Subgroups — #30652883

Order 16256.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550619	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550615	C₂	1	2	yes	maximal, complemented
3	#22550554	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550551	C₂	1	2	yes	maximal, complemented
5	#22550523	C₂	1	2	yes	maximal, complemented
6	#22550518	C₂	1	2	yes	maximal, complemented
7	#22550515	C₂	1	2	yes	maximal, complemented
8	#22550511	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550510	C₂	1	2	yes	maximal, complemented
10	#22550465	C₂	1	2	yes	maximal, complemented
11	#22550462	C₂	1	2	yes	maximal, complemented
12	#22550458	C₂	1	2	yes	maximal, complemented
13	#22550442	C₂	1	2	yes	maximal, complemented
14	#22550439	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550437	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550434	C₂	1	2	yes	maximal, complemented
17	#120×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#120×D₁₂₇	C₂	1	2	yes	maximal, complemented
19	#560×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14523248	C₂²	1	2	yes	complemented
22	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
30	#16861205	C₂²	1	2	yes	complemented
31	#16861205	C₂²	1	1	yes	characteristic, complemented
32	#16861204	C₂²	1	2	yes	complemented
33	#16861202	C₂²	1	2	yes	complemented
34	#16861202	C₂²	1	2	yes	complemented
35	#16861197	C₂²	1	1	yes	characteristic, complemented
36	#16861196	C₂²	1	1	yes	characteristic, complemented
37	#16861196	C₂²	1	2	yes	complemented
38	#16861195	C₂²	1	2	yes	complemented
39	#16861195	C₂²	1	2	yes	complemented
40	#16861195	C₂²	1	2	yes	complemented
41	#16861195	C₂²	1	2	yes	complemented
42	#16861194	C₂²	1	2	yes	complemented
43	#16861194	C₂²	1	2	yes	complemented
44	#16861194	C₂²	1	2	yes	complemented
45	#16861192	C₂²	1	1	yes	characteristic, complemented
46	#16861191	C₂²	1	2	yes	complemented
47	#16861191	C₂²	1	2	yes	complemented
48	#16861191	C₂²	1	2	yes	complemented
49	#16861190	C₂²	1	2	yes	complemented
50	#16861189	C₂²	1	2	yes	complemented
51	#16861187	C₂²	1	2	yes	complemented
52	#16861187	C₂²	1	2	yes	complemented
53	#16861184	C₂²	1	2	yes	complemented
54	#16861184	C₂²	1	2	yes	complemented
55	#16861183	C₂²	1	2	yes	complemented
56	#16861182	C₂²	1	2	yes	complemented
57	#16861182	C₂²	1	2	yes	complemented
58	#16861182	C₂²	1	2	yes	complemented
59	#16861181	C₂²	1	2	yes	complemented
60	#16861181	C₂²	1	2	yes	complemented
61	#16861181	C₂²	1	2	yes	complemented
62	#16861180	C₂²	1	2	yes	complemented
63	#16861180	C₂²	1	2	yes	complemented
64	#16861180	C₂²	1	2	yes	complemented
65	#16861179	C₂²	1	2	yes	—
66	#16861179	C₂²	1	2	yes	complemented
67	#16861179	C₂²	1	2	yes	complemented
68	#16861179	C₂²	1	2	yes	complemented
69	#16861179	C₂²	1	1	yes	characteristic, complemented
70	#16861179	C₂²	1	2	yes	complemented
71	#16861179	C₂²	1	1	yes	characteristic, complemented
72	#16861178	C₂²	1	1	yes	characteristic, complemented
73	#16861178	C₂²	1	2	yes	complemented
74	#16861177	C₂²	1	1	yes	characteristic
75	#16861177	C₂²	1	2	yes	complemented
76	#16861177	C₂²	1	2	yes	complemented
77	#16861177	C₂²	1	2	yes	complemented
78	#16861177	C₂²	1	2	yes	complemented
79	#16861177	C₂²	1	2	yes	complemented
80	#16861177	C₂²	1	1	yes	characteristic, complemented
81	#16861177	C₂²	1	2	yes	complemented
82	#16861177	C₂²	1	2	yes	complemented
83	C₄×D₅₀₈	C₂²	1	2	yes	complemented
84	#16861171	C₂²	1	2	yes	complemented
85	#16861171	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
88	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
89	#16861167	C₂²	1	2	yes	complemented
90	#16861166	C₂²	1	1	yes	characteristic, complemented
91	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
98	#127×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
99	#126×C₁₂₇	C₂²	1	2	yes	complemented
100	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
101	#123×C₁₂₇	C₂²	1	2	yes	complemented
102	#121×C₁₂₇	C₂²	1	2	yes	complemented
103	#121×C₁₂₇	C₂²	1	2	yes	complemented
104	#121×C₁₂₇	C₂²	1	2	yes	complemented
105	#120×C₁₂₇	C₂²	1	2	yes	complemented
106	#120×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₂₇	—	4	4	no	—
108	C₂³×D₁₂₇	—	4	2	no	—
109	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
110	C₂³×D₁₂₇	C₂³	1	2	yes	—
111	C₂³×D₁₂₇	C₂³	1	2	yes	—
112	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
113	C₂³×D₁₂₇	C₂³	1	2	yes	—
114	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
115	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
116	#14523248	—	4	4	no	—
117	#14523247	—	4	2	no	—
118	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic, complemented
119	C₂×Dic₂₅₄	C₂³	1	2	yes	complemented
120	C₂×D₅₀₈	—	4	2	no	—
121	C₂×D₅₀₈	C₂³	1	2	yes	—
122	C₂×D₅₀₈	C₂³	1	2	yes	—
123	C₂×D₅₀₈	C₂³	1	2	yes	—
124	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
125	C₂×D₅₀₈	C₂³	1	2	yes	—
126	C₂×D₅₀₈	C₂³	1	2	yes	complemented
127	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₂₇	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	complemented
138	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
139	D₄×D₁₂₇	—	4	2	no	—
140	D₄×D₁₂₇	—	4	4	no	—
141	D₄×D₁₂₇	—	4	4	no	—
142	D₄×D₁₂₇	—	4	4	no	—
143	D₄×D₁₂₇	—	4	4	no	—
144	D₄×D₁₂₇	—	4	4	no	—
145	C₂²×Dic₁₂₇	C₂³	1	2	yes	complemented
146	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
149	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
151	C₂×C₄×D₁₂₇	C₂³	1	2	yes	complemented
152	C₂×C₄×D₁₂₇	C₂³	1	2	yes	complemented
153	C₄⋊Dic₁₂₇	C₂³	1	2	yes	complemented
154	C₄⋊Dic₁₂₇	C₂³	1	2	yes	complemented
155	Dic₁₂₇⋊C₄	C₂³	1	2	yes	complemented
156	Dic₁₂₇⋊C₄	C₂³	1	2	yes	complemented
157	Dic₁₂₇⋊C₄	C₂³	1	2	yes	complemented
158	Dic₁₂₇⋊C₄	C₂³	1	2	yes	complemented
159	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
162	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
163	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
165	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
166	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
167	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
177	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
178	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
179	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
180	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
181	C₄×Dic₁₂₇	C₂³	1	2	yes	complemented
182	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
183	C₄×Dic₁₂₇	C₂³	1	2	yes	complemented
184	C₂⁴×C₁₂₇	C₂³	1	1	yes	characteristic
185	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
186	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
187	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
188	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
189	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
190	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
191	C₂×D₄×C₁₂₇	C₂³	1	2	yes	complemented
192	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
193	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	complemented
194	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
195	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
196	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
197	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
200	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
203	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
204	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
205	C₂²×D₁₂₇	—	2	4	no	—
206	C₂²×D₁₂₇	—	2	4	no	—
207	C₂²×D₁₂₇	—	2	4	no	—
208	C₂²×D₁₂₇	—	2	2	no	—
209	C₂²×D₁₂₇	—	2	4	no	—
210	C₂²×D₁₂₇	—	2	4	no	—
211	C₂²×D₁₂₇	—	2	2	no	—
212	C₂²×D₁₂₇	—	4	1	no	—
213	C₂²×D₁₂₇	—	4	2	no	—
214	C₂²×D₁₂₇	—	4	2	no	—
215	C₂²×D₁₂₇	—	4	2	no	—
216	C₂²×D₁₂₇	—	4	2	no	—
217	C₂²×D₁₂₇	—	4	2	no	—
218	C₂²×D₁₂₇	—	4	2	no	—
219	C₂²×D₁₂₇	—	4	2	no	—
220	C₂²×D₁₂₇	—	4	2	no	—
221	C₂²×D₁₂₇	—	4	1	no	—
222	C₂²×D₁₂₇	—	4	16	no	—
223	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
224	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
225	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
227	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
228	Dic₂₅₄	—	4	1	no	—
229	Dic₂₅₄	—	4	2	no	—
230	D₅₀₈	—	2	4	no	—
231	D₅₀₈	—	2	4	no	—
232	D₅₀₈	—	2	4	no	—
233	D₅₀₈	—	4	2	no	—
234	D₅₀₈	—	4	1	no	—
235	D₅₀₈	—	4	2	no	—
236	C₂²⋊D₁₂₇	—	2	4	no	—
237	C₂²⋊D₁₂₇	—	2	4	no	—
238	C₂²⋊D₁₂₇	—	2	4	no	—
239	C₂²⋊D₁₂₇	—	4	1	no	—
240	C₂²⋊D₁₂₇	—	4	1	no	—
241	C₂²⋊D₁₂₇	—	4	2	no	—
242	C₂²⋊D₁₂₇	—	4	2	no	—
243	C₂²⋊D₁₂₇	—	4	2	no	—
244	C₂²⋊D₁₂₇	—	4	2	no	—
245	C₂²⋊D₁₂₇	—	4	2	no	—
246	C₂²⋊D₁₂₇	—	4	2	no	—
247	C₂²⋊D₁₂₇	—	4	2	no	—
248	C₂×Dic₁₂₇	—	4	2	no	—
249	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
250	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
251	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
252	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
253	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₂₇	—	2	2	no	—
255	C₄×D₁₂₇	—	2	4	no	—
256	C₄×D₁₂₇	—	4	2	no	—
257	C₄×D₁₂₇	—	4	2	no	—
258	C₄×D₁₂₇	—	4	2	no	—
259	C₄×D₁₂₇	—	4	2	no	—
260	C₄×D₁₂₇	—	4	2	no	—
261	C₂³×C₁₂₇	—	4	1	no	—
262	C₂³×C₁₂₇	—	4	2	no	—
263	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
264	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
265	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
266	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
267	D₄×C₁₂₇	—	4	2	no	—
268	D₄×C₁₂₇	—	4	2	no	—
269	D₄×C₁₂₇	—	4	2	no	—
270	D₄×C₁₂₇	—	4	1	no	—
271	D₄×C₁₂₇	—	4	2	no	—
272	D₄×C₁₂₇	—	4	2	no	—
273	D₄×C₁₂₇	—	4	1	no	—
274	C₂×C₄×C₁₂₇	—	4	1	no	—
275	C₂×C₄×C₁₂₇	—	4	2	no	—
276	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
279	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
280	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
281	C₂²×C₁₂₇	—	2	2	no	—
282	C₂²×C₁₂₇	—	2	1	no	—
283	C₂²×C₁₂₇	—	2	2	no	—
284	C₂²×C₁₂₇	—	2	2	no	—
285	C₂²×C₁₂₇	—	2	2	no	—
286	C₂²×C₁₂₇	—	2	2	no	—
287	C₂²×C₁₂₇	—	2	1	no	—
288	C₂²×C₁₂₇	—	2	2	no	—
289	C₂²×C₁₂₇	—	2	2	no	—
290	C₂²×C₁₂₇	—	2	2	no	—
291	C₂²×C₁₂₇	—	4	4	no	—
292	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₂₇	—	2	2	no	—
294	C₂×D₁₂₇	—	2	2	no	—
295	C₂×D₁₂₇	—	2	2	no	—
296	C₂×D₁₂₇	—	2	2	no	—
297	C₂×D₁₂₇	—	2	2	no	—
298	C₂×D₁₂₇	—	2	2	no	—
299	C₂×D₁₂₇	—	2	2	no	—
300	C₂×D₁₂₇	—	2	1	no	—
301	C₂×D₁₂₇	—	2	1	no	—
302	C₂×D₁₂₇	—	2	2	no	—
303	C₂×D₁₂₇	—	4	4	no	—
304	C₂×D₁₂₇	—	4	8	no	—
305	C₂×D₁₂₇	—	4	4	no	—
306	C₂×D₁₂₇	—	4	8	no	—
307	C₂×D₁₂₇	—	8	2	no	—
308	C₂×D₁₂₇	—	8	4	no	—
309	C₂×D₁₂₇	—	8	2	no	—
310	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
311	C₂×D₁₂₇	H(5,𝔽₂)	1	4	yes	—
312	C₄×C₁₂₇	—	2	2	no	—
313	C₄×C₁₂₇	—	2	2	no	—
314	C₄×C₁₂₇	—	2	2	no	—
315	C₄×C₁₂₇	—	2	1	no	—
316	C₄×C₁₂₇	—	2	2	no	—
317	Dic₁₂₇	—	2	1	no	—
318	Dic₁₂₇	—	2	2	no	—
319	Dic₁₂₇	—	2	2	no	—
320	Dic₁₂₇	—	2	2	no	—
321	Dic₁₂₇	—	2	2	no	—
322	C₂×C₁₂₇	—	4	1	no	—
323	C₂×C₁₂₇	—	4	2	no	—
324	C₂×C₁₂₇	—	4	1	no	—
325	C₂×C₁₂₇	—	4	2	no	—
326	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	2	yes	—
328	D₁₂₇	—	2	2	no	—
329	D₁₂₇	—	2	4	no	—
330	D₁₂₇	—	4	1	no	—
331	D₁₂₇	—	4	1	no	—
332	D₁₂₇	—	4	2	no	—
333	#3532	—	127	1	no	maximal, Sylow
334	C₁₂₇	#3532	1	1	yes	characteristic, complemented, Sylow
335	H(3,𝔽₄)	—	127	1	no	—
336	#560	—	127	2	no	—
337	#560	D₁₂₇	1	1	yes	characteristic, complemented
338	#551	—	127	2	no	—
339	#551	—	127	1	no	—
340	#546	—	127	2	no	—
341	#546	—	127	2	no	—
342	#546	—	127	2	no	—
343	D₄²	—	127	1	no	—
344	D₄²	—	127	2	no	—
345	#538	—	127	2	no	—
346	#538	—	127	2	no	—
347	#538	—	127	2	no	—
348	#535	—	127	1	no	—
349	#535	—	127	2	no	—
350	#534	—	127	1	no	—
351	#534	—	127	2	no	—
352	C₂×#120	—	127	1	no	—
353	C₂×#120	—	127	2	no	—
354	C₂⁵	—	127	1	no	—
355	C₂×#41	—	127	1	no	—
356	C₂×#41	—	127	2	no	—
357	C₂²×D₄	—	127	1	no	—
358	C₂²×D₄	—	127	2	no	—
359	C₂²×D₄	—	127	2	no	—
360	C₂²×D₄	—	127	2	no	—
361	C₂²×D₄	—	127	2	no	—
362	C₂²×D₄	—	127	2	no	—
363	C₂²×D₄	—	127	1	no	—
364	#127	—	127	2	no	—
365	#127	—	127	1	no	—
366	#127	C₂×D₁₂₇	1	1	yes	characteristic, complemented
367	#126	—	127	2	no	—
368	#126	—	127	2	no	—
369	#126	—	127	2	no	—
370	#126	C₂×D₁₂₇	1	2	yes	complemented
371	#124	—	127	1	no	—
372	#124	—	127	2	no	—
373	#124	—	127	2	no	—
374	#124	—	127	2	no	—
375	#124	—	127	2	no	—
376	#124	—	127	2	no	—
377	#124	—	127	1	no	—
378	#123	—	127	2	no	—
379	#123	—	127	1	no	—
380	#123	—	127	2	no	—
381	#123	—	127	2	no	—
382	#123	—	127	2	no	—
383	#123	—	127	2	no	—
384	#123	—	127	2	no	—
385	#123	—	127	2	no	—
386	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
387	#123	C₂×D₁₂₇	1	2	yes	complemented
388	C₂²⋊Q₈	—	127	2	no	—
389	C₂²⋊Q₈	—	127	2	no	—
390	C₂²⋊Q₈	—	127	2	no	—
391	#121	—	127	2	no	—
392	#121	—	127	2	no	—
393	#121	—	127	2	no	—
394	#121	—	127	2	no	—
395	#121	—	127	2	no	—
396	#121	—	127	2	no	—
397	#121	—	127	2	no	—
398	#121	—	127	2	no	—
399	#121	—	127	2	no	—
400	#121	—	127	2	no	—
401	#121	—	127	2	no	—
402	#121	—	127	2	no	—
403	#121	C₂×D₁₂₇	1	2	yes	complemented
404	#121	C₂×D₁₂₇	1	2	yes	complemented
405	#121	C₂×D₁₂₇	1	2	yes	complemented
406	#120	—	127	1	no	—
407	#120	—	127	2	no	—
408	#120	—	127	2	no	—
409	#120	—	127	2	no	—
410	#120	—	127	2	no	—
411	#120	—	127	1	no	—
412	#120	—	127	2	no	—
413	#120	—	127	1	no	—
414	#120	—	127	2	no	—
415	#120	—	127	2	no	—
416	#120	—	127	2	no	—
417	#120	—	127	2	no	—
418	#120	—	127	2	no	—
419	#120	—	127	2	no	—
420	#120	—	127	2	no	—
421	#120	—	127	1	no	—
422	#120	—	127	1	no	—
423	#120	—	127	2	no	—
424	#120	C₂×D₁₂₇	1	2	yes	complemented
425	#120	C₂×D₁₂₇	1	1	yes	characteristic, complemented
426	C₄×D₄	—	127	2	no	—
427	C₄×D₄	—	127	2	no	—
428	C₄×D₄	—	127	2	no	—
429	C₄×D₄	—	127	2	no	—
430	C₄×D₄	—	127	2	no	—
431	C₄×D₄	—	127	2	no	—
432	#117	—	127	2	no	—
433	#117	—	127	1	no	—
434	C₂×C₂²⋊C₄	—	127	2	no	—
435	C₂×C₂²⋊C₄	—	127	1	no	—
436	C₂×C₂²⋊C₄	—	127	2	no	—
437	C₂×C₂²⋊C₄	—	127	2	no	—
438	C₂×C₂²⋊C₄	—	127	2	no	—
439	C₂×C₂²⋊C₄	—	127	2	no	—
440	C₂×C₂²⋊C₄	—	127	1	no	—
441	C₂⁴	—	127	1	no	—
442	C₂⁴	—	127	2	no	—
443	C₂⁴	—	127	1	no	—
444	C₂⁴	—	127	2	no	—
445	C₂⁴	—	127	1	no	—
446	C₂⁴	—	127	1	no	—
447	C₂⁴	—	127	2	no	—
448	C₂⁴	—	508	2	no	—
449	C₂⁴	—	508	4	no	—
450	C₂⁴	C₂²×D₁₂₇	1	1	yes	characteristic
451	#41	—	508	4	no	—
452	#41	—	508	2	no	—
453	C₂×Q₈	—	127	2	no	—
454	C₂×Q₈	—	127	1	no	—
455	C₂×D₄	—	127	1	no	—
456	C₂×D₄	—	127	2	no	—
457	C₂×D₄	—	127	2	no	—
458	C₂×D₄	—	127	2	no	—
459	C₂×D₄	—	127	1	no	—
460	C₂×D₄	—	127	2	no	—
461	C₂×D₄	—	127	2	no	—
462	C₂×D₄	—	127	2	no	—
463	C₂×D₄	—	127	2	no	—
464	C₂×D₄	—	127	2	no	—
465	C₂×D₄	—	127	2	no	—
466	C₂×D₄	—	127	2	no	—
467	C₂×D₄	—	127	2	no	—
468	C₂×D₄	—	127	1	no	—
469	C₂×D₄	—	127	2	no	—
470	C₂×D₄	—	127	2	no	—
471	C₂×D₄	—	127	2	no	—
472	C₂×D₄	—	127	2	no	—
473	C₂×D₄	—	508	2	no	—
474	C₂×D₄	—	508	4	no	—
475	C₂×D₄	—	508	4	no	—
476	C₂×D₄	—	508	4	no	—
477	C₂×D₄	—	508	4	no	—
478	C₂×D₄	—	508	4	no	—
479	C₂×D₄	—	508	2	no	—
480	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
481	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
483	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
484	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
485	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
486	C₂×D₄	C₂²×D₁₂₇	1	2	yes	complemented
487	C₂²×C₄	—	127	2	no	—
488	C₂²×C₄	—	127	2	no	—
489	C₂²×C₄	—	127	2	no	—
490	C₂²×C₄	—	127	2	no	—
491	C₂²×C₄	—	127	2	no	—
492	C₂²×C₄	—	127	2	no	—
493	C₂²×C₄	—	127	2	no	—
494	C₂²×C₄	—	127	1	no	—
495	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	complemented
496	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
497	C₄⋊C₄	—	127	2	no	—
498	C₄⋊C₄	—	127	2	no	—
499	C₄⋊C₄	—	127	2	no	—
500	C₄⋊C₄	—	127	2	no	—
501	C₄⋊C₄	—	127	2	no	—
502	C₄⋊C₄	—	127	2	no	—
503	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
504	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
505	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
506	C₂²⋊C₄	—	127	1	no	—
507	C₂²⋊C₄	—	127	2	no	—
508	C₂²⋊C₄	—	127	2	no	—
509	C₂²⋊C₄	—	127	2	no	—
510	C₂²⋊C₄	—	127	2	no	—
511	C₂²⋊C₄	—	127	1	no	—
512	C₂²⋊C₄	—	127	2	no	—
513	C₂²⋊C₄	—	127	2	no	—
514	C₂²⋊C₄	—	127	2	no	—
515	C₂²⋊C₄	—	127	2	no	—
516	C₂²⋊C₄	—	127	2	no	—
517	C₂²⋊C₄	—	127	2	no	—
518	C₂²⋊C₄	—	127	2	no	—
519	C₂²⋊C₄	—	127	2	no	—
520	C₂²⋊C₄	—	127	2	no	—
521	C₂²⋊C₄	—	127	2	no	—
522	C₂²⋊C₄	—	127	2	no	—
523	C₂²⋊C₄	—	127	2	no	—
524	C₂²⋊C₄	—	127	2	no	—
525	C₂²⋊C₄	—	127	2	no	—
526	C₂²⋊C₄	—	127	2	no	—
527	C₂²⋊C₄	—	127	2	no	—
528	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
534	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
535	C₄²	—	127	1	no	—
536	C₄²	—	127	2	no	—
537	C₄²	—	127	2	no	—
538	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
539	C₂³	—	4	2	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	127	1	no	—
542	C₂³	—	127	2	no	—
543	C₂³	—	127	1	no	—
544	C₂³	—	127	2	no	—
545	C₂³	—	127	1	no	—
546	C₂³	—	508	2	no	—
547	C₂³	—	508	1	no	—
548	C₂³	—	508	2	no	—
549	C₂³	—	508	2	no	—
550	C₂³	—	508	2	no	—
551	C₂³	—	508	2	no	—
552	C₂³	—	508	2	no	—
553	C₂³	—	508	2	no	—
554	C₂³	—	508	1	no	—
555	C₂³	—	508	2	no	—
556	C₂³	—	508	16	no	—
557	C₂³	—	254	2	no	—
558	C₂³	—	254	4	no	—
559	C₂³	—	254	2	no	—
560	C₂³	—	254	4	no	—
561	C₂³	—	254	4	no	—
562	C₂³	—	254	4	no	—
563	C₂³	—	254	4	no	—
564	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
565	C₂³	C₂³×D₁₂₇	1	2	yes	—
566	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
567	C₂³	C₂³×D₁₂₇	1	2	yes	—
568	Q₈	—	508	2	no	—
569	Q₈	—	508	1	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	1	no	—
577	D₄	—	508	2	no	—
578	D₄	—	508	2	no	—
579	D₄	—	508	1	no	—
580	D₄	—	508	1	no	—
581	D₄	—	508	1	no	—
582	D₄	—	508	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	—	254	4	no	—
590	D₄	—	254	4	no	—
591	D₄	—	254	4	no	—
592	D₄	—	254	4	no	—
593	D₄	—	254	4	no	—
594	D₄	—	254	4	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	127	2	no	—
598	C₂×C₄	—	127	2	no	—
599	C₂×C₄	—	127	2	no	—
600	C₂×C₄	—	127	2	no	—
601	C₂×C₄	—	127	1	no	—
602	C₂×C₄	—	508	2	no	—
603	C₂×C₄	—	508	2	no	—
604	C₂×C₄	—	508	2	no	—
605	C₂×C₄	—	508	2	no	—
606	C₂×C₄	—	508	2	no	—
607	C₂×C₄	—	508	2	no	—
608	C₂×C₄	—	254	4	no	—
609	C₂×C₄	—	254	2	no	—
610	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
612	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
613	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
614	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	127	2	no	—
627	C₂²	—	127	4	no	—
628	C₂²	—	1016	2	no	—
629	C₂²	—	1016	2	no	—
630	C₂²	—	1016	4	no	—
631	C₂²	—	508	4	no	—
632	C₂²	—	508	8	no	—
633	C₂²	—	508	8	no	—
634	C₂²	—	508	4	no	—
635	C₂²	—	254	2	no	—
636	C₂²	—	254	2	no	—
637	C₂²	—	254	1	no	—
638	C₂²	—	254	2	no	—
639	C₂²	—	254	2	no	—
640	C₂²	—	254	2	no	—
641	C₂²	—	254	1	no	—
642	C₂²	—	254	2	no	—
643	C₂²	—	254	2	no	—
644	C₂²	—	254	2	no	—
645	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	254	1	no	—
652	C₄	—	254	2	no	—
653	C₄	—	254	2	no	—
654	C₄	—	254	2	no	—
655	C₄	—	254	2	no	—
656	C₂	—	4	2	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	2	no	—
660	C₂	—	508	2	no	—
661	C₂	—	508	1	no	—
662	C₂	—	508	1	no	—
663	C₂	—	254	2	no	—
664	C₂	—	254	4	no	—
665	C₂	H(5,𝔽₂)×D₁₂₇	1	2	yes	—
666	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#560×C₁₂₇	C₂
hypercenter	#560	D₁₂₇
hypocenter	C₁₂₇	#3532
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #560

Complements

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

N	H ≅ G/N	type
1. #22550619	C₂	semidirect
2. #22550615	C₂	semidirect
3. #22550554	C₂	semidirect
4. #22550551	C₂	semidirect
5. #22550523	C₂	semidirect
6. #22550518	C₂	semidirect
7. #22550515	C₂	semidirect
8. #22550511	C₂	semidirect
9. #22550510	C₂	semidirect
10. #22550465	C₂	semidirect
11. #22550462	C₂	semidirect
12. #22550458	C₂	semidirect
13. #22550442	C₂	semidirect
14. #22550439	C₂	semidirect
15. #22550437	C₂	semidirect
16. #22550434	C₂	semidirect
17. #120×D₁₂₇	C₂	semidirect
18. #120×D₁₂₇	C₂	semidirect
19. #560×C₁₂₇	C₂	semidirect
20. C₂⁴×D₁₂₇	C₂²	semidirect
21. C₂×#14523248	C₂²	semidirect
22. C₂×#14523247	C₂²	semidirect
23. C₂²×D₅₀₈	C₂²	semidirect
24. C₂×D₄×D₁₂₇	C₂²	semidirect
25. C₂×D₄×D₁₂₇	C₂²	semidirect
26. C₂×D₄×D₁₂₇	C₂²	semidirect
27. C₂×D₄×D₁₂₇	C₂²	semidirect
28. C₂×D₄×D₁₂₇	C₂²	semidirect
29. C₂×D₄×D₁₂₇	C₂²	semidirect
30. #16861205	C₂²	semidirect
31. #16861205	C₂²	semidirect
32. #16861204	C₂²	semidirect
33. #16861202	C₂²	semidirect
34. #16861202	C₂²	semidirect
35. #16861197	C₂²	semidirect
36. #16861196	C₂²	semidirect
37. #16861196	C₂²	semidirect
38. #16861195	C₂²	semidirect
39. #16861195	C₂²	semidirect
40. #16861195	C₂²	semidirect
41. #16861195	C₂²	semidirect
42. #16861194	C₂²	semidirect
43. #16861194	C₂²	semidirect
44. #16861194	C₂²	semidirect
45. #16861192	C₂²	semidirect
46. #16861191	C₂²	semidirect
47. #16861191	C₂²	semidirect
48. #16861191	C₂²	semidirect
49. #16861190	C₂²	semidirect
50. #16861189	C₂²	semidirect
51. #16861187	C₂²	semidirect
52. #16861187	C₂²	semidirect
53. #16861184	C₂²	semidirect
54. #16861184	C₂²	semidirect
55. #16861183	C₂²	semidirect
56. #16861182	C₂²	semidirect
57. #16861182	C₂²	semidirect
58. #16861182	C₂²	semidirect
59. #16861181	C₂²	semidirect
60. #16861181	C₂²	semidirect
61. #16861181	C₂²	semidirect
62. #16861180	C₂²	semidirect
63. #16861180	C₂²	semidirect
64. #16861180	C₂²	semidirect
66. #16861179	C₂²	semidirect
67. #16861179	C₂²	semidirect
68. #16861179	C₂²	semidirect
69. #16861179	C₂²	semidirect
70. #16861179	C₂²	semidirect
71. #16861179	C₂²	semidirect
72. #16861178	C₂²	semidirect
73. #16861178	C₂²	semidirect
75. #16861177	C₂²	semidirect
76. #16861177	C₂²	semidirect
77. #16861177	C₂²	semidirect
78. #16861177	C₂²	semidirect
79. #16861177	C₂²	semidirect
80. #16861177	C₂²	semidirect
81. #16861177	C₂²	semidirect
82. #16861177	C₂²	semidirect
83. C₄×D₅₀₈	C₂²	semidirect
84. #16861171	C₂²	semidirect
85. #16861171	C₂²	semidirect
86. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
87. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
88. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
89. #16861167	C₂²	semidirect
90. #16861166	C₂²	semidirect
91. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
92. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
93. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
94. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
95. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
96. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
97. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
98. #127×C₁₂₇	C₂²	semidirect
99. #126×C₁₂₇	C₂²	semidirect
100. #123×C₁₂₇	C₂²	semidirect
101. #123×C₁₂₇	C₂²	semidirect
102. #121×C₁₂₇	C₂²	semidirect
103. #121×C₁₂₇	C₂²	semidirect
104. #121×C₁₂₇	C₂²	semidirect
105. #120×C₁₂₇	C₂²	semidirect
106. #120×C₁₂₇	C₂²	semidirect
115. C₂³×D₁₂₇	C₂³	semidirect
118. C₂×Dic₂₅₄	C₂³	semidirect
119. C₂×Dic₂₅₄	C₂³	semidirect
126. C₂×D₅₀₈	C₂³	semidirect
137. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
138. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
145. C₂²×Dic₁₂₇	C₂³	semidirect
151. C₂×C₄×D₁₂₇	C₂³	semidirect
152. C₂×C₄×D₁₂₇	C₂³	semidirect
153. C₄⋊Dic₁₂₇	C₂³	semidirect
154. C₄⋊Dic₁₂₇	C₂³	semidirect
155. Dic₁₂₇⋊C₄	C₂³	semidirect
156. Dic₁₂₇⋊C₄	C₂³	semidirect
157. Dic₁₂₇⋊C₄	C₂³	semidirect
158. Dic₁₂₇⋊C₄	C₂³	semidirect
164. C₂²⋊Dic₁₂₇	C₂³	semidirect
165. C₂²⋊Dic₁₂₇	C₂³	semidirect
166. C₂²⋊Dic₁₂₇	C₂³	semidirect
176. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
177. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
178. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
179. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
180. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
181. C₄×Dic₁₂₇	C₂³	semidirect
182. C₄×Dic₁₂₇	C₂³	semidirect
183. C₄×Dic₁₂₇	C₂³	semidirect
190. C₂×D₄×C₁₂₇	C₂³	semidirect
191. C₂×D₄×C₁₂₇	C₂³	semidirect
192. C₂²×C₄×C₁₂₇	C₂³	semidirect
193. C₂²×C₄×C₁₂₇	C₂³	semidirect
194. C₄⋊C₄×C₁₂₇	C₂³	semidirect
195. C₄⋊C₄×C₁₂₇	C₂³	semidirect
196. C₄⋊C₄×C₁₂₇	C₂³	semidirect
202. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
203. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
204. C₄²×C₁₂₇	C₂³	semidirect
334. C₁₂₇	#3532	semidirect
337. #560	D₁₂₇	semidirect
366. #127	C₂×D₁₂₇	semidirect
370. #126	C₂×D₁₂₇	semidirect
386. #123	C₂×D₁₂₇	semidirect
387. #123	C₂×D₁₂₇	semidirect
403. #121	C₂×D₁₂₇	semidirect
404. #121	C₂×D₁₂₇	semidirect
405. #121	C₂×D₁₂₇	semidirect
424. #120	C₂×D₁₂₇	semidirect
425. #120	C₂×D₁₂₇	semidirect
485. C₂×D₄	C₂²×D₁₂₇	semidirect
486. C₂×D₄	C₂²×D₁₂₇	semidirect
495. C₂²×C₄	C₂²×D₁₂₇	semidirect
496. C₂²×C₄	C₂²×D₁₂₇	semidirect
503. C₄⋊C₄	C₂²×D₁₂₇	semidirect
504. C₄⋊C₄	C₂²×D₁₂₇	semidirect
505. C₄⋊C₄	C₂²×D₁₂₇	semidirect
533. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
534. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
538. C₄²	C₂²×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550619	2
#22550615	2
#22550554	2
#22550551	2
#22550523	2
#22550518	2
#22550515	2
#22550511	2
#22550510	2
#22550465	2
#22550462	2
#22550458	2
#22550442	2
#22550439	2
#22550437	2
#22550434	2
#120×D₁₂₇	2
#560×C₁₂₇	2
#3532	127