Subgroups — C₄×#470×C₁₂₇ #44585207

Order 32512.

1002 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#470×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂²⋊Q₈×C₁₂₇	C₂	1	2	yes	maximal
5	C₁₂₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₂₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1935	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1894	C₂	1	2	yes	maximal
9	C₁₂₇×#1809	C₂	1	1	yes	maximal, characteristic
10	C₄×#106×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₁₂₇	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₂₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
18	#470×C₁₂₇	C₄	1	8	yes	direct product factor
19	C₄×Q₁₆×C₁₂₇	—	2	4	no	—
20	C₂×#107×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₁₂₇	C₂²	1	2	yes	—
24	C₂×#103×C₁₂₇	C₂²	1	2	yes	—
25	C₂×#103×C₁₂₇	C₂²	1	2	yes	—
26	C₄×M₁₆×C₁₂₇	—	2	4	no	—
27	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
28	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
31	#391×C₁₂₇	C₂²	1	2	yes	—
32	#389×C₁₂₇	C₂²	1	2	yes	—
33	#387×C₁₂₇	—	2	2	no	—
34	#385×C₁₂₇	—	2	2	no	—
35	#380×C₁₂₇	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₂₇	—	2	2	no	—
37	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
39	#340×C₁₂₇	C₂²	1	2	yes	—
40	#340×C₁₂₇	C₂²	1	2	yes	—
41	#340×C₁₂₇	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₂₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₂₇	—	2	2	no	—
47	C₂×Q₁₆×C₁₂₇	—	2	2	no	—
48	C₂×Q₁₆×C₁₂₇	C₂×C₄	1	4	yes	complemented
49	C₂×M₁₆×C₁₂₇	—	2	2	no	—
50	C₂×M₁₆×C₁₂₇	—	2	2	no	—
51	C₂×M₁₆×C₁₂₇	—	2	2	no	—
52	C₂×M₁₆×C₁₂₇	—	2	2	no	—
53	C₂×M₁₆×C₁₂₇	—	2	2	no	—
54	C₂×M₁₆×C₁₂₇	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
59	C₂²⋊Q₈×C₁₂₇	—	2	4	no	—
60	C₂²⋊Q₈×C₁₂₇	C₂×C₄	1	8	yes	—
61	C₄×Q₈×C₁₂₇	—	2	4	no	—
62	C₄×Q₈×C₁₂₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
71	C₂×C₄²×C₁₂₇	—	2	2	no	—
72	C₂×C₄²×C₁₂₇	—	2	2	no	—
73	C₂×C₄²×C₁₂₇	—	2	2	no	—
74	C₂×C₄²×C₁₂₇	—	2	2	no	—
75	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₂₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
79	#107×C₁₂₇	—	2	2	no	—
80	#106×C₁₂₇	—	2	2	no	—
81	#106×C₁₂₇	C₂×C₄	1	4	yes	complemented
82	#103×C₁₂₇	—	2	4	no	—
83	#103×C₁₂₇	—	2	4	no	—
84	#103×C₁₂₇	C₂×C₄	1	8	yes	complemented
85	#97×C₁₂₇	—	2	2	no	—
86	#97×C₁₂₇	—	2	2	no	—
87	C₄×C₈×C₁₂₇	—	2	2	no	—
88	C₄×C₈×C₁₂₇	D₄	1	4	yes	—
89	#95×C₁₂₇	—	2	2	no	—
90	#95×C₁₂₇	—	2	2	no	—
91	#95×C₁₂₇	—	2	2	no	—
92	#95×C₁₂₇	—	2	2	no	—
93	#95×C₁₂₇	—	2	2	no	—
94	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₂₇	—	2	2	no	—
96	C₂×Q₈×C₁₂₇	—	2	2	no	—
97	C₂×Q₈×C₁₂₇	—	2	2	no	—
98	C₂×Q₈×C₁₂₇	—	2	2	no	—
99	C₂×Q₈×C₁₂₇	—	2	2	no	—
100	C₂×Q₈×C₁₂₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₂₇	—	2	1	no	—
102	C₂²×C₄×C₁₂₇	—	2	1	no	—
103	C₂²×C₄×C₁₂₇	—	2	1	no	—
104	C₂²×C₄×C₁₂₇	—	2	1	no	—
105	C₂²×C₄×C₁₂₇	—	2	2	no	—
106	C₂²×C₄×C₁₂₇	—	2	2	no	—
107	C₂²×C₄×C₁₂₇	—	2	2	no	—
108	C₂²×C₄×C₁₂₇	—	2	2	no	—
109	C₂²×C₄×C₁₂₇	—	2	4	no	—
110	C₂²×C₄×C₁₂₇	—	2	2	no	—
111	C₂²×C₄×C₁₂₇	—	2	2	no	—
112	C₂²×C₄×C₁₂₇	—	4	2	no	—
113	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
120	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
121	Q₁₆×C₁₂₇	—	2	8	no	—
122	M₁₆×C₁₂₇	—	2	8	no	—
123	M₁₆×C₁₂₇	—	2	8	no	—
124	C₂×C₈×C₁₂₇	—	2	1	no	—
125	C₂×C₈×C₁₂₇	—	2	1	no	—
126	C₂×C₈×C₁₂₇	—	2	1	no	—
127	C₂×C₈×C₁₂₇	—	2	1	no	—
128	C₂×C₈×C₁₂₇	—	2	1	no	—
129	C₂×C₈×C₁₂₇	—	2	1	no	—
130	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₂₇	#41	1	2	yes	—
135	C₂×C₈×C₁₂₇	#41	1	2	yes	—
136	C₄⋊C₄×C₁₂₇	—	2	8	no	—
137	C₄⋊C₄×C₁₂₇	—	2	2	no	—
138	C₄⋊C₄×C₁₂₇	—	2	2	no	—
139	C₄⋊C₄×C₁₂₇	—	2	2	no	—
140	C₄⋊C₄×C₁₂₇	—	2	2	no	—
141	C₄⋊C₄×C₁₂₇	—	2	2	no	—
142	C₄⋊C₄×C₁₂₇	—	4	4	no	—
143	C₄⋊C₄×C₁₂₇	—	4	4	no	—
144	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₁₂₇	—	2	8	no	—
146	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
147	C₄²×C₁₂₇	—	2	2	no	—
148	C₄²×C₁₂₇	—	2	2	no	—
149	C₄²×C₁₂₇	—	2	1	no	—
150	C₄²×C₁₂₇	—	2	1	no	—
151	C₄²×C₁₂₇	—	4	4	no	—
152	C₄²×C₁₂₇	—	4	4	no	—
153	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
154	C₄²×C₁₂₇	#41	1	2	yes	—
155	C₂³×C₁₂₇	—	2	1	no	—
156	C₂³×C₁₂₇	—	2	1	no	—
157	C₂³×C₁₂₇	—	2	2	no	—
158	C₂³×C₁₂₇	—	2	2	no	—
159	C₂³×C₁₂₇	C₄×D₄	1	2	yes	—
160	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₁₂₇	—	2	4	no	—
162	Q₈×C₁₂₇	—	2	4	no	—
163	Q₈×C₁₂₇	—	4	2	no	—
164	Q₈×C₁₂₇	—	4	2	no	—
165	C₂×C₄×C₁₂₇	—	2	1	no	—
166	C₂×C₄×C₁₂₇	—	2	1	no	—
167	C₂×C₄×C₁₂₇	—	2	2	no	—
168	C₂×C₄×C₁₂₇	—	2	2	no	—
169	C₂×C₄×C₁₂₇	—	2	2	no	—
170	C₂×C₄×C₁₂₇	—	2	2	no	—
171	C₂×C₄×C₁₂₇	—	2	2	no	—
172	C₂×C₄×C₁₂₇	—	2	4	no	—
173	C₂×C₄×C₁₂₇	—	2	4	no	—
174	C₂×C₄×C₁₂₇	—	2	1	no	—
175	C₂×C₄×C₁₂₇	—	2	1	no	—
176	C₂×C₄×C₁₂₇	—	2	2	no	—
177	C₂×C₄×C₁₂₇	—	2	2	no	—
178	C₂×C₄×C₁₂₇	—	4	4	no	—
179	C₂×C₄×C₁₂₇	—	4	2	no	—
180	C₂×C₄×C₁₂₇	—	4	2	no	—
181	C₂×C₄×C₁₂₇	—	4	2	no	—
182	C₂×C₄×C₁₂₇	—	4	2	no	—
183	C₂×C₄×C₁₂₇	—	4	4	no	—
184	C₂×C₄×C₁₂₇	—	4	2	no	—
185	C₂×C₄×C₁₂₇	—	4	2	no	—
186	C₂×C₄×C₁₂₇	—	4	2	no	—
187	C₂×C₄×C₁₂₇	—	4	2	no	—
188	C₂×C₄×C₁₂₇	—	4	2	no	—
189	C₂×C₄×C₁₂₇	—	4	2	no	—
190	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₂₇	#121	1	2	yes	—
192	C₂×C₄×C₁₂₇	#121	1	2	yes	—
193	C₂×C₄×C₁₂₇	#137	1	4	yes	—
194	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
200	C₈×C₁₂₇	—	2	2	no	—
201	C₈×C₁₂₇	—	2	2	no	—
202	C₈×C₁₂₇	—	2	2	no	—
203	C₈×C₁₂₇	C₄×D₄	1	4	yes	—
204	C₂²×C₁₂₇	—	2	4	no	—
205	C₂²×C₁₂₇	—	2	2	no	—
206	C₂²×C₁₂₇	—	4	2	no	—
207	C₂²×C₁₂₇	—	4	1	no	—
208	C₂²×C₁₂₇	—	4	1	no	—
209	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₁₂₇	C₂×#121	1	1	yes	characteristic
211	C₂²×C₁₂₇	#532	1	1	yes	characteristic
212	C₂²×C₁₂₇	C₂×#137	1	2	yes	—
213	C₂²×C₁₂₇	#575	1	2	yes	—
214	C₄×C₁₂₇	—	2	2	no	—
215	C₄×C₁₂₇	—	2	2	no	—
216	C₄×C₁₂₇	—	4	4	no	—
217	C₄×C₁₂₇	—	4	1	no	—
218	C₄×C₁₂₇	—	4	1	no	—
219	C₄×C₁₂₇	—	4	4	no	—
220	C₄×C₁₂₇	—	8	2	no	—
221	C₄×C₁₂₇	—	8	2	no	—
222	C₄×C₁₂₇	#470	1	4	yes	direct product factor
223	C₄×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
225	C₄×C₁₂₇	#525	1	1	yes	characteristic
226	C₄×C₁₂₇	#529	1	1	yes	characteristic
227	C₄×#470	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₁₂₇	—	4	2	no	—
229	C₂×C₁₂₇	C₄×#121	1	1	yes	characteristic
230	C₂×C₁₂₇	C₄×#137	1	2	yes	—
231	C₂×C₁₂₇	C₂×#470	1	1	yes	characteristic
232	C₂×C₁₂₇	#3054	1	1	yes	characteristic
233	C₂×C₁₂₇	#3172	1	2	yes	—
234	C₂×#470	C₂×C₁₂₇	1	1	yes	characteristic
235	C₂×C₄×Q₁₆	C₂×C₁₂₇	1	1	yes	characteristic, complemented
236	C₂×C₄×M₁₆	C₂×C₁₂₇	1	1	yes	characteristic
237	C₄×C₂²⋊Q₈	C₂×C₁₂₇	1	2	yes	—
238	#1971	C₂×C₁₂₇	1	1	yes	characteristic, complemented
239	#1944	C₂×C₁₂₇	1	1	yes	characteristic, complemented
240	#1935	C₂×C₁₂₇	1	2	yes	complemented
241	#1894	C₂×C₁₂₇	1	2	yes	—
242	#1809	C₂×C₁₂₇	1	1	yes	characteristic
243	C₄×#106	C₂×C₁₂₇	1	1	yes	characteristic, complemented
244	C₄×#103	C₂×C₁₂₇	1	2	yes	complemented
245	C₁₂₇	C₄×#470	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₁₂₇	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₁₂₇	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₁₂₇	1	2	yes	—
251	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
252	#470	C₄×C₁₂₇	1	8	yes	direct product factor
253	C₄×Q₁₆	—	2	4	no	—
254	C₂×#107	C₂²×C₁₂₇	1	1	yes	characteristic
255	C₂×#106	C₂²×C₁₂₇	1	1	yes	characteristic
256	C₂×#106	C₂²×C₁₂₇	1	1	yes	characteristic
257	C₂×#103	C₂²×C₁₂₇	1	2	yes	—
258	C₂×#103	C₂²×C₁₂₇	1	2	yes	—
259	C₂×#103	C₂²×C₁₂₇	1	2	yes	—
260	C₄×M₁₆	—	2	4	no	—
261	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
262	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
265	#391	C₂²×C₁₂₇	1	2	yes	—
266	#389	C₂²×C₁₂₇	1	2	yes	—
267	#387	—	2	2	no	—
268	#385	—	2	2	no	—
269	#380	C₂²×C₁₂₇	1	2	yes	—
270	C₄×C₄⋊C₄	—	2	2	no	—
271	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
272	C₄×C₂²⋊C₄	—	2	2	no	—
273	#340	C₂²×C₁₂₇	1	2	yes	—
274	#340	C₂²×C₁₂₇	1	2	yes	—
275	#340	C₂²×C₁₂₇	1	2	yes	—
276	C₂²×Q₈	C₂³×C₁₂₇	1	2	yes	—
277	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
278	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
280	C₂×Q₁₆	—	2	2	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	C₂×C₄×C₁₂₇	1	4	yes	complemented
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	C₂×C₄×C₁₂₇	1	4	yes	—
289	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	C₂×C₄×C₁₂₇	1	8	yes	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
310	C₂×C₄²	D₄×C₁₂₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
313	#107	—	2	2	no	—
314	#106	—	2	2	no	—
315	#106	C₂×C₄×C₁₂₇	1	4	yes	complemented
316	#103	—	2	4	no	—
317	#103	—	2	4	no	—
318	#103	C₂×C₄×C₁₂₇	1	8	yes	complemented
319	#97	—	2	2	no	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	D₄×C₁₂₇	1	4	yes	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²×C₄×C₁₂₇	1	4	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
353	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
355	Q₁₆	—	2	8	no	—
356	M₁₆	—	2	8	no	—
357	M₁₆	—	2	8	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
365	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
366	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
367	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
368	C₂×C₈	#41×C₁₂₇	1	2	yes	—
369	C₂×C₈	#41×C₁₂₇	1	2	yes	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	4	4	no	—
386	C₄²	—	4	4	no	—
387	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
388	C₄²	#41×C₁₂₇	1	2	yes	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₄×D₄×C₁₂₇	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
425	C₂×C₄	#121×C₁₂₇	1	2	yes	—
426	C₂×C₄	#121×C₁₂₇	1	2	yes	—
427	C₂×C₄	#137×C₁₂₇	1	4	yes	—
428	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	2	no	—
437	C₈	C₄×D₄×C₁₂₇	1	4	yes	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
444	C₂²	C₂×#121×C₁₂₇	1	1	yes	characteristic
445	C₂²	#532×C₁₂₇	1	1	yes	characteristic
446	C₂²	C₂×#137×C₁₂₇	1	2	yes	—
447	C₂²	#575×C₁₂₇	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	4	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	2	no	—
456	C₄	#470×C₁₂₇	1	4	yes	direct product factor
457	C₄	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
458	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
459	C₄	#525×C₁₂₇	1	1	yes	characteristic
460	C₄	#529×C₁₂₇	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	C₄×#121×C₁₂₇	1	1	yes	characteristic
463	C₂	C₄×#137×C₁₂₇	1	2	yes	—
464	C₂	C₂×#470×C₁₂₇	1	1	yes	characteristic
465	C₂	C₁₂₇×#3054	1	1	yes	characteristic
466	C₂	C₁₂₇×#3172	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂²×D₄
prime radical	C₂⁴×C₁₂₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₂₇ ◁ C₂²×C₄²×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1971	C₂	semidirect
6. C₁₂₇×#1944	C₂	semidirect
7. C₁₂₇×#1935	C₂	semidirect
10. C₄×#106×C₁₂₇	C₂	semidirect
11. C₄×#103×C₁₂₇	C₂	semidirect
18. #470×C₁₂₇	C₄	direct (N × H)
48. C₂×Q₁₆×C₁₂₇	C₂×C₄	semidirect
81. #106×C₁₂₇	C₂×C₄	semidirect
84. #103×C₁₂₇	C₂×C₄	semidirect
222. C₄×C₁₂₇	#470	direct (N × H)
227. C₄×#470	C₁₂₇	direct (N × H)
235. C₂×C₄×Q₁₆	C₂×C₁₂₇	semidirect
238. #1971	C₂×C₁₂₇	semidirect
239. #1944	C₂×C₁₂₇	semidirect
240. #1935	C₂×C₁₂₇	semidirect
243. C₄×#106	C₂×C₁₂₇	semidirect
244. C₄×#103	C₂×C₁₂₇	semidirect
245. C₁₂₇	C₄×#470	direct (N × H)
252. #470	C₄×C₁₂₇	direct (N × H)
282. C₂×Q₁₆	C₂×C₄×C₁₂₇	semidirect
315. #106	C₂×C₄×C₁₂₇	semidirect
318. #103	C₂×C₄×C₁₂₇	semidirect
456. C₄	#470×C₁₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#470×C₁₂₇	2
C₂×C₄×Q₁₆×C₁₂₇	2
C₂×C₄×M₁₆×C₁₂₇	2
C₄×C₂²⋊Q₈×C₁₂₇	2
C₁₂₇×#1971	2
C₁₂₇×#1944	2
C₁₂₇×#1935	2
C₁₂₇×#1894	2
C₁₂₇×#1809	2
C₄×#106×C₁₂₇	2
C₄×#103×C₁₂₇	2
C₄×#470	127

Subgroups — C4×#470×C127 #44585207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#470×C₁₂₇ #44585207