Subgroups — C₁₂₇×#21652 #44585325

Order 32512.

882 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#490×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₂₇×#2328	C₂	1	1	yes	maximal, characteristic
4	C₁₂₇×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1957	C₂	1	1	yes	maximal, characteristic
6	C₁₂₇×#1936	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1934	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1836	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1762	C₂	1	2	yes	maximal, complemented
10	C₄×#102×C₁₂₇	C₂	1	2	yes	maximal, complemented
11	C₁₂₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₂₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
15	#490×C₁₂₇	C₄	1	8	yes	complemented
16	C₂×#102×C₁₂₇	C₂²	1	2	yes	—
17	C₂×#102×C₁₂₇	C₂²	1	2	yes	—
18	C₂×#102×C₁₂₇	C₂²	1	2	yes	—
19	C₂×#102×C₁₂₇	C₂²	1	2	yes	—
20	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
26	#390×C₁₂₇	C₂²	1	2	yes	—
27	#389×C₁₂₇	—	2	2	no	—
28	#389×C₁₂₇	C₂²	1	2	yes	—
29	#387×C₁₂₇	—	2	2	no	—
30	#386×C₁₂₇	—	2	2	no	—
31	#386×C₁₂₇	—	2	2	no	—
32	#384×C₁₂₇	C₂²	1	1	yes	characteristic
33	#382×C₁₂₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
35	#376×C₁₂₇	C₂²	1	1	yes	characteristic
36	#340×C₁₂₇	C₂²	1	2	yes	—
37	#340×C₁₂₇	C₂²	1	2	yes	—
38	#340×C₁₂₇	C₂²	1	2	yes	—
39	#340×C₁₂₇	C₂²	1	2	yes	—
40	C₂²×D₄×C₁₂₇	—	2	2	no	—
41	C₂²×D₄×C₁₂₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₂₇	—	2	2	no	—
43	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
47	#127×C₁₂₇	—	2	2	no	—
48	#127×C₁₂₇	C₂×C₄	1	4	yes	—
49	#125×C₁₂₇	—	2	2	no	—
50	#125×C₁₂₇	C₂×C₄	1	4	yes	complemented
51	C₄×D₄×C₁₂₇	—	2	4	no	—
52	C₄×D₄×C₁₂₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₂₇	—	2	2	no	—
62	C₂×C₄²×C₁₂₇	—	2	2	no	—
63	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
66	#102×C₁₂₇	—	2	4	no	—
67	#102×C₁₂₇	—	2	4	no	—
68	#102×C₁₂₇	C₂×C₄	1	8	yes	complemented
69	#102×C₁₂₇	C₂×C₄	1	8	yes	complemented
70	#97×C₁₂₇	—	2	2	no	—
71	#97×C₁₂₇	—	2	2	no	—
72	#97×C₁₂₇	C₂×C₄	1	4	yes	complemented
73	C₄×C₈×C₁₂₇	—	2	2	no	—
74	C₄×C₈×C₁₂₇	—	2	2	no	—
75	C₄×C₈×C₁₂₇	—	2	2	no	—
76	#95×C₁₂₇	—	2	2	no	—
77	#95×C₁₂₇	—	2	2	no	—
78	#95×C₁₂₇	—	2	2	no	—
79	#95×C₁₂₇	D₄	1	2	yes	—
80	#95×C₁₂₇	D₄	1	2	yes	—
81	C₂⁴×C₁₂₇	—	2	2	no	—
82	C₂×D₄×C₁₂₇	—	2	8	no	—
83	C₂×D₄×C₁₂₇	—	2	2	no	—
84	C₂×D₄×C₁₂₇	—	2	2	no	—
85	C₂×D₄×C₁₂₇	—	2	2	no	—
86	C₂×D₄×C₁₂₇	—	2	2	no	—
87	C₂×D₄×C₁₂₇	—	2	2	no	—
88	C₂×D₄×C₁₂₇	—	8	2	no	—
89	C₂×D₄×C₁₂₇	—	8	2	no	—
90	C₂×D₄×C₁₂₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₂₇	—	2	2	no	—
92	C₂²×C₄×C₁₂₇	—	2	2	no	—
93	C₂²×C₄×C₁₂₇	—	2	2	no	—
94	C₂²×C₄×C₁₂₇	—	4	4	no	—
95	C₂²×C₄×C₁₂₇	—	8	2	no	—
96	C₂²×C₄×C₁₂₇	—	8	2	no	—
97	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₁₂₇	—	2	1	no	—
103	C₂×C₈×C₁₂₇	—	2	1	no	—
104	C₂×C₈×C₁₂₇	—	2	1	no	—
105	C₂×C₈×C₁₂₇	—	2	1	no	—
106	C₂×C₈×C₁₂₇	—	2	1	no	—
107	C₂×C₈×C₁₂₇	—	2	1	no	—
108	C₂×C₈×C₁₂₇	—	2	1	no	—
109	C₂×C₈×C₁₂₇	—	2	1	no	—
110	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₁₂₇	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₂₇	#41	1	2	yes	—
113	C₂×C₈×C₁₂₇	#41	1	2	yes	—
114	C₄⋊C₄×C₁₂₇	—	2	8	no	—
115	C₄⋊C₄×C₁₂₇	—	2	2	no	—
116	C₄⋊C₄×C₁₂₇	—	2	2	no	—
117	C₄⋊C₄×C₁₂₇	—	2	2	no	—
118	C₄⋊C₄×C₁₂₇	—	2	2	no	—
119	C₄⋊C₄×C₁₂₇	—	2	2	no	—
120	C₄⋊C₄×C₁₂₇	—	8	2	no	—
121	C₄⋊C₄×C₁₂₇	—	8	2	no	—
122	C₄⋊C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
124	C₂²⋊C₄×C₁₂₇	—	8	2	no	—
125	C₂²⋊C₄×C₁₂₇	—	8	2	no	—
126	C₄²×C₁₂₇	—	2	1	no	—
127	C₄²×C₁₂₇	—	2	1	no	—
128	C₄²×C₁₂₇	—	8	2	no	—
129	C₄²×C₁₂₇	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₂₇	#41	1	2	yes	—
131	C₄²×C₁₂₇	#41	1	2	yes	—
132	C₄²×C₁₂₇	#41	1	2	yes	—
133	C₂³×C₁₂₇	—	2	4	no	—
134	C₂³×C₁₂₇	—	4	2	no	—
135	C₂³×C₁₂₇	—	4	2	no	—
136	C₂³×C₁₂₇	—	4	2	no	—
137	C₂³×C₁₂₇	—	4	2	no	—
138	C₂³×C₁₂₇	—	4	2	no	—
139	C₂³×C₁₂₇	—	4	2	no	—
140	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₁₂₇	—	2	4	no	—
142	D₄×C₁₂₇	—	2	4	no	—
143	D₄×C₁₂₇	—	4	2	no	—
144	D₄×C₁₂₇	—	4	2	no	—
145	D₄×C₁₂₇	—	8	8	no	—
146	C₂×C₄×C₁₂₇	—	2	2	no	—
147	C₂×C₄×C₁₂₇	—	2	2	no	—
148	C₂×C₄×C₁₂₇	—	2	2	no	—
149	C₂×C₄×C₁₂₇	—	2	2	no	—
150	C₂×C₄×C₁₂₇	—	2	4	no	—
151	C₂×C₄×C₁₂₇	—	2	1	no	—
152	C₂×C₄×C₁₂₇	—	2	1	no	—
153	C₂×C₄×C₁₂₇	—	2	2	no	—
154	C₂×C₄×C₁₂₇	—	2	2	no	—
155	C₂×C₄×C₁₂₇	—	4	2	no	—
156	C₂×C₄×C₁₂₇	—	4	2	no	—
157	C₂×C₄×C₁₂₇	—	4	2	no	—
158	C₂×C₄×C₁₂₇	—	4	2	no	—
159	C₂×C₄×C₁₂₇	—	4	2	no	—
160	C₂×C₄×C₁₂₇	—	4	2	no	—
161	C₂×C₄×C₁₂₇	—	4	2	no	—
162	C₂×C₄×C₁₂₇	—	4	2	no	—
163	C₂×C₄×C₁₂₇	—	8	8	no	—
164	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
165	C₂×C₄×C₁₂₇	#124	1	4	yes	—
166	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
172	C₈×C₁₂₇	—	2	2	no	—
173	C₈×C₁₂₇	—	2	2	no	—
174	C₈×C₁₂₇	—	2	2	no	—
175	C₈×C₁₂₇	—	2	2	no	—
176	C₂²×C₁₂₇	—	4	4	no	—
177	C₂²×C₁₂₇	—	4	4	no	—
178	C₂²×C₁₂₇	—	4	4	no	—
179	C₂²×C₁₂₇	—	8	2	no	—
180	C₂²×C₁₂₇	—	8	2	no	—
181	C₂²×C₁₂₇	—	8	2	no	—
182	C₂²×C₁₂₇	—	8	2	no	—
183	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₁₂₇	C₂×#124	1	1	yes	characteristic
185	C₂²×C₁₂₇	#532	1	1	yes	characteristic
186	C₂²×C₁₂₇	#576	1	2	yes	—
187	C₂²×C₁₂₇	#577	1	2	yes	—
188	C₄×C₁₂₇	—	2	4	no	—
189	C₄×C₁₂₇	—	2	4	no	—
190	C₄×C₁₂₇	—	4	1	no	—
191	C₄×C₁₂₇	—	4	1	no	—
192	C₄×C₁₂₇	—	4	4	no	—
193	C₄×C₁₂₇	—	8	2	no	—
194	C₄×C₁₂₇	—	8	2	no	—
195	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
196	C₄×C₁₂₇	C₄×#41	1	1	yes	characteristic
197	C₄×C₁₂₇	#529	1	1	yes	characteristic
198	C₄×C₁₂₇	#529	1	1	yes	characteristic
199	#21652	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₁₂₇	—	8	4	no	—
201	C₂×C₁₂₇	C₄×#124	1	1	yes	characteristic
202	C₂×C₁₂₇	#2946	1	2	yes	—
203	C₂×C₁₂₇	#3136	1	2	yes	—
204	C₂×C₁₂₇	#3174	1	1	yes	characteristic
205	C₂×C₁₂₇	#3176	1	1	yes	characteristic
206	C₂×#490	C₂×C₁₂₇	1	1	yes	characteristic
207	#2330	C₂×C₁₂₇	1	1	yes	characteristic, complemented
208	#2328	C₂×C₁₂₇	1	1	yes	characteristic
209	#1991	C₂×C₁₂₇	1	1	yes	characteristic, complemented
210	#1957	C₂×C₁₂₇	1	1	yes	characteristic
211	#1936	C₂×C₁₂₇	1	2	yes	complemented
212	#1934	C₂×C₁₂₇	1	2	yes	complemented
213	#1836	C₂×C₁₂₇	1	1	yes	characteristic, complemented
214	#1762	C₂×C₁₂₇	1	2	yes	complemented
215	C₄×#102	C₂×C₁₂₇	1	2	yes	complemented
216	#1726	C₂×C₁₂₇	1	1	yes	characteristic, complemented
217	C₁₂₇	#21652	1	1	yes	characteristic, direct product factor, Sylow
218	C₂×#127	C₂²×C₁₂₇	1	1	yes	characteristic
219	C₂×#125	C₂²×C₁₂₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
221	#490	C₄×C₁₂₇	1	8	yes	complemented
222	C₂×#102	C₂²×C₁₂₇	1	2	yes	—
223	C₂×#102	C₂²×C₁₂₇	1	2	yes	—
224	C₂×#102	C₂²×C₁₂₇	1	2	yes	—
225	C₂×#102	C₂²×C₁₂₇	1	2	yes	—
226	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
227	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
228	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
232	#390	C₂²×C₁₂₇	1	2	yes	—
233	#389	—	2	2	no	—
234	#389	C₂²×C₁₂₇	1	2	yes	—
235	#387	—	2	2	no	—
236	#386	—	2	2	no	—
237	#386	—	2	2	no	—
238	#384	C₂²×C₁₂₇	1	1	yes	characteristic
239	#382	C₂²×C₁₂₇	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
241	#376	C₂²×C₁₂₇	1	1	yes	characteristic
242	#340	C₂²×C₁₂₇	1	2	yes	—
243	#340	C₂²×C₁₂₇	1	2	yes	—
244	#340	C₂²×C₁₂₇	1	2	yes	—
245	#340	C₂²×C₁₂₇	1	2	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₁₂₇	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
253	#127	—	2	2	no	—
254	#127	C₂×C₄×C₁₂₇	1	4	yes	—
255	#125	—	2	2	no	—
256	#125	C₂×C₄×C₁₂₇	1	4	yes	complemented
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
272	#102	—	2	4	no	—
273	#102	—	2	4	no	—
274	#102	C₂×C₄×C₁₂₇	1	8	yes	complemented
275	#102	C₂×C₄×C₁₂₇	1	8	yes	complemented
276	#97	—	2	2	no	—
277	#97	—	2	2	no	—
278	#97	C₂×C₄×C₁₂₇	1	4	yes	complemented
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	D₄×C₁₂₇	1	2	yes	—
286	#95	D₄×C₁₂₇	1	2	yes	—
287	C₂⁴	—	2	2	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	8	2	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	C₂²×C₄×C₁₂₇	1	4	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	8	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₁₂₇	1	2	yes	—
318	C₂×C₈	#41×C₁₂₇	1	2	yes	—
319	C₂×C₈	#41×C₁₂₇	1	2	yes	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₄⋊C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂²×C₄×C₁₂₇	1	2	yes	—
336	C₄²	#41×C₁₂₇	1	2	yes	—
337	C₄²	#41×C₁₂₇	1	2	yes	—
338	C₄²	#41×C₁₂₇	1	2	yes	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
347	D₄	—	2	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	8	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	8	no	—
370	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
371	C₂×C₄	#124×C₁₂₇	1	4	yes	—
372	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
390	C₂²	C₂×#124×C₁₂₇	1	1	yes	characteristic
391	C₂²	#532×C₁₂₇	1	1	yes	characteristic
392	C₂²	#576×C₁₂₇	1	2	yes	—
393	C₂²	#577×C₁₂₇	1	2	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
402	C₄	C₄×#41×C₁₂₇	1	1	yes	characteristic
403	C₄	#529×C₁₂₇	1	1	yes	characteristic
404	C₄	#529×C₁₂₇	1	1	yes	characteristic
405	C₂	—	8	4	no	—
406	C₂	C₄×#124×C₁₂₇	1	1	yes	characteristic
407	C₂	C₁₂₇×#2946	1	2	yes	—
408	C₂	C₁₂₇×#3136	1	2	yes	—
409	C₂	C₁₂₇×#3174	1	1	yes	characteristic
410	C₂	C₁₂₇×#3176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₂₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
prime radical	C₂×#127×C₁₂₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₂₇ ◁ #376×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₂₇×#2330	C₂	semidirect
4. C₁₂₇×#1991	C₂	semidirect
6. C₁₂₇×#1936	C₂	semidirect
7. C₁₂₇×#1934	C₂	semidirect
8. C₁₂₇×#1836	C₂	semidirect
9. C₁₂₇×#1762	C₂	semidirect
10. C₄×#102×C₁₂₇	C₂	semidirect
11. C₁₂₇×#1726	C₂	semidirect
15. #490×C₁₂₇	C₄	semidirect
50. #125×C₁₂₇	C₂×C₄	semidirect
68. #102×C₁₂₇	C₂×C₄	semidirect
69. #102×C₁₂₇	C₂×C₄	semidirect
72. #97×C₁₂₇	C₂×C₄	semidirect
199. #21652	C₁₂₇	direct (N × H)
207. #2330	C₂×C₁₂₇	semidirect
209. #1991	C₂×C₁₂₇	semidirect
211. #1936	C₂×C₁₂₇	semidirect
212. #1934	C₂×C₁₂₇	semidirect
213. #1836	C₂×C₁₂₇	semidirect
214. #1762	C₂×C₁₂₇	semidirect
215. C₄×#102	C₂×C₁₂₇	semidirect
216. #1726	C₂×C₁₂₇	semidirect
217. C₁₂₇	#21652	direct (N × H)
221. #490	C₄×C₁₂₇	semidirect
256. #125	C₂×C₄×C₁₂₇	semidirect
274. #102	C₂×C₄×C₁₂₇	semidirect
275. #102	C₂×C₄×C₁₂₇	semidirect
278. #97	C₂×C₄×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#490×C₁₂₇	2
C₁₂₇×#2330	2
C₁₂₇×#2328	2
C₁₂₇×#1991	2
C₁₂₇×#1957	2
C₁₂₇×#1936	2
C₁₂₇×#1934	2
C₁₂₇×#1836	2
C₁₂₇×#1762	2
C₄×#102×C₁₂₇	2
C₁₂₇×#1726	2
#21652	127

Subgroups — C127×#21652 #44585325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#21652 #44585325