Subgroups — C₁₁₃×#10720 #43278740

Order 28928.

1414 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₁₃×#2280	C₂	1	1	yes	maximal, characteristic
4	C₂×#339×C₁₁₃	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
7	C₂×#117×C₁₁₃	—	2	2	no	—
8	C₂×#117×C₁₁₃	—	2	8	no	—
9	C₂×#117×C₁₁₃	C₄	1	4	yes	complemented
10	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₁₃	—	2	1	no	—
12	C₂²×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
13	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
14	#407×C₁₁₃	—	2	2	no	—
15	#407×C₁₁₃	C₄	1	4	yes	complemented
16	C₂×C₂²⋊C₈×C₁₁₃	—	2	2	no	—
17	#381×C₁₁₃	—	2	1	no	—
18	#380×C₁₁₃	C₄	1	4	yes	complemented
19	#379×C₁₁₃	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
21	#339×C₁₁₃	—	2	8	no	—
22	C₂⁵×C₁₁₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₁₃	—	2	4	no	—
24	C₂³×C₄×C₁₁₃	—	2	4	no	—
25	C₂³×C₄×C₁₁₃	—	2	2	no	—
26	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
31	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
32	C₂³×C₄×C₁₁₃	Q₈	1	2	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₁₃	—	2	2	no	—
35	C₂×M₁₆×C₁₁₃	—	2	4	no	—
36	C₂×M₁₆×C₁₁₃	—	2	4	no	—
37	C₂×M₁₆×C₁₁₃	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₁₁₃	—	2	2	no	—
39	#117×C₁₁₃	—	2	16	no	—
40	#117×C₁₁₃	—	2	16	no	—
41	#117×C₁₁₃	—	2	4	no	—
42	#117×C₁₁₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
46	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₁₃	—	2	4	no	—
51	C₂×C₄²×C₁₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₁₃	—	2	2	no	—
53	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₁₁₃	D₄	1	8	yes	—
55	C₂²⋊C₈×C₁₁₃	—	2	8	no	—
56	#95×C₁₁₃	—	2	4	no	—
57	C₂⁴×C₁₁₃	—	2	2	no	—
58	C₂⁴×C₁₁₃	—	2	2	no	—
59	C₂⁴×C₁₁₃	—	4	4	no	—
60	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
61	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
62	C₂⁴×C₁₁₃	C₄⋊C₄	1	2	yes	—
63	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁₃	—	2	2	no	—
65	C₂²×C₄×C₁₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₁₃	—	2	8	no	—
69	C₂²×C₄×C₁₁₃	—	2	8	no	—
70	C₂²×C₄×C₁₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₁₃	—	2	8	no	—
72	C₂²×C₄×C₁₁₃	—	2	8	no	—
73	C₂²×C₄×C₁₁₃	—	2	4	no	—
74	C₂²×C₄×C₁₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₁₃	—	2	8	no	—
76	C₂²×C₄×C₁₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₁₃	—	4	8	no	—
78	C₂²×C₄×C₁₁₃	C₄²	1	4	yes	—
79	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
82	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
93	M₁₆×C₁₁₃	—	2	8	no	—
94	M₁₆×C₁₁₃	—	4	2	no	—
95	M₁₆×C₁₁₃	—	4	2	no	—
96	C₂×C₈×C₁₁₃	—	2	4	no	—
97	C₂×C₈×C₁₁₃	—	4	4	no	—
98	C₄⋊C₄×C₁₁₃	—	2	16	no	—
99	C₄⋊C₄×C₁₁₃	—	2	8	no	—
100	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
101	C₂²⋊C₄×C₁₁₃	—	4	8	no	—
102	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
103	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
104	C₄²×C₁₁₃	—	2	4	no	—
105	C₄²×C₁₁₃	—	2	8	no	—
106	C₄²×C₁₁₃	—	4	4	no	—
107	C₄²×C₁₁₃	C₂²⋊C₄	1	8	yes	complemented
108	C₂³×C₁₁₃	—	2	4	no	—
109	C₂³×C₁₁₃	—	2	2	no	—
110	C₂³×C₁₁₃	—	2	2	no	—
111	C₂³×C₁₁₃	—	2	4	no	—
112	C₂³×C₁₁₃	—	2	4	no	—
113	C₂³×C₁₁₃	—	2	4	no	—
114	C₂³×C₁₁₃	—	2	4	no	—
115	C₂³×C₁₁₃	—	4	4	no	—
116	C₂³×C₁₁₃	—	4	4	no	—
117	C₂³×C₁₁₃	—	4	8	no	—
118	C₂³×C₁₁₃	—	4	8	no	—
119	C₂³×C₁₁₃	#95	1	4	yes	—
120	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂³×C₁₁₃	#120	1	2	yes	—
124	C₂³×C₁₁₃	#123	1	2	yes	—
125	C₂×C₄×C₁₁₃	—	2	2	no	—
126	C₂×C₄×C₁₁₃	—	2	2	no	—
127	C₂×C₄×C₁₁₃	—	2	4	no	—
128	C₂×C₄×C₁₁₃	—	2	4	no	—
129	C₂×C₄×C₁₁₃	—	2	8	no	—
130	C₂×C₄×C₁₁₃	—	2	8	no	—
131	C₂×C₄×C₁₁₃	—	2	8	no	—
132	C₂×C₄×C₁₁₃	—	2	8	no	—
133	C₂×C₄×C₁₁₃	—	2	8	no	—
134	C₂×C₄×C₁₁₃	—	4	16	no	—
135	C₂×C₄×C₁₁₃	—	4	8	no	—
136	C₂×C₄×C₁₁₃	—	4	4	no	—
137	C₂×C₄×C₁₁₃	—	4	8	no	—
138	C₂×C₄×C₁₁₃	#95	1	4	yes	—
139	C₂×C₄×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁₃	#117	1	2	yes	—
145	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
147	C₂×C₄×C₁₁₃	#120	1	2	yes	—
148	C₂×C₄×C₁₁₃	#121	1	4	yes	—
149	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₁₁₃	#123	1	2	yes	—
151	C₈×C₁₁₃	—	4	4	no	—
152	C₂²×C₁₁₃	—	2	4	no	—
153	C₂²×C₁₁₃	—	2	4	no	—
154	C₂²×C₁₁₃	—	2	2	no	—
155	C₂²×C₁₁₃	—	2	2	no	—
156	C₂²×C₁₁₃	—	2	4	no	—
157	C₂²×C₁₁₃	—	2	4	no	—
158	C₂²×C₁₁₃	—	2	4	no	—
159	C₂²×C₁₁₃	—	4	4	no	—
160	C₂²×C₁₁₃	—	4	4	no	—
161	C₂²×C₁₁₃	—	4	8	no	—
162	C₂²×C₁₁₃	—	4	8	no	—
163	C₂²×C₁₁₃	C₂×#95	1	1	yes	characteristic
164	C₂²×C₁₁₃	#379	1	1	yes	characteristic
165	C₂²×C₁₁₃	#381	1	1	yes	characteristic
166	C₂²×C₁₁₃	#385	1	2	yes	—
167	C₂²×C₁₁₃	#386	1	2	yes	—
168	C₂²×C₁₁₃	#421	1	4	yes	—
169	C₄×C₁₁₃	—	2	4	no	—
170	C₄×C₁₁₃	—	4	8	no	—
171	C₄×C₁₁₃	—	8	4	no	—
172	C₄×C₁₁₃	C₄×C₂²⋊C₄	1	2	yes	—
173	C₄×C₁₁₃	#380	1	2	yes	—
174	C₄×C₁₁₃	#385	1	2	yes	—
175	C₄×C₁₁₃	#386	1	2	yes	—
176	#10720	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₁₁₃	—	2	1	no	—
178	C₂×C₁₁₃	—	2	1	no	—
179	C₂×C₁₁₃	—	2	2	no	—
180	C₂×C₁₁₃	—	4	4	no	—
181	C₂×C₁₁₃	C₂²⋊#95	1	1	yes	characteristic
182	C₂×C₁₁₃	#1733	1	2	yes	—
183	C₂×C₁₁₃	#1897	1	4	yes	—
184	C₂²×#117	C₂×C₁₁₃	1	1	yes	characteristic
185	C₂×#407	C₂×C₁₁₃	1	1	yes	characteristic
186	#2280	C₂×C₁₁₃	1	1	yes	characteristic
187	C₂×#339	C₂×C₁₁₃	1	4	yes	complemented
188	C₁₁₃	#10720	1	1	yes	characteristic, direct product factor, Sylow
189	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
190	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
191	C₂×#117	—	2	2	no	—
192	C₂×#117	—	2	8	no	—
193	C₂×#117	C₄×C₁₁₃	1	4	yes	complemented
194	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
195	C₂²×C₄⋊C₄	—	2	1	no	—
196	C₂²×C₂²⋊C₄	—	2	1	no	—
197	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
198	#407	—	2	2	no	—
199	#407	C₄×C₁₁₃	1	4	yes	complemented
200	C₂×C₂²⋊C₈	—	2	2	no	—
201	#381	—	2	1	no	—
202	#380	C₄×C₁₁₃	1	4	yes	complemented
203	#379	—	2	1	no	—
204	C₄×C₂²⋊C₄	—	2	2	no	—
205	#339	—	2	8	no	—
206	C₂⁵	D₄×C₁₁₃	1	1	yes	characteristic
207	C₂³×C₄	—	2	4	no	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
211	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
212	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
213	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
215	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
216	C₂³×C₄	Q₈×C₁₁₃	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂×M₁₆	—	2	4	no	—
221	C₂×M₁₆	C₂×C₄×C₁₁₃	1	4	yes	—
222	C₂²×C₈	—	2	2	no	—
223	#117	—	2	16	no	—
224	#117	—	2	16	no	—
225	#117	—	2	4	no	—
226	#117	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
230	C₂×C₂²⋊C₄	—	2	8	no	—
231	C₂×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
238	C₂×C₄²	D₄×C₁₁₃	1	8	yes	—
239	C₂²⋊C₈	—	2	8	no	—
240	#95	—	2	4	no	—
241	C₂⁴	—	2	2	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	4	4	no	—
244	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
245	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
246	C₂⁴	C₄⋊C₄×C₁₁₃	1	2	yes	—
247	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	8	no	—
262	C₂²×C₄	C₄²×C₁₁₃	1	4	yes	—
263	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
264	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
265	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
266	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
267	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
268	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
275	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
276	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
277	M₁₆	—	2	8	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	—	4	2	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₄⋊C₄	—	2	16	no	—
283	C₄⋊C₄	—	2	8	no	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₂²⋊C₄	—	4	8	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₄²	—	2	4	no	—
289	C₄²	—	2	8	no	—
290	C₄²	—	4	4	no	—
291	C₄²	C₂²⋊C₄×C₁₁₃	1	8	yes	complemented
292	C₂³	—	2	4	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	4	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	8	no	—
303	C₂³	#95×C₁₁₃	1	4	yes	—
304	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
305	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
306	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
307	C₂³	#120×C₁₁₃	1	2	yes	—
308	C₂³	#123×C₁₁₃	1	2	yes	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	—	4	8	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	#95×C₁₁₃	1	4	yes	—
323	C₂×C₄	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
328	C₂×C₄	#117×C₁₁₃	1	2	yes	—
329	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
330	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
331	C₂×C₄	#120×C₁₁₃	1	2	yes	—
332	C₂×C₄	#121×C₁₁₃	1	4	yes	—
333	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
334	C₂×C₄	#123×C₁₁₃	1	2	yes	—
335	C₈	—	4	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	8	no	—
346	C₂²	—	4	8	no	—
347	C₂²	C₂×#95×C₁₁₃	1	1	yes	characteristic
348	C₂²	#379×C₁₁₃	1	1	yes	characteristic
349	C₂²	#381×C₁₁₃	1	1	yes	characteristic
350	C₂²	#385×C₁₁₃	1	2	yes	—
351	C₂²	#386×C₁₁₃	1	2	yes	—
352	C₂²	#421×C₁₁₃	1	4	yes	—
353	C₄	—	2	4	no	—
354	C₄	—	4	8	no	—
355	C₄	—	8	4	no	—
356	C₄	C₄×C₂²⋊C₄×C₁₁₃	1	2	yes	—
357	C₄	#380×C₁₁₃	1	2	yes	—
358	C₄	#385×C₁₁₃	1	2	yes	—
359	C₄	#386×C₁₁₃	1	2	yes	—
360	C₂	—	2	1	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	2	no	—
363	C₂	—	4	4	no	—
364	C₂	C₁₁₃×C₂²⋊#95	1	1	yes	characteristic
365	C₂	C₁₁₃×#1733	1	2	yes	—
366	C₂	C₁₁₃×#1897	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁₃
socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁₃ ◁ C₂⁴×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#339×C₁₁₃	C₂	semidirect
9. C₂×#117×C₁₁₃	C₄	semidirect
15. #407×C₁₁₃	C₄	semidirect
18. #380×C₁₁₃	C₄	semidirect
107. C₄²×C₁₁₃	C₂²⋊C₄	semidirect
176. #10720	C₁₁₃	direct (N × H)
187. C₂×#339	C₂×C₁₁₃	semidirect
188. C₁₁₃	#10720	direct (N × H)
193. C₂×#117	C₄×C₁₁₃	semidirect
199. #407	C₄×C₁₁₃	semidirect
202. #380	C₄×C₁₁₃	semidirect
291. C₄²	C₂²⋊C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#117×C₁₁₃	2
C₂×#407×C₁₁₃	2
C₁₁₃×#2280	2
C₂×#339×C₁₁₃	2
#10720	113

Subgroups — C113×#10720 #43278740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#10720 #43278740