Subgroups — C₁₂₇×#10730 #44574403

Order 32512.

1822 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₁₂₇	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₂₇	—	2	1	no	—
6	C₂⁴×C₄×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₂₇	—	2	1	no	—
9	C₂²×C₄⋊C₄×C₁₂₇	—	2	2	no	—
10	C₂²×C₄⋊C₄×C₁₂₇	—	2	8	no	—
11	C₂²×C₄⋊C₄×C₁₂₇	C₄	1	4	yes	complemented
12	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₁₂₇	—	2	2	no	—
16	C₂×C₂²⋊C₈×C₁₂₇	—	2	2	no	—
17	C₂×C₂²⋊C₈×C₁₂₇	C₄	1	4	yes	complemented
18	#380×C₁₂₇	—	2	2	no	—
19	#380×C₁₂₇	C₄	1	4	yes	complemented
20	C₂×#95×C₁₂₇	—	2	1	no	—
21	#340×C₁₂₇	—	2	8	no	—
22	C₂⁵×C₁₂₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₂₇	—	2	4	no	—
24	C₂³×C₄×C₁₂₇	—	2	4	no	—
25	C₂³×C₄×C₁₂₇	—	2	8	no	—
26	C₂³×C₄×C₁₂₇	—	2	4	no	—
27	C₂³×C₄×C₁₂₇	—	2	2	no	—
28	C₂³×C₄×C₁₂₇	—	2	2	no	—
29	C₂³×C₄×C₁₂₇	—	4	4	no	—
30	C₂³×C₄×C₁₂₇	—	4	2	no	—
31	C₂³×C₄×C₁₂₇	—	4	2	no	—
32	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₂₇	D₄	1	2	yes	—
37	C₂³×C₄×C₁₂₇	D₄	1	2	yes	—
38	C₂³×C₄×C₁₂₇	Q₈	1	2	yes	—
39	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₂₇	—	2	4	no	—
41	C₂²×C₈×C₁₂₇	—	2	2	no	—
42	C₂²×C₈×C₁₂₇	—	2	2	no	—
43	C₂²×C₈×C₁₂₇	—	2	4	no	—
44	C₂²×C₈×C₁₂₇	C₂×C₄	1	4	yes	complemented
45	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₂₇	—	2	16	no	—
47	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₂₇	—	2	16	no	—
51	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₂₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	complemented
56	C₂×C₄⋊C₄×C₁₂₇	D₄	1	8	yes	—
57	C₂×C₂²⋊C₄×C₁₂₇	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₂₇	—	4	2	no	—
59	C₂×C₂²⋊C₄×C₁₂₇	—	4	2	no	—
60	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
61	#95×C₁₂₇	—	2	4	no	—
62	C₂⁴×C₁₂₇	—	2	2	no	—
63	C₂⁴×C₁₂₇	—	2	2	no	—
64	C₂⁴×C₁₂₇	—	2	2	no	—
65	C₂⁴×C₁₂₇	—	2	2	no	—
66	C₂⁴×C₁₂₇	C₂²⋊C₄	1	2	yes	—
67	C₂⁴×C₁₂₇	C₂²⋊C₄	1	2	yes	—
68	C₂⁴×C₁₂₇	C₄⋊C₄	1	2	yes	—
69	C₂⁴×C₁₂₇	D₈	1	2	yes	—
70	C₂⁴×C₁₂₇	SD₁₆	1	2	yes	—
71	C₂⁴×C₁₂₇	SD₁₆	1	2	yes	—
72	C₂⁴×C₁₂₇	Q₁₆	1	2	yes	—
73	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₂₇	—	2	2	no	—
75	C₂²×C₄×C₁₂₇	—	2	2	no	—
76	C₂²×C₄×C₁₂₇	—	2	4	no	—
77	C₂²×C₄×C₁₂₇	—	2	4	no	—
78	C₂²×C₄×C₁₂₇	—	2	8	no	—
79	C₂²×C₄×C₁₂₇	—	2	8	no	—
80	C₂²×C₄×C₁₂₇	—	2	4	no	—
81	C₂²×C₄×C₁₂₇	—	2	8	no	—
82	C₂²×C₄×C₁₂₇	—	2	8	no	—
83	C₂²×C₄×C₁₂₇	—	2	4	no	—
84	C₂²×C₄×C₁₂₇	—	2	16	no	—
85	C₂²×C₄×C₁₂₇	—	2	4	no	—
86	C₂²×C₄×C₁₂₇	—	2	8	no	—
87	C₂²×C₄×C₁₂₇	—	2	4	no	—
88	C₂²×C₄×C₁₂₇	—	4	8	no	—
89	C₂²×C₄×C₁₂₇	—	4	16	no	—
90	C₂²×C₄×C₁₂₇	—	4	16	no	—
91	C₂²×C₄×C₁₂₇	—	4	8	no	—
92	C₂²×C₄×C₁₂₇	—	4	2	no	—
93	C₂²×C₄×C₁₂₇	—	4	2	no	—
94	C₂²×C₄×C₁₂₇	—	4	4	no	—
95	C₂²×C₄×C₁₂₇	—	4	2	no	—
96	C₂²×C₄×C₁₂₇	—	4	2	no	—
97	C₂²×C₄×C₁₂₇	—	4	2	no	—
98	C₂²×C₄×C₁₂₇	—	4	2	no	—
99	C₂²×C₄×C₁₂₇	—	4	2	no	—
100	C₂²×C₄×C₁₂₇	—	4	2	no	—
101	C₂²×C₄×C₁₂₇	C₄²	1	4	yes	—
102	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	2	yes	—
106	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	4	yes	—
107	C₂²×C₄×C₁₂₇	C₄⋊C₄	1	4	yes	—
108	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₂₇	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₂₇	#41	1	4	yes	—
116	C₂×C₈×C₁₂₇	—	2	4	no	—
117	C₂×C₈×C₁₂₇	—	2	8	no	—
118	C₂×C₈×C₁₂₇	—	4	2	no	—
119	C₂×C₈×C₁₂₇	—	4	4	no	—
120	C₂×C₈×C₁₂₇	—	4	2	no	—
121	C₄⋊C₄×C₁₂₇	—	2	16	no	—
122	C₄⋊C₄×C₁₂₇	—	2	4	no	—
123	C₄⋊C₄×C₁₂₇	—	2	8	no	—
124	C₄⋊C₄×C₁₂₇	—	2	8	no	—
125	C₄⋊C₄×C₁₂₇	—	4	4	no	—
126	C₄⋊C₄×C₁₂₇	C₂²⋊C₄	1	8	yes	complemented
127	C₂²⋊C₄×C₁₂₇	—	4	8	no	—
128	C₂³×C₁₂₇	—	2	2	no	—
129	C₂³×C₁₂₇	—	2	2	no	—
130	C₂³×C₁₂₇	—	2	4	no	—
131	C₂³×C₁₂₇	—	2	4	no	—
132	C₂³×C₁₂₇	—	2	4	no	—
133	C₂³×C₁₂₇	—	2	2	no	—
134	C₂³×C₁₂₇	—	2	2	no	—
135	C₂³×C₁₂₇	—	2	4	no	—
136	C₂³×C₁₂₇	—	2	4	no	—
137	C₂³×C₁₂₇	—	2	4	no	—
138	C₂³×C₁₂₇	—	2	4	no	—
139	C₂³×C₁₂₇	—	2	4	no	—
140	C₂³×C₁₂₇	—	2	4	no	—
141	C₂³×C₁₂₇	—	2	4	no	—
142	C₂³×C₁₂₇	—	2	4	no	—
143	C₂³×C₁₂₇	—	2	4	no	—
144	C₂³×C₁₂₇	#95	1	4	yes	—
145	C₂³×C₁₂₇	#102	1	4	yes	—
146	C₂³×C₁₂₇	#102	1	4	yes	—
147	C₂³×C₁₂₇	#103	1	4	yes	—
148	C₂³×C₁₂₇	#103	1	4	yes	—
149	C₂³×C₁₂₇	#106	1	4	yes	—
150	C₂³×C₁₂₇	#107	1	4	yes	—
151	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂³×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂³×C₁₂₇	#120	1	2	yes	—
155	C₂³×C₁₂₇	#123	1	2	yes	—
156	C₂³×C₁₂₇	C₂×D₈	1	1	yes	characteristic
157	C₂³×C₁₂₇	C₂×SD₁₆	1	1	yes	characteristic
158	C₂³×C₁₂₇	C₂×SD₁₆	1	1	yes	characteristic
159	C₂³×C₁₂₇	C₂×Q₁₆	1	1	yes	characteristic
160	C₂³×C₁₂₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂³×C₁₂₇	#137	1	2	yes	—
162	C₂×C₄×C₁₂₇	—	2	2	no	—
163	C₂×C₄×C₁₂₇	—	2	2	no	—
164	C₂×C₄×C₁₂₇	—	2	4	no	—
165	C₂×C₄×C₁₂₇	—	2	4	no	—
166	C₂×C₄×C₁₂₇	—	2	8	no	—
167	C₂×C₄×C₁₂₇	—	2	8	no	—
168	C₂×C₄×C₁₂₇	—	2	8	no	—
169	C₂×C₄×C₁₂₇	—	2	8	no	—
170	C₂×C₄×C₁₂₇	—	2	8	no	—
171	C₂×C₄×C₁₂₇	—	4	32	no	—
172	C₂×C₄×C₁₂₇	—	4	4	no	—
173	C₂×C₄×C₁₂₇	—	4	4	no	—
174	C₂×C₄×C₁₂₇	—	4	8	no	—
175	C₂×C₄×C₁₂₇	—	4	8	no	—
176	C₂×C₄×C₁₂₇	—	4	4	no	—
177	C₂×C₄×C₁₂₇	—	4	4	no	—
178	C₂×C₄×C₁₂₇	—	4	4	no	—
179	C₂×C₄×C₁₂₇	—	8	2	no	—
180	C₂×C₄×C₁₂₇	—	8	2	no	—
181	C₂×C₄×C₁₂₇	—	8	2	no	—
182	C₂×C₄×C₁₂₇	—	8	2	no	—
183	C₂×C₄×C₁₂₇	#95	1	4	yes	—
184	C₂×C₄×C₁₂₇	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₂₇	#117	1	2	yes	—
190	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
191	C₂×C₄×C₁₂₇	C₄×D₄	1	4	yes	—
192	C₂×C₄×C₁₂₇	#120	1	2	yes	—
193	C₂×C₄×C₁₂₇	#121	1	4	yes	—
194	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	4	yes	—
195	C₂×C₄×C₁₂₇	#123	1	2	yes	—
196	C₈×C₁₂₇	—	4	4	no	—
197	C₂²×C₁₂₇	—	2	4	no	—
198	C₂²×C₁₂₇	—	2	4	no	—
199	C₂²×C₁₂₇	—	2	8	no	—
200	C₂²×C₁₂₇	—	2	8	no	—
201	C₂²×C₁₂₇	—	2	8	no	—
202	C₂²×C₁₂₇	—	2	8	no	—
203	C₂²×C₁₂₇	—	2	4	no	—
204	C₂²×C₁₂₇	—	2	4	no	—
205	C₂²×C₁₂₇	—	2	4	no	—
206	C₂²×C₁₂₇	—	2	4	no	—
207	C₂²×C₁₂₇	#340	1	8	yes	complemented
208	C₂²×C₁₂₇	C₂×#95	1	1	yes	characteristic
209	C₂²×C₁₂₇	#379	1	1	yes	characteristic
210	C₂²×C₁₂₇	#381	1	1	yes	characteristic
211	C₂²×C₁₂₇	#385	1	2	yes	—
212	C₂²×C₁₂₇	#386	1	2	yes	—
213	C₂²×C₁₂₇	C₂×#102	1	1	yes	characteristic
214	C₂²×C₁₂₇	C₂×#102	1	1	yes	characteristic
215	C₂²×C₁₂₇	C₂×#103	1	1	yes	characteristic
216	C₂²×C₁₂₇	C₂×#103	1	1	yes	characteristic
217	C₂²×C₁₂₇	#417	1	2	yes	—
218	C₂²×C₁₂₇	#418	1	1	yes	characteristic
219	C₂²×C₁₂₇	#419	1	1	yes	characteristic
220	C₂²×C₁₂₇	C₂×#106	1	1	yes	characteristic
221	C₂²×C₁₂₇	C₂×#107	1	1	yes	characteristic
222	C₂²×C₁₂₇	#428	1	2	yes	—
223	C₂²×C₁₂₇	#447	1	2	yes	—
224	C₂²×C₁₂₇	#448	1	2	yes	—
225	C₂²×C₁₂₇	#450	1	2	yes	—
226	C₂²×C₁₂₇	#451	1	2	yes	—
227	C₂²×C₁₂₇	#480	1	2	yes	—
228	C₂²×C₁₂₇	#481	1	2	yes	—
229	C₂²×C₁₂₇	#483	1	2	yes	—
230	C₂²×C₁₂₇	#484	1	2	yes	—
231	C₄×C₁₂₇	—	2	4	no	—
232	C₄×C₁₂₇	—	4	8	no	—
233	C₄×C₁₂₇	—	8	4	no	—
234	C₄×C₁₂₇	C₄×C₂²⋊C₄	1	2	yes	—
235	C₄×C₁₂₇	#380	1	2	yes	—
236	C₄×C₁₂₇	#385	1	2	yes	—
237	C₄×C₁₂₇	#386	1	2	yes	—
238	#10730	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂×C₁₂₇	—	2	8	no	—
240	C₂×C₁₂₇	C₂²⋊#95	1	1	yes	characteristic
241	C₂×C₁₂₇	C₂×#340	1	1	yes	characteristic
242	C₂×C₁₂₇	#1736	1	1	yes	characteristic
243	C₂×C₁₂₇	#1786	1	1	yes	characteristic
244	C₂×C₁₂₇	#1787	1	1	yes	characteristic
245	C₂×C₁₂₇	#1823	1	1	yes	characteristic
246	C₂×C₁₂₇	#1824	1	1	yes	characteristic
247	C₂×C₁₂₇	#1852	1	2	yes	—
248	C₂×C₁₂₇	#1853	1	2	yes	—
249	C₂×C₁₂₇	#1872	1	2	yes	—
250	C₂×C₁₂₇	#1874	1	2	yes	—
251	C₂³×C₄⋊C₄	C₂×C₁₂₇	1	1	yes	characteristic
252	C₂²×C₂²⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic
253	C₂×#380	C₂×C₁₂₇	1	1	yes	characteristic
254	C₂×#340	C₂×C₁₂₇	1	4	yes	complemented
255	C₁₂₇	#10730	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴×C₄	—	2	1	no	—
257	C₂⁴×C₄	C₂²×C₁₂₇	1	1	yes	characteristic
258	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
259	C₂²×C₄⋊C₄	—	2	1	no	—
260	C₂²×C₄⋊C₄	—	2	2	no	—
261	C₂²×C₄⋊C₄	—	2	8	no	—
262	C₂²×C₄⋊C₄	C₄×C₁₂₇	1	4	yes	complemented
263	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
265	C₂²×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₈	—	2	2	no	—
267	C₂×C₂²⋊C₈	—	2	2	no	—
268	C₂×C₂²⋊C₈	C₄×C₁₂₇	1	4	yes	complemented
269	#380	—	2	2	no	—
270	#380	C₄×C₁₂₇	1	4	yes	complemented
271	C₂×#95	—	2	1	no	—
272	#340	—	2	8	no	—
273	C₂⁵	D₄×C₁₂₇	1	1	yes	characteristic
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	8	no	—
277	C₂³×C₄	—	2	4	no	—
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	—	2	2	no	—
280	C₂³×C₄	—	4	4	no	—
281	C₂³×C₄	—	4	2	no	—
282	C₂³×C₄	—	4	2	no	—
283	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
284	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
285	C₂³×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
286	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₁₂₇	1	2	yes	—
288	C₂³×C₄	D₄×C₁₂₇	1	2	yes	—
289	C₂³×C₄	Q₈×C₁₂₇	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	C₂×C₄×C₁₂₇	1	4	yes	complemented
296	C₂×C₄⋊C₄	—	2	8	no	—
297	C₂×C₄⋊C₄	—	2	16	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	16	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
306	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	complemented
307	C₂×C₄⋊C₄	D₄×C₁₂₇	1	8	yes	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₂²⋊C₄	—	4	2	no	—
310	C₂×C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₈	—	2	8	no	—
312	#95	—	2	4	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	C₂²⋊C₄×C₁₂₇	1	2	yes	—
318	C₂⁴	C₂²⋊C₄×C₁₂₇	1	2	yes	—
319	C₂⁴	C₄⋊C₄×C₁₂₇	1	2	yes	—
320	C₂⁴	D₈×C₁₂₇	1	2	yes	—
321	C₂⁴	SD₁₆×C₁₂₇	1	2	yes	—
322	C₂⁴	SD₁₆×C₁₂₇	1	2	yes	—
323	C₂⁴	Q₁₆×C₁₂₇	1	2	yes	—
324	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	16	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	16	no	—
341	C₂²×C₄	—	4	16	no	—
342	C₂²×C₄	—	4	8	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₄²×C₁₂₇	1	4	yes	—
353	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
354	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	2	yes	—
355	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
356	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	2	yes	—
357	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	4	yes	—
358	C₂²×C₄	C₄⋊C₄×C₁₂₇	1	4	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₂₇	1	4	yes	—
365	C₂²×C₄	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
366	C₂²×C₄	#41×C₁₂₇	1	4	yes	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	8	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	4	no	—
371	C₂×C₈	—	4	2	no	—
372	C₄⋊C₄	—	2	16	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	C₂²⋊C₄×C₁₂₇	1	8	yes	complemented
378	C₂²⋊C₄	—	4	8	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	#95×C₁₂₇	1	4	yes	—
396	C₂³	#102×C₁₂₇	1	4	yes	—
397	C₂³	#102×C₁₂₇	1	4	yes	—
398	C₂³	#103×C₁₂₇	1	4	yes	—
399	C₂³	#103×C₁₂₇	1	4	yes	—
400	C₂³	#106×C₁₂₇	1	4	yes	—
401	C₂³	#107×C₁₂₇	1	4	yes	—
402	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
403	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
404	C₂³	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
405	C₂³	#120×C₁₂₇	1	2	yes	—
406	C₂³	#123×C₁₂₇	1	2	yes	—
407	C₂³	C₂×D₈×C₁₂₇	1	1	yes	characteristic
408	C₂³	C₂×SD₁₆×C₁₂₇	1	1	yes	characteristic
409	C₂³	C₂×SD₁₆×C₁₂₇	1	1	yes	characteristic
410	C₂³	C₂×Q₁₆×C₁₂₇	1	1	yes	characteristic
411	C₂³	AGL(1,ℤ/8)×C₁₂₇	1	2	yes	—
412	C₂³	#137×C₁₂₇	1	2	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	4	32	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#95×C₁₂₇	1	4	yes	—
435	C₂×C₄	C₂×C₄²×C₁₂₇	1	1	yes	characteristic
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
438	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
439	C₂×C₄	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
440	C₂×C₄	#117×C₁₂₇	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
442	C₂×C₄	C₄×D₄×C₁₂₇	1	4	yes	—
443	C₂×C₄	#120×C₁₂₇	1	2	yes	—
444	C₂×C₄	#121×C₁₂₇	1	4	yes	—
445	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	4	yes	—
446	C₂×C₄	#123×C₁₂₇	1	2	yes	—
447	C₈	—	4	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	8	no	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	#340×C₁₂₇	1	8	yes	complemented
459	C₂²	C₂×#95×C₁₂₇	1	1	yes	characteristic
460	C₂²	#379×C₁₂₇	1	1	yes	characteristic
461	C₂²	#381×C₁₂₇	1	1	yes	characteristic
462	C₂²	#385×C₁₂₇	1	2	yes	—
463	C₂²	#386×C₁₂₇	1	2	yes	—
464	C₂²	C₂×#102×C₁₂₇	1	1	yes	characteristic
465	C₂²	C₂×#102×C₁₂₇	1	1	yes	characteristic
466	C₂²	C₂×#103×C₁₂₇	1	1	yes	characteristic
467	C₂²	C₂×#103×C₁₂₇	1	1	yes	characteristic
468	C₂²	#417×C₁₂₇	1	2	yes	—
469	C₂²	#418×C₁₂₇	1	1	yes	characteristic
470	C₂²	#419×C₁₂₇	1	1	yes	characteristic
471	C₂²	C₂×#106×C₁₂₇	1	1	yes	characteristic
472	C₂²	C₂×#107×C₁₂₇	1	1	yes	characteristic
473	C₂²	#428×C₁₂₇	1	2	yes	—
474	C₂²	#447×C₁₂₇	1	2	yes	—
475	C₂²	#448×C₁₂₇	1	2	yes	—
476	C₂²	#450×C₁₂₇	1	2	yes	—
477	C₂²	#451×C₁₂₇	1	2	yes	—
478	C₂²	#480×C₁₂₇	1	2	yes	—
479	C₂²	#481×C₁₂₇	1	2	yes	—
480	C₂²	#483×C₁₂₇	1	2	yes	—
481	C₂²	#484×C₁₂₇	1	2	yes	—
482	C₄	—	2	4	no	—
483	C₄	—	4	8	no	—
484	C₄	—	8	4	no	—
485	C₄	C₄×C₂²⋊C₄×C₁₂₇	1	2	yes	—
486	C₄	#380×C₁₂₇	1	2	yes	—
487	C₄	#385×C₁₂₇	1	2	yes	—
488	C₄	#386×C₁₂₇	1	2	yes	—
489	C₂	—	2	8	no	—
490	C₂	C₁₂₇×C₂²⋊#95	1	1	yes	characteristic
491	C₂	C₂×#340×C₁₂₇	1	1	yes	characteristic
492	C₂	C₁₂₇×#1736	1	1	yes	characteristic
493	C₂	C₁₂₇×#1786	1	1	yes	characteristic
494	C₂	C₁₂₇×#1787	1	1	yes	characteristic
495	C₂	C₁₂₇×#1823	1	1	yes	characteristic
496	C₂	C₁₂₇×#1824	1	1	yes	characteristic
497	C₂	C₁₂₇×#1852	1	2	yes	—
498	C₂	C₁₂₇×#1853	1	2	yes	—
499	C₂	C₁₂₇×#1872	1	2	yes	—
500	C₂	C₁₂₇×#1874	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₂₇	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₂₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₂₇
prime radical	C₂⁵×C₁₂₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₂₇ ◁ C₂⁴×C₄×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#340×C₁₂₇	C₂	semidirect
11. C₂²×C₄⋊C₄×C₁₂₇	C₄	semidirect
17. C₂×C₂²⋊C₈×C₁₂₇	C₄	semidirect
19. #380×C₁₂₇	C₄	semidirect
44. C₂²×C₈×C₁₂₇	C₂×C₄	semidirect
55. C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	semidirect
126. C₄⋊C₄×C₁₂₇	C₂²⋊C₄	semidirect
207. C₂²×C₁₂₇	#340	semidirect
238. #10730	C₁₂₇	direct (N × H)
254. C₂×#340	C₂×C₁₂₇	semidirect
255. C₁₂₇	#10730	direct (N × H)
262. C₂²×C₄⋊C₄	C₄×C₁₂₇	semidirect
268. C₂×C₂²⋊C₈	C₄×C₁₂₇	semidirect
270. #380	C₄×C₁₂₇	semidirect
295. C₂²×C₈	C₂×C₄×C₁₂₇	semidirect
306. C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	semidirect
377. C₄⋊C₄	C₂²⋊C₄×C₁₂₇	semidirect
458. C₂²	#340×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₂₇	2
C₂²×C₂²⋊C₈×C₁₂₇	2
C₂×#380×C₁₂₇	2
C₂×#340×C₁₂₇	2
#10730	127

Subgroups — C127×#10730 #44574403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#10730 #44574403