Subgroups — #30653505

Order 16256.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550711	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550688	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550687	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550686	C₂	1	3	yes	maximal, complemented
6	#22550683	C₂	1	3	yes	maximal, complemented
7	#22550680	C₂	1	3	yes	maximal, complemented
8	#22550679	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550677	C₂	1	3	yes	maximal, complemented
10	#22550673	C₂	1	3	yes	maximal, complemented
11	#22550672	C₂	1	3	yes	maximal, complemented
12	C₂×#16861233	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₁₂₇	C₂	1	3	yes	maximal, complemented
14	#22550641	C₂	1	1	yes	maximal, characteristic, complemented
15	#576×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#16861256	—	2	1	no	—
17	#16861256	C₂²	1	1	yes	characteristic, complemented
18	#16861256	C₂²	1	3	yes	complemented
19	#16861255	—	2	1	no	—
20	#16861255	C₂²	1	1	yes	characteristic, complemented
21	#16861255	C₂²	1	3	yes	complemented
22	#16861254	—	2	3	no	—
23	#16861254	—	2	3	no	—
24	#16861254	C₂²	1	3	yes	complemented
25	#16861254	C₂²	1	3	yes	complemented
26	C₂×#14523247	—	2	3	no	—
27	C₂×#14523247	C₂²	1	3	yes	complemented
28	#41×D₁₂₇	—	2	1	no	—
29	#41×D₁₂₇	—	2	1	no	—
30	#41×D₁₂₇	C₂²	1	1	yes	characteristic
31	#41×D₁₂₇	C₂²	1	3	yes	complemented
32	#41×D₁₂₇	C₂²	1	3	yes	complemented
33	C₂×D₄×D₁₂₇	—	2	3	no	—
34	C₂×D₄×D₁₂₇	C₂²	1	3	yes	complemented
35	#16861242	C₂²	1	3	yes	complemented
36	#16861241	C₂²	1	1	yes	characteristic, complemented
37	#16861241	C₂²	1	3	yes	complemented
38	#16861239	C₂²	1	3	yes	complemented
39	#16861238	C₂²	1	3	yes	complemented
40	#16861238	C₂²	1	3	yes	complemented
41	#16861237	C₂²	1	3	yes	complemented
42	#16861236	C₂²	1	3	yes	complemented
43	#16861236	C₂²	1	3	yes	complemented
44	#16861235	C₂²	1	3	yes	complemented
45	#16861235	C₂²	1	3	yes	complemented
46	#16861234	C₂²	1	3	yes	complemented
47	#16861233	C₂²	1	6	yes	complemented
48	#16861233	C₂²	1	3	yes	complemented
49	#16861233	C₂²	1	6	yes	complemented
50	#16861233	C₂²	1	6	yes	complemented
51	#16861233	C₂²	1	3	yes	complemented
52	#16861231	C₂²	1	3	yes	complemented
53	#16861230	C₂²	1	6	yes	complemented
54	#16861229	C₂²	1	3	yes	complemented
55	#16861229	C₂²	1	3	yes	complemented
56	#16861228	C₂²	1	6	yes	complemented
57	C₂×#14523237	C₂²	1	3	yes	complemented
58	C₂×#14523236	C₂²	1	3	yes	complemented
59	SD₁₆×D₁₂₇	C₂²	1	6	yes	complemented
60	C₂×#14523233	C₂²	1	3	yes	complemented
61	D₈×D₁₂₇	C₂²	1	6	yes	complemented
62	#16861217	C₂²	1	3	yes	complemented
63	#16861216	C₂²	1	1	yes	characteristic, complemented
64	#16861215	C₂²	1	3	yes	complemented
65	C₂×#14523231	C₂²	1	3	yes	complemented
66	M₁₆×D₁₂₇	C₂²	1	3	yes	complemented
67	H(5,𝔽₂)×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
69	AGL(1,ℤ/8)×C₁₂₇	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₁₂₇	C₂²	1	3	yes	complemented
71	#135×C₁₂₇	C₂²	1	3	yes	complemented
72	C₂×D₈×C₁₂₇	C₂²	1	3	yes	complemented
73	#131×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₁₂₇	—	2	3	no	—
75	#14523249	—	2	1	no	—
76	#14523249	D₄	1	1	yes	characteristic
77	#14523249	C₂³	1	3	yes	—
78	#14523249	C₂³	1	1	yes	characteristic
79	#14523248	—	2	3	no	—
80	#14523248	—	2	3	no	—
81	#14523248	—	2	3	no	—
82	#14523248	—	2	3	no	—
83	#14523248	C₂³	1	3	yes	—
84	#14523248	C₂³	1	3	yes	—
85	#14523248	C₂³	1	3	yes	complemented
86	#14523247	—	2	3	no	—
87	#14523247	—	2	3	no	—
88	#14523247	—	2	6	no	—
89	#14523247	—	2	3	no	—
90	#14523247	—	2	3	no	—
91	#14523247	—	2	3	no	—
92	#14523247	—	2	3	no	—
93	#14523247	—	2	3	no	—
94	#14523247	D₄	1	3	yes	—
95	#14523247	C₂³	1	3	yes	—
96	#14523247	C₂³	1	3	yes	—
97	#14523247	C₂³	1	6	yes	complemented
98	C₂×Dic₂₅₄	—	2	3	no	—
99	C₂×Dic₂₅₄	C₂³	1	3	yes	complemented
100	Q₈×D₁₂₇	—	2	1	no	—
101	Q₈×D₁₂₇	D₄	1	1	yes	characteristic
102	Q₈×D₁₂₇	C₂³	1	1	yes	characteristic
103	Q₈×D₁₂₇	C₂³	1	3	yes	complemented
104	C₂×D₅₀₈	—	2	3	no	—
105	C₂×D₅₀₈	C₂³	1	3	yes	—
106	C₂×C₂²⋊D₁₂₇	—	2	3	no	—
107	C₂×C₂²⋊D₁₂₇	—	2	6	no	—
108	C₂×C₂²⋊D₁₂₇	—	2	6	no	—
109	C₂×C₂²⋊D₁₂₇	—	2	3	no	—
110	D₄×D₁₂₇	—	2	3	no	—
111	D₄×D₁₂₇	—	2	3	no	—
112	D₄×D₁₂₇	—	2	3	no	—
113	D₄×D₁₂₇	—	2	3	no	—
114	D₄×D₁₂₇	—	2	6	no	—
115	D₄×D₁₂₇	—	2	3	no	—
116	D₄×D₁₂₇	—	2	3	no	—
117	D₄×D₁₂₇	—	2	3	no	—
118	D₄×D₁₂₇	D₄	1	3	yes	—
119	D₄×D₁₂₇	C₂³	1	6	yes	—
120	D₄×D₁₂₇	C₂³	1	3	yes	—
121	D₄×D₁₂₇	C₂³	1	3	yes	complemented
122	C₂²×Dic₁₂₇	—	2	3	no	—
123	C₂×C₄×D₁₂₇	—	2	3	no	—
124	C₂×C₄×D₁₂₇	—	2	3	no	—
125	C₂×C₄×D₁₂₇	C₂³	1	3	yes	—
126	Dic₅₀₈	C₂³	1	3	yes	complemented
127	#14523238	C₂³	1	1	yes	characteristic, complemented
128	#14523238	C₂³	1	3	yes	complemented
129	#14523237	C₂³	1	6	yes	complemented
130	#14523237	C₂³	1	3	yes	complemented
131	#14523237	C₂³	1	1	yes	characteristic, complemented
132	#14523236	C₂³	1	6	yes	complemented
133	#14523236	C₂³	1	3	yes	complemented
134	#14523236	C₂³	1	3	yes	complemented
135	#14523235	C₂³	1	3	yes	complemented
136	#14523235	C₂³	1	1	yes	characteristic, complemented
137	D₁₀₁₆	C₂³	1	3	yes	complemented
138	#14523233	C₂³	1	3	yes	complemented
139	#14523233	C₂³	1	6	yes	complemented
140	#14523233	C₂³	1	3	yes	complemented
141	#14523232	C₂³	1	3	yes	complemented
142	#14523231	C₂³	1	3	yes	—
143	#14523231	C₂³	1	1	yes	characteristic
144	#14523231	C₂³	1	3	yes	complemented
145	#14523231	C₂³	1	3	yes	complemented
146	C₂×C₁₂₇⋊C₈	C₂³	1	3	yes	complemented
147	C₈×D₁₂₇	C₂³	1	6	yes	complemented
148	#41×C₁₂₇	—	2	1	no	—
149	#41×C₁₂₇	—	2	1	no	—
150	#41×C₁₂₇	C₂³	1	3	yes	—
151	#41×C₁₂₇	C₂³	1	1	yes	characteristic
152	#41×C₁₂₇	C₂³	1	3	yes	complemented
153	C₂×D₄×C₁₂₇	—	2	3	no	—
154	C₂×D₄×C₁₂₇	—	2	3	no	—
155	C₂×D₄×C₁₂₇	C₂³	1	3	yes	—
156	C₂×D₄×C₁₂₇	C₂³	1	3	yes	complemented
157	Q₁₆×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
158	SD₁₆×C₁₂₇	C₂³	1	3	yes	complemented
159	SD₁₆×C₁₂₇	C₂³	1	3	yes	complemented
160	D₈×C₁₂₇	C₂³	1	6	yes	complemented
161	D₈×C₁₂₇	C₂³	1	3	yes	complemented
162	M₁₆×C₁₂₇	C₂³	1	3	yes	complemented
163	C₂×C₈×C₁₂₇	C₂³	1	3	yes	complemented
164	C₂²×D₁₂₇	—	2	3	no	—
165	C₂²×D₁₂₇	—	2	3	no	—
166	C₂²×D₁₂₇	—	2	3	no	—
167	C₂²×D₁₂₇	—	2	6	no	—
168	C₂²×D₁₂₇	—	8	6	no	—
169	C₂²×D₁₂₇	C₂×D₄	1	3	yes	—
170	Dic₂₅₄	—	2	3	no	—
171	Dic₂₅₄	—	2	1	no	—
172	Dic₂₅₄	—	2	3	no	—
173	Dic₂₅₄	C₂×D₄	1	3	yes	—
174	Dic₂₅₄	C₂⁴	1	3	yes	—
175	Dic₂₅₄	C₂⁴	1	1	yes	characteristic
176	D₅₀₈	—	2	3	no	—
177	D₅₀₈	—	2	1	no	—
178	D₅₀₈	—	2	3	no	—
179	D₅₀₈	C₂×D₄	1	3	yes	—
180	D₅₀₈	C₂⁴	1	1	yes	characteristic
181	D₅₀₈	C₂⁴	1	3	yes	—
182	C₂²⋊D₁₂₇	—	2	3	no	—
183	C₂²⋊D₁₂₇	—	2	3	no	—
184	C₂²⋊D₁₂₇	—	2	3	no	—
185	C₂²⋊D₁₂₇	—	2	3	no	—
186	C₂²⋊D₁₂₇	—	2	6	no	—
187	C₂²⋊D₁₂₇	—	2	3	no	—
188	C₂²⋊D₁₂₇	—	2	6	no	—
189	C₂²⋊D₁₂₇	—	2	3	no	—
190	C₂²⋊D₁₂₇	C₂×D₄	1	6	yes	—
191	C₂×Dic₁₂₇	—	2	3	no	—
192	C₂×Dic₁₂₇	—	2	3	no	—
193	C₂×Dic₁₂₇	—	2	3	no	—
194	C₂×Dic₁₂₇	—	2	6	no	—
195	C₂×Dic₁₂₇	C₂×D₄	1	3	yes	—
196	C₄×D₁₂₇	—	2	1	no	—
197	C₄×D₁₂₇	—	2	3	no	—
198	C₄×D₁₂₇	—	2	3	no	—
199	C₄×D₁₂₇	—	2	3	no	—
200	C₄×D₁₂₇	—	2	1	no	—
201	C₄×D₁₂₇	—	2	3	no	—
202	C₄×D₁₂₇	C₂×D₄	1	3	yes	—
203	C₄×D₁₂₇	C₂×D₄	1	3	yes	—
204	C₄×D₁₂₇	C₂⁴	1	3	yes	—
205	C₄×D₁₂₇	C₂⁴	1	1	yes	characteristic
206	C₁₂₇⋊C₈	C₂⁴	1	3	yes	—
207	C₁₂₇⋊C₈	C₂⁴	1	1	yes	characteristic
208	C₂³×C₁₂₇	—	2	3	no	—
209	C₂³×C₁₂₇	—	2	3	no	—
210	Q₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
211	Q₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
212	Q₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
213	D₄×C₁₂₇	—	2	3	no	—
214	D₄×C₁₂₇	—	2	3	no	—
215	D₄×C₁₂₇	—	2	3	no	—
216	D₄×C₁₂₇	—	2	3	no	—
217	D₄×C₁₂₇	C₂×D₄	1	3	yes	—
218	D₄×C₁₂₇	C₂⁴	1	3	yes	—
219	D₄×C₁₂₇	C₂⁴	1	3	yes	—
220	C₂×C₄×C₁₂₇	—	2	3	no	—
221	C₂×C₄×C₁₂₇	—	2	3	no	—
222	C₂×C₄×C₁₂₇	C₂⁴	1	3	yes	—
223	C₈×C₁₂₇	C₂⁴	1	1	yes	characteristic
224	C₈×C₁₂₇	C₂⁴	1	3	yes	—
225	C₂²×C₁₂₇	—	2	3	no	—
226	C₂²×C₁₂₇	—	2	3	no	—
227	C₂²×C₁₂₇	—	8	3	no	—
228	C₂²×C₁₂₇	—	8	3	no	—
229	C₂²×C₁₂₇	C₂²×D₄	1	3	yes	—
230	C₂×D₁₂₇	—	2	1	no	—
231	C₂×D₁₂₇	—	2	3	no	—
232	C₂×D₁₂₇	—	4	3	no	—
233	C₂×D₁₂₇	—	4	6	no	—
234	C₂×D₁₂₇	—	8	3	no	—
235	C₂×D₁₂₇	—	8	6	no	—
236	C₂×D₁₂₇	—	8	3	no	—
237	C₂×D₁₂₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₁₂₇	C₂²×D₄	1	3	yes	—
239	C₄×C₁₂₇	—	2	1	no	—
240	C₄×C₁₂₇	—	2	1	no	—
241	C₄×C₁₂₇	C₂²×D₄	1	3	yes	—
242	C₄×C₁₂₇	C₂⁵	1	1	yes	characteristic
243	Dic₁₂₇	—	2	1	no	—
244	Dic₁₂₇	—	2	3	no	—
245	Dic₁₂₇	C₂²×D₄	1	1	yes	characteristic
246	Dic₁₂₇	C₂²×D₄	1	3	yes	—
247	C₂×C₁₂₇	—	2	3	no	—
248	C₂×C₁₂₇	—	4	3	no	—
249	C₂×C₁₂₇	—	4	3	no	—
250	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
251	D₁₂₇	—	2	1	no	—
252	D₁₂₇	—	2	3	no	—
253	D₁₂₇	—	4	3	no	—
254	D₁₂₇	—	4	1	no	—
255	#3585	—	127	1	no	maximal, Sylow
256	C₁₂₇	#3585	1	1	yes	characteristic, complemented, Sylow
257	#585	—	127	1	no	—
258	C₂×H(5,𝔽₂)	—	127	1	no	—
259	#577	—	127	1	no	—
260	#577	—	127	3	no	—
261	#577	—	127	3	no	—
262	#577	—	127	1	no	—
263	#576	—	127	1	no	—
264	#576	—	127	3	no	—
265	#576	—	127	3	no	—
266	#576	D₁₂₇	1	1	yes	characteristic, complemented
267	#575	—	127	3	no	—
268	#575	—	127	3	no	—
269	C₂×AGL(1,ℤ/8)	—	127	3	no	—
270	C₂×AGL(1,ℤ/8)	—	127	3	no	—
271	#568	—	127	1	no	—
272	2₋¹⁺⁴	—	127	1	no	—
273	2₋¹⁺⁴	—	127	3	no	—
274	2₋¹⁺⁴	—	254	1	no	—
275	H(5,𝔽₂)	—	127	3	no	—
276	H(5,𝔽₂)	—	127	1	no	—
277	H(5,𝔽₂)	—	127	3	no	—
278	H(5,𝔽₂)	—	127	3	no	—
279	H(5,𝔽₂)	—	254	3	no	—
280	H(5,𝔽₂)	—	254	3	no	—
281	H(5,𝔽₂)	—	254	1	no	—
282	H(5,𝔽₂)	C₂×D₁₂₇	1	1	yes	characteristic, complemented
283	H(5,𝔽₂)	C₂×D₁₂₇	1	1	yes	characteristic, complemented
284	C₂×#41	—	127	1	no	—
285	C₂×#41	—	127	3	no	—
286	C₂×#41	—	127	3	no	—
287	C₂×#41	—	127	3	no	—
288	C₂×#41	—	254	3	no	—
289	C₂×#41	—	254	1	no	—
290	C₂×#41	—	254	1	no	—
291	C₂²×D₄	—	127	3	no	—
292	C₂²×D₄	—	254	3	no	—
293	#137	—	127	3	no	—
294	#137	—	127	1	no	—
295	#137	—	127	3	no	—
296	#137	—	127	3	no	—
297	#137	—	127	3	no	—
298	#137	—	127	3	no	—
299	AGL(1,ℤ/8)	—	127	3	no	—
300	AGL(1,ℤ/8)	—	127	3	no	—
301	AGL(1,ℤ/8)	—	127	3	no	—
302	AGL(1,ℤ/8)	—	127	3	no	—
303	AGL(1,ℤ/8)	—	127	3	no	—
304	AGL(1,ℤ/8)	—	127	6	no	—
305	AGL(1,ℤ/8)	—	127	3	no	—
306	AGL(1,ℤ/8)	—	127	6	no	—
307	AGL(1,ℤ/8)	—	127	6	no	—
308	AGL(1,ℤ/8)	—	127	3	no	—
309	AGL(1,ℤ/8)	—	127	3	no	—
310	AGL(1,ℤ/8)	C₂×D₁₂₇	1	3	yes	complemented
311	AGL(1,ℤ/8)	C₂×D₁₂₇	1	3	yes	complemented
312	#135	—	127	3	no	—
313	#135	—	127	3	no	—
314	#135	—	127	6	no	—
315	#135	—	127	6	no	—
316	#135	—	127	3	no	—
317	#135	C₂×D₁₂₇	1	3	yes	complemented
318	C₂×SD₁₆	—	127	3	no	—
319	C₂×SD₁₆	—	127	6	no	—
320	C₂×SD₁₆	—	127	3	no	—
321	C₂×D₈	—	127	3	no	—
322	C₂×D₈	—	127	6	no	—
323	C₂×D₈	C₂×D₁₂₇	1	3	yes	complemented
324	#131	—	127	1	no	—
325	#131	—	127	3	no	—
326	#131	—	127	3	no	—
327	#131	C₂×D₁₂₇	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	127	3	no	—
329	C₂×M₁₆	—	127	3	no	—
330	C₂⁴	—	254	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	127	1	no	—
334	#41	—	127	3	no	—
335	#41	—	127	3	no	—
336	#41	—	127	3	no	—
337	#41	—	127	1	no	—
338	#41	—	127	3	no	—
339	#41	—	127	3	no	—
340	#41	—	127	6	no	—
341	#41	—	127	3	no	—
342	#41	—	127	3	no	—
343	#41	—	254	3	no	—
344	#41	—	254	3	no	—
345	#41	—	254	3	no	—
346	#41	—	254	3	no	—
347	#41	—	254	3	no	—
348	#41	—	254	3	no	—
349	#41	—	254	3	no	—
350	#41	—	254	3	no	—
351	#41	—	254	6	no	—
352	#41	—	254	3	no	—
353	#41	—	254	3	no	—
354	#41	—	254	1	no	—
355	#41	—	254	3	no	—
356	#41	C₂²×D₁₂₇	1	3	yes	—
357	#41	C₂²×D₁₂₇	1	1	yes	characteristic
358	#41	C₂²×D₁₂₇	1	3	yes	complemented
359	C₂×Q₈	—	127	1	no	—
360	C₂×Q₈	—	127	1	no	—
361	C₂×Q₈	—	127	3	no	—
362	C₂×Q₈	—	127	3	no	—
363	C₂×Q₈	—	254	3	no	—
364	C₂×Q₈	—	254	1	no	—
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	—	127	3	no	—
368	C₂×D₄	—	127	6	no	—
369	C₂×D₄	—	127	3	no	—
370	C₂×D₄	—	127	3	no	—
371	C₂×D₄	—	127	3	no	—
372	C₂×D₄	—	254	3	no	—
373	C₂×D₄	—	254	3	no	—
374	C₂×D₄	—	254	3	no	—
375	C₂×D₄	—	254	3	no	—
376	C₂×D₄	—	254	6	no	—
377	C₂×D₄	—	254	3	no	—
378	C₂×D₄	—	254	3	no	—
379	C₂×D₄	—	254	3	no	—
380	C₂×D₄	—	254	3	no	—
381	C₂×D₄	—	254	6	no	—
382	C₂×D₄	—	254	6	no	—
383	C₂×D₄	—	254	3	no	—
384	C₂×D₄	—	254	3	no	—
385	C₂×D₄	C₂²×D₁₂₇	1	3	yes	—
386	C₂×D₄	C₂²×D₁₂₇	1	3	yes	complemented
387	C₂²×C₄	—	127	3	no	—
388	C₂²×C₄	—	254	3	no	—
389	C₂²×C₄	—	254	3	no	—
390	C₂²×C₄	—	254	3	no	—
391	Q₁₆	—	127	3	no	—
392	Q₁₆	—	127	1	no	—
393	Q₁₆	—	127	3	no	—
394	Q₁₆	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
395	SD₁₆	—	127	3	no	—
396	SD₁₆	—	127	1	no	—
397	SD₁₆	—	127	6	no	—
398	SD₁₆	—	127	3	no	—
399	SD₁₆	—	127	3	no	—
400	SD₁₆	—	127	6	no	—
401	SD₁₆	—	127	3	no	—
402	SD₁₆	—	127	1	no	—
403	SD₁₆	C₂²×D₁₂₇	1	3	yes	complemented
404	SD₁₆	C₂²×D₁₂₇	1	3	yes	complemented
405	D₈	—	127	3	no	—
406	D₈	—	127	6	no	—
407	D₈	—	127	3	no	—
408	D₈	—	127	3	no	—
409	D₈	C₂²×D₁₂₇	1	6	yes	complemented
410	D₈	C₂²×D₁₂₇	1	3	yes	complemented
411	M₁₆	—	127	3	no	—
412	M₁₆	—	127	3	no	—
413	M₁₆	—	127	1	no	—
414	M₁₆	—	127	3	no	—
415	M₁₆	—	127	3	no	—
416	M₁₆	C₂²×D₁₂₇	1	3	yes	complemented
417	C₂×C₈	—	127	3	no	—
418	C₂×C₈	—	127	6	no	—
419	C₂×C₈	C₂²×D₁₂₇	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	2	3	no	—
422	C₂³	—	127	3	no	—
423	C₂³	—	1016	6	no	—
424	C₂³	—	254	3	no	—
425	C₂³	—	254	6	no	—
426	C₂³	—	254	3	no	—
427	C₂³	—	254	3	no	—
428	Q₈	—	127	3	no	—
429	Q₈	—	127	3	no	—
430	Q₈	—	127	1	no	—
431	Q₈	—	254	3	no	—
432	Q₈	—	254	1	no	—
433	Q₈	—	254	3	no	—
434	Q₈	D₄×D₁₂₇	1	1	yes	characteristic
435	Q₈	C₂³×D₁₂₇	1	1	yes	characteristic
436	Q₈	C₂³×D₁₂₇	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	2	3	no	—
441	D₄	—	127	6	no	—
442	D₄	—	127	3	no	—
443	D₄	—	127	1	no	—
444	D₄	—	127	3	no	—
445	D₄	—	254	3	no	—
446	D₄	—	254	1	no	—
447	D₄	—	254	3	no	—
448	D₄	—	254	6	no	—
449	D₄	—	254	3	no	—
450	D₄	—	254	3	no	—
451	D₄	—	254	3	no	—
452	D₄	—	254	6	no	—
453	D₄	—	254	3	no	—
454	D₄	—	254	3	no	—
455	D₄	—	254	3	no	—
456	D₄	D₄×D₁₂₇	1	3	yes	—
457	D₄	C₂³×D₁₂₇	1	3	yes	—
458	D₄	C₂³×D₁₂₇	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	127	3	no	—
462	C₂×C₄	—	127	3	no	—
463	C₂×C₄	—	127	3	no	—
464	C₂×C₄	—	127	3	no	—
465	C₂×C₄	—	127	1	no	—
466	C₂×C₄	—	254	1	no	—
467	C₂×C₄	—	254	3	no	—
468	C₂×C₄	—	254	1	no	—
469	C₂×C₄	—	254	3	no	—
470	C₂×C₄	—	254	3	no	—
471	C₂×C₄	—	254	3	no	—
472	C₂×C₄	—	254	6	no	—
473	C₂×C₄	—	254	3	no	—
474	C₂×C₄	—	254	3	no	—
475	C₂×C₄	—	254	3	no	—
476	C₂×C₄	C₂³×D₁₂₇	1	3	yes	—
477	C₈	—	127	1	no	—
478	C₈	—	127	3	no	—
479	C₈	C₂³×D₁₂₇	1	3	yes	—
480	C₈	C₂³×D₁₂₇	1	1	yes	characteristic
481	C₂²	—	2	3	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	8	3	no	—
485	C₂²	—	127	1	no	—
486	C₂²	—	127	3	no	—
487	C₂²	—	1016	3	no	—
488	C₂²	—	1016	6	no	—
489	C₂²	—	1016	3	no	—
490	C₂²	—	508	3	no	—
491	C₂²	—	508	6	no	—
492	C₂²	—	254	1	no	—
493	C₂²	—	254	3	no	—
494	C₂²	C₂×D₄×D₁₂₇	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	127	1	no	—
498	C₄	—	127	3	no	—
499	C₄	—	254	1	no	—
500	C₄	—	254	3	no	—
501	C₄	C₂×D₄×D₁₂₇	1	3	yes	—
502	C₄	C₂⁴×D₁₂₇	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	3	no	—
506	C₂	—	508	3	no	—
507	C₂	—	508	1	no	—
508	C₂	—	254	3	no	—
509	C₂	—	254	1	no	—
510	C₂	C₂²×D₄×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₂₇
commutator, cosocle	C₄×C₁₂₇	C₂⁵
Frattini	C₄	C₂⁴×D₁₂₇
Fitting	#576×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂³×D₄
hypercenter	#576	D₁₂₇
hypocenter	C₁₂₇	#3585
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. #22550711	C₂	semidirect
2. H(5,𝔽₂)×D₁₂₇	C₂	semidirect
3. #22550688	C₂	semidirect
4. #22550687	C₂	semidirect
5. #22550686	C₂	semidirect
6. #22550683	C₂	semidirect
7. #22550680	C₂	semidirect
8. #22550679	C₂	semidirect
9. #22550677	C₂	semidirect
10. #22550673	C₂	semidirect
11. #22550672	C₂	semidirect
12. C₂×#16861233	C₂	semidirect
13. AGL(1,ℤ/8)×D₁₂₇	C₂	semidirect
14. #22550641	C₂	semidirect
15. #576×C₁₂₇	C₂	semidirect
17. #16861256	C₂²	semidirect
18. #16861256	C₂²	semidirect
20. #16861255	C₂²	semidirect
21. #16861255	C₂²	semidirect
24. #16861254	C₂²	semidirect
25. #16861254	C₂²	semidirect
27. C₂×#14523247	C₂²	semidirect
31. #41×D₁₂₇	C₂²	semidirect
32. #41×D₁₂₇	C₂²	semidirect
34. C₂×D₄×D₁₂₇	C₂²	semidirect
35. #16861242	C₂²	semidirect
36. #16861241	C₂²	semidirect
37. #16861241	C₂²	semidirect
38. #16861239	C₂²	semidirect
39. #16861238	C₂²	semidirect
40. #16861238	C₂²	semidirect
41. #16861237	C₂²	semidirect
42. #16861236	C₂²	semidirect
43. #16861236	C₂²	semidirect
44. #16861235	C₂²	semidirect
45. #16861235	C₂²	semidirect
46. #16861234	C₂²	semidirect
47. #16861233	C₂²	semidirect
48. #16861233	C₂²	semidirect
49. #16861233	C₂²	semidirect
50. #16861233	C₂²	semidirect
51. #16861233	C₂²	semidirect
52. #16861231	C₂²	semidirect
53. #16861230	C₂²	semidirect
54. #16861229	C₂²	semidirect
55. #16861229	C₂²	semidirect
56. #16861228	C₂²	semidirect
57. C₂×#14523237	C₂²	semidirect
58. C₂×#14523236	C₂²	semidirect
59. SD₁₆×D₁₂₇	C₂²	semidirect
60. C₂×#14523233	C₂²	semidirect
61. D₈×D₁₂₇	C₂²	semidirect
62. #16861217	C₂²	semidirect
63. #16861216	C₂²	semidirect
64. #16861215	C₂²	semidirect
65. C₂×#14523231	C₂²	semidirect
66. M₁₆×D₁₂₇	C₂²	semidirect
67. H(5,𝔽₂)×C₁₂₇	C₂²	semidirect
68. H(5,𝔽₂)×C₁₂₇	C₂²	semidirect
69. AGL(1,ℤ/8)×C₁₂₇	C₂²	semidirect
70. AGL(1,ℤ/8)×C₁₂₇	C₂²	semidirect
71. #135×C₁₂₇	C₂²	semidirect
72. C₂×D₈×C₁₂₇	C₂²	semidirect
73. #131×C₁₂₇	C₂²	semidirect
85. #14523248	C₂³	semidirect
97. #14523247	C₂³	semidirect
99. C₂×Dic₂₅₄	C₂³	semidirect
103. Q₈×D₁₂₇	C₂³	semidirect
121. D₄×D₁₂₇	C₂³	semidirect
126. Dic₅₀₈	C₂³	semidirect
127. #14523238	C₂³	semidirect
128. #14523238	C₂³	semidirect
129. #14523237	C₂³	semidirect
130. #14523237	C₂³	semidirect
131. #14523237	C₂³	semidirect
132. #14523236	C₂³	semidirect
133. #14523236	C₂³	semidirect
134. #14523236	C₂³	semidirect
135. #14523235	C₂³	semidirect
136. #14523235	C₂³	semidirect
137. D₁₀₁₆	C₂³	semidirect
138. #14523233	C₂³	semidirect
139. #14523233	C₂³	semidirect
140. #14523233	C₂³	semidirect
141. #14523232	C₂³	semidirect
144. #14523231	C₂³	semidirect
145. #14523231	C₂³	semidirect
146. C₂×C₁₂₇⋊C₈	C₂³	semidirect
147. C₈×D₁₂₇	C₂³	semidirect
152. #41×C₁₂₇	C₂³	semidirect
156. C₂×D₄×C₁₂₇	C₂³	semidirect
157. Q₁₆×C₁₂₇	C₂³	semidirect
158. SD₁₆×C₁₂₇	C₂³	semidirect
159. SD₁₆×C₁₂₇	C₂³	semidirect
160. D₈×C₁₂₇	C₂³	semidirect
161. D₈×C₁₂₇	C₂³	semidirect
162. M₁₆×C₁₂₇	C₂³	semidirect
163. C₂×C₈×C₁₂₇	C₂³	semidirect
256. C₁₂₇	#3585	semidirect
266. #576	D₁₂₇	semidirect
282. H(5,𝔽₂)	C₂×D₁₂₇	semidirect
283. H(5,𝔽₂)	C₂×D₁₂₇	semidirect
310. AGL(1,ℤ/8)	C₂×D₁₂₇	semidirect
311. AGL(1,ℤ/8)	C₂×D₁₂₇	semidirect
317. #135	C₂×D₁₂₇	semidirect
323. C₂×D₈	C₂×D₁₂₇	semidirect
327. #131	C₂×D₁₂₇	semidirect
358. #41	C₂²×D₁₂₇	semidirect
386. C₂×D₄	C₂²×D₁₂₇	semidirect
394. Q₁₆	C₂²×D₁₂₇	semidirect
403. SD₁₆	C₂²×D₁₂₇	semidirect
404. SD₁₆	C₂²×D₁₂₇	semidirect
409. D₈	C₂²×D₁₂₇	semidirect
410. D₈	C₂²×D₁₂₇	semidirect
416. M₁₆	C₂²×D₁₂₇	semidirect
419. C₂×C₈	C₂²×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550711	2
H(5,𝔽₂)×D₁₂₇	2
#22550688	2
#22550687	2
#22550686	2
#22550683	2
#22550680	2
#22550679	2
#22550677	2
#22550673	2
#22550672	2
C₂×#16861233	2
AGL(1,ℤ/8)×D₁₂₇	2
#22550641	2
#576×C₁₂₇	2
#3585	127