Subgroups — C₁₂₇×#20563 #44584236

Order 32512.

954 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#435×C₁₂₇	C₂	1	2	yes	maximal
2	C₁₂₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₂₇×#1771	C₂	1	2	yes	maximal, complemented
4	C₁₂₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₂₇×#1753	C₂	1	2	yes	maximal, complemented
6	C₁₂₇×#1752	C₂	1	2	yes	maximal, complemented
7	C₁₂₇×#1750	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1745	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₂₇×#1729	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₁₂₇	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₂₇	C₂²	1	2	yes	—
14	#435×C₁₂₇	C₄	1	16	yes	complemented
15	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
18	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
19	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
20	C₂×#97×C₁₂₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₂₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
23	#390×C₁₂₇	C₄	1	2	yes	—
24	#389×C₁₂₇	C₄	1	2	yes	—
25	#388×C₁₂₇	C₄	1	4	yes	—
26	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	—
28	C₄³×C₁₂₇	C₂²	1	1	yes	characteristic
29	#336×C₁₂₇	C₂²	1	1	yes	characteristic
30	#336×C₁₂₇	C₂²	1	2	yes	—
31	#336×C₁₂₇	C₂²	1	2	yes	—
32	#336×C₁₂₇	C₂²	1	2	yes	—
33	#336×C₁₂₇	C₂²	1	1	yes	characteristic
34	#336×C₁₂₇	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
37	C₂×M₁₆×C₁₂₇	—	4	2	no	—
38	C₂×M₁₆×C₁₂₇	—	4	2	no	—
39	C₂×M₁₆×C₁₂₇	C₂×C₄	1	8	yes	—
40	C₂²×C₈×C₁₂₇	—	4	2	no	—
41	C₂²×C₈×C₁₂₇	—	4	2	no	—
42	C₂²×C₈×C₁₂₇	C₂×C₄	1	8	yes	—
43	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
47	C₄×D₄×C₁₂₇	C₂×C₄	1	8	yes	—
48	#117×C₁₂₇	—	4	2	no	—
49	#117×C₁₂₇	—	4	2	no	—
50	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₂₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
63	C₂²⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
64	C₂²⋊C₈×C₁₂₇	C₂×C₄	1	8	yes	—
65	#97×C₁₂₇	—	4	1	no	—
66	#97×C₁₂₇	—	4	1	no	—
67	#97×C₁₂₇	—	4	2	no	—
68	#97×C₁₂₇	C₂×C₄	1	8	yes	—
69	C₄×C₈×C₁₂₇	—	4	2	no	—
70	#95×C₁₂₇	C₂×C₄	1	4	yes	—
71	#95×C₁₂₇	C₂×C₄	1	2	yes	—
72	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
73	C₂×D₄×C₁₂₇	—	4	2	no	—
74	C₂×D₄×C₁₂₇	C₄²	1	4	yes	—
75	C₂²×C₄×C₁₂₇	—	2	2	no	—
76	C₂²×C₄×C₁₂₇	—	2	2	no	—
77	C₂²×C₄×C₁₂₇	—	2	2	no	—
78	C₂²×C₄×C₁₂₇	—	2	2	no	—
79	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₂₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
88	M₁₆×C₁₂₇	—	4	8	no	—
89	C₂×C₈×C₁₂₇	—	2	2	no	—
90	C₂×C₈×C₁₂₇	—	2	2	no	—
91	C₂×C₈×C₁₂₇	—	2	2	no	—
92	C₂×C₈×C₁₂₇	—	2	2	no	—
93	C₂×C₈×C₁₂₇	—	2	2	no	—
94	C₂×C₈×C₁₂₇	—	2	2	no	—
95	C₂×C₈×C₁₂₇	—	2	2	no	—
96	C₂×C₈×C₁₂₇	—	2	2	no	—
97	C₂×C₈×C₁₂₇	—	4	8	no	—
98	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
99	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₂₇	C₂²×C₄	1	4	yes	—
102	C₄⋊C₄×C₁₂₇	—	4	2	no	—
103	C₄⋊C₄×C₁₂₇	—	4	4	no	—
104	C₄⋊C₄×C₁₂₇	C₄²	1	4	yes	—
105	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
106	C₂²⋊C₄×C₁₂₇	—	4	4	no	—
107	C₂²⋊C₄×C₁₂₇	C₄²	1	8	yes	—
108	C₄²×C₁₂₇	—	2	2	no	—
109	C₄²×C₁₂₇	—	2	1	no	—
110	C₄²×C₁₂₇	—	2	2	no	—
111	C₄²×C₁₂₇	—	2	2	no	—
112	C₄²×C₁₂₇	—	2	1	no	—
113	C₄²×C₁₂₇	—	4	2	no	—
114	C₄²×C₁₂₇	—	4	2	no	—
115	C₄²×C₁₂₇	C₂²×C₄	1	4	yes	—
116	C₂³×C₁₂₇	—	2	2	no	—
117	C₂³×C₁₂₇	—	2	2	no	—
118	C₂³×C₁₂₇	—	2	4	no	—
119	C₂³×C₁₂₇	—	2	4	no	—
120	C₂³×C₁₂₇	C₂×C₄²	1	4	yes	—
121	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
122	D₄×C₁₂₇	—	4	4	no	—
123	C₂×C₄×C₁₂₇	—	2	2	no	—
124	C₂×C₄×C₁₂₇	—	2	2	no	—
125	C₂×C₄×C₁₂₇	—	2	2	no	—
126	C₂×C₄×C₁₂₇	—	2	2	no	—
127	C₂×C₄×C₁₂₇	—	2	4	no	—
128	C₂×C₄×C₁₂₇	—	2	4	no	—
129	C₂×C₄×C₁₂₇	—	2	4	no	—
130	C₂×C₄×C₁₂₇	—	2	4	no	—
131	C₂×C₄×C₁₂₇	—	2	2	no	—
132	C₂×C₄×C₁₂₇	—	2	4	no	—
133	C₂×C₄×C₁₂₇	—	2	2	no	—
134	C₂×C₄×C₁₂₇	—	2	2	no	—
135	C₂×C₄×C₁₂₇	—	2	2	no	—
136	C₂×C₄×C₁₂₇	—	2	2	no	—
137	C₂×C₄×C₁₂₇	—	2	2	no	—
138	C₂×C₄×C₁₂₇	—	2	4	no	—
139	C₂×C₄×C₁₂₇	—	2	4	no	—
140	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
141	C₂×C₄×C₁₂₇	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₁₂₇	C₂×C₄²	1	4	yes	—
143	C₂×C₄×C₁₂₇	C₂³×C₄	1	2	yes	—
144	C₂×C₄×C₁₂₇	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
146	C₂×C₄×C₁₂₇	2₋¹⁺⁴	1	1	yes	characteristic
147	C₈×C₁₂₇	—	2	4	no	—
148	C₈×C₁₂₇	—	2	4	no	—
149	C₈×C₁₂₇	—	2	4	no	—
150	C₈×C₁₂₇	—	2	4	no	—
151	C₂²×C₁₂₇	—	2	4	no	—
152	C₂²×C₁₂₇	—	2	4	no	—
153	C₂²×C₁₂₇	—	2	4	no	—
154	C₂²×C₁₂₇	—	4	4	no	—
155	C₂²×C₁₂₇	—	4	4	no	—
156	C₂²×C₁₂₇	C₂²×C₄²	1	1	yes	characteristic
157	C₂²×C₁₂₇	#518	1	1	yes	characteristic
158	C₂²×C₁₂₇	#520	1	1	yes	characteristic
159	C₂²×C₁₂₇	#568	1	2	yes	—
160	C₂²×C₁₂₇	#568	1	2	yes	—
161	C₄×C₁₂₇	—	2	2	no	—
162	C₄×C₁₂₇	—	2	2	no	—
163	C₄×C₁₂₇	—	2	4	no	—
164	C₄×C₁₂₇	—	4	2	no	—
165	C₄×C₁₂₇	—	4	4	no	—
166	C₄×C₁₂₇	—	4	2	no	—
167	C₄×C₁₂₇	#518	1	2	yes	—
168	C₄×C₁₂₇	#520	1	2	yes	—
169	#20563	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂×C₁₂₇	—	4	4	no	—
171	C₂×C₁₂₇	#2275	1	1	yes	characteristic
172	C₂×C₁₂₇	#2873	1	1	yes	characteristic
173	C₂×C₁₂₇	#2875	1	1	yes	characteristic
174	C₂×C₁₂₇	#2980	1	2	yes	—
175	C₂×C₁₂₇	#2995	1	2	yes	—
176	C₂×#435	C₂×C₁₂₇	1	2	yes	—
177	#2293	C₂×C₁₂₇	1	1	yes	characteristic
178	#1771	C₂×C₁₂₇	1	2	yes	complemented
179	#1767	C₂×C₁₂₇	1	1	yes	characteristic, complemented
180	#1753	C₂×C₁₂₇	1	2	yes	complemented
181	#1752	C₂×C₁₂₇	1	2	yes	complemented
182	#1750	C₂×C₁₂₇	1	2	yes	complemented
183	#1745	C₂×C₁₂₇	1	1	yes	characteristic, complemented
184	#1729	C₂×C₁₂₇	1	2	yes	complemented
185	C₁₂₇	#20563	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×M₁₆	C₂²×C₁₂₇	1	2	yes	—
187	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
188	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
189	C₂×#117	C₂²×C₁₂₇	1	2	yes	—
190	#435	C₄×C₁₂₇	1	16	yes	complemented
191	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
192	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
194	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
195	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
196	C₂×#97	C₂²×C₁₂₇	1	1	yes	characteristic
197	C₂×#97	C₂²×C₁₂₇	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
199	#390	C₄×C₁₂₇	1	2	yes	—
200	#389	C₄×C₁₂₇	1	2	yes	—
201	#388	C₄×C₁₂₇	1	4	yes	—
202	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
203	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	2	yes	—
204	C₄³	C₂²×C₁₂₇	1	1	yes	characteristic
205	#336	C₂²×C₁₂₇	1	1	yes	characteristic
206	#336	C₂²×C₁₂₇	1	2	yes	—
207	#336	C₂²×C₁₂₇	1	2	yes	—
208	#336	C₂²×C₁₂₇	1	2	yes	—
209	#336	C₂²×C₁₂₇	1	1	yes	characteristic
210	#336	C₂²×C₁₂₇	1	2	yes	—
211	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
213	C₂×M₁₆	—	4	2	no	—
214	C₂×M₁₆	—	4	2	no	—
215	C₂×M₁₆	C₂×C₄×C₁₂₇	1	8	yes	—
216	C₂²×C₈	—	4	2	no	—
217	C₂²×C₈	—	4	2	no	—
218	C₂²×C₈	C₂×C₄×C₁₂₇	1	8	yes	—
219	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
221	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
222	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
223	C₄×D₄	C₂×C₄×C₁₂₇	1	8	yes	—
224	#117	—	4	2	no	—
225	#117	—	4	2	no	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
229	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	4	yes	—
231	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
232	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
233	C₂×C₄²	C₂×C₄×C₁₂₇	1	2	yes	—
234	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
236	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
238	C₄⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
239	C₂²⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
240	C₂²⋊C₈	C₂×C₄×C₁₂₇	1	8	yes	—
241	#97	—	4	1	no	—
242	#97	—	4	1	no	—
243	#97	—	4	2	no	—
244	#97	C₂×C₄×C₁₂₇	1	8	yes	—
245	C₄×C₈	—	4	2	no	—
246	#95	C₂×C₄×C₁₂₇	1	4	yes	—
247	#95	C₂×C₄×C₁₂₇	1	2	yes	—
248	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
249	C₂×D₄	—	4	2	no	—
250	C₂×D₄	C₄²×C₁₂₇	1	4	yes	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₂₇	1	4	yes	—
263	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
264	M₁₆	—	4	8	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	4	8	no	—
274	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
275	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
276	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
277	C₂×C₈	C₂²×C₄×C₁₂₇	1	4	yes	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	C₄²×C₁₂₇	1	4	yes	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₂²⋊C₄	—	4	4	no	—
283	C₂²⋊C₄	C₄²×C₁₂₇	1	8	yes	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	4	2	no	—
290	C₄²	—	4	2	no	—
291	C₄²	C₂²×C₄×C₁₂₇	1	4	yes	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	C₂×C₄²×C₁₂₇	1	4	yes	—
297	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
298	D₄	—	4	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
317	C₂×C₄	C₂×C₄²×C₁₂₇	1	2	yes	—
318	C₂×C₄	C₂×C₄²×C₁₂₇	1	4	yes	—
319	C₂×C₄	C₂³×C₄×C₁₂₇	1	2	yes	—
320	C₂×C₄	H(5,𝔽₂)×C₁₂₇	1	1	yes	characteristic
321	C₂×C₄	H(5,𝔽₂)×C₁₂₇	1	2	yes	—
322	C₂×C₄	2₋¹⁺⁴×C₁₂₇	1	1	yes	characteristic
323	C₈	—	2	4	no	—
324	C₈	—	2	4	no	—
325	C₈	—	2	4	no	—
326	C₈	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	4	no	—
332	C₂²	C₂²×C₄²×C₁₂₇	1	1	yes	characteristic
333	C₂²	#518×C₁₂₇	1	1	yes	characteristic
334	C₂²	#520×C₁₂₇	1	1	yes	characteristic
335	C₂²	#568×C₁₂₇	1	2	yes	—
336	C₂²	#568×C₁₂₇	1	2	yes	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	4	no	—
340	C₄	—	4	2	no	—
341	C₄	—	4	4	no	—
342	C₄	—	4	2	no	—
343	C₄	#518×C₁₂₇	1	2	yes	—
344	C₄	#520×C₁₂₇	1	2	yes	—
345	C₂	—	4	4	no	—
346	C₂	C₁₂₇×#2275	1	1	yes	characteristic
347	C₂	C₁₂₇×#2873	1	1	yes	characteristic
348	C₂	C₁₂₇×#2875	1	1	yes	characteristic
349	C₂	C₁₂₇×#2980	1	2	yes	—
350	C₂	C₁₂₇×#2995	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₂₇×#1771	C₂	semidirect
4. C₁₂₇×#1767	C₂	semidirect
5. C₁₂₇×#1753	C₂	semidirect
6. C₁₂₇×#1752	C₂	semidirect
7. C₁₂₇×#1750	C₂	semidirect
8. C₁₂₇×#1745	C₂	semidirect
9. C₁₂₇×#1729	C₂	semidirect
14. #435×C₁₂₇	C₄	semidirect
169. #20563	C₁₂₇	direct (N × H)
178. #1771	C₂×C₁₂₇	semidirect
179. #1767	C₂×C₁₂₇	semidirect
180. #1753	C₂×C₁₂₇	semidirect
181. #1752	C₂×C₁₂₇	semidirect
182. #1750	C₂×C₁₂₇	semidirect
183. #1745	C₂×C₁₂₇	semidirect
184. #1729	C₂×C₁₂₇	semidirect
185. C₁₂₇	#20563	direct (N × H)
190. #435	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×#435×C₁₂₇	2
C₁₂₇×#2293	2
C₁₂₇×#1771	2
C₁₂₇×#1767	2
C₁₂₇×#1753	2
C₁₂₇×#1752	2
C₁₂₇×#1750	2
C₁₂₇×#1745	2
C₁₂₇×#1729	2
#20563	127

Subgroups — C127×#20563 #44584236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#20563 #44584236