Subgroups — C₁₁₃×#7913 #43275933

Order 28928.

982 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	C₂×#407×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#381×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1280	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₁₃	—	2	1	no	—
7	C₂³×C₈×C₁₁₃	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₁₃	C₄	1	2	yes	—
9	#407×C₁₁₃	—	2	2	no	—
10	#407×C₁₁₃	C₄	1	4	yes	complemented
11	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₁₁₃	—	2	2	no	—
13	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
14	C₂×C₂²⋊C₈×C₁₁₃	C₄	1	4	yes	complemented
15	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
17	#381×C₁₁₃	—	2	1	no	—
18	#381×C₁₁₃	—	2	1	no	—
19	#381×C₁₁₃	—	2	1	no	—
20	#381×C₁₁₃	—	2	1	no	—
21	C₂×#95×C₁₁₃	C₄	1	2	yes	—
22	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
23	C₂⁵×C₁₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₁₃	—	4	4	no	—
25	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
26	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
31	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
32	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₁₃	Q₈	1	2	yes	—
35	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₁₃	—	2	4	no	—
37	C₂×M₁₆×C₁₁₃	—	4	4	no	—
38	C₂²×C₈×C₁₁₃	—	2	4	no	—
39	C₂²×C₈×C₁₁₃	—	2	2	no	—
40	C₂²×C₈×C₁₁₃	—	2	2	no	—
41	C₂²×C₈×C₁₁₃	—	4	4	no	—
42	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
45	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
46	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
47	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
48	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
49	C₂²⋊C₈×C₁₁₃	C₂×C₄	1	4	yes	—
50	C₂²⋊C₈×C₁₁₃	C₂×C₄	1	4	yes	—
51	#95×C₁₁₃	—	2	2	no	—
52	#95×C₁₁₃	—	2	2	no	—
53	#95×C₁₁₃	—	2	2	no	—
54	#95×C₁₁₃	—	2	2	no	—
55	C₂⁴×C₁₁₃	—	2	4	no	—
56	C₂⁴×C₁₁₃	—	2	4	no	—
57	C₂⁴×C₁₁₃	—	4	2	no	—
58	C₂⁴×C₁₁₃	C₄²	1	2	yes	—
59	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂⁴×C₁₁₃	C₄⋊C₄	1	2	yes	—
62	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₁₃	—	2	4	no	—
66	C₂²×C₄×C₁₁₃	—	2	8	no	—
67	C₂²×C₄×C₁₁₃	—	4	4	no	—
68	C₂²×C₄×C₁₁₃	—	4	4	no	—
69	C₂²×C₄×C₁₁₃	—	4	2	no	—
70	C₂²×C₄×C₁₁₃	—	4	4	no	—
71	C₂²×C₄×C₁₁₃	—	4	2	no	—
72	C₂²×C₄×C₁₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₁₃	—	4	4	no	—
74	C₂²×C₄×C₁₁₃	—	4	2	no	—
75	C₂²×C₄×C₁₁₃	—	4	4	no	—
76	C₂²×C₄×C₁₁₃	—	4	4	no	—
77	C₂²×C₄×C₁₁₃	C₄²	1	2	yes	—
78	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
88	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
95	M₁₆×C₁₁₃	—	4	8	no	—
96	C₂×C₈×C₁₁₃	—	2	4	no	—
97	C₂×C₈×C₁₁₃	—	2	4	no	—
98	C₂×C₈×C₁₁₃	—	4	8	no	—
99	C₂×C₈×C₁₁₃	—	4	4	no	—
100	C₂×C₈×C₁₁₃	—	4	4	no	—
101	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
102	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
103	C₂³×C₁₁₃	—	2	2	no	—
104	C₂³×C₁₁₃	—	2	2	no	—
105	C₂³×C₁₁₃	—	2	2	no	—
106	C₂³×C₁₁₃	—	2	2	no	—
107	C₂³×C₁₁₃	—	2	4	no	—
108	C₂³×C₁₁₃	—	2	4	no	—
109	C₂³×C₁₁₃	—	2	4	no	—
110	C₂³×C₁₁₃	—	2	2	no	—
111	C₂³×C₁₁₃	—	2	2	no	—
112	C₂³×C₁₁₃	—	2	2	no	—
113	C₂³×C₁₁₃	—	2	4	no	—
114	C₂³×C₁₁₃	—	4	2	no	—
115	C₂³×C₁₁₃	—	4	2	no	—
116	C₂³×C₁₁₃	—	4	16	no	—
117	C₂³×C₁₁₃	#95	1	2	yes	—
118	C₂³×C₁₁₃	#95	1	2	yes	—
119	C₂³×C₁₁₃	#99	1	4	yes	—
120	C₂³×C₁₁₃	C₂×C₄²	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	#131	1	4	yes	—
124	C₂×C₄×C₁₁₃	—	2	4	no	—
125	C₂×C₄×C₁₁₃	—	2	4	no	—
126	C₂×C₄×C₁₁₃	—	2	4	no	—
127	C₂×C₄×C₁₁₃	—	2	4	no	—
128	C₂×C₄×C₁₁₃	—	2	2	no	—
129	C₂×C₄×C₁₁₃	—	2	2	no	—
130	C₂×C₄×C₁₁₃	—	2	2	no	—
131	C₂×C₄×C₁₁₃	—	2	2	no	—
132	C₂×C₄×C₁₁₃	—	4	2	no	—
133	C₂×C₄×C₁₁₃	—	4	2	no	—
134	C₂×C₄×C₁₁₃	—	4	2	no	—
135	C₂×C₄×C₁₁₃	—	4	2	no	—
136	C₂×C₄×C₁₁₃	—	4	2	no	—
137	C₂×C₄×C₁₁₃	—	4	2	no	—
138	C₂×C₄×C₁₁₃	—	4	1	no	—
139	C₂×C₄×C₁₁₃	—	4	1	no	—
140	C₂×C₄×C₁₁₃	—	4	1	no	—
141	C₂×C₄×C₁₁₃	—	4	1	no	—
142	C₂×C₄×C₁₁₃	—	4	4	no	—
143	C₂×C₄×C₁₁₃	—	4	4	no	—
144	C₂×C₄×C₁₁₃	—	4	4	no	—
145	C₂×C₄×C₁₁₃	—	8	8	no	—
146	C₂×C₄×C₁₁₃	#95	1	2	yes	—
147	C₂×C₄×C₁₁₃	#95	1	2	yes	—
148	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₈×C₁₁₃	—	4	4	no	—
153	C₈×C₁₁₃	—	4	4	no	—
154	C₂²×C₁₁₃	—	2	8	no	—
155	C₂²×C₁₁₃	—	2	8	no	—
156	C₂²×C₁₁₃	—	2	2	no	—
157	C₂²×C₁₁₃	—	2	1	no	—
158	C₂²×C₁₁₃	—	2	1	no	—
159	C₂²×C₁₁₃	—	2	2	no	—
160	C₂²×C₁₁₃	—	2	1	no	—
161	C₂²×C₁₁₃	—	2	1	no	—
162	C₂²×C₁₁₃	—	2	2	no	—
163	C₂²×C₁₁₃	—	2	2	no	—
164	C₂²×C₁₁₃	—	2	2	no	—
165	C₂²×C₁₁₃	—	4	8	no	—
166	C₂²×C₁₁₃	—	4	8	no	—
167	C₂²×C₁₁₃	—	4	4	no	—
168	C₂²×C₁₁₃	#342	1	4	yes	—
169	C₂²×C₁₁₃	C₂×#95	1	1	yes	characteristic
170	C₂²×C₁₁₃	#405	1	2	yes	—
171	C₂²×C₁₁₃	#408	1	2	yes	—
172	C₂²×C₁₁₃	C₂×#99	1	2	yes	—
173	C₂²×C₁₁₃	#413	1	2	yes	—
174	C₂²×C₁₁₃	#424	1	2	yes	—
175	C₄×C₁₁₃	—	2	1	no	—
176	C₄×C₁₁₃	—	2	1	no	—
177	C₄×C₁₁₃	—	2	2	no	—
178	C₄×C₁₁₃	—	2	2	no	—
179	C₄×C₁₁₃	—	2	1	no	—
180	C₄×C₁₁₃	—	2	1	no	—
181	C₄×C₁₁₃	—	8	4	no	—
182	#7913	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₁₁₃	—	2	4	no	—
184	C₂×C₁₁₃	—	2	2	no	—
185	C₂×C₁₁₃	—	2	2	no	—
186	C₂×C₁₁₃	—	4	2	no	—
187	C₂×C₁₁₃	#1468	1	4	yes	—
188	C₂×C₁₁₃	#1729	1	1	yes	characteristic
189	C₂×C₁₁₃	C₂×#342	1	1	yes	characteristic
190	C₂×C₁₁₃	#1742	1	1	yes	characteristic
191	C₂×#407	C₂×C₁₁₃	1	1	yes	characteristic
192	C₂²×C₂²⋊C₈	C₂×C₁₁₃	1	1	yes	characteristic
193	C₂×#381	C₂×C₁₁₃	1	1	yes	characteristic
194	#1280	C₂×C₁₁₃	1	4	yes	complemented
195	C₁₁₃	#7913	1	1	yes	characteristic, direct product factor, Sylow
196	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
197	C₂²×M₁₆	—	2	1	no	—
198	C₂³×C₈	—	2	1	no	—
199	C₂²×C₂²⋊C₄	C₄×C₁₁₃	1	2	yes	—
200	#407	—	2	2	no	—
201	#407	C₄×C₁₁₃	1	4	yes	complemented
202	C₂×C₂²⋊C₈	—	2	1	no	—
203	C₂×C₂²⋊C₈	—	2	2	no	—
204	C₂×C₂²⋊C₈	—	2	1	no	—
205	C₂×C₂²⋊C₈	C₄×C₁₁₃	1	4	yes	complemented
206	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
207	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
208	#381	—	2	1	no	—
209	#381	—	2	1	no	—
210	#381	—	2	1	no	—
211	#381	—	2	1	no	—
212	C₂×#95	C₄×C₁₁₃	1	2	yes	—
213	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
214	C₂⁵	C₂×C₄×C₁₁₃	1	1	yes	characteristic
215	C₂³×C₄	—	4	4	no	—
216	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
217	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
219	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
220	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
223	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
225	C₂³×C₄	Q₈×C₁₁₃	1	2	yes	—
226	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	—	4	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	4	4	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	4	4	no	—
236	C₂²⋊C₈	—	2	4	no	—
237	C₂²⋊C₈	—	2	4	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	C₂×C₄×C₁₁₃	1	4	yes	—
241	C₂²⋊C₈	C₂×C₄×C₁₁₃	1	4	yes	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	C₂⁴	—	2	4	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	4	2	no	—
249	C₂⁴	C₄²×C₁₁₃	1	2	yes	—
250	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
251	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
252	C₂⁴	C₄⋊C₄×C₁₁₃	1	2	yes	—
253	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	—	4	4	no	—
268	C₂²×C₄	C₄²×C₁₁₃	1	2	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	2	yes	—
272	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
274	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
275	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
276	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
277	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
278	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
279	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
286	M₁₆	—	4	8	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	8	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	16	no	—
308	C₂³	#95×C₁₁₃	1	2	yes	—
309	C₂³	#95×C₁₁₃	1	2	yes	—
310	C₂³	#99×C₁₁₃	1	4	yes	—
311	C₂³	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
312	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
313	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
314	C₂³	#131×C₁₁₃	1	4	yes	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	8	8	no	—
337	C₂×C₄	#95×C₁₁₃	1	2	yes	—
338	C₂×C₄	#95×C₁₁₃	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
343	C₈	—	4	4	no	—
344	C₈	—	4	4	no	—
345	C₂²	—	2	8	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	8	no	—
358	C₂²	—	4	4	no	—
359	C₂²	#342×C₁₁₃	1	4	yes	—
360	C₂²	C₂×#95×C₁₁₃	1	1	yes	characteristic
361	C₂²	#405×C₁₁₃	1	2	yes	—
362	C₂²	#408×C₁₁₃	1	2	yes	—
363	C₂²	C₂×#99×C₁₁₃	1	2	yes	—
364	C₂²	#413×C₁₁₃	1	2	yes	—
365	C₂²	#424×C₁₁₃	1	2	yes	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	4	no	—
373	C₂	—	2	4	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	—	4	2	no	—
377	C₂	C₁₁₃×#1468	1	4	yes	—
378	C₂	C₁₁₃×#1729	1	1	yes	characteristic
379	C₂	C₂×#342×C₁₁₃	1	1	yes	characteristic
380	C₂	C₁₁₃×#1742	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₁₃×#1280	C₂	semidirect
10. #407×C₁₁₃	C₄	semidirect
14. C₂×C₂²⋊C₈×C₁₁₃	C₄	semidirect
182. #7913	C₁₁₃	direct (N × H)
194. #1280	C₂×C₁₁₃	semidirect
195. C₁₁₃	#7913	direct (N × H)
201. #407	C₄×C₁₁₃	semidirect
205. C₂×C₂²⋊C₈	C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#407×C₁₁₃	2
C₂²×C₂²⋊C₈×C₁₁₃	2
C₂×#381×C₁₁₃	2
C₁₁₃×#1280	2
#7913	113

Subgroups — C113×#7913 #43275933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#7913 #43275933