Subgroups — #553×D₁₂₇ #30652245

Order 16256.

1252 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550579	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550578	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550577	C₂	1	2	yes	maximal, complemented
4	#22550576	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550575	C₂	1	2	yes	maximal, complemented
6	#22550574	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550573	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550572	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550571	C₂	1	2	yes	maximal, complemented
10	#22550570	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550569	C₂	1	2	yes	maximal, complemented
12	#126×D₁₂₇	C₂	1	2	yes	maximal, complemented
13	#125×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#123×D₁₂₇	C₂	1	2	yes	maximal, complemented
15	#121×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#121×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₁₂₇	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₁₂₇	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#117×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₂₇	C₂²	1	2	yes	—
27	C₂×D₄×D₁₂₇	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	—
31	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	—
32	#16861204	C₂²	1	2	yes	complemented
33	#16861204	C₂²	1	2	yes	complemented
34	#16861204	C₂²	1	2	yes	complemented
35	#16861203	C₂²	1	2	yes	complemented
36	#16861202	C₂²	1	2	yes	complemented
37	#16861202	C₂²	1	2	yes	complemented
38	#16861202	C₂²	1	2	yes	complemented
39	#16861201	C₂²	1	1	yes	characteristic, complemented
40	#16861200	C₂²	1	1	yes	characteristic, complemented
41	#16861200	C₂²	1	1	yes	characteristic, complemented
42	#16861199	C₂²	1	2	yes	complemented
43	#16861199	C₂²	1	2	yes	complemented
44	#16861194	C₂²	1	2	yes	complemented
45	#16861194	C₂²	1	2	yes	complemented
46	#16861193	C₂²	1	2	yes	complemented
47	#16861192	C₂²	1	2	yes	complemented
48	#16861191	C₂²	1	2	yes	complemented
49	#16861191	C₂²	1	2	yes	complemented
50	#16861190	C₂²	1	2	yes	complemented
51	#16861184	C₂²	1	1	yes	characteristic, complemented
52	#16861184	C₂²	1	1	yes	characteristic, complemented
53	#16861184	C₂²	1	2	yes	complemented
54	#16861183	C₂²	1	1	yes	characteristic, complemented
55	#16861183	C₂²	1	1	yes	characteristic, complemented
56	#16861183	C₂²	1	2	yes	complemented
57	#16861182	C₂²	1	2	yes	complemented
58	#16861182	C₂²	1	2	yes	complemented
59	#16861182	C₂²	1	2	yes	complemented
60	#16861182	C₂²	1	2	yes	complemented
61	#16861181	C₂²	1	2	yes	complemented
62	#16861181	C₂²	1	2	yes	complemented
63	#16861181	C₂²	1	2	yes	complemented
64	#16861181	C₂²	1	2	yes	complemented
65	#16861180	C₂²	1	2	yes	complemented
66	#16861180	C₂²	1	1	yes	characteristic, complemented
67	#16861180	C₂²	1	1	yes	characteristic, complemented
68	C₄×D₅₀₈	C₂²	1	2	yes	complemented
69	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
73	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
74	#16861171	C₂²	1	1	yes	characteristic, complemented
75	#16861171	C₂²	1	2	yes	complemented
76	#16861171	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
82	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
83	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
85	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
86	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	#16861168	C₂²	1	1	yes	characteristic, complemented
88	#16861167	C₂²	1	1	yes	characteristic, complemented
89	#16861167	C₂²	1	1	yes	characteristic, complemented
90	#16861166	C₂²	1	2	yes	complemented
91	#16861165	C₂²	1	2	yes	complemented
92	C₂×C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
93	C₂×Dic₁₂₇⋊C₄	C₂²	1	2	yes	complemented
94	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
95	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	—
97	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	—
99	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
100	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	—
101	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
102	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
109	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
110	C₄²×D₁₂₇	C₂²	1	2	yes	—
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
112	#126×C₁₂₇	C₂²	1	2	yes	complemented
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₂₇	C₂²	1	2	yes	complemented
115	#121×C₁₂₇	C₂²	1	2	yes	complemented
116	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
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	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
126	C₂×D₅₀₈	C₂³	1	2	yes	—
127	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
128	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
129	C₂×D₅₀₈	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
137	D₄×D₁₂₇	—	2	4	no	—
138	D₄×D₁₂₇	—	2	8	no	—
139	D₄×D₁₂₇	—	2	4	no	—
140	D₄×D₁₂₇	—	4	4	no	—
141	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
144	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
145	C₂×C₄×D₁₂₇	—	2	4	no	—
146	C₂×C₄×D₁₂₇	—	2	4	no	—
147	C₂×C₄×D₁₂₇	—	4	4	no	—
148	C₂×C₄×D₁₂₇	—	4	4	no	—
149	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
159	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
161	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
162	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
163	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
164	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
166	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
167	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
168	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
172	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
178	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
179	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
180	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
181	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
182	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
195	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₁₂₇)⋊C₄	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	2	yes	—
205	C₄×Dic₁₂₇	C₂³	1	2	yes	—
206	C₄×Dic₁₂₇	C₂³	1	2	yes	—
207	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
210	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
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	1	yes	characteristic
221	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
228	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
229	C₄²×C₁₂₇	C₂³	1	2	yes	—
230	C₂²×D₁₂₇	—	2	2	no	—
231	C₂²×D₁₂₇	—	2	2	no	—
232	C₂²×D₁₂₇	—	2	2	no	—
233	C₂²×D₁₂₇	—	2	2	no	—
234	C₂²×D₁₂₇	—	2	4	no	—
235	C₂²×D₁₂₇	—	2	4	no	—
236	C₂²×D₁₂₇	—	2	4	no	—
237	C₂²×D₁₂₇	—	2	2	no	—
238	C₂²×D₁₂₇	#41	1	4	yes	—
239	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
241	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
243	D₅₀₈	—	2	4	no	—
244	D₅₀₈	—	2	2	no	—
245	D₅₀₈	—	2	2	no	—
246	D₅₀₈	—	4	2	no	—
247	C₂²⋊D₁₂₇	—	2	4	no	—
248	C₂²⋊D₁₂₇	—	2	2	no	—
249	C₂²⋊D₁₂₇	—	2	2	no	—
250	C₂²⋊D₁₂₇	—	2	4	no	—
251	C₂²⋊D₁₂₇	—	2	4	no	—
252	C₂²⋊D₁₂₇	—	4	2	no	—
253	C₂²⋊D₁₂₇	—	4	2	no	—
254	C₂×Dic₁₂₇	—	2	2	no	—
255	C₂×Dic₁₂₇	—	2	2	no	—
256	C₂×Dic₁₂₇	—	4	2	no	—
257	C₂×Dic₁₂₇	—	4	2	no	—
258	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
261	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
263	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
265	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
266	C₄×D₁₂₇	—	2	2	no	—
267	C₄×D₁₂₇	—	2	2	no	—
268	C₄×D₁₂₇	—	2	4	no	—
269	C₄×D₁₂₇	—	2	2	no	—
270	C₄×D₁₂₇	—	2	2	no	—
271	C₄×D₁₂₇	—	2	4	no	—
272	C₄×D₁₂₇	—	2	4	no	—
273	C₄×D₁₂₇	—	2	2	no	—
274	C₄×D₁₂₇	—	2	2	no	—
275	C₄×D₁₂₇	—	2	2	no	—
276	C₄×D₁₂₇	—	2	2	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	#41	1	4	yes	—
282	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
283	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
284	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
285	D₄×C₁₂₇	—	2	2	no	—
286	D₄×C₁₂₇	—	2	4	no	—
287	D₄×C₁₂₇	—	2	2	no	—
288	D₄×C₁₂₇	—	4	2	no	—
289	C₂×C₄×C₁₂₇	—	2	2	no	—
290	C₂×C₄×C₁₂₇	—	2	2	no	—
291	C₂×C₄×C₁₂₇	—	4	2	no	—
292	C₂×C₄×C₁₂₇	—	4	2	no	—
293	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
298	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
306	C₂²×C₁₂₇	—	2	2	no	—
307	C₂²×C₁₂₇	—	2	2	no	—
308	C₂²×C₁₂₇	—	2	1	no	—
309	C₂²×C₁₂₇	C₂×#41	1	2	yes	—
310	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
311	C₂×D₁₂₇	—	2	1	no	—
312	C₂×D₁₂₇	—	2	1	no	—
313	C₂×D₁₂₇	—	2	8	no	—
314	C₂×D₁₂₇	—	2	1	no	—
315	C₂×D₁₂₇	—	2	1	no	—
316	C₂×D₁₂₇	—	2	2	no	—
317	C₂×D₁₂₇	—	2	2	no	—
318	C₂×D₁₂₇	—	2	2	no	—
319	C₂×D₁₂₇	—	2	1	no	—
320	C₂×D₁₂₇	—	4	4	no	—
321	C₂×D₁₂₇	—	4	8	no	—
322	C₂×D₁₂₇	C₂×#41	1	2	yes	—
323	C₂×D₁₂₇	C₂×#41	1	2	yes	—
324	C₂×D₁₂₇	C₂×#41	1	2	yes	—
325	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
326	C₄×C₁₂₇	—	2	1	no	—
327	C₄×C₁₂₇	—	2	1	no	—
328	C₄×C₁₂₇	—	2	1	no	—
329	C₄×C₁₂₇	—	2	2	no	—
330	C₄×C₁₂₇	—	2	1	no	—
331	C₄×C₁₂₇	—	2	2	no	—
332	C₄×C₁₂₇	—	2	2	no	—
333	C₄×C₁₂₇	C₂×#41	1	2	yes	—
334	Dic₁₂₇	—	2	1	no	—
335	Dic₁₂₇	—	2	1	no	—
336	Dic₁₂₇	—	2	1	no	—
337	Dic₁₂₇	—	2	2	no	—
338	Dic₁₂₇	—	2	1	no	—
339	Dic₁₂₇	—	2	2	no	—
340	Dic₁₂₇	—	2	2	no	—
341	Dic₁₂₇	C₂×#41	1	2	yes	—
342	C₂×C₁₂₇	—	2	2	no	—
343	C₂×C₁₂₇	—	4	1	no	—
344	C₂×C₁₂₇	—	4	2	no	—
345	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
346	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
347	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	D₁₂₇	—	2	2	no	—
349	D₁₂₇	—	4	1	no	—
350	D₁₂₇	—	4	2	no	—
351	D₁₂₇	#553	1	4	yes	direct product factor
352	C₂×#553	—	127	1	no	maximal, Sylow
353	C₁₂₇	C₂×#553	1	1	yes	characteristic, complemented, Sylow
354	#553	—	127	2	no	—
355	#553	—	127	1	no	—
356	#553	—	127	2	no	—
357	#553	—	127	2	no	—
358	#553	—	127	1	no	—
359	#553	—	127	1	no	—
360	#553	—	127	1	no	—
361	#553	—	127	2	no	—
362	#553	—	127	1	no	—
363	#553	—	127	1	no	—
364	#553	—	127	1	no	—
365	#553	D₁₂₇	1	1	yes	characteristic, direct product factor
366	C₂×#126	—	127	2	no	—
367	C₂×#125	—	127	1	no	—
368	C₂×#123	—	127	2	no	—
369	C₂×#121	—	127	2	no	—
370	C₂×#121	—	127	1	no	—
371	C₂×#121	—	127	1	no	—
372	C₂×C₄×D₄	—	127	2	no	—
373	C₂×C₄×D₄	—	127	1	no	—
374	C₂×C₄×D₄	—	127	1	no	—
375	C₂×#117	—	127	1	no	—
376	C₂²×C₄⋊C₄	—	127	1	no	—
377	C₂²×D₄	—	127	2	no	—
378	C₂²×D₄	—	127	1	no	—
379	C₂²×D₄	—	127	2	no	—
380	C₂²×D₄	—	127	1	no	—
381	C₂³×C₄	—	127	2	no	—
382	C₂³×C₄	—	127	2	no	—
383	C₂³×C₄	—	127	1	no	—
384	C₂³×C₄	—	127	1	no	—
385	#126	—	127	2	no	—
386	#126	—	127	2	no	—
387	#126	—	127	2	no	—
388	#126	—	127	2	no	—
389	#126	—	127	2	no	—
390	#126	—	127	2	no	—
391	#126	—	127	2	no	—
392	#126	C₂×D₁₂₇	1	2	yes	complemented
393	#125	—	127	2	no	—
394	#125	—	127	2	no	—
395	#125	—	127	1	no	—
396	#125	—	127	1	no	—
397	#125	—	127	1	no	—
398	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
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	C₂×D₁₂₇	1	2	yes	complemented
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	2	no	—
413	#121	—	127	2	no	—
414	#121	—	127	2	no	—
415	#121	—	127	1	no	—
416	#121	—	127	1	no	—
417	#121	—	127	2	no	—
418	#121	—	127	1	no	—
419	#121	—	127	1	no	—
420	#121	—	127	2	no	—
421	#121	—	127	2	no	—
422	#121	—	127	2	no	—
423	#121	—	127	2	no	—
424	#121	C₂×D₁₂₇	1	2	yes	complemented
425	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
426	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
427	C₄×D₄	—	127	2	no	—
428	C₄×D₄	—	127	1	no	—
429	C₄×D₄	—	127	1	no	—
430	C₄×D₄	—	127	2	no	—
431	C₄×D₄	—	127	2	no	—
432	C₄×D₄	—	127	1	no	—
433	C₄×D₄	—	127	2	no	—
434	C₄×D₄	—	127	1	no	—
435	C₄×D₄	—	127	2	no	—
436	C₄×D₄	—	127	1	no	—
437	C₄×D₄	—	127	1	no	—
438	C₄×D₄	—	127	2	no	—
439	C₄×D₄	—	127	2	no	—
440	C₄×D₄	—	127	1	no	—
441	C₄×D₄	—	127	2	no	—
442	C₄×D₄	—	127	1	no	—
443	C₄×D₄	—	127	2	no	—
444	C₄×D₄	—	127	1	no	—
445	C₄×D₄	—	127	1	no	—
446	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
447	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
448	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
449	#117	—	127	1	no	—
450	#117	—	127	1	no	—
451	#117	—	127	1	no	—
452	#117	—	127	2	no	—
453	#117	—	127	2	no	—
454	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	127	2	no	—
456	C₂×C₄⋊C₄	—	127	1	no	—
457	C₂×C₄⋊C₄	—	127	1	no	—
458	C₂×C₄⋊C₄	—	127	1	no	—
459	C₂×C₄⋊C₄	—	127	2	no	—
460	C₂×C₄⋊C₄	—	127	2	no	—
461	C₂×C₄⋊C₄	—	127	1	no	—
462	C₂×C₄⋊C₄	—	127	1	no	—
463	C₂×C₄⋊C₄	—	127	1	no	—
464	C₂×C₄⋊C₄	—	127	2	no	—
465	C₂×C₄⋊C₄	—	127	1	no	—
466	C₂×C₄⋊C₄	—	127	2	no	—
467	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
468	C₂×C₂²⋊C₄	—	127	2	no	—
469	C₂×C₂²⋊C₄	—	127	1	no	—
470	C₂×C₂²⋊C₄	—	127	2	no	—
471	C₂×C₂²⋊C₄	—	127	2	no	—
472	C₂×C₂²⋊C₄	—	127	1	no	—
473	C₂×C₂²⋊C₄	—	127	2	no	—
474	C₂×C₄²	—	127	2	no	—
475	C₂×C₄²	—	127	1	no	—
476	C₂⁴	—	127	1	no	—
477	C₂⁴	—	127	2	no	—
478	C₂⁴	—	127	1	no	—
479	C₂×D₄	—	127	2	no	—
480	C₂×D₄	—	127	2	no	—
481	C₂×D₄	—	127	2	no	—
482	C₂×D₄	—	127	2	no	—
483	C₂×D₄	—	127	1	no	—
484	C₂×D₄	—	127	2	no	—
485	C₂×D₄	—	127	1	no	—
486	C₂×D₄	—	127	2	no	—
487	C₂×D₄	—	127	2	no	—
488	C₂×D₄	—	127	1	no	—
489	C₂×D₄	—	127	1	no	—
490	C₂×D₄	—	508	4	no	—
491	C₂×D₄	—	254	4	no	—
492	C₂×D₄	—	254	8	no	—
493	C₂×D₄	—	254	4	no	—
494	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
495	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
498	C₂²×C₄	—	127	1	no	—
499	C₂²×C₄	—	127	2	no	—
500	C₂²×C₄	—	127	2	no	—
501	C₂²×C₄	—	127	1	no	—
502	C₂²×C₄	—	127	1	no	—
503	C₂²×C₄	—	127	2	no	—
504	C₂²×C₄	—	127	2	no	—
505	C₂²×C₄	—	127	2	no	—
506	C₂²×C₄	—	127	2	no	—
507	C₂²×C₄	—	127	1	no	—
508	C₂²×C₄	—	127	2	no	—
509	C₂²×C₄	—	127	1	no	—
510	C₂²×C₄	—	127	2	no	—
511	C₂²×C₄	—	127	1	no	—
512	C₂²×C₄	—	127	1	no	—
513	C₂²×C₄	—	127	2	no	—
514	C₂²×C₄	—	127	1	no	—
515	C₂²×C₄	—	127	1	no	—
516	C₂²×C₄	—	127	1	no	—
517	C₂²×C₄	—	127	1	no	—
518	C₂²×C₄	—	508	4	no	—
519	C₂²×C₄	—	508	4	no	—
520	C₂²×C₄	—	254	4	no	—
521	C₂²×C₄	—	254	4	no	—
522	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
525	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
526	C₄⋊C₄	—	127	2	no	—
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	2	no	—
532	C₄⋊C₄	—	127	2	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	1	no	—
539	C₄⋊C₄	—	127	2	no	—
540	C₄⋊C₄	—	127	1	no	—
541	C₄⋊C₄	—	127	2	no	—
542	C₄⋊C₄	—	127	1	no	—
543	C₄⋊C₄	—	127	2	no	—
544	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
549	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
550	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
551	C₂²⋊C₄	—	127	2	no	—
552	C₂²⋊C₄	—	127	1	no	—
553	C₂²⋊C₄	—	127	2	no	—
554	C₂²⋊C₄	—	127	2	no	—
555	C₂²⋊C₄	—	127	1	no	—
556	C₂²⋊C₄	—	127	2	no	—
557	C₂²⋊C₄	—	127	2	no	—
558	C₂²⋊C₄	—	127	2	no	—
559	C₂²⋊C₄	—	127	1	no	—
560	C₂²⋊C₄	—	127	1	no	—
561	C₂²⋊C₄	—	127	2	no	—
562	C₂²⋊C₄	—	127	2	no	—
563	C₂²⋊C₄	—	127	2	no	—
564	C₂²⋊C₄	—	127	2	no	—
565	C₂²⋊C₄	—	127	1	no	—
566	C₂²⋊C₄	—	127	1	no	—
567	C₂²⋊C₄	—	127	2	no	—
568	C₂²⋊C₄	—	127	2	no	—
569	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
575	C₄²	—	127	2	no	—
576	C₄²	—	127	2	no	—
577	C₄²	—	127	2	no	—
578	C₄²	—	127	1	no	—
579	C₄²	—	127	1	no	—
580	C₄²	—	127	1	no	—
581	C₄²	C₂²×D₁₂₇	1	2	yes	—
582	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
583	C₂³	—	127	1	no	—
584	C₂³	—	127	4	no	—
585	C₂³	—	127	1	no	—
586	C₂³	—	127	1	no	—
587	C₂³	—	127	2	no	—
588	C₂³	—	254	4	no	—
589	C₂³	—	254	2	no	—
590	C₂³	—	254	2	no	—
591	C₂³	—	254	4	no	—
592	C₂³	—	254	4	no	—
593	C₂³	—	254	2	no	—
594	C₂³	—	254	2	no	—
595	C₂³	—	254	2	no	—
596	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
597	C₂³	C₂³×D₁₂₇	1	2	yes	—
598	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
599	D₄	—	2	4	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	508	2	no	—
604	D₄	—	508	2	no	—
605	D₄	—	508	2	no	—
606	D₄	—	254	4	no	—
607	D₄	—	254	2	no	—
608	D₄	—	254	4	no	—
609	D₄	—	254	4	no	—
610	D₄	—	254	2	no	—
611	D₄	—	254	4	no	—
612	D₄	—	254	2	no	—
613	D₄	—	254	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	127	1	no	—
619	C₂×C₄	—	127	4	no	—
620	C₂×C₄	—	127	1	no	—
621	C₂×C₄	—	127	2	no	—
622	C₂×C₄	—	127	1	no	—
623	C₂×C₄	—	127	2	no	—
624	C₂×C₄	—	127	1	no	—
625	C₂×C₄	—	127	1	no	—
626	C₂×C₄	—	127	2	no	—
627	C₂×C₄	—	508	2	no	—
628	C₂×C₄	—	508	2	no	—
629	C₂×C₄	—	508	2	no	—
630	C₂×C₄	—	508	2	no	—
631	C₂×C₄	—	508	2	no	—
632	C₂×C₄	—	508	2	no	—
633	C₂×C₄	—	254	2	no	—
634	C₂×C₄	—	254	2	no	—
635	C₂×C₄	—	254	4	no	—
636	C₂×C₄	—	254	2	no	—
637	C₂×C₄	—	254	4	no	—
638	C₂×C₄	—	254	2	no	—
639	C₂×C₄	—	254	2	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	—	254	2	no	—
645	C₂×C₄	—	254	2	no	—
646	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
648	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
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	2	yes	—
653	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	127	2	no	—
663	C₂²	—	127	2	no	—
664	C₂²	—	127	2	no	—
665	C₂²	—	127	2	no	—
666	C₂²	—	508	8	no	—
667	C₂²	—	508	4	no	—
668	C₂²	—	254	8	no	—
669	C₂²	—	254	1	no	—
670	C₂²	—	254	1	no	—
671	C₂²	—	254	2	no	—
672	C₂²	—	254	2	no	—
673	C₂²	—	254	2	no	—
674	C₂²	—	254	1	no	—
675	C₂²	—	254	1	no	—
676	C₂²	—	254	1	no	—
677	C₂²	#41×D₁₂₇	1	2	yes	—
678	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	127	2	no	—
687	C₄	—	254	1	no	—
688	C₄	—	254	1	no	—
689	C₄	—	254	2	no	—
690	C₄	—	254	1	no	—
691	C₄	—	254	2	no	—
692	C₄	—	254	1	no	—
693	C₄	—	254	2	no	—
694	C₄	#41×D₁₂₇	1	2	yes	—
695	C₂	—	2	2	no	—
696	C₂	—	4	1	no	—
697	C₂	—	4	2	no	—
698	C₂	—	127	4	no	—
699	C₂	—	508	1	no	—
700	C₂	—	508	2	no	—
701	C₂	—	254	2	no	—
702	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
703	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
704	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#553×C₁₂₇	C₂
hypercenter	#553	D₁₂₇
hypocenter	C₁₂₇	C₂×#553
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #22550579	C₂	semidirect
2. #22550578	C₂	semidirect
3. #22550577	C₂	semidirect
4. #22550576	C₂	semidirect
5. #22550575	C₂	semidirect
6. #22550574	C₂	semidirect
7. #22550573	C₂	semidirect
8. #22550572	C₂	semidirect
9. #22550571	C₂	semidirect
10. #22550570	C₂	semidirect
11. #22550569	C₂	semidirect
12. #126×D₁₂₇	C₂	semidirect
13. #125×D₁₂₇	C₂	semidirect
14. #123×D₁₂₇	C₂	semidirect
15. #121×D₁₂₇	C₂	semidirect
16. #121×D₁₂₇	C₂	semidirect
17. #121×D₁₂₇	C₂	semidirect
18. C₄×D₄×D₁₂₇	C₂	semidirect
19. C₄×D₄×D₁₂₇	C₂	semidirect
20. C₄×D₄×D₁₂₇	C₂	semidirect
21. #117×D₁₂₇	C₂	semidirect
22. C₂×C₄⋊C₄×D₁₂₇	C₂	semidirect
23. #553×C₁₂₇	C₂	semidirect
32. #16861204	C₂²	semidirect
33. #16861204	C₂²	semidirect
34. #16861204	C₂²	semidirect
35. #16861203	C₂²	semidirect
36. #16861202	C₂²	semidirect
37. #16861202	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861201	C₂²	semidirect
40. #16861200	C₂²	semidirect
41. #16861200	C₂²	semidirect
42. #16861199	C₂²	semidirect
43. #16861199	C₂²	semidirect
44. #16861194	C₂²	semidirect
45. #16861194	C₂²	semidirect
46. #16861193	C₂²	semidirect
47. #16861192	C₂²	semidirect
48. #16861191	C₂²	semidirect
49. #16861191	C₂²	semidirect
50. #16861190	C₂²	semidirect
51. #16861184	C₂²	semidirect
52. #16861184	C₂²	semidirect
53. #16861184	C₂²	semidirect
54. #16861183	C₂²	semidirect
55. #16861183	C₂²	semidirect
56. #16861183	C₂²	semidirect
57. #16861182	C₂²	semidirect
58. #16861182	C₂²	semidirect
59. #16861182	C₂²	semidirect
60. #16861182	C₂²	semidirect
61. #16861181	C₂²	semidirect
62. #16861181	C₂²	semidirect
63. #16861181	C₂²	semidirect
64. #16861181	C₂²	semidirect
65. #16861180	C₂²	semidirect
66. #16861180	C₂²	semidirect
67. #16861180	C₂²	semidirect
68. C₄×D₅₀₈	C₂²	semidirect
69. C₄×D₅₀₈	C₂²	semidirect
70. C₄×D₅₀₈	C₂²	semidirect
71. D₄×Dic₁₂₇	C₂²	semidirect
72. D₄×Dic₁₂₇	C₂²	semidirect
73. D₄×Dic₁₂₇	C₂²	semidirect
74. #16861171	C₂²	semidirect
75. #16861171	C₂²	semidirect
76. #16861171	C₂²	semidirect
77. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
78. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
79. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
80. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
81. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
82. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
83. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
84. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
85. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
86. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
87. #16861168	C₂²	semidirect
88. #16861167	C₂²	semidirect
89. #16861167	C₂²	semidirect
90. #16861166	C₂²	semidirect
91. #16861165	C₂²	semidirect
92. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
93. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
101. C₄⋊C₄×D₁₂₇	C₂²	semidirect
102. C₄⋊C₄×D₁₂₇	C₂²	semidirect
103. C₄⋊C₄×D₁₂₇	C₂²	semidirect
112. #126×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
114. #123×C₁₂₇	C₂²	semidirect
115. #121×C₁₂₇	C₂²	semidirect
116. #121×C₁₂₇	C₂²	semidirect
117. #121×C₁₂₇	C₂²	semidirect
118. C₄×D₄×C₁₂₇	C₂²	semidirect
119. C₄×D₄×C₁₂₇	C₂²	semidirect
120. C₄×D₄×C₁₂₇	C₂²	semidirect
121. #117×C₁₂₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
351. D₁₂₇	#553	direct (N × H)
353. C₁₂₇	C₂×#553	semidirect
365. #553	D₁₂₇	direct (N × H)
392. #126	C₂×D₁₂₇	semidirect
398. #125	C₂×D₁₂₇	semidirect
406. #123	C₂×D₁₂₇	semidirect
424. #121	C₂×D₁₂₇	semidirect
425. #121	C₂×D₁₂₇	semidirect
426. #121	C₂×D₁₂₇	semidirect
446. C₄×D₄	C₂×D₁₂₇	semidirect
447. C₄×D₄	C₂×D₁₂₇	semidirect
448. C₄×D₄	C₂×D₁₂₇	semidirect
454. #117	C₂×D₁₂₇	semidirect
467. 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
#22550579	2
#22550578	2
#22550577	2
#22550576	2
#22550575	2
#22550574	2
#22550573	2
#22550572	2
#22550571	2
#22550570	2
#22550569	2
#126×D₁₂₇	2
#125×D₁₂₇	2
#123×D₁₂₇	2
#121×D₁₂₇	2
C₄×D₄×D₁₂₇	2
#117×D₁₂₇	2
C₂×C₄⋊C₄×D₁₂₇	2
#553×C₁₂₇	2
C₂×#553	127

Subgroups — #553×D127 #30652245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #553×D₁₂₇ #30652245