	—
317	C₄×C₁₂₇	—	2	1	no	—
318	C₄×C₁₂₇	—	2	2	no	—
319	C₄×C₁₂₇	—	2	1	no	—
320	C₄×C₁₂₇	C₂×#41	1	2	yes	—
321	Dic₁₂₇	—	2	1	no	—
322	Dic₁₂₇	—	2	2	no	—
323	Dic₁₂₇	—	2	2	no	—
324	Dic₁₂₇	—	2	2	no	—
325	Dic₁₂₇	—	2	1	no	—
326	Dic₁₂₇	—	2	1	no	—
327	Dic₁₂₇	—	2	1	no	—
328	Dic₁₂₇	C₂×#41	1	2	yes	—
329	Dic₁₂₇	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₁₂₇	—	4	2	no	—
331	C₂×C₁₂₇	—	4	1	no	—
332	C₂×C₁₂₇	—	4	2	no	—
333	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
334	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₁₂₇	#585	1	1	yes	characteristic
336	D₁₂₇	—	2	2	no	—
337	D₁₂₇	—	4	1	no	—
338	D₁₂₇	—	4	2	no	—
339	#3460	—	127	1	no	maximal, Sylow
340	C₁₂₇	#3460	1	1	yes	characteristic, complemented, Sylow
341	#544	—	127	1	no	—
342	#542	—	127	2	no	—
343	#542	—	127	1	no	—
344	#542	—	127	1	no	—
345	#540	—	127	2	no	—
346	#540	—	127	1	no	—
347	#540	D₁₂₇	1	1	yes	characteristic, complemented
348	#538	—	127	2	no	—
349	#538	—	127	2	no	—
350	#537	—	127	1	no	—
351	#535	—	127	1	no	—
352	#535	—	127	1	no	—
353	#532	—	127	1	no	—
354	#532	—	127	1	no	—
355	#532	—	127	2	no	—
356	#529	—	127	1	no	—
357	#529	—	127	2	no	—
358	#529	—	127	1	no	—
359	#525	—	127	2	no	—
360	#525	—	127	2	no	—
361	C₄×#41	—	127	1	no	—
362	C₄×#41	—	127	1	no	—
363	C₂×C₄×D₄	—	127	1	no	—
364	C₂×#41	—	127	2	no	—
365	C₂×#41	—	127	2	no	—
366	C₂×#41	—	127	1	no	—
367	C₂×#41	—	127	1	no	—
368	C₂²×D₄	—	127	1	no	—
369	C₂³×C₄	—	127	2	no	—
370	C₄⋊Q₈	—	127	2	no	—
371	C₄⋊Q₈	—	127	1	no	—
372	C₄⋊Q₈	—	127	1	no	—
373	#127	—	127	1	no	—
374	#127	—	127	2	no	—
375	#127	C₂×D₁₂₇	1	1	yes	characteristic
376	#126	—	127	2	no	—
377	#126	—	127	2	no	—
378	#126	—	127	2	no	—
379	#126	—	127	2	no	—
380	#125	—	127	2	no	—
381	#125	—	127	1	no	—
382	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
383	#124	—	127	1	no	—
384	#124	—	127	2	no	—
385	#124	—	127	2	no	—
386	#124	—	127	2	no	—
387	#124	—	127	2	no	—
388	#124	—	127	2	no	—
389	#124	—	127	1	no	—
390	#123	—	127	2	no	—
391	#123	—	127	2	no	—
392	#123	—	127	2	no	—
393	#123	—	127	2	no	—
394	#123	—	127	2	no	—
395	#123	—	127	2	no	—
396	#123	C₂×D₁₂₇	1	2	yes	complemented
397	#123	C₂×D₁₂₇	1	2	yes	complemented
398	C₂²⋊Q₈	—	127	2	no	—
399	C₂²⋊Q₈	—	127	1	no	—
400	C₂²⋊Q₈	—	127	2	no	—
401	C₂²⋊Q₈	—	127	2	no	—
402	C₂²⋊Q₈	—	127	2	no	—
403	C₂²⋊Q₈	—	127	1	no	—
404	C₂²⋊Q₈	—	127	2	no	—
405	#121	—	127	2	no	—
406	#121	—	127	2	no	—
407	#121	—	127	1	no	—
408	#121	—	127	2	no	—
409	#121	—	127	1	no	—
410	#121	—	127	2	no	—
411	#121	—	127	2	no	—
412	#121	—	127	2	no	—
413	#121	—	127	1	no	—
414	#121	—	127	2	no	—
415	#121	—	127	1	no	—
416	#121	—	127	2	no	—
417	#121	—	127	2	no	—
418	#121	C₂×D₁₂₇	1	1	yes	characteristic
419	#121	C₂×D₁₂₇	1	2	yes	complemented
420	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
421	#121	C₂×D₁₂₇	1	2	yes	complemented
422	#120	—	127	2	no	—
423	#120	—	127	2	no	—
424	#120	—	127	2	no	—
425	#120	—	127	2	no	—
426	C₄×Q₈	—	127	1	no	—
427	C₄×Q₈	—	127	1	no	—
428	C₄×Q₈	—	127	1	no	—
429	C₄×Q₈	—	127	1	no	—
430	C₄×D₄	—	127	1	no	—
431	C₄×D₄	—	127	1	no	—
432	C₄×D₄	—	127	2	no	—
433	C₄×D₄	—	127	2	no	—
434	C₄×D₄	—	127	2	no	—
435	C₄×D₄	—	127	2	no	—
436	C₄×D₄	—	127	1	no	—
437	C₄×D₄	—	127	1	no	—
438	C₄×D₄	—	127	1	no	—
439	C₄×D₄	—	127	2	no	—
440	C₄×D₄	—	127	2	no	—
441	C₄×D₄	—	127	2	no	—
442	C₄×D₄	—	127	1	no	—
443	C₄×D₄	—	127	1	no	—
444	C₄×D₄	—	127	1	no	—
445	C₄×D₄	—	127	1	no	—
446	C₄×D₄	—	127	2	no	—
447	C₄×D₄	—	127	1	no	—
448	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
450	#117	—	127	1	no	—
451	#117	—	127	2	no	—
452	#117	—	127	2	no	—
453	#117	—	127	2	no	—
454	#117	—	127	1	no	—
455	#117	—	127	1	no	—
456	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	127	1	no	—
458	C₂×C₂²⋊C₄	—	127	2	no	—
459	C₂×C₄²	—	127	1	no	—
460	C₂×C₄²	—	127	2	no	—
461	C₂×C₄²	—	127	1	no	—
462	C₂×C₄²	—	127	1	no	—
463	C₂⁴	—	127	2	no	—
464	#41	—	508	4	no	—
465	#41	—	508	4	no	—
466	#41	—	254	4	no	—
467	#41	—	254	4	no	—
468	C₂×Q₈	—	127	2	no	—
469	C₂×Q₈	—	127	2	no	—
470	C₂×Q₈	—	127	1	no	—
471	C₂×Q₈	—	127	1	no	—
472	C₂×D₄	—	127	2	no	—
473	C₂×D₄	—	127	2	no	—
474	C₂×D₄	—	127	2	no	—
475	C₂×D₄	—	127	2	no	—
476	C₂×D₄	—	127	2	no	—
477	C₂×D₄	—	127	2	no	—
478	C₂×D₄	—	127	1	no	—
479	C₂×D₄	—	127	2	no	—
480	C₂×D₄	—	127	1	no	—
481	C₂×D₄	—	127	2	no	—
482	C₂×D₄	—	127	1	no	—
483	C₂×D₄	—	127	1	no	—
484	C₂×D₄	—	254	4	no	—
485	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
488	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
489	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
490	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
491	C₂²×C₄	—	127	1	no	—
492	C₂²×C₄	—	127	1	no	—
493	C₂²×C₄	—	127	2	no	—
494	C₂²×C₄	—	127	2	no	—
495	C₂²×C₄	—	127	1	no	—
496	C₂²×C₄	—	127	2	no	—
497	C₂²×C₄	—	127	1	no	—
498	C₂²×C₄	—	127	1	no	—
499	C₂²×C₄	—	127	2	no	—
500	C₂²×C₄	—	127	2	no	—
501	C₂²×C₄	—	127	1	no	—
502	C₂²×C₄	—	127	1	no	—
503	C₂²×C₄	—	127	1	no	—
504	C₂²×C₄	—	127	2	no	—
505	C₂²×C₄	—	508	4	no	—
506	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
508	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
509	C₄⋊C₄	—	127	2	no	—
510	C₄⋊C₄	—	127	1	no	—
511	C₄⋊C₄	—	127	1	no	—
512	C₄⋊C₄	—	127	2	no	—
513	C₄⋊C₄	—	127	1	no	—
514	C₄⋊C₄	—	127	2	no	—
515	C₄⋊C₄	—	127	1	no	—
516	C₄⋊C₄	—	127	2	no	—
517	C₄⋊C₄	—	127	2	no	—
518	C₄⋊C₄	—	127	2	no	—
519	C₄⋊C₄	—	127	1	no	—
520	C₄⋊C₄	—	127	1	no	—
521	C₄⋊C₄	—	127	2	no	—
522	C₄⋊C₄	—	127	2	no	—
523	C₄⋊C₄	—	127	2	no	—
524	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
530	C₂²⋊C₄	—	127	2	no	—
531	C₂²⋊C₄	—	127	2	no	—
532	C₂²⋊C₄	—	127	2	no	—
533	C₂²⋊C₄	—	127	2	no	—
534	C₂²⋊C₄	—	127	2	no	—
535	C₂²⋊C₄	—	127	2	no	—
536	C₂²⋊C₄	—	127	2	no	—
537	C₂²⋊C₄	—	127	2	no	—
538	C₂²⋊C₄	—	127	2	no	—
539	C₂²⋊C₄	—	127	1	no	—
540	C₂²⋊C₄	—	127	2	no	—
541	C₂²⋊C₄	—	127	1	no	—
542	C₂²⋊C₄	—	127	1	no	—
543	C₂²⋊C₄	—	127	1	no	—
544	C₂²⋊C₄	—	127	2	no	—
545	C₂²⋊C₄	—	127	2	no	—
546	C₂²⋊C₄	—	127	2	no	—
547	C₂²⋊C₄	—	127	2	no	—
548	C₂²⋊C₄	—	127	2	no	—
549	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
555	C₄²	—	127	1	no	—
556	C₄²	—	127	1	no	—
557	C₄²	—	127	2	no	—
558	C₄²	—	127	1	no	—
559	C₄²	—	127	1	no	—
560	C₄²	—	127	1	no	—
561	C₄²	—	127	2	no	—
562	C₄²	—	127	1	no	—
563	C₄²	—	127	1	no	—
564	C₄²	—	127	1	no	—
565	C₄²	—	127	2	no	—
566	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
567	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
568	C₂³	—	127	1	no	—
569	C₂³	—	127	2	no	—
570	C₂³	—	127	1	no	—
571	C₂³	—	508	2	no	—
572	C₂³	—	508	2	no	—
573	C₂³	—	254	4	no	—
574	C₂³	C₂³×D₁₂₇	1	2	yes	—
575	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
576	C₂³	C₂³×D₁₂₇	1	2	yes	—
577	Q₈	—	508	2	no	—
578	Q₈	—	508	2	no	—
579	Q₈	—	254	2	no	—
580	Q₈	—	254	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	508	2	no	—
588	D₄	—	508	2	no	—
589	D₄	—	508	2	no	—
590	D₄	—	508	2	no	—
591	D₄	—	508	2	no	—
592	D₄	—	508	2	no	—
593	D₄	—	254	2	no	—
594	D₄	—	254	4	no	—
595	D₄	—	254	2	no	—
596	D₄	—	254	2	no	—
597	D₄	—	254	4	no	—
598	D₄	—	254	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	127	1	no	—
603	C₂×C₄	—	127	1	no	—
604	C₂×C₄	—	127	4	no	—
605	C₂×C₄	—	127	1	no	—
606	C₂×C₄	—	127	2	no	—
607	C₂×C₄	—	127	1	no	—
608	C₂×C₄	—	127	1	no	—
609	C₂×C₄	—	127	2	no	—
610	C₂×C₄	—	127	1	no	—
611	C₂×C₄	—	127	2	no	—
612	C₂×C₄	—	508	2	no	—
613	C₂×C₄	—	508	2	no	—
614	C₂×C₄	—	508	1	no	—
615	C₂×C₄	—	508	1	no	—
616	C₂×C₄	—	508	1	no	—
617	C₂×C₄	—	254	2	no	—
618	C₂×C₄	—	254	4	no	—
619	C₂×C₄	—	254	2	no	—
620	C₂×C₄	—	254	4	no	—
621	C₂×C₄	—	254	4	no	—
622	C₂×C₄	—	254	2	no	—
623	C₂×C₄	—	254	4	no	—
624	C₂×C₄	—	254	2	no	—
625	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
628	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
632	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	127	2	no	—
643	C₂²	—	508	8	no	—
644	C₂²	—	254	1	no	—
645	C₂²	—	254	2	no	—
646	C₂²	—	254	2	no	—
647	C₂²	—	254	1	no	—
648	C₂²	—	254	1	no	—
649	C₂²	—	254	2	no	—
650	C₂²	—	254	1	no	—
651	C₂²	—	254	1	no	—
652	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	127	2	no	—
661	C₄	—	127	2	no	—
662	C₄	—	254	2	no	—
663	C₄	—	254	1	no	—
664	C₄	—	254	2	no	—
665	C₄	—	254	2	no	—
666	C₄	—	254	1	no	—
667	C₄	—	254	1	no	—
668	C₄	—	254	1	no	—
669	C₄	#41×D₁₂₇	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	508	2	no	—
674	C₂	—	508	1	no	—
675	C₂	—	254	2	no	—
676	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
678	C₂	#22550711	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#540×C₁₂₇	C₂
hypercenter	#540	D₁₂₇
hypocenter	C₁₂₇	#3460
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #22550506	C₂	semidirect
2. #22550497	C₂	semidirect
3. #22550494	C₂	semidirect
4. #22550491	C₂	semidirect
5. #22550477	C₂	semidirect
6. #22550476	C₂	semidirect
7. #22550462	C₂	semidirect
8. #22550458	C₂	semidirect
9. #22550455	C₂	semidirect
10. #22550442	C₂	semidirect
11. #22550439	C₂	semidirect
12. #22550424	C₂	semidirect
13. #22550421	C₂	semidirect
14. #22550421	C₂	semidirect
15. #22550411	C₂	semidirect
16. #22550407	C₂	semidirect
17. #22550403	C₂	semidirect
18. #22550386	C₂	semidirect
19. #22550384	C₂	semidirect
20. #22550344	C₂	semidirect
21. C₄×#14523247	C₂	semidirect
22. C₄×D₄×D₁₂₇	C₂	semidirect
23. #540×C₁₂₇	C₂	semidirect
26. C₂×#14523247	C₂²	semidirect
27. C₂×#14523247	C₂²	semidirect
30. #16861209	C₂²	semidirect
31. #16861208	C₂²	semidirect
32. #16861208	C₂²	semidirect
35. #16861204	C₂²	semidirect
36. #16861204	C₂²	semidirect
37. #16861202	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861200	C₂²	semidirect
40. #16861199	C₂²	semidirect
43. #16861196	C₂²	semidirect
45. #16861195	C₂²	semidirect
46. #16861195	C₂²	semidirect
47. #16861195	C₂²	semidirect
48. #16861194	C₂²	semidirect
49. #16861192	C₂²	semidirect
50. #16861192	C₂²	semidirect
51. #16861191	C₂²	semidirect
52. #16861191	C₂²	semidirect
53. #16861190	C₂²	semidirect
55. #16861189	C₂²	semidirect
56. #16861188	C₂²	semidirect
57. #16861188	C₂²	semidirect
59. #16861187	C₂²	semidirect
60. #16861186	C₂²	semidirect
63. #16861183	C₂²	semidirect
65. #16861182	C₂²	semidirect
68. #16861181	C₂²	semidirect
69. #16861181	C₂²	semidirect
72. #16861180	C₂²	semidirect
73. #16861180	C₂²	semidirect
78. C₄×Dic₂₅₄	C₂²	semidirect
79. #16861174	C₂²	semidirect
80. #16861174	C₂²	semidirect
81. #16861174	C₂²	semidirect
84. D₄×Dic₁₂₇	C₂²	semidirect
85. D₄×Dic₁₂₇	C₂²	semidirect
86. D₄×Dic₁₂₇	C₂²	semidirect
90. #16861171	C₂²	semidirect
97. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
101. #16861167	C₂²	semidirect
103. #16861166	C₂²	semidirect
104. #16861165	C₂²	semidirect
105. #16861165	C₂²	semidirect
108. C₂×C₄×Dic₁₂₇	C₂²	semidirect
109. C₂×C₄×Dic₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
114. #123×C₁₂₇	C₂²	semidirect
115. #123×C₁₂₇	C₂²	semidirect
117. #121×C₁₂₇	C₂²	semidirect
118. #121×C₁₂₇	C₂²	semidirect
119. #121×C₁₂₇	C₂²	semidirect
121. C₄×D₄×C₁₂₇	C₂²	semidirect
122. #117×C₁₂₇	C₂²	semidirect
272. C₄×D₁₂₇	#41	semidirect
340. C₁₂₇	#3460	semidirect
347. #540	D₁₂₇	semidirect
382. #125	C₂×D₁₂₇	semidirect
396. #123	C₂×D₁₂₇	semidirect
397. #123	C₂×D₁₂₇	semidirect
419. #121	C₂×D₁₂₇	semidirect
420. #121	C₂×D₁₂₇	semidirect
421. #121	C₂×D₁₂₇	semidirect
449. C₄×D₄	C₂×D₁₂₇	semidirect
456. #117	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550506	2
#22550497	2
#22550494	2
#22550491	2
#22550477	2
#22550476	2
#22550462	2
#22550458	2
#22550455	2
#22550442	2
#22550439	2
#22550424	2
#22550421	2
#22550411	2
#22550407	2
#22550403	2
#22550386	2
#22550384	2
#22550344	2
C₄×#14523247	2
C₄×D₄×D₁₂₇	2
#540×C₁₂₇	2
#3460	127