Subgroups — C₂×C₁₂₇×#1787 #44584268

Order 32512.

3942 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₁₂₇	C₂	1	4	yes	maximal, complemented
3	C₂²×C₂²⋊C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#380×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1787	C₂	1	8	yes	maximal, direct product factor
6	C₂³×Q₈×C₁₂₇	—	2	16	no	—
7	C₂³×Q₈×C₁₂₇	—	2	4	no	—
8	C₂³×Q₈×C₁₂₇	—	2	2	no	—
9	C₂³×Q₈×C₁₂₇	—	2	1	no	—
10	C₂³×Q₈×C₁₂₇	C₄	1	8	yes	complemented
11	C₂³×Q₈×C₁₂₇	C₂²	1	4	yes	—
12	C₂³×Q₈×C₁₂₇	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₂₇	—	2	1	no	—
14	C₂⁴×C₄×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₂₇	—	2	1	no	—
18	C₂×#103×C₁₂₇	—	2	16	no	—
19	C₂×#103×C₁₂₇	C₂²	1	16	yes	complemented
20	C₂×C₂²⋊C₈×C₁₂₇	—	2	4	no	—
21	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	4	yes	—
22	#380×C₁₂₇	—	2	2	no	—
23	#380×C₁₂₇	C₂²	1	4	yes	—
24	C₂×#95×C₁₂₇	—	2	1	no	—
25	C₂⁵×C₁₂₇	D₄	1	1	yes	characteristic
26	C₂²×Q₈×C₁₂₇	—	2	32	no	—
27	C₂²×Q₈×C₁₂₇	—	2	64	no	—
28	C₂²×Q₈×C₁₂₇	—	2	16	no	—
29	C₂²×Q₈×C₁₂₇	—	2	64	no	—
30	C₂²×Q₈×C₁₂₇	—	2	32	no	—
31	C₂²×Q₈×C₁₂₇	—	2	8	no	—
32	C₂²×Q₈×C₁₂₇	—	2	16	no	—
33	C₂²×Q₈×C₁₂₇	—	2	4	no	—
34	C₂²×Q₈×C₁₂₇	—	2	8	no	—
35	C₂²×Q₈×C₁₂₇	—	2	8	no	—
36	C₂²×Q₈×C₁₂₇	—	2	4	no	—
37	C₂²×Q₈×C₁₂₇	—	2	2	no	—
38	C₂²×Q₈×C₁₂₇	C₂×C₄	1	8	yes	—
39	C₂²×Q₈×C₁₂₇	C₂×C₄	1	16	yes	complemented
40	C₂²×Q₈×C₁₂₇	D₄	1	16	yes	—
41	C₂²×Q₈×C₁₂₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₂₇	—	2	16	no	—
43	C₂³×C₄×C₁₂₇	—	2	8	no	—
44	C₂³×C₄×C₁₂₇	—	2	4	no	—
45	C₂³×C₄×C₁₂₇	—	2	2	no	—
46	C₂³×C₄×C₁₂₇	—	2	8	no	—
47	C₂³×C₄×C₁₂₇	—	2	2	no	—
48	C₂³×C₄×C₁₂₇	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₁₂₇	D₄	1	2	yes	—
50	C₂³×C₄×C₁₂₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₂₇	D₄	1	4	yes	—
52	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₂₇	—	2	4	no	—
55	C₂²×C₈×C₁₂₇	—	2	8	no	—
56	C₂²×C₈×C₁₂₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₂₇	—	2	8	no	—
58	C₂×C₄⋊C₄×C₁₂₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₂₇	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₂₇	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₂₇	—	4	4	no	—
62	#103×C₁₂₇	—	2	32	no	—
63	C₂²⋊C₈×C₁₂₇	—	2	8	no	—
64	#95×C₁₂₇	—	2	4	no	—
65	C₂⁴×C₁₂₇	—	2	4	no	—
66	C₂⁴×C₁₂₇	—	2	4	no	—
67	C₂⁴×C₁₂₇	C₂²⋊C₄	1	4	yes	—
68	C₂⁴×C₁₂₇	SD₁₆	1	4	yes	—
69	C₂⁴×C₁₂₇	Q₁₆	1	4	yes	—
70	C₂⁴×C₁₂₇	C₂×D₄	1	2	yes	—
71	C₂⁴×C₁₂₇	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₂₇	—	2	64	no	—
73	C₂×Q₈×C₁₂₇	—	2	128	no	—
74	C₂×Q₈×C₁₂₇	—	2	32	no	—
75	C₂×Q₈×C₁₂₇	—	2	64	no	—
76	C₂×Q₈×C₁₂₇	—	2	64	no	—
77	C₂×Q₈×C₁₂₇	—	2	8	no	—
78	C₂×Q₈×C₁₂₇	—	2	16	no	—
79	C₂×Q₈×C₁₂₇	—	2	16	no	—
80	C₂×Q₈×C₁₂₇	—	2	16	no	—
81	C₂×Q₈×C₁₂₇	—	2	32	no	—
82	C₂×Q₈×C₁₂₇	—	2	4	no	—
83	C₂×Q₈×C₁₂₇	—	2	8	no	—
84	C₂×Q₈×C₁₂₇	C₂²⋊C₄	1	32	yes	complemented
85	C₂×Q₈×C₁₂₇	C₂²×C₄	1	8	yes	—
86	C₂×Q₈×C₁₂₇	C₂×D₄	1	16	yes	—
87	C₂²×C₄×C₁₂₇	—	2	32	no	—
88	C₂²×C₄×C₁₂₇	—	2	64	no	—
89	C₂²×C₄×C₁₂₇	—	2	8	no	—
90	C₂²×C₄×C₁₂₇	—	2	16	no	—
91	C₂²×C₄×C₁₂₇	—	2	16	no	—
92	C₂²×C₄×C₁₂₇	—	2	4	no	—
93	C₂²×C₄×C₁₂₇	—	2	4	no	—
94	C₂²×C₄×C₁₂₇	—	2	16	no	—
95	C₂²×C₄×C₁₂₇	—	2	8	no	—
96	C₂²×C₄×C₁₂₇	—	2	16	no	—
97	C₂²×C₄×C₁₂₇	—	2	8	no	—
98	C₂²×C₄×C₁₂₇	—	2	4	no	—
99	C₂²×C₄×C₁₂₇	—	4	4	no	—
100	C₂²×C₄×C₁₂₇	—	4	4	no	—
101	C₂²×C₄×C₁₂₇	—	4	4	no	—
102	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₁₂₇	C₂²⋊C₄	1	8	yes	—
104	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₂₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₂₇	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₂₇	—	2	4	no	—
113	C₂×C₈×C₁₂₇	—	2	8	no	—
114	C₂×C₈×C₁₂₇	—	4	8	no	—
115	C₄⋊C₄×C₁₂₇	—	2	8	no	—
116	C₄⋊C₄×C₁₂₇	—	4	4	no	—
117	C₂²⋊C₄×C₁₂₇	—	4	8	no	—
118	C₂³×C₁₂₇	—	2	4	no	—
119	C₂³×C₁₂₇	—	2	4	no	—
120	C₂³×C₁₂₇	—	2	8	no	—
121	C₂³×C₁₂₇	—	2	8	no	—
122	C₂³×C₁₂₇	—	2	16	no	—
123	C₂³×C₁₂₇	—	2	16	no	—
124	C₂³×C₁₂₇	#103	1	16	yes	complemented
125	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂³×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂³×C₁₂₇	#120	1	4	yes	—
128	C₂³×C₁₂₇	C₂×SD₁₆	1	4	yes	—
129	C₂³×C₁₂₇	C₂×SD₁₆	1	2	yes	—
130	C₂³×C₁₂₇	C₂×Q₁₆	1	4	yes	—
131	C₂³×C₁₂₇	C₂×Q₁₆	1	2	yes	—
132	C₂³×C₁₂₇	#137	1	4	yes	—
133	C₂³×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₂₇	—	2	64	no	—
135	Q₈×C₁₂₇	—	2	8	no	—
136	Q₈×C₁₂₇	—	2	16	no	—
137	Q₈×C₁₂₇	—	2	32	no	—
138	Q₈×C₁₂₇	C₂×C₂²⋊C₄	1	16	yes	complemented
139	C₂×C₄×C₁₂₇	—	2	64	no	—
140	C₂×C₄×C₁₂₇	—	2	8	no	—
141	C₂×C₄×C₁₂₇	—	2	16	no	—
142	C₂×C₄×C₁₂₇	—	2	4	no	—
143	C₂×C₄×C₁₂₇	—	2	32	no	—
144	C₂×C₄×C₁₂₇	—	2	8	no	—
145	C₂×C₄×C₁₂₇	—	2	8	no	—
146	C₂×C₄×C₁₂₇	—	2	8	no	—
147	C₂×C₄×C₁₂₇	—	2	16	no	—
148	C₂×C₄×C₁₂₇	—	4	4	no	—
149	C₂×C₄×C₁₂₇	—	4	4	no	—
150	C₂×C₄×C₁₂₇	—	4	4	no	—
151	C₂×C₄×C₁₂₇	—	8	8	no	—
152	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	8	yes	—
154	C₂×C₄×C₁₂₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₂₇	#120	1	8	yes	—
156	C₂×C₄×C₁₂₇	#120	1	4	yes	—
157	C₂×C₄×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₂₇	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₁₂₇	—	4	4	no	—
161	C₂²×C₁₂₇	—	2	4	no	—
162	C₂²×C₁₂₇	—	2	8	no	—
163	C₂²×C₁₂₇	—	2	8	no	—
164	C₂²×C₁₂₇	—	2	4	no	—
165	C₂²×C₁₂₇	—	2	32	no	—
166	C₂²×C₁₂₇	#379	1	4	yes	—
167	C₂²×C₁₂₇	C₂×#103	1	4	yes	—
168	C₂²×C₁₂₇	C₂×#103	1	8	yes	complemented
169	C₂²×C₁₂₇	#419	1	4	yes	—
170	C₂²×C₁₂₇	#448	1	8	yes	—
171	C₂²×C₁₂₇	#451	1	8	yes	—
172	C₂²×C₁₂₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₂₇	C₂×#120	1	2	yes	—
174	C₂²×C₁₂₇	C₂²×SD₁₆	1	1	yes	characteristic
175	C₂²×C₁₂₇	C₂²×Q₁₆	1	1	yes	characteristic
176	C₂²×C₁₂₇	C₂×#137	1	2	yes	—
177	C₄×C₁₂₇	—	2	16	no	—
178	C₄×C₁₂₇	—	2	4	no	—
179	C₄×C₁₂₇	—	8	4	no	—
180	C₄×C₁₂₇	#379	1	4	yes	—
181	C₄×C₁₂₇	C₂²×C₂²⋊C₄	1	2	yes	—
182	C₄×C₁₂₇	C₂×#120	1	2	yes	—
183	C₂×#1787	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂×C₁₂₇	—	2	8	no	—
185	C₂×C₁₂₇	#1787	1	8	yes	direct product factor
186	C₂×C₁₂₇	C₂×#379	1	1	yes	characteristic
187	C₂×C₁₂₇	C₂²×#103	1	1	yes	characteristic
188	C₂×C₁₂₇	C₂×#419	1	1	yes	characteristic
189	C₂×C₁₂₇	C₂×#448	1	2	yes	—
190	C₂×C₁₂₇	C₂×#451	1	2	yes	—
191	C₂⁴×Q₈	C₂×C₁₂₇	1	1	yes	characteristic
192	C₂²×#103	C₂×C₁₂₇	1	4	yes	complemented
193	C₂²×C₂²⋊C₈	C₂×C₁₂₇	1	1	yes	characteristic
194	C₂×#380	C₂×C₁₂₇	1	1	yes	characteristic
195	#1787	C₂×C₁₂₇	1	8	yes	direct product factor
196	C₁₂₇	C₂×#1787	1	1	yes	characteristic, direct product factor, Sylow
197	C₂³×Q₈	—	2	16	no	—
198	C₂³×Q₈	—	2	4	no	—
199	C₂³×Q₈	—	2	1	no	—
200	C₂³×Q₈	—	2	2	no	—
201	C₂³×Q₈	C₄×C₁₂₇	1	8	yes	complemented
202	C₂³×Q₈	C₂²×C₁₂₇	1	4	yes	—
203	C₂³×Q₈	C₂²×C₁₂₇	1	2	yes	—
204	C₂⁴×C₄	—	2	1	no	—
205	C₂⁴×C₄	C₂²×C₁₂₇	1	1	yes	characteristic
206	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₁₂₇	1	2	yes	—
208	C₂²×C₂²⋊C₄	—	2	1	no	—
209	C₂×#103	—	2	16	no	—
210	C₂×#103	C₂²×C₁₂₇	1	16	yes	complemented
211	C₂×C₂²⋊C₈	—	2	4	no	—
212	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	4	yes	—
213	#380	—	2	2	no	—
214	#380	C₂²×C₁₂₇	1	4	yes	—
215	C₂×#95	—	2	1	no	—
216	C₂⁵	D₄×C₁₂₇	1	1	yes	characteristic
217	C₂²×Q₈	—	2	32	no	—
218	C₂²×Q₈	—	2	64	no	—
219	C₂²×Q₈	—	2	16	no	—
220	C₂²×Q₈	—	2	64	no	—
221	C₂²×Q₈	—	2	32	no	—
222	C₂²×Q₈	—	2	8	no	—
223	C₂²×Q₈	—	2	16	no	—
224	C₂²×Q₈	—	2	4	no	—
225	C₂²×Q₈	—	2	8	no	—
226	C₂²×Q₈	—	2	8	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×Q₈	C₂×C₄×C₁₂₇	1	8	yes	—
230	C₂²×Q₈	C₂×C₄×C₁₂₇	1	16	yes	complemented
231	C₂²×Q₈	D₄×C₁₂₇	1	16	yes	—
232	C₂²×Q₈	C₂³×C₁₂₇	1	4	yes	—
233	C₂³×C₄	—	2	16	no	—
234	C₂³×C₄	—	2	8	no	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	—	2	8	no	—
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	C₂×C₄×C₁₂₇	1	4	yes	—
240	C₂³×C₄	D₄×C₁₂₇	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₁₂₇	1	2	yes	—
242	C₂³×C₄	D₄×C₁₂₇	1	4	yes	—
243	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
245	C₂²×C₈	—	2	4	no	—
246	C₂²×C₈	—	2	8	no	—
247	C₂²×C₈	C₂³×C₁₂₇	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂³×C₁₂₇	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	4	4	no	—
253	#103	—	2	32	no	—
254	C₂²⋊C₈	—	2	8	no	—
255	#95	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	C₂²⋊C₄×C₁₂₇	1	4	yes	—
259	C₂⁴	SD₁₆×C₁₂₇	1	4	yes	—
260	C₂⁴	Q₁₆×C₁₂₇	1	4	yes	—
261	C₂⁴	C₂×D₄×C₁₂₇	1	2	yes	—
262	C₂⁴	C₂×D₄×C₁₂₇	1	1	yes	characteristic
263	C₂×Q₈	—	2	64	no	—
264	C₂×Q₈	—	2	128	no	—
265	C₂×Q₈	—	2	32	no	—
266	C₂×Q₈	—	2	64	no	—
267	C₂×Q₈	—	2	64	no	—
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	2	16	no	—
270	C₂×Q₈	—	2	16	no	—
271	C₂×Q₈	—	2	16	no	—
272	C₂×Q₈	—	2	32	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	C₂²⋊C₄×C₁₂₇	1	32	yes	complemented
276	C₂×Q₈	C₂²×C₄×C₁₂₇	1	8	yes	—
277	C₂×Q₈	C₂×D₄×C₁₂₇	1	16	yes	—
278	C₂²×C₄	—	2	32	no	—
279	C₂²×C₄	—	2	64	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	16	no	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	16	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	16	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	4	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₁₂₇	1	8	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₂₇	1	4	yes	—
299	C₂²×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₂₇	1	8	yes	—
301	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	8	no	—
305	C₂×C₈	—	4	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	4	4	no	—
308	C₂²⋊C₄	—	4	8	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	2	16	no	—
314	C₂³	—	2	16	no	—
315	C₂³	#103×C₁₂₇	1	16	yes	complemented
316	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	4	yes	—
317	C₂³	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
318	C₂³	#120×C₁₂₇	1	4	yes	—
319	C₂³	C₂×SD₁₆×C₁₂₇	1	4	yes	—
320	C₂³	C₂×SD₁₆×C₁₂₇	1	2	yes	—
321	C₂³	C₂×Q₁₆×C₁₂₇	1	4	yes	—
322	C₂³	C₂×Q₁₆×C₁₂₇	1	2	yes	—
323	C₂³	#137×C₁₂₇	1	4	yes	—
324	C₂³	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
325	Q₈	—	2	64	no	—
326	Q₈	—	2	8	no	—
327	Q₈	—	2	16	no	—
328	Q₈	—	2	32	no	—
329	Q₈	C₂×C₂²⋊C₄×C₁₂₇	1	16	yes	complemented
330	C₂×C₄	—	2	64	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	32	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	16	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	8	no	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	4	yes	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	8	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₂₇	1	2	yes	—
346	C₂×C₄	#120×C₁₂₇	1	8	yes	—
347	C₂×C₄	#120×C₁₂₇	1	4	yes	—
348	C₂×C₄	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₂₇	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	8	no	—
354	C₂²	—	2	8	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	32	no	—
357	C₂²	#379×C₁₂₇	1	4	yes	—
358	C₂²	C₂×#103×C₁₂₇	1	4	yes	—
359	C₂²	C₂×#103×C₁₂₇	1	8	yes	complemented
360	C₂²	#419×C₁₂₇	1	4	yes	—
361	C₂²	#448×C₁₂₇	1	8	yes	—
362	C₂²	#451×C₁₂₇	1	8	yes	—
363	C₂²	C₂²×C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
364	C₂²	C₂×#120×C₁₂₇	1	2	yes	—
365	C₂²	C₂²×SD₁₆×C₁₂₇	1	1	yes	characteristic
366	C₂²	C₂²×Q₁₆×C₁₂₇	1	1	yes	characteristic
367	C₂²	C₂×#137×C₁₂₇	1	2	yes	—
368	C₄	—	2	16	no	—
369	C₄	—	2	4	no	—
370	C₄	—	8	4	no	—
371	C₄	#379×C₁₂₇	1	4	yes	—
372	C₄	C₂²×C₂²⋊C₄×C₁₂₇	1	2	yes	—
373	C₄	C₂×#120×C₁₂₇	1	2	yes	—
374	C₂	—	2	8	no	—
375	C₂	C₁₂₇×#1787	1	8	yes	direct product factor
376	C₂	C₂×#379×C₁₂₇	1	1	yes	characteristic
377	C₂	C₂²×#103×C₁₂₇	1	1	yes	characteristic
378	C₂	C₂×#419×C₁₂₇	1	1	yes	characteristic
379	C₂	C₂×#448×C₁₂₇	1	2	yes	—
380	C₂	C₂×#451×C₁₂₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₂₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×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
2. C₂²×#103×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1787	C₂	direct (N × H)
10. C₂³×Q₈×C₁₂₇	C₄	semidirect
19. C₂×#103×C₁₂₇	C₂²	semidirect
39. C₂²×Q₈×C₁₂₇	C₂×C₄	semidirect
84. C₂×Q₈×C₁₂₇	C₂²⋊C₄	semidirect
124. C₂³×C₁₂₇	#103	semidirect
138. Q₈×C₁₂₇	C₂×C₂²⋊C₄	semidirect
168. C₂²×C₁₂₇	C₂×#103	semidirect
183. C₂×#1787	C₁₂₇	direct (N × H)
185. C₂×C₁₂₇	#1787	direct (N × H)
192. C₂²×#103	C₂×C₁₂₇	semidirect
195. #1787	C₂×C₁₂₇	direct (N × H)
196. C₁₂₇	C₂×#1787	direct (N × H)
201. C₂³×Q₈	C₄×C₁₂₇	semidirect
210. C₂×#103	C₂²×C₁₂₇	semidirect
230. C₂²×Q₈	C₂×C₄×C₁₂₇	semidirect
275. C₂×Q₈	C₂²⋊C₄×C₁₂₇	semidirect
315. C₂³	#103×C₁₂₇	semidirect
329. Q₈	C₂×C₂²⋊C₄×C₁₂₇	semidirect
359. C₂²	C₂×#103×C₁₂₇	semidirect
375. C₂	C₁₂₇×#1787	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₁₂₇	2
C₂²×#103×C₁₂₇	2
C₂²×C₂²⋊C₈×C₁₂₇	2
C₂×#380×C₁₂₇	2
C₁₂₇×#1787	2
C₂×#1787	127

Subgroups — C2×C127×#1787 #44584268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₂₇×#1787 #44584268