Subgroups — #30652151

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	#22550499	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550495	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550492	C₂	1	2	yes	maximal, complemented
5	#22550482	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550479	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550478	C₂	1	2	yes	maximal, complemented
8	#22550465	C₂	1	2	yes	maximal, complemented
9	#22550462	C₂	1	2	yes	maximal, complemented
10	#22550456	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550444	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550442	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550426	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550423	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550423	C₂	1	2	yes	maximal, complemented
16	#22550413	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550404	C₂	1	2	yes	maximal, complemented
18	#22550388	C₂	1	2	yes	maximal, complemented
19	#22550385	C₂	1	2	yes	maximal, complemented
20	C₄×#14523249	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#14523248	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523249	C₂²	1	1	yes	characteristic
25	C₂×#14523248	C₂²	1	1	yes	characteristic
26	C₂×#14523248	C₂²	1	2	yes	complemented
27	C₂×#14523248	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	2	yes	complemented
32	#16861208	C₂²	1	1	yes	characteristic, complemented
33	#16861206	C₂²	1	1	yes	characteristic
34	#16861205	C₂²	1	2	yes	—
35	#16861205	C₂²	1	1	yes	characteristic
36	#16861204	C₂²	1	2	yes	complemented
37	#16861204	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	#16861198	C₂²	1	1	yes	characteristic
42	#16861197	C₂²	1	2	yes	complemented
43	#16861195	C₂²	1	2	yes	—
44	#16861195	C₂²	1	2	yes	complemented
45	#16861195	C₂²	1	2	yes	complemented
46	#16861195	C₂²	1	2	yes	complemented
47	#16861194	C₂²	1	2	yes	complemented
48	#16861194	C₂²	1	2	yes	complemented
49	#16861194	C₂²	1	2	yes	complemented
50	#16861193	C₂²	1	2	yes	complemented
51	#16861193	C₂²	1	2	yes	complemented
52	#16861191	C₂²	1	2	yes	complemented
53	#16861191	C₂²	1	2	yes	complemented
54	#16861189	C₂²	1	2	yes	—
55	#16861189	C₂²	1	2	yes	complemented
56	#16861187	C₂²	1	2	yes	—
57	#16861187	C₂²	1	2	yes	complemented
58	#16861186	C₂²	1	2	yes	complemented
59	#16861185	C₂²	1	1	yes	characteristic, complemented
60	#16861184	C₂²	1	2	yes	—
61	#16861184	C₂²	1	1	yes	characteristic
62	#16861184	C₂²	1	2	yes	complemented
63	#16861184	C₂²	1	1	yes	characteristic, complemented
64	#16861184	C₂²	1	2	yes	complemented
65	#16861183	C₂²	1	1	yes	characteristic
66	#16861183	C₂²	1	1	yes	characteristic, complemented
67	#16861183	C₂²	1	2	yes	complemented
68	#16861182	C₂²	1	2	yes	—
69	#16861182	C₂²	1	2	yes	—
70	#16861182	C₂²	1	2	yes	—
71	#16861182	C₂²	1	2	yes	complemented
72	#16861182	C₂²	1	2	yes	complemented
73	#16861181	C₂²	1	2	yes	complemented
74	#16861180	C₂²	1	1	yes	characteristic
75	#16861180	C₂²	1	2	yes	complemented
76	#16861179	C₂²	1	2	yes	—
77	#16861179	C₂²	1	2	yes	—
78	#16861179	C₂²	1	2	yes	—
79	#16861177	C₂²	1	2	yes	—
80	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
84	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
85	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
86	C₄×D₅₀₈	C₂²	1	2	yes	—
87	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₅₀₈	C₂²	1	2	yes	complemented
89	C₄×D₅₀₈	C₂²	1	2	yes	complemented
90	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
91	#16861171	C₂²	1	1	yes	characteristic
92	#16861171	C₂²	1	2	yes	—
93	#16861171	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
95	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
100	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
101	#16861168	C₂²	1	1	yes	characteristic, complemented
102	#16861167	C₂²	1	1	yes	characteristic
103	#16861167	C₂²	1	2	yes	complemented
104	#16861166	C₂²	1	1	yes	characteristic
105	#16861166	C₂²	1	1	yes	characteristic, complemented
106	#16861166	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
109	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
110	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₁₂₇	C₂²	1	2	yes	complemented
112	#126×C₁₂₇	C₂²	1	2	yes	complemented
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#124×C₁₂₇	C₂²	1	1	yes	characteristic
115	#123×C₁₂₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₂₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
121	#117×C₁₂₇	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	2	yes	—
124	#14523249	—	2	4	no	—
125	#14523248	—	2	4	no	—
126	#14523248	—	4	4	no	—
127	#14523248	—	4	4	no	—
128	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₅₄	C₂³	1	2	yes	—
130	C₂×Dic₂₅₄	C₂³	1	2	yes	—
131	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
132	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
133	C₂×D₅₀₈	C₂³	1	2	yes	—
134	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
135	C₂×D₅₀₈	C₂³	1	2	yes	—
136	C₂×D₅₀₈	C₂³	1	2	yes	—
137	C₂×D₅₀₈	C₂³	1	2	yes	—
138	C₂×D₅₀₈	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
147	D₄×D₁₂₇	—	2	4	no	—
148	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
149	C₂×C₄×D₁₂₇	—	4	4	no	—
150	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
152	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
154	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
155	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
157	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
158	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
159	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
164	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
165	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
166	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
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	2	yes	—
173	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
174	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
181	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
197	C₄×Dic₁₂₇	C₂³	1	2	yes	—
198	C₄×Dic₁₂₇	C₂³	1	2	yes	—
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	1	yes	characteristic
205	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
223	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
224	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
225	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
226	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
227	C₄²×C₁₂₇	C₂³	1	2	yes	—
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	2	yes	—
234	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
235	Dic₂₅₄	—	2	2	no	—
236	Dic₂₅₄	—	4	2	no	—
237	Dic₂₅₄	—	4	2	no	—
238	D₅₀₈	—	2	2	no	—
239	D₅₀₈	—	2	4	no	—
240	D₅₀₈	—	2	2	no	—
241	D₅₀₈	—	2	2	no	—
242	D₅₀₈	—	4	2	no	—
243	D₅₀₈	—	4	2	no	—
244	D₅₀₈	—	4	2	no	—
245	D₅₀₈	—	4	2	no	—
246	C₂²⋊D₁₂₇	—	2	2	no	—
247	C₂²⋊D₁₂₇	—	2	4	no	—
248	C₂²⋊D₁₂₇	—	2	2	no	—
249	C₂²⋊D₁₂₇	—	4	2	no	—
250	C₂²⋊D₁₂₇	—	4	2	no	—
251	C₂²⋊D₁₂₇	—	4	2	no	—
252	C₂²⋊D₁₂₇	—	4	2	no	—
253	C₂²⋊D₁₂₇	—	4	2	no	—
254	C₂×Dic₁₂₇	—	4	2	no	—
255	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
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	C₄×D₁₂₇	—	2	2	no	—
264	C₄×D₁₂₇	—	2	2	no	—
265	C₄×D₁₂₇	—	2	4	no	—
266	C₄×D₁₂₇	—	2	4	no	—
267	C₄×D₁₂₇	—	2	2	no	—
268	C₄×D₁₂₇	—	2	4	no	—
269	C₄×D₁₂₇	—	4	2	no	—
270	C₄×D₁₂₇	—	4	2	no	—
271	C₄×D₁₂₇	—	4	1	no	—
272	C₄×D₁₂₇	—	4	2	no	—
273	C₄×D₁₂₇	—	4	1	no	—
274	C₄×D₁₂₇	#41	1	4	yes	complemented
275	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
276	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
277	Q₈×C₁₂₇	—	2	2	no	—
278	D₄×C₁₂₇	—	2	2	no	—
279	D₄×C₁₂₇	—	4	2	no	—
280	C₂×C₄×C₁₂₇	—	2	2	no	—
281	C₂×C₄×C₁₂₇	—	2	4	no	—
282	C₂×C₄×C₁₂₇	—	2	2	no	—
283	C₂×C₄×C₁₂₇	—	4	1	no	—
284	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
289	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
290	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
297	C₂²×C₁₂₇	—	2	1	no	—
298	C₂²×C₁₂₇	—	2	2	no	—
299	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₂₇	—	2	1	no	—
301	C₂×D₁₂₇	—	2	1	no	—
302	C₂×D₁₂₇	—	2	1	no	—
303	C₂×D₁₂₇	—	2	2	no	—
304	C₂×D₁₂₇	—	2	2	no	—
305	C₂×D₁₂₇	—	2	2	no	—
306	C₂×D₁₂₇	—	2	1	no	—
307	C₂×D₁₂₇	—	2	2	no	—
308	C₂×D₁₂₇	—	2	2	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	2	no	—
315	C₄×C₁₂₇	—	2	2	no	—
316	C₄×C₁₂₇	—	2	1	no	—
317	C₄×C₁₂₇	—	2	1	no	—
318	C₄×C₁₂₇	—	2	1	no	—
319	C₄×C₁₂₇	—	2	2	no	—
320	C₄×C₁₂₇	C₂×#41	1	2	yes	—
321	C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
322	Dic₁₂₇	—	2	1	no	—
323	Dic₁₂₇	—	2	1	no	—
324	Dic₁₂₇	—	2	2	no	—
325	Dic₁₂₇	—	2	2	no	—
326	Dic₁₂₇	—	2	1	no	—
327	Dic₁₂₇	—	2	1	no	—
328	Dic₁₂₇	—	2	1	no	—
329	Dic₁₂₇	C₂×#41	1	2	yes	—
330	C₂×C₁₂₇	—	4	2	no	—
331	C₂×C₁₂₇	—	4	1	no	—
332	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
333	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₁₂₇	#585	1	1	yes	characteristic
335	D₁₂₇	—	2	2	no	—
336	D₁₂₇	—	4	1	no	—
337	D₁₂₇	—	4	2	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	1	no	—
346	#540	—	127	2	no	—
347	#540	—	127	1	no	—
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	2	no	—
355	#532	—	127	1	no	—
356	#529	—	127	1	no	—
357	#529	—	127	2	no	—
358	#529	D₁₂₇	1	1	yes	characteristic, complemented
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	1	no	—
365	C₂×#41	—	127	2	no	—
366	C₂×#41	—	127	2	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	—	127	1	no	—
376	#126	—	127	2	no	—
377	#126	—	127	2	no	—
378	#126	—	127	2	no	—
379	#126	C₂×D₁₂₇	1	2	yes	complemented
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	C₂×D₁₂₇	1	1	yes	characteristic
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	—	127	2	no	—
397	#123	C₂×D₁₂₇	1	2	yes	complemented
398	C₂²⋊Q₈	—	127	1	no	—
399	C₂²⋊Q₈	—	127	2	no	—
400	C₂²⋊Q₈	—	127	2	no	—
401	C₂²⋊Q₈	—	127	2	no	—
402	C₂²⋊Q₈	—	127	2	no	—
403	C₂²⋊Q₈	—	127	2	no	—
404	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
405	#121	—	127	2	no	—
406	#121	—	127	1	no	—
407	#121	—	127	2	no	—
408	#121	—	127	1	no	—
409	#121	—	127	1	no	—
410	#121	—	127	2	no	—
411	#121	—	127	2	no	—
412	#121	—	127	1	no	—
413	#121	—	127	2	no	—
414	#121	—	127	1	no	—
415	#121	—	127	2	no	—
416	#121	—	127	2	no	—
417	#121	—	127	2	no	—
418	#121	—	127	2	no	—
419	#121	—	127	2	no	—
420	#121	—	127	2	no	—
421	#121	C₂×D₁₂₇	1	1	yes	characteristic
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	C₂×D₁₂₇	1	1	yes	characteristic, complemented
430	C₄×D₄	—	127	1	no	—
431	C₄×D₄	—	127	2	no	—
432	C₄×D₄	—	127	1	no	—
433	C₄×D₄	—	127	1	no	—
434	C₄×D₄	—	127	1	no	—
435	C₄×D₄	—	127	1	no	—
436	C₄×D₄	—	127	2	no	—
437	C₄×D₄	—	127	1	no	—
438	C₄×D₄	—	127	2	no	—
439	C₄×D₄	—	127	1	no	—
440	C₄×D₄	—	127	2	no	—
441	C₄×D₄	—	127	1	no	—
442	C₄×D₄	—	127	2	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	2	no	—
448	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
450	#117	—	127	1	no	—
451	#117	—	127	1	no	—
452	#117	—	127	2	no	—
453	#117	—	127	1	no	—
454	#117	—	127	1	no	—
455	#117	—	127	2	no	—
456	#117	C₂×D₁₂₇	1	2	yes	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	C₂×D₁₂₇	1	1	yes	characteristic, complemented
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	C₂²×D₁₂₇	1	1	yes	characteristic
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	1	no	—
478	C₂×D₄	—	127	2	no	—
479	C₂×D₄	—	127	1	no	—
480	C₂×D₄	—	127	2	no	—
481	C₂×D₄	—	127	2	no	—
482	C₂×D₄	—	127	2	no	—
483	C₂×D₄	—	127	2	no	—
484	C₂×D₄	—	127	2	no	—
485	C₂×D₄	—	127	1	no	—
486	C₂×D₄	—	127	1	no	—
487	C₂×D₄	—	127	1	no	—
488	C₂×D₄	—	254	4	no	—
489	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
490	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
491	C₂²×C₄	—	127	1	no	—
492	C₂²×C₄	—	127	2	no	—
493	C₂²×C₄	—	127	1	no	—
494	C₂²×C₄	—	127	2	no	—
495	C₂²×C₄	—	127	1	no	—
496	C₂²×C₄	—	127	2	no	—
497	C₂²×C₄	—	127	2	no	—
498	C₂²×C₄	—	127	2	no	—
499	C₂²×C₄	—	127	1	no	—
500	C₂²×C₄	—	127	1	no	—
501	C₂²×C₄	—	127	1	no	—
502	C₂²×C₄	—	127	2	no	—
503	C₂²×C₄	—	127	2	no	—
504	C₂²×C₄	—	508	4	no	—
505	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
508	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
509	C₄⋊C₄	—	127	2	no	—
510	C₄⋊C₄	—	127	1	no	—
511	C₄⋊C₄	—	127	1	no	—
512	C₄⋊C₄	—	127	1	no	—
513	C₄⋊C₄	—	127	1	no	—
514	C₄⋊C₄	—	127	2	no	—
515	C₄⋊C₄	—	127	2	no	—
516	C₄⋊C₄	—	127	2	no	—
517	C₄⋊C₄	—	127	1	no	—
518	C₄⋊C₄	—	127	1	no	—
519	C₄⋊C₄	—	127	2	no	—
520	C₄⋊C₄	—	127	1	no	—
521	C₄⋊C₄	—	127	1	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	2	yes	—
528	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
530	C₂²⋊C₄	—	127	2	no	—
531	C₂²⋊C₄	—	127	1	no	—
532	C₂²⋊C₄	—	127	1	no	—
533	C₂²⋊C₄	—	127	2	no	—
534	C₂²⋊C₄	—	127	2	no	—
535	C₂²⋊C₄	—	127	2	no	—
536	C₂²⋊C₄	—	127	1	no	—
537	C₂²⋊C₄	—	127	2	no	—
538	C₂²⋊C₄	—	127	1	no	—
539	C₂²⋊C₄	—	127	2	no	—
540	C₂²⋊C₄	—	127	1	no	—
541	C₂²⋊C₄	—	127	1	no	—
542	C₂²⋊C₄	—	127	2	no	—
543	C₂²⋊C₄	—	127	2	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	—	127	2	no	—
550	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
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	2	no	—
560	C₄²	—	127	1	no	—
561	C₄²	—	127	1	no	—
562	C₄²	—	127	1	no	—
563	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
564	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
565	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
566	C₄²	C₂²×D₁₂₇	1	2	yes	—
567	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
568	C₂³	—	127	1	no	—
569	C₂³	—	127	2	no	—
570	C₂³	—	127	2	no	—
571	C₂³	—	127	1	no	—
572	C₂³	—	508	2	no	—
573	C₂³	—	508	2	no	—
574	C₂³	—	254	4	no	—
575	C₂³	C₂³×D₁₂₇	1	2	yes	—
576	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	508	2	no	—
579	Q₈	—	508	2	no	—
580	Q₈	—	254	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	508	2	no	—
584	D₄	—	508	2	no	—
585	D₄	—	508	2	no	—
586	D₄	—	508	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	—	254	2	no	—
593	D₄	—	254	4	no	—
594	D₄	—	254	4	no	—
595	D₄	—	254	2	no	—
596	D₄	—	254	2	no	—
597	D₄	—	254	2	no	—
598	D₄	—	254	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	127	1	no	—
604	C₂×C₄	—	127	4	no	—
605	C₂×C₄	—	127	1	no	—
606	C₂×C₄	—	127	1	no	—
607	C₂×C₄	—	127	1	no	—
608	C₂×C₄	—	127	1	no	—
609	C₂×C₄	—	127	1	no	—
610	C₂×C₄	—	127	2	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	2	no	—
617	C₂×C₄	—	508	2	no	—
618	C₂×C₄	—	254	4	no	—
619	C₂×C₄	—	254	2	no	—
620	C₂×C₄	—	254	2	no	—
621	C₂×C₄	—	254	4	no	—
622	C₂×C₄	—	254	2	no	—
623	C₂×C₄	—	254	4	no	—
624	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
626	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
627	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
631	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
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	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	127	2	no	—
640	C₂²	—	508	8	no	—
641	C₂²	—	254	2	no	—
642	C₂²	—	254	1	no	—
643	C₂²	—	254	2	no	—
644	C₂²	—	254	2	no	—
645	C₂²	—	254	1	no	—
646	C₂²	—	254	2	no	—
647	C₂²	—	254	1	no	—
648	C₂²	—	254	2	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	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	2	no	—
660	C₄	—	127	2	no	—
661	C₄	—	254	1	no	—
662	C₄	—	254	1	no	—
663	C₄	—	254	2	no	—
664	C₄	—	254	1	no	—
665	C₄	—	254	2	no	—
666	C₄	—	254	1	no	—
667	C₄	—	254	1	no	—
668	C₄	#41×D₁₂₇	1	2	yes	—
669	C₄	#16861255	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	508	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	C₂×#16861255	1	1	yes	characteristic
678	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	#3460
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. #22550506	C₂	semidirect
2. #22550499	C₂	semidirect
3. #22550495	C₂	semidirect
4. #22550492	C₂	semidirect
5. #22550482	C₂	semidirect
6. #22550479	C₂	semidirect
7. #22550478	C₂	semidirect
8. #22550465	C₂	semidirect
9. #22550462	C₂	semidirect
10. #22550456	C₂	semidirect
11. #22550444	C₂	semidirect
12. #22550442	C₂	semidirect
13. #22550426	C₂	semidirect
14. #22550423	C₂	semidirect
15. #22550423	C₂	semidirect
16. #22550413	C₂	semidirect
17. #22550404	C₂	semidirect
18. #22550388	C₂	semidirect
19. #22550385	C₂	semidirect
20. C₄×#14523249	C₂	semidirect
21. C₄×#14523248	C₂	semidirect
22. C₄×D₄×D₁₂₇	C₂	semidirect
23. #529×C₁₂₇	C₂	semidirect
26. C₂×#14523248	C₂²	semidirect
27. C₂×#14523248	C₂²	semidirect
30. #16861209	C₂²	semidirect
31. #16861208	C₂²	semidirect
32. #16861208	C₂²	semidirect
36. #16861204	C₂²	semidirect
37. #16861204	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861200	C₂²	semidirect
40. #16861199	C₂²	semidirect
42. #16861197	C₂²	semidirect
44. #16861195	C₂²	semidirect
45. #16861195	C₂²	semidirect
46. #16861195	C₂²	semidirect
47. #16861194	C₂²	semidirect
48. #16861194	C₂²	semidirect
49. #16861194	C₂²	semidirect
50. #16861193	C₂²	semidirect
51. #16861193	C₂²	semidirect
52. #16861191	C₂²	semidirect
53. #16861191	C₂²	semidirect
55. #16861189	C₂²	semidirect
57. #16861187	C₂²	semidirect
58. #16861186	C₂²	semidirect
59. #16861185	C₂²	semidirect
62. #16861184	C₂²	semidirect
63. #16861184	C₂²	semidirect
64. #16861184	C₂²	semidirect
66. #16861183	C₂²	semidirect
67. #16861183	C₂²	semidirect
71. #16861182	C₂²	semidirect
72. #16861182	C₂²	semidirect
73. #16861181	C₂²	semidirect
75. #16861180	C₂²	semidirect
80. Q₈×Dic₁₂₇	C₂²	semidirect
81. C₄×Dic₂₅₄	C₂²	semidirect
82. C₄×Dic₂₅₄	C₂²	semidirect
87. C₄×D₅₀₈	C₂²	semidirect
88. C₄×D₅₀₈	C₂²	semidirect
89. C₄×D₅₀₈	C₂²	semidirect
93. #16861171	C₂²	semidirect
97. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
98. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
99. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
101. #16861168	C₂²	semidirect
103. #16861167	C₂²	semidirect
105. #16861166	C₂²	semidirect
106. #16861166	C₂²	semidirect
110. C₄²×D₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
112. #126×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
115. #123×C₁₂₇	C₂²	semidirect
116. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
118. C₄×Q₈×C₁₂₇	C₂²	semidirect
120. C₄×D₄×C₁₂₇	C₂²	semidirect
121. #117×C₁₂₇	C₂²	semidirect
122. C₂×C₄²×C₁₂₇	C₂²	semidirect
274. C₄×D₁₂₇	#41	semidirect
340. C₁₂₇	#3460	semidirect
358. #529	D₁₂₇	semidirect
379. #126	C₂×D₁₂₇	semidirect
382. #125	C₂×D₁₂₇	semidirect
397. #123	C₂×D₁₂₇	semidirect
404. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
429. C₄×Q₈	C₂×D₁₂₇	semidirect
449. C₄×D₄	C₂×D₁₂₇	semidirect
456. #117	C₂×D₁₂₇	semidirect
462. 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
#22550506	2
#22550499	2
#22550495	2
#22550492	2
#22550482	2
#22550479	2
#22550478	2
#22550465	2
#22550462	2
#22550456	2
#22550444	2
#22550442	2
#22550426	2
#22550423	2
#22550413	2
#22550404	2
#22550388	2
#22550385	2
C₄×#14523249	2
C₄×#14523248	2
C₄×D₄×D₁₂₇	2
#529×C₁₂₇	2
#3460	127