Subgroups — #30652764

Order 16256.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550591	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550586	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550579	C₂	1	2	yes	maximal, complemented
4	#22550572	C₂	1	2	yes	maximal, complemented
5	#22550548	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550519	C₂	1	2	yes	maximal, complemented
7	#22550518	C₂	1	4	yes	maximal, complemented
8	D₄×D₅₀₈	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×D₅₀₈	C₂	1	2	yes	maximal, complemented
10	#22550481	C₂	1	2	yes	maximal, complemented
11	#22550465	C₂	1	4	yes	maximal, complemented
12	#22550426	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550389	C₂	1	2	yes	maximal, complemented
14	#121×D₁₂₇	C₂	1	2	yes	maximal, complemented
15	#22550350	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₅₀₈	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14523249	C₂²	1	2	yes	complemented
19	C₂×#14523248	C₂²	1	2	yes	complemented
20	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic
21	C₂²×D₅₀₈	C₂²	1	2	yes	—
22	C₂×D₄×D₁₂₇	C₂²	1	4	yes	complemented
23	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
24	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	complemented
25	#16861209	C₂²	1	1	yes	characteristic, complemented
26	#16861206	C₂²	1	1	yes	characteristic, complemented
27	#16861206	C₂²	1	2	yes	complemented
28	#16861204	C₂²	1	4	yes	complemented
29	#16861201	C₂²	1	2	yes	complemented
30	#16861197	C₂²	1	2	yes	complemented
31	#16861195	C₂²	1	4	yes	complemented
32	#16861194	C₂²	1	4	yes	complemented
33	#16861194	C₂²	1	4	yes	complemented
34	#16861191	C₂²	1	4	yes	complemented
35	#16861187	C₂²	1	4	yes	complemented
36	#16861185	C₂²	1	2	yes	complemented
37	#16861184	C₂²	1	2	yes	complemented
38	#16861184	C₂²	1	4	yes	complemented
39	#16861184	C₂²	1	2	yes	complemented
40	#16861184	C₂²	1	4	yes	complemented
41	#16861183	C₂²	1	2	yes	complemented
42	#16861183	C₂²	1	2	yes	complemented
43	#16861183	C₂²	1	2	yes	complemented
44	#16861183	C₂²	1	2	yes	complemented
45	#16861182	C₂²	1	4	yes	complemented
46	#16861182	C₂²	1	4	yes	complemented
47	#16861181	C₂²	1	4	yes	complemented
48	#16861180	C₂²	1	2	yes	complemented
49	#16861179	C₂²	1	4	yes	complemented
50	#16861179	C₂²	1	4	yes	complemented
51	#16861179	C₂²	1	4	yes	complemented
52	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
53	C₄×D₅₀₈	C₂²	1	2	yes	—
54	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
55	C₄×D₅₀₈	C₂²	1	2	yes	complemented
56	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₅₀₈	C₂²	1	2	yes	complemented
58	C₄×D₅₀₈	C₂²	1	2	yes	complemented
59	C₄×D₅₀₈	C₂²	1	2	yes	complemented
60	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
61	C₄×D₅₀₈	C₂²	1	2	yes	complemented
62	#16861171	C₂²	1	4	yes	complemented
63	#16861171	C₂²	1	4	yes	complemented
64	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	4	yes	complemented
65	#16861168	C₂²	1	2	yes	complemented
66	#16861167	C₂²	1	2	yes	complemented
67	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
68	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
69	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
70	C₂²⋊C₄×D₁₂₇	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₁₂₇	C₂²	1	4	yes	complemented
72	#126×C₁₂₇	C₂²	1	2	yes	complemented
73	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
74	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
75	#123×C₁₂₇	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
77	#121×C₁₂₇	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
80	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
81	#117×C₁₂₇	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₂₇	C₂³	1	2	yes	—
84	C₂³×D₁₂₇	C₂³	1	4	yes	—
85	#14523249	—	4	4	no	—
86	#14523248	—	4	4	no	—
87	C₂×Dic₂₅₄	C₂³	1	2	yes	—
88	C₂×D₅₀₈	—	2	4	no	—
89	C₂×D₅₀₈	—	2	8	no	—
90	C₂×D₅₀₈	C₂³	1	2	yes	—
91	C₂×D₅₀₈	C₂³	1	4	yes	—
92	C₂×D₅₀₈	C₂³	1	2	yes	—
93	C₂×D₅₀₈	C₂³	1	2	yes	—
94	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
95	C₂×D₅₀₈	C₂³	1	4	yes	—
96	C₂×D₅₀₈	C₂³	1	2	yes	—
97	C₂×D₅₀₈	C₂³	1	4	yes	—
98	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₂₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₂₇	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₂₇	C₂³	1	4	yes	—
102	D₄×D₁₂₇	—	4	4	no	—
103	D₄×D₁₂₇	—	4	8	no	—
104	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
105	C₂×C₄×D₁₂₇	—	4	4	no	—
106	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
107	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
108	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
109	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
110	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
111	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
112	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
113	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
114	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
115	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
117	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
118	Dic₁₂₇⋊C₄	C₂³	1	4	yes	—
119	Dic₁₂₇⋊C₄	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₂₇	C₂³	1	4	yes	—
121	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
122	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
131	C₄×Dic₁₂₇	C₂³	1	4	yes	—
132	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
134	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
150	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
151	C₄²×C₁₂₇	C₂³	1	2	yes	—
152	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
153	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
154	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
155	C₂²×D₁₂₇	—	2	4	no	—
156	C₂²×D₁₂₇	—	2	4	no	—
157	C₂²×D₁₂₇	—	2	8	no	—
158	C₂²×D₁₂₇	—	4	2	no	—
159	C₂²×D₁₂₇	—	4	4	no	—
160	C₂²×D₁₂₇	—	4	4	no	—
161	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
162	C₂²×D₁₂₇	C₂⁴	1	4	yes	—
163	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
164	Dic₂₅₄	—	4	2	no	—
165	D₅₀₈	—	2	8	no	—
166	D₅₀₈	—	2	4	no	—
167	D₅₀₈	—	2	2	no	—
168	D₅₀₈	—	2	4	no	—
169	D₅₀₈	—	2	4	no	—
170	D₅₀₈	—	4	4	no	—
171	D₅₀₈	—	4	2	no	—
172	D₅₀₈	—	4	4	no	—
173	D₅₀₈	#41	1	4	yes	complemented
174	C₂²⋊D₁₂₇	—	2	8	no	—
175	C₂²⋊D₁₂₇	—	4	4	no	—
176	C₂²⋊D₁₂₇	—	4	4	no	—
177	C₂×Dic₁₂₇	—	4	2	no	—
178	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
179	C₂×Dic₁₂₇	C₂⁴	1	4	yes	—
180	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
181	C₄×D₁₂₇	—	2	4	no	—
182	C₄×D₁₂₇	—	2	4	no	—
183	C₄×D₁₂₇	—	4	2	no	—
184	C₄×D₁₂₇	—	4	2	no	—
185	C₄×D₁₂₇	—	4	4	no	—
186	C₄×D₁₂₇	—	4	4	no	—
187	C₄×D₁₂₇	—	4	4	no	—
188	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
189	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
190	Q₈×C₁₂₇	—	2	2	no	—
191	D₄×C₁₂₇	—	2	4	no	—
192	D₄×C₁₂₇	—	2	2	no	—
193	C₂×C₄×C₁₂₇	—	2	2	no	—
194	C₂×C₄×C₁₂₇	—	2	2	no	—
195	C₂×C₄×C₁₂₇	—	2	4	no	—
196	C₂×C₄×C₁₂₇	—	2	2	no	—
197	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
200	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
201	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
202	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
203	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
204	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
205	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₁₂₇	—	2	1	no	—
207	C₂²×C₁₂₇	—	2	1	no	—
208	C₂²×C₁₂₇	—	2	2	no	—
209	C₂²×C₁₂₇	—	2	2	no	—
210	C₂²×C₁₂₇	—	2	2	no	—
211	C₂²×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
212	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
213	C₂×D₁₂₇	—	2	2	no	—
214	C₂×D₁₂₇	—	2	2	no	—
215	C₂×D₁₂₇	—	2	2	no	—
216	C₂×D₁₂₇	—	2	4	no	—
217	C₂×D₁₂₇	—	2	2	no	—
218	C₂×D₁₂₇	—	2	4	no	—
219	C₂×D₁₂₇	—	2	4	no	—
220	C₂×D₁₂₇	—	2	2	no	—
221	C₂×D₁₂₇	—	4	8	no	—
222	C₂×D₁₂₇	—	8	8	no	—
223	C₂×D₁₂₇	C₂×#41	1	4	yes	—
224	C₄×C₁₂₇	—	2	1	no	—
225	C₄×C₁₂₇	—	2	2	no	—
226	C₄×C₁₂₇	—	2	1	no	—
227	C₄×C₁₂₇	—	2	1	no	—
228	C₄×C₁₂₇	—	2	1	no	—
229	C₄×C₁₂₇	—	2	2	no	—
230	C₄×C₁₂₇	—	2	2	no	—
231	C₄×C₁₂₇	C₂×#41	1	2	yes	—
232	C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
233	Dic₁₂₇	—	2	2	no	—
234	Dic₁₂₇	—	2	2	no	—
235	Dic₁₂₇	—	2	4	no	—
236	C₂×C₁₂₇	—	2	2	no	—
237	C₂×C₁₂₇	—	4	2	no	—
238	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
239	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	D₁₂₇	—	2	4	no	—
242	D₁₂₇	—	4	2	no	—
243	D₁₂₇	—	4	4	no	—
244	#3519	—	127	1	no	maximal, Sylow
245	C₁₂₇	#3519	1	1	yes	characteristic, complemented, Sylow
246	#555	—	127	1	no	—
247	#554	—	127	1	no	—
248	#553	—	127	2	no	—
249	#553	—	127	2	no	—
250	#550	—	127	1	no	—
251	#546	—	127	2	no	—
252	#546	—	127	4	no	—
253	D₄²	—	127	1	no	—
254	D₄²	—	127	2	no	—
255	#540	—	127	2	no	—
256	#538	—	127	4	no	—
257	#532	—	127	1	no	—
258	#529	D₁₂₇	1	1	yes	characteristic, complemented
259	#525	—	127	2	no	—
260	C₂×#121	—	127	2	no	—
261	#518	—	127	2	no	—
262	C₂×C₄×D₄	—	127	1	no	—
263	C₂×#41	—	127	2	no	—
264	C₂×#41	—	127	2	no	—
265	C₂²×D₄	—	127	4	no	—
266	C₂²×D₄	—	127	2	no	—
267	C₂²×D₄	—	127	1	no	—
268	C₂²×D₄	—	127	2	no	—
269	C₂³×C₄	—	127	2	no	—
270	C₄⋊Q₈	—	127	1	no	—
271	#127	—	127	1	no	—
272	#127	—	127	2	no	—
273	#126	—	127	4	no	—
274	#126	C₂×D₁₂₇	1	2	yes	complemented
275	#125	—	127	2	no	—
276	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
277	#124	—	127	4	no	—
278	#124	—	127	2	no	—
279	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
280	#123	—	127	4	no	—
281	#123	—	127	4	no	—
282	#123	—	127	4	no	—
283	#123	C₂×D₁₂₇	1	2	yes	complemented
284	C₂²⋊Q₈	—	127	2	no	—
285	C₂²⋊Q₈	—	127	4	no	—
286	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
287	#121	—	127	4	no	—
288	#121	—	127	2	no	—
289	#121	—	127	2	no	—
290	#121	—	127	2	no	—
291	#121	—	127	2	no	—
292	#121	—	127	2	no	—
293	#121	—	127	2	no	—
294	#121	—	127	2	no	—
295	#121	—	127	4	no	—
296	#121	—	127	4	no	—
297	#121	—	127	4	no	—
298	#121	—	127	4	no	—
299	#121	C₂×D₁₂₇	1	1	yes	characteristic
300	#120	—	127	4	no	—
301	#120	—	127	4	no	—
302	#120	—	127	4	no	—
303	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
304	C₄×D₄	—	127	4	no	—
305	C₄×D₄	—	127	4	no	—
306	C₄×D₄	—	127	4	no	—
307	C₄×D₄	—	127	1	no	—
308	C₄×D₄	—	127	2	no	—
309	C₄×D₄	—	127	1	no	—
310	C₄×D₄	—	127	1	no	—
311	C₄×D₄	—	127	2	no	—
312	C₄×D₄	—	127	1	no	—
313	C₄×D₄	—	127	2	no	—
314	C₄×D₄	—	127	2	no	—
315	C₄×D₄	—	127	2	no	—
316	C₄×D₄	—	127	2	no	—
317	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
318	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
319	#117	—	127	2	no	—
320	#117	—	127	2	no	—
321	#117	C₂×D₁₂₇	1	2	yes	complemented
322	C₂×C₄⋊C₄	—	127	1	no	—
323	C₂×C₄⋊C₄	—	127	2	no	—
324	C₂×C₂²⋊C₄	—	127	2	no	—
325	C₂×C₂²⋊C₄	—	127	4	no	—
326	C₂×C₂²⋊C₄	—	127	4	no	—
327	C₂×C₄²	C₂×D₁₂₇	1	1	yes	characteristic, complemented
328	C₂⁴	—	127	4	no	—
329	C₂⁴	—	127	2	no	—
330	#41	—	508	4	no	—
331	#41	—	508	4	no	—
332	C₂×Q₈	—	127	2	no	—
333	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
334	C₂×D₄	—	127	4	no	—
335	C₂×D₄	—	127	4	no	—
336	C₂×D₄	—	127	4	no	—
337	C₂×D₄	—	127	1	no	—
338	C₂×D₄	—	127	4	no	—
339	C₂×D₄	—	127	2	no	—
340	C₂×D₄	—	127	4	no	—
341	C₂×D₄	—	127	4	no	—
342	C₂×D₄	—	127	2	no	—
343	C₂×D₄	—	127	1	no	—
344	C₂×D₄	—	127	2	no	—
345	C₂×D₄	—	127	2	no	—
346	C₂×D₄	—	508	8	no	—
347	C₂×D₄	—	508	4	no	—
348	C₂×D₄	—	254	8	no	—
349	C₂×D₄	—	254	4	no	—
350	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
351	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
352	C₂²×C₄	—	127	2	no	—
353	C₂²×C₄	—	127	2	no	—
354	C₂²×C₄	—	127	4	no	—
355	C₂²×C₄	—	127	4	no	—
356	C₂²×C₄	—	127	4	no	—
357	C₂²×C₄	—	127	2	no	—
358	C₂²×C₄	—	127	2	no	—
359	C₂²×C₄	—	127	2	no	—
360	C₂²×C₄	—	508	4	no	—
361	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
362	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
363	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
365	C₄⋊C₄	—	127	4	no	—
366	C₄⋊C₄	—	127	4	no	—
367	C₄⋊C₄	—	127	1	no	—
368	C₄⋊C₄	—	127	2	no	—
369	C₄⋊C₄	—	127	1	no	—
370	C₄⋊C₄	—	127	2	no	—
371	C₄⋊C₄	—	127	2	no	—
372	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
374	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
375	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
376	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
377	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
378	C₂²⋊C₄	—	127	4	no	—
379	C₂²⋊C₄	—	127	2	no	—
380	C₂²⋊C₄	—	127	4	no	—
381	C₂²⋊C₄	—	127	2	no	—
382	C₂²⋊C₄	—	127	4	no	—
383	C₂²⋊C₄	—	127	2	no	—
384	C₂²⋊C₄	—	127	4	no	—
385	C₂²⋊C₄	—	127	2	no	—
386	C₂²⋊C₄	—	127	4	no	—
387	C₂²⋊C₄	—	127	4	no	—
388	C₂²⋊C₄	—	127	4	no	—
389	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
390	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
391	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
394	C₄²	—	127	4	no	—
395	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
396	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
397	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
398	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
399	C₄²	C₂²×D₁₂₇	1	2	yes	—
400	C₂³	—	127	2	no	—
401	C₂³	—	127	2	no	—
402	C₂³	—	127	4	no	—
403	C₂³	—	508	4	no	—
404	C₂³	—	508	4	no	—
405	C₂³	—	508	2	no	—
406	C₂³	—	254	8	no	—
407	C₂³	—	254	4	no	—
408	C₂³	—	254	4	no	—
409	C₂³	C₂³×D₁₂₇	1	2	yes	—
410	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	508	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	127	4	no	—
416	D₄	—	508	4	no	—
417	D₄	—	508	2	no	—
418	D₄	—	508	4	no	—
419	D₄	—	508	4	no	—
420	D₄	—	508	4	no	—
421	D₄	—	254	8	no	—
422	D₄	—	254	4	no	—
423	D₄	—	254	8	no	—
424	D₄	—	254	4	no	—
425	D₄	—	254	2	no	—
426	D₄	—	254	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	127	2	no	—
432	C₂×C₄	—	127	4	no	—
433	C₂×C₄	—	127	2	no	—
434	C₂×C₄	—	508	2	no	—
435	C₂×C₄	—	508	2	no	—
436	C₂×C₄	—	508	4	no	—
437	C₂×C₄	—	508	4	no	—
438	C₂×C₄	—	508	4	no	—
439	C₂×C₄	—	508	2	no	—
440	C₂×C₄	—	254	4	no	—
441	C₂×C₄	—	254	4	no	—
442	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
443	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
444	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
448	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
449	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	127	4	no	—
457	C₂²	—	1016	8	no	—
458	C₂²	—	508	8	no	—
459	C₂²	—	254	4	no	—
460	C₂²	—	254	2	no	—
461	C₂²	—	254	2	no	—
462	C₂²	—	254	4	no	—
463	C₂²	—	254	4	no	—
464	C₂²	—	254	2	no	—
465	C₂²	—	254	2	no	—
466	C₂²	—	254	2	no	—
467	C₂²	#16861255	1	2	yes	—
468	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	254	2	no	—
477	C₄	—	254	2	no	—
478	C₄	—	254	4	no	—
479	C₄	#41×D₁₂₇	1	2	yes	—
480	C₄	#16861255	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	508	4	no	—
484	C₂	—	508	2	no	—
485	C₂	—	254	4	no	—
486	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
487	C₂	C₂×#16861255	1	1	yes	characteristic
488	C₂	C₂×#16861255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#529×C₁₂₇	C₂
hypercenter	#529	D₁₂₇
hypocenter	C₁₂₇	#3519
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #22550591	C₂	semidirect
2. #22550586	C₂	semidirect
3. #22550579	C₂	semidirect
4. #22550572	C₂	semidirect
5. #22550548	C₂	semidirect
6. #22550519	C₂	semidirect
7. #22550518	C₂	semidirect
8. D₄×D₅₀₈	C₂	semidirect
9. D₄×D₅₀₈	C₂	semidirect
10. #22550481	C₂	semidirect
11. #22550465	C₂	semidirect
12. #22550426	C₂	semidirect
13. #22550389	C₂	semidirect
14. #121×D₁₂₇	C₂	semidirect
15. #22550350	C₂	semidirect
16. C₂×C₄×D₅₀₈	C₂	semidirect
17. #529×C₁₂₇	C₂	semidirect
18. C₂×#14523249	C₂²	semidirect
19. C₂×#14523248	C₂²	semidirect
22. C₂×D₄×D₁₂₇	C₂²	semidirect
23. C₂×D₄×D₁₂₇	C₂²	semidirect
24. C₂²×C₄×D₁₂₇	C₂²	semidirect
25. #16861209	C₂²	semidirect
26. #16861206	C₂²	semidirect
27. #16861206	C₂²	semidirect
28. #16861204	C₂²	semidirect
29. #16861201	C₂²	semidirect
30. #16861197	C₂²	semidirect
31. #16861195	C₂²	semidirect
32. #16861194	C₂²	semidirect
33. #16861194	C₂²	semidirect
34. #16861191	C₂²	semidirect
35. #16861187	C₂²	semidirect
36. #16861185	C₂²	semidirect
37. #16861184	C₂²	semidirect
38. #16861184	C₂²	semidirect
39. #16861184	C₂²	semidirect
40. #16861184	C₂²	semidirect
41. #16861183	C₂²	semidirect
42. #16861183	C₂²	semidirect
43. #16861183	C₂²	semidirect
44. #16861183	C₂²	semidirect
45. #16861182	C₂²	semidirect
46. #16861182	C₂²	semidirect
47. #16861181	C₂²	semidirect
48. #16861180	C₂²	semidirect
49. #16861179	C₂²	semidirect
50. #16861179	C₂²	semidirect
51. #16861179	C₂²	semidirect
55. C₄×D₅₀₈	C₂²	semidirect
56. C₄×D₅₀₈	C₂²	semidirect
57. C₄×D₅₀₈	C₂²	semidirect
58. C₄×D₅₀₈	C₂²	semidirect
59. C₄×D₅₀₈	C₂²	semidirect
60. C₄×D₅₀₈	C₂²	semidirect
61. C₄×D₅₀₈	C₂²	semidirect
62. #16861171	C₂²	semidirect
63. #16861171	C₂²	semidirect
64. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
65. #16861168	C₂²	semidirect
66. #16861167	C₂²	semidirect
67. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
68. C₄⋊C₄×D₁₂₇	C₂²	semidirect
69. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
70. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
71. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
72. #126×C₁₂₇	C₂²	semidirect
73. #125×C₁₂₇	C₂²	semidirect
74. #124×C₁₂₇	C₂²	semidirect
75. #123×C₁₂₇	C₂²	semidirect
76. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
78. C₄×Q₈×C₁₂₇	C₂²	semidirect
79. C₄×D₄×C₁₂₇	C₂²	semidirect
80. C₄×D₄×C₁₂₇	C₂²	semidirect
81. #117×C₁₂₇	C₂²	semidirect
82. C₂×C₄²×C₁₂₇	C₂²	semidirect
173. D₅₀₈	#41	semidirect
245. C₁₂₇	#3519	semidirect
258. #529	D₁₂₇	semidirect
274. #126	C₂×D₁₂₇	semidirect
276. #125	C₂×D₁₂₇	semidirect
279. #124	C₂×D₁₂₇	semidirect
283. #123	C₂×D₁₂₇	semidirect
286. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
303. C₄×Q₈	C₂×D₁₂₇	semidirect
317. C₄×D₄	C₂×D₁₂₇	semidirect
318. C₄×D₄	C₂×D₁₂₇	semidirect
321. #117	C₂×D₁₂₇	semidirect
327. 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
#22550591	2
#22550586	2
#22550579	2
#22550572	2
#22550548	2
#22550519	2
#22550518	2
D₄×D₅₀₈	2
#22550481	2
#22550465	2
#22550426	2
#22550389	2
#121×D₁₂₇	2
#22550350	2
C₂×C₄×D₅₀₈	2
#529×C₁₂₇	2
#3519	127