Subgroups — #30652958

Order 16256.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550624	C₂	1	2	yes	maximal, complemented
2	#22550622	C₂	1	2	yes	maximal, complemented
3	#22550581	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550538	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550536	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550529	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550527	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550522	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550522	C₂	1	2	yes	maximal, complemented
10	#22550517	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550517	C₂	1	2	yes	maximal, complemented
12	#22550501	C₂	1	2	yes	maximal, complemented
13	#22550500	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550498	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550474	C₂	1	2	yes	maximal, complemented
16	#22550459	C₂	1	2	yes	maximal, complemented
17	#22550457	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550456	C₂	1	2	yes	maximal, complemented
19	#22550456	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550385	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²⋊Q₈×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16861184	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523249	C₂²	1	2	yes	complemented
25	C₂×#14523249	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
28	C₂×#14523248	C₂²	1	2	yes	complemented
29	C₂×Q₈×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic
31	C₂²×D₅₀₈	C₂²	1	2	yes	—
32	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
33	#16861208	C₂²	1	1	yes	characteristic, complemented
34	#16861204	C₂²	1	2	yes	complemented
35	#16861203	C₂²	1	2	yes	complemented
36	#16861199	C₂²	1	2	yes	complemented
37	#16861198	C₂²	1	1	yes	characteristic, complemented
38	#16861198	C₂²	1	2	yes	complemented
39	#16861197	C₂²	1	2	yes	complemented
40	#16861197	C₂²	1	1	yes	characteristic, complemented
41	#16861197	C₂²	1	2	yes	complemented
42	#16861195	C₂²	1	2	yes	complemented
43	#16861194	C₂²	1	2	yes	complemented
44	#16861194	C₂²	1	2	yes	complemented
45	#16861194	C₂²	1	2	yes	complemented
46	#16861194	C₂²	1	2	yes	complemented
47	#16861194	C₂²	1	1	yes	characteristic, complemented
48	#16861194	C₂²	1	2	yes	complemented
49	#16861194	C₂²	1	2	yes	complemented
50	#16861194	C₂²	1	2	yes	complemented
51	#16861192	C₂²	1	2	yes	complemented
52	#16861191	C₂²	1	1	yes	characteristic, complemented
53	#16861189	C₂²	1	1	yes	characteristic, complemented
54	#16861189	C₂²	1	2	yes	complemented
55	#16861189	C₂²	1	1	yes	characteristic, complemented
56	#16861189	C₂²	1	2	yes	complemented
57	#16861188	C₂²	1	1	yes	characteristic
58	#16861188	C₂²	1	2	yes	—
59	#16861187	C₂²	1	2	yes	complemented
60	#16861187	C₂²	1	2	yes	complemented
61	#16861187	C₂²	1	2	yes	complemented
62	#16861187	C₂²	1	2	yes	complemented
63	#16861187	C₂²	1	1	yes	characteristic, complemented
64	#16861187	C₂²	1	2	yes	complemented
65	#16861187	C₂²	1	2	yes	complemented
66	#16861186	C₂²	1	2	yes	—
67	#16861186	C₂²	1	1	yes	characteristic
68	#16861185	C₂²	1	2	yes	complemented
69	#16861185	C₂²	1	1	yes	characteristic, complemented
70	#16861185	C₂²	1	2	yes	complemented
71	#16861184	C₂²	1	1	yes	characteristic
72	#16861184	C₂²	1	1	yes	characteristic
73	#16861184	C₂²	1	2	yes	—
74	#16861184	C₂²	1	2	yes	—
75	#16861184	C₂²	1	1	yes	characteristic
76	#16861184	C₂²	1	1	yes	characteristic
77	#16861184	C₂²	1	1	yes	characteristic, complemented
78	#16861184	C₂²	1	2	yes	complemented
79	#16861184	C₂²	1	2	yes	complemented
80	#16861184	C₂²	1	2	yes	complemented
81	#16861184	C₂²	1	2	yes	complemented
82	#16861183	C₂²	1	2	yes	complemented
83	#16861183	C₂²	1	2	yes	complemented
84	#16861183	C₂²	1	1	yes	characteristic, complemented
85	#16861182	C₂²	1	2	yes	complemented
86	#16861182	C₂²	1	2	yes	complemented
87	#16861182	C₂²	1	2	yes	complemented
88	#16861182	C₂²	1	1	yes	characteristic, complemented
89	#16861182	C₂²	1	2	yes	complemented
90	#16861181	C₂²	1	1	yes	characteristic
91	#16861179	C₂²	1	1	yes	characteristic
92	#16861179	C₂²	1	2	yes	—
93	#16861177	C₂²	1	1	yes	characteristic
94	#16861177	C₂²	1	2	yes	—
95	#16861174	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₅₀₈	C₂²	1	2	yes	complemented
99	#16861171	C₂²	1	2	yes	complemented
100	#16861171	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
104	#16861166	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
108	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₂₇	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
115	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	complemented
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	—
121	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₂₇	C₂³	1	2	yes	—
125	#14523249	—	4	2	no	—
126	#14523249	—	4	4	no	—
127	#14523248	—	4	2	no	—
128	#14523248	—	4	2	no	—
129	#14523248	—	4	4	no	—
130	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
132	C₂×Dic₂₅₄	C₂³	1	2	yes	—
133	C₂×Dic₂₅₄	C₂³	1	2	yes	—
134	Q₈×D₁₂₇	—	4	2	no	—
135	C₂×D₅₀₈	—	4	2	no	—
136	C₂×D₅₀₈	—	4	4	no	—
137	C₂×D₅₀₈	C₂³	1	2	yes	—
138	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
139	C₂×D₅₀₈	C₂³	1	2	yes	—
140	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
141	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
142	C₂×D₅₀₈	C₂³	1	2	yes	—
143	C₂×D₅₀₈	C₂³	1	2	yes	—
144	C₂×D₅₀₈	C₂³	1	2	yes	—
145	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
146	C₂×D₅₀₈	C₂³	1	2	yes	—
147	C₂×D₅₀₈	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
154	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₂₇	—	4	2	no	—
156	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
163	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
164	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
165	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
166	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
167	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
168	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
170	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
172	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
174	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
175	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
176	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
177	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
178	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
179	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
180	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
181	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
206	C₄×Dic₁₂₇	C₂³	1	2	yes	—
207	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₁₂₇	C₂³	1	2	yes	—
210	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
214	C₂²×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	1	yes	characteristic
218	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
222	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
229	C₄²×C₁₂₇	C₂³	1	2	yes	—
230	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
231	C₂²×D₁₂₇	—	2	2	no	—
232	C₂²×D₁₂₇	—	2	4	no	—
233	C₂²×D₁₂₇	—	2	2	no	—
234	C₂²×D₁₂₇	—	4	1	no	—
235	C₂²×D₁₂₇	—	4	2	no	—
236	C₂²×D₁₂₇	—	4	2	no	—
237	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
239	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
240	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
242	Dic₂₅₄	—	2	2	no	—
243	Dic₂₅₄	—	4	2	no	—
244	Dic₂₅₄	—	4	1	no	—
245	Dic₂₅₄	—	4	2	no	—
246	D₅₀₈	—	2	4	no	—
247	D₅₀₈	—	2	4	no	—
248	D₅₀₈	—	2	2	no	—
249	D₅₀₈	—	2	2	no	—
250	D₅₀₈	—	2	2	no	—
251	D₅₀₈	—	4	2	no	—
252	D₅₀₈	—	4	2	no	—
253	D₅₀₈	—	4	2	no	—
254	D₅₀₈	—	4	1	no	—
255	D₅₀₈	—	4	2	no	—
256	D₅₀₈	—	4	2	no	—
257	C₂²⋊D₁₂₇	—	2	2	no	—
258	C₂²⋊D₁₂₇	—	2	2	no	—
259	C₂²⋊D₁₂₇	—	4	1	no	—
260	C₂²⋊D₁₂₇	—	4	2	no	—
261	C₂²⋊D₁₂₇	—	4	1	no	—
262	C₂²⋊D₁₂₇	—	4	2	no	—
263	C₂×Dic₁₂₇	—	4	1	no	—
264	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
267	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
270	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
271	C₄×D₁₂₇	—	2	4	no	—
272	C₄×D₁₂₇	—	2	2	no	—
273	C₄×D₁₂₇	—	2	2	no	—
274	C₄×D₁₂₇	—	2	2	no	—
275	C₄×D₁₂₇	—	4	1	no	—
276	C₄×D₁₂₇	—	4	1	no	—
277	C₄×D₁₂₇	—	4	2	no	—
278	C₄×D₁₂₇	—	4	2	no	—
279	C₄×D₁₂₇	—	4	2	no	—
280	C₄×D₁₂₇	—	4	2	no	—
281	C₄×D₁₂₇	—	4	2	no	—
282	C₄×D₁₂₇	—	4	2	no	—
283	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
284	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
285	Q₈×C₁₂₇	—	2	2	no	—
286	Q₈×C₁₂₇	—	4	2	no	—
287	D₄×C₁₂₇	—	2	2	no	—
288	C₂×C₄×C₁₂₇	—	2	2	no	—
289	C₂×C₄×C₁₂₇	—	2	2	no	—
290	C₂×C₄×C₁₂₇	—	4	2	no	—
291	C₂×C₄×C₁₂₇	—	4	2	no	—
292	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
294	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
295	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
296	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
299	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
300	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₁₂₇	—	2	1	no	—
302	C₂²×C₁₂₇	—	2	1	no	—
303	C₂²×C₁₂₇	—	2	1	no	—
304	C₂²×C₁₂₇	—	2	1	no	—
305	C₂²×C₁₂₇	—	2	1	no	—
306	C₂²×C₁₂₇	2₋¹⁺⁴	1	2	yes	—
307	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
308	C₂×D₁₂₇	—	2	1	no	—
309	C₂×D₁₂₇	—	2	1	no	—
310	C₂×D₁₂₇	—	2	1	no	—
311	C₂×D₁₂₇	—	2	1	no	—
312	C₂×D₁₂₇	—	2	1	no	—
313	C₂×D₁₂₇	—	2	2	no	—
314	C₂×D₁₂₇	—	2	2	no	—
315	C₂×D₁₂₇	—	2	2	no	—
316	C₂×D₁₂₇	—	2	2	no	—
317	C₂×D₁₂₇	—	2	1	no	—
318	C₂×D₁₂₇	—	2	1	no	—
319	C₂×D₁₂₇	—	2	1	no	—
320	C₂×D₁₂₇	—	2	2	no	—
321	C₂×D₁₂₇	—	2	2	no	—
322	C₂×D₁₂₇	—	4	4	no	—
323	C₂×D₁₂₇	—	8	4	no	—
324	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
325	C₄×C₁₂₇	—	2	1	no	—
326	C₄×C₁₂₇	—	2	1	no	—
327	C₄×C₁₂₇	—	2	2	no	—
328	C₄×C₁₂₇	—	2	2	no	—
329	C₄×C₁₂₇	—	2	2	no	—
330	C₄×C₁₂₇	—	2	2	no	—
331	C₄×C₁₂₇	—	2	1	no	—
332	C₄×C₁₂₇	—	2	1	no	—
333	C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₂₇	—	2	2	no	—
335	Dic₁₂₇	—	2	1	no	—
336	Dic₁₂₇	—	2	1	no	—
337	Dic₁₂₇	—	2	1	no	—
338	Dic₁₂₇	—	2	1	no	—
339	Dic₁₂₇	—	2	2	no	—
340	Dic₁₂₇	—	2	1	no	—
341	C₂×C₁₂₇	—	2	2	no	—
342	C₂×C₁₂₇	—	4	1	no	—
343	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₁₂₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	D₁₂₇	—	2	2	no	—
347	D₁₂₇	—	4	1	no	—
348	D₁₂₇	—	4	1	no	—
349	D₁₂₇	—	4	2	no	—
350	D₁₂₇	—	4	2	no	—
351	#3536	—	127	1	no	maximal, Sylow
352	C₁₂₇	#3536	1	1	yes	characteristic, complemented, Sylow
353	#562	—	127	2	no	—
354	#562	—	127	2	no	—
355	#554	—	127	1	no	—
356	#554	D₁₂₇	1	1	yes	characteristic, complemented
357	#548	—	127	1	no	—
358	#548	—	127	1	no	—
359	#547	—	127	1	no	—
360	#547	—	127	1	no	—
361	#546	—	127	2	no	—
362	#546	—	127	1	no	—
363	#546	—	127	2	no	—
364	#546	—	127	1	no	—
365	#543	—	127	2	no	—
366	#542	—	127	1	no	—
367	#542	—	127	1	no	—
368	#539	—	127	2	no	—
369	#538	—	127	2	no	—
370	#537	—	127	2	no	—
371	#537	—	127	1	no	—
372	#537	—	127	1	no	—
373	#525	—	127	1	no	—
374	C₂×C₂²⋊Q₈	—	127	1	no	—
375	C₂×#121	—	127	1	no	—
376	C₂×#41	—	127	2	no	—
377	C₂×#41	—	127	1	no	—
378	C₂×#41	—	127	1	no	—
379	C₂×#41	—	127	2	no	—
380	C₂×#41	—	127	1	no	—
381	C₂²×Q₈	—	127	1	no	—
382	C₂²×D₄	—	127	1	no	—
383	C₂²×D₄	—	127	2	no	—
384	C₂³×C₄	—	127	1	no	—
385	C₄⋊Q₈	—	127	1	no	—
386	C₄⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
387	#126	—	127	2	no	—
388	#126	—	127	2	no	—
389	#125	—	127	2	no	—
390	#125	C₂×D₁₂₇	1	2	yes	complemented
391	#124	—	127	1	no	—
392	#124	—	127	2	no	—
393	#124	—	127	2	no	—
394	#124	—	127	2	no	—
395	#124	—	127	1	no	—
396	#124	—	127	2	no	—
397	#123	—	127	2	no	—
398	#123	—	127	1	no	—
399	#123	—	127	2	no	—
400	#123	—	127	2	no	—
401	#123	—	127	2	no	—
402	#123	—	127	2	no	—
403	#123	—	127	2	no	—
404	#123	—	127	2	no	—
405	#123	—	127	2	no	—
406	#123	—	127	1	no	—
407	C₂²⋊Q₈	—	127	1	no	—
408	C₂²⋊Q₈	—	127	2	no	—
409	C₂²⋊Q₈	—	127	2	no	—
410	C₂²⋊Q₈	—	127	1	no	—
411	C₂²⋊Q₈	—	127	2	no	—
412	C₂²⋊Q₈	—	127	2	no	—
413	C₂²⋊Q₈	—	127	1	no	—
414	C₂²⋊Q₈	—	127	2	no	—
415	C₂²⋊Q₈	—	127	2	no	—
416	C₂²⋊Q₈	—	127	2	no	—
417	C₂²⋊Q₈	—	127	2	no	—
418	C₂²⋊Q₈	—	127	2	no	—
419	C₂²⋊Q₈	—	127	1	no	—
420	C₂²⋊Q₈	—	127	2	no	—
421	C₂²⋊Q₈	—	127	1	no	—
422	C₂²⋊Q₈	—	127	2	no	—
423	C₂²⋊Q₈	—	127	2	no	—
424	C₂²⋊Q₈	—	127	1	no	—
425	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic
426	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	—
427	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
428	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	complemented
429	#121	—	127	1	no	—
430	#121	—	127	2	no	—
431	#121	—	127	1	no	—
432	#121	—	127	2	no	—
433	#121	—	127	2	no	—
434	#121	—	127	1	no	—
435	#121	—	127	1	no	—
436	#121	—	127	1	no	—
437	#121	—	127	1	no	—
438	#121	—	127	2	no	—
439	#121	—	127	1	no	—
440	#121	—	127	2	no	—
441	#121	—	127	2	no	—
442	#121	—	127	2	no	—
443	#121	—	127	2	no	—
444	#121	—	127	1	no	—
445	#121	—	127	2	no	—
446	#121	—	127	2	no	—
447	#121	—	127	2	no	—
448	#121	—	127	2	no	—
449	#120	—	127	1	no	—
450	#120	—	127	2	no	—
451	#120	—	127	1	no	—
452	#120	—	127	2	no	—
453	C₄×Q₈	—	127	1	no	—
454	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
455	C₄×D₄	—	127	1	no	—
456	C₄×D₄	—	127	1	no	—
457	C₄×D₄	—	127	2	no	—
458	C₄×D₄	—	127	2	no	—
459	C₄×D₄	—	127	1	no	—
460	C₄×D₄	—	127	1	no	—
461	C₄×D₄	—	127	2	no	—
462	C₄×D₄	—	127	1	no	—
463	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
464	C₄×D₄	C₂×D₁₂₇	1	2	yes	—
465	#117	—	127	1	no	—
466	C₂×C₄⋊C₄	—	127	2	no	—
467	C₂×C₄⋊C₄	—	127	1	no	—
468	C₂×C₄⋊C₄	—	127	1	no	—
469	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₄	—	127	2	no	—
472	C₂×C₂²⋊C₄	—	127	2	no	—
473	C₂×C₂²⋊C₄	—	127	2	no	—
474	C₂×C₂²⋊C₄	—	127	2	no	—
475	C₂⁴	—	127	2	no	—
476	C₂⁴	—	127	1	no	—
477	#41	—	508	2	no	—
478	#41	—	508	2	no	—
479	#41	—	508	4	no	—
480	#41	—	508	2	no	—
481	#41	—	508	4	no	—
482	C₂×Q₈	—	127	1	no	—
483	C₂×Q₈	—	127	2	no	—
484	C₂×Q₈	—	127	2	no	—
485	C₂×Q₈	—	127	1	no	—
486	C₂×Q₈	—	508	2	no	—
487	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₁₂₇	1	2	yes	—
489	C₂×D₄	—	127	1	no	—
490	C₂×D₄	—	127	2	no	—
491	C₂×D₄	—	127	2	no	—
492	C₂×D₄	—	127	1	no	—
493	C₂×D₄	—	127	1	no	—
494	C₂×D₄	—	127	1	no	—
495	C₂×D₄	—	127	2	no	—
496	C₂×D₄	—	127	1	no	—
497	C₂×D₄	—	127	2	no	—
498	C₂×D₄	—	127	2	no	—
499	C₂×D₄	—	127	2	no	—
500	C₂×D₄	—	127	2	no	—
501	C₂×D₄	—	127	1	no	—
502	C₂×D₄	—	127	2	no	—
503	C₂×D₄	—	127	2	no	—
504	C₂×D₄	—	127	1	no	—
505	C₂×D₄	—	127	1	no	—
506	C₂×D₄	—	508	2	no	—
507	C₂×D₄	—	508	4	no	—
508	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
509	C₂²×C₄	—	127	1	no	—
510	C₂²×C₄	—	127	2	no	—
511	C₂²×C₄	—	127	2	no	—
512	C₂²×C₄	—	127	2	no	—
513	C₂²×C₄	—	127	2	no	—
514	C₂²×C₄	—	127	2	no	—
515	C₂²×C₄	—	127	1	no	—
516	C₂²×C₄	—	127	2	no	—
517	C₂²×C₄	—	127	1	no	—
518	C₂²×C₄	—	127	2	no	—
519	C₂²×C₄	—	127	1	no	—
520	C₂²×C₄	—	127	1	no	—
521	C₂²×C₄	—	127	1	no	—
522	C₂²×C₄	—	508	2	no	—
523	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
526	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
527	C₄⋊C₄	—	127	2	no	—
528	C₄⋊C₄	—	127	2	no	—
529	C₄⋊C₄	—	127	2	no	—
530	C₄⋊C₄	—	127	2	no	—
531	C₄⋊C₄	—	127	1	no	—
532	C₄⋊C₄	—	127	1	no	—
533	C₄⋊C₄	—	127	1	no	—
534	C₄⋊C₄	—	127	1	no	—
535	C₄⋊C₄	—	127	2	no	—
536	C₄⋊C₄	—	127	2	no	—
537	C₄⋊C₄	—	127	1	no	—
538	C₄⋊C₄	—	127	2	no	—
539	C₄⋊C₄	—	127	2	no	—
540	C₄⋊C₄	—	127	1	no	—
541	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
544	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
546	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
548	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
550	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
551	C₂²⋊C₄	—	127	2	no	—
552	C₂²⋊C₄	—	127	1	no	—
553	C₂²⋊C₄	—	127	1	no	—
554	C₂²⋊C₄	—	127	2	no	—
555	C₂²⋊C₄	—	127	2	no	—
556	C₂²⋊C₄	—	127	2	no	—
557	C₂²⋊C₄	—	127	2	no	—
558	C₂²⋊C₄	—	127	2	no	—
559	C₂²⋊C₄	—	127	2	no	—
560	C₂²⋊C₄	—	127	2	no	—
561	C₂²⋊C₄	—	127	2	no	—
562	C₂²⋊C₄	—	127	2	no	—
563	C₂²⋊C₄	—	127	2	no	—
564	C₂²⋊C₄	—	127	1	no	—
565	C₂²⋊C₄	—	127	1	no	—
566	C₂²⋊C₄	—	127	1	no	—
567	C₂²⋊C₄	—	127	1	no	—
568	C₂²⋊C₄	—	127	2	no	—
569	C₂²⋊C₄	—	127	2	no	—
570	C₂²⋊C₄	—	127	2	no	—
571	C₂²⋊C₄	—	127	2	no	—
572	C₂²⋊C₄	—	127	1	no	—
573	C₂²⋊C₄	—	127	2	no	—
574	C₂²⋊C₄	—	127	1	no	—
575	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
579	C₄²	—	127	1	no	—
580	C₄²	—	127	2	no	—
581	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
582	C₄²	C₂²×D₁₂₇	1	2	yes	—
583	C₂³	—	127	1	no	—
584	C₂³	—	127	2	no	—
585	C₂³	—	127	2	no	—
586	C₂³	—	127	1	no	—
587	C₂³	—	127	1	no	—
588	C₂³	—	508	2	no	—
589	C₂³	—	508	2	no	—
590	C₂³	—	508	1	no	—
591	C₂³	—	254	2	no	—
592	C₂³	—	254	4	no	—
593	C₂³	—	254	2	no	—
594	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
595	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	508	2	no	—
599	Q₈	—	508	2	no	—
600	Q₈	—	508	1	no	—
601	Q₈	—	254	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	508	2	no	—
604	D₄	—	508	2	no	—
605	D₄	—	508	2	no	—
606	D₄	—	508	2	no	—
607	D₄	—	508	1	no	—
608	D₄	—	508	2	no	—
609	D₄	—	508	2	no	—
610	D₄	—	508	1	no	—
611	D₄	—	508	1	no	—
612	D₄	—	508	2	no	—
613	D₄	—	254	4	no	—
614	D₄	—	254	4	no	—
615	D₄	—	254	2	no	—
616	D₄	—	254	2	no	—
617	D₄	—	254	2	no	—
618	D₄	—	254	2	no	—
619	D₄	—	254	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	127	1	no	—
625	C₂×C₄	—	127	1	no	—
626	C₂×C₄	—	127	2	no	—
627	C₂×C₄	—	127	1	no	—
628	C₂×C₄	—	127	2	no	—
629	C₂×C₄	—	127	1	no	—
630	C₂×C₄	—	127	1	no	—
631	C₂×C₄	—	508	1	no	—
632	C₂×C₄	—	508	1	no	—
633	C₂×C₄	—	508	2	no	—
634	C₂×C₄	—	508	2	no	—
635	C₂×C₄	—	508	2	no	—
636	C₂×C₄	—	508	2	no	—
637	C₂×C₄	—	508	2	no	—
638	C₂×C₄	—	508	2	no	—
639	C₂×C₄	—	508	1	no	—
640	C₂×C₄	—	254	4	no	—
641	C₂×C₄	—	254	2	no	—
642	C₂×C₄	—	254	2	no	—
643	C₂×C₄	—	254	2	no	—
644	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
645	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
648	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
649	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
650	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	127	2	no	—
659	C₂²	—	1016	4	no	—
660	C₂²	—	508	4	no	—
661	C₂²	—	254	1	no	—
662	C₂²	—	254	2	no	—
663	C₂²	—	254	2	no	—
664	C₂²	—	254	1	no	—
665	C₂²	—	254	1	no	—
666	C₂²	—	254	2	no	—
667	C₂²	—	254	2	no	—
668	C₂²	—	254	1	no	—
669	C₂²	—	254	1	no	—
670	C₂²	—	254	2	no	—
671	C₂²	—	254	2	no	—
672	C₂²	—	254	1	no	—
673	C₂²	—	254	1	no	—
674	C₂²	—	254	1	no	—
675	C₂²	#16861257	1	2	yes	—
676	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	254	2	no	—
686	C₄	—	254	1	no	—
687	C₄	—	254	1	no	—
688	C₄	—	254	1	no	—
689	C₄	—	254	1	no	—
690	C₄	—	254	2	no	—
691	C₄	—	254	1	no	—
692	C₄	#16861255	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	508	2	no	—
696	C₂	—	508	2	no	—
697	C₂	—	508	1	no	—
698	C₂	—	508	1	no	—
699	C₂	—	254	2	no	—
700	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
701	C₂	C₂×#16861255	1	1	yes	characteristic
702	C₂	C₂×#16861257	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#554×C₁₂₇	C₂
hypercenter	#554	D₁₂₇
hypocenter	C₁₂₇	#3536
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #22550624	C₂	semidirect
2. #22550622	C₂	semidirect
3. #22550581	C₂	semidirect
4. #22550538	C₂	semidirect
5. #22550536	C₂	semidirect
6. #22550529	C₂	semidirect
7. #22550527	C₂	semidirect
8. #22550522	C₂	semidirect
9. #22550522	C₂	semidirect
10. #22550517	C₂	semidirect
11. #22550517	C₂	semidirect
12. #22550501	C₂	semidirect
13. #22550500	C₂	semidirect
14. #22550498	C₂	semidirect
15. #22550474	C₂	semidirect
16. #22550459	C₂	semidirect
17. #22550457	C₂	semidirect
18. #22550456	C₂	semidirect
19. #22550456	C₂	semidirect
20. #22550385	C₂	semidirect
21. C₂²⋊Q₈×D₁₂₇	C₂	semidirect
22. C₂×#16861184	C₂	semidirect
23. #554×C₁₂₇	C₂	semidirect
24. C₂×#14523249	C₂²	semidirect
25. C₂×#14523249	C₂²	semidirect
26. C₂×#14523248	C₂²	semidirect
27. C₂×#14523248	C₂²	semidirect
28. C₂×#14523248	C₂²	semidirect
29. C₂×Q₈×D₁₂₇	C₂²	semidirect
33. #16861208	C₂²	semidirect
34. #16861204	C₂²	semidirect
35. #16861203	C₂²	semidirect
36. #16861199	C₂²	semidirect
37. #16861198	C₂²	semidirect
38. #16861198	C₂²	semidirect
39. #16861197	C₂²	semidirect
40. #16861197	C₂²	semidirect
41. #16861197	C₂²	semidirect
42. #16861195	C₂²	semidirect
43. #16861194	C₂²	semidirect
44. #16861194	C₂²	semidirect
45. #16861194	C₂²	semidirect
46. #16861194	C₂²	semidirect
47. #16861194	C₂²	semidirect
48. #16861194	C₂²	semidirect
49. #16861194	C₂²	semidirect
50. #16861194	C₂²	semidirect
51. #16861192	C₂²	semidirect
52. #16861191	C₂²	semidirect
53. #16861189	C₂²	semidirect
54. #16861189	C₂²	semidirect
55. #16861189	C₂²	semidirect
56. #16861189	C₂²	semidirect
59. #16861187	C₂²	semidirect
60. #16861187	C₂²	semidirect
61. #16861187	C₂²	semidirect
62. #16861187	C₂²	semidirect
63. #16861187	C₂²	semidirect
64. #16861187	C₂²	semidirect
65. #16861187	C₂²	semidirect
68. #16861185	C₂²	semidirect
69. #16861185	C₂²	semidirect
70. #16861185	C₂²	semidirect
77. #16861184	C₂²	semidirect
78. #16861184	C₂²	semidirect
79. #16861184	C₂²	semidirect
80. #16861184	C₂²	semidirect
81. #16861184	C₂²	semidirect
82. #16861183	C₂²	semidirect
83. #16861183	C₂²	semidirect
84. #16861183	C₂²	semidirect
85. #16861182	C₂²	semidirect
86. #16861182	C₂²	semidirect
87. #16861182	C₂²	semidirect
88. #16861182	C₂²	semidirect
89. #16861182	C₂²	semidirect
95. #16861174	C₂²	semidirect
96. C₄×D₅₀₈	C₂²	semidirect
97. C₄×D₅₀₈	C₂²	semidirect
98. C₄×D₅₀₈	C₂²	semidirect
99. #16861171	C₂²	semidirect
100. #16861171	C₂²	semidirect
103. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
104. #16861166	C₂²	semidirect
105. C₄⋊C₄×D₁₂₇	C₂²	semidirect
106. C₄⋊C₄×D₁₂₇	C₂²	semidirect
107. C₄⋊C₄×D₁₂₇	C₂²	semidirect
112. C₄⋊Q₈×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
116. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
117. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
118. C₄×Q₈×C₁₂₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
352. C₁₂₇	#3536	semidirect
356. #554	D₁₂₇	semidirect
386. C₄⋊Q₈	C₂×D₁₂₇	semidirect
390. #125	C₂×D₁₂₇	semidirect
427. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
428. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
454. C₄×Q₈	C₂×D₁₂₇	semidirect
470. C₂×C₄⋊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
#22550624	2
#22550622	2
#22550581	2
#22550538	2
#22550536	2
#22550529	2
#22550527	2
#22550522	2
#22550517	2
#22550501	2
#22550500	2
#22550498	2
#22550474	2
#22550459	2
#22550457	2
#22550456	2
#22550385	2
C₂²⋊Q₈×D₁₂₇	2
C₂×#16861184	2
#554×C₁₂₇	2
#3536	127