Subgroups — C₁₁₃×#20731 #43288751

Order 28928.

1242 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2921	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#1821	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#1801	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1800	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1785	C₂	1	2	yes	maximal
7	C₄×#101×C₁₁₃	C₂	1	2	yes	maximal, complemented
8	C₄×#100×C₁₁₃	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
10	#520×C₁₁₃	—	2	8	no	—
11	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₁₃	C₄	1	2	yes	—
18	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₁₃	C₄	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
21	#433×C₁₁₃	—	2	8	no	—
22	#423×C₁₁₃	C₂²	1	4	yes	—
23	C₂×#101×C₁₁₃	C₂²	1	4	yes	—
24	C₂×#100×C₁₁₃	C₂²	1	4	yes	—
25	#407×C₁₁₃	C₂²	1	4	yes	—
26	C₄×M₁₆×C₁₁₃	C₂²	1	4	yes	—
27	#343×C₁₁₃	C₂²	1	4	yes	—
28	#343×C₁₁₃	C₂²	1	4	yes	—
29	C₂×#41×C₁₁₃	—	2	4	no	—
30	C₂×#41×C₁₁₃	—	2	4	no	—
31	C₂×#41×C₁₁₃	—	2	4	no	—
32	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₁₃	C₂³	1	8	yes	—
41	C₄×Q₈×C₁₁₃	—	2	4	no	—
42	C₄×Q₈×C₁₁₃	—	2	4	no	—
43	C₄×D₄×C₁₁₃	—	2	8	no	—
44	C₄×D₄×C₁₁₃	—	2	8	no	—
45	C₄×D₄×C₁₁₃	—	2	4	no	—
46	C₄×D₄×C₁₁₃	—	2	4	no	—
47	#117×C₁₁₃	—	2	8	no	—
48	#117×C₁₁₃	D₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₁₁₃	—	2	8	no	—
67	#101×C₁₁₃	—	2	8	no	—
68	#100×C₁₁₃	—	2	8	no	—
69	C₂²⋊C₈×C₁₁₃	—	2	8	no	—
70	#97×C₁₁₃	—	2	4	no	—
71	C₄×C₈×C₁₁₃	—	2	4	no	—
72	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
74	#41×C₁₁₃	—	2	32	no	—
75	C₂×Q₈×C₁₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₁₃	#41	1	4	yes	—
78	C₂×D₄×C₁₁₃	—	2	4	no	—
79	C₂×D₄×C₁₁₃	—	2	4	no	—
80	C₂×D₄×C₁₁₃	—	2	4	no	—
81	C₂×D₄×C₁₁₃	—	2	2	no	—
82	C₂×D₄×C₁₁₃	—	2	2	no	—
83	C₂×D₄×C₁₁₃	#41	1	4	yes	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₁₃	—	8	2	no	—
93	C₂²×C₄×C₁₁₃	—	8	2	no	—
94	C₂²×C₄×C₁₁₃	—	8	2	no	—
95	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₁₁₃	—	2	8	no	—
106	M₁₆×C₁₁₃	—	2	8	no	—
107	C₂×C₈×C₁₁₃	—	2	8	no	—
108	C₄⋊C₄×C₁₁₃	—	2	4	no	—
109	C₄⋊C₄×C₁₁₃	—	2	4	no	—
110	C₄⋊C₄×C₁₁₃	—	2	4	no	—
111	C₄⋊C₄×C₁₁₃	—	2	2	no	—
112	C₄⋊C₄×C₁₁₃	—	2	2	no	—
113	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
114	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
115	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
116	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
117	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
118	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₁₁₃	—	2	4	no	—
120	C₄²×C₁₁₃	—	2	4	no	—
121	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
122	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
123	C₂³×C₁₁₃	—	2	2	no	—
124	C₂³×C₁₁₃	—	2	1	no	—
125	C₂³×C₁₁₃	—	2	1	no	—
126	C₂³×C₁₁₃	—	2	2	no	—
127	C₂³×C₁₁₃	—	4	1	no	—
128	C₂³×C₁₁₃	—	4	1	no	—
129	C₂³×C₁₁₃	—	4	2	no	—
130	C₂³×C₁₁₃	—	4	2	no	—
131	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂³×C₁₁₃	#117	1	4	yes	—
133	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
134	Q₈×C₁₁₃	—	2	8	no	—
135	D₄×C₁₁₃	—	2	16	no	—
136	D₄×C₁₁₃	—	2	8	no	—
137	C₂×C₄×C₁₁₃	—	2	16	no	—
138	C₂×C₄×C₁₁₃	—	2	2	no	—
139	C₂×C₄×C₁₁₃	—	2	1	no	—
140	C₂×C₄×C₁₁₃	—	2	1	no	—
141	C₂×C₄×C₁₁₃	—	2	2	no	—
142	C₂×C₄×C₁₁₃	—	2	8	no	—
143	C₂×C₄×C₁₁₃	—	2	2	no	—
144	C₂×C₄×C₁₁₃	—	2	2	no	—
145	C₂×C₄×C₁₁₃	—	4	1	no	—
146	C₂×C₄×C₁₁₃	—	4	1	no	—
147	C₂×C₄×C₁₁₃	—	4	1	no	—
148	C₂×C₄×C₁₁₃	—	4	1	no	—
149	C₂×C₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	4	2	no	—
151	C₂×C₄×C₁₁₃	—	8	4	no	—
152	C₂×C₄×C₁₁₃	—	8	4	no	—
153	C₂×C₄×C₁₁₃	—	8	4	no	—
154	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₁₃	#117	1	4	yes	—
160	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
163	C₈×C₁₁₃	—	4	8	no	—
164	C₂²×C₁₁₃	—	2	1	no	—
165	C₂²×C₁₁₃	—	2	1	no	—
166	C₂²×C₁₁₃	—	2	2	no	—
167	C₂²×C₁₁₃	—	2	2	no	—
168	C₂²×C₁₁₃	—	2	2	no	—
169	C₂²×C₁₁₃	—	2	4	no	—
170	C₂²×C₁₁₃	—	4	4	no	—
171	C₂²×C₁₁₃	—	4	2	no	—
172	C₂²×C₁₁₃	—	4	2	no	—
173	C₂²×C₁₁₃	—	4	4	no	—
174	C₂²×C₁₁₃	—	4	2	no	—
175	C₂²×C₁₁₃	—	4	2	no	—
176	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
178	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
179	C₄×C₁₁₃	—	2	2	no	—
180	C₄×C₁₁₃	—	2	2	no	—
181	C₄×C₁₁₃	—	2	2	no	—
182	C₄×C₁₁₃	—	2	2	no	—
183	C₄×C₁₁₃	—	2	2	no	—
184	C₄×C₁₁₃	—	2	4	no	—
185	C₄×C₁₁₃	—	4	2	no	—
186	C₄×C₁₁₃	—	4	2	no	—
187	C₄×C₁₁₃	#525	1	4	yes	—
188	#20731	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂×C₁₁₃	—	2	1	no	—
190	C₂×C₁₁₃	—	2	1	no	—
191	C₂×C₁₁₃	—	4	2	no	—
192	C₂×C₁₁₃	—	4	4	no	—
193	C₂×C₁₁₃	#2280	1	1	yes	characteristic
194	C₂×C₁₁₃	#2888	1	1	yes	characteristic
195	C₂×C₁₁₃	#2889	1	1	yes	characteristic
196	C₂×#520	C₂×C₁₁₃	1	1	yes	characteristic
197	#2921	C₂×C₁₁₃	1	2	yes	complemented
198	#1821	C₂×C₁₁₃	1	2	yes	complemented
199	#1801	C₂×C₁₁₃	1	2	yes	complemented
200	#1800	C₂×C₁₁₃	1	2	yes	complemented
201	#1785	C₂×C₁₁₃	1	2	yes	—
202	C₄×#101	C₂×C₁₁₃	1	2	yes	complemented
203	C₄×#100	C₂×C₁₁₃	1	2	yes	complemented
204	C₁₁₃	#20731	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
206	#520	—	2	8	no	—
207	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
208	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
209	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	—
210	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
213	C₂×#117	C₄×C₁₁₃	1	2	yes	—
214	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	C₄×C₁₁₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
217	#433	—	2	8	no	—
218	#423	C₂²×C₁₁₃	1	4	yes	—
219	C₂×#101	C₂²×C₁₁₃	1	4	yes	—
220	C₂×#100	C₂²×C₁₁₃	1	4	yes	—
221	#407	C₂²×C₁₁₃	1	4	yes	—
222	C₄×M₁₆	C₂²×C₁₁₃	1	4	yes	—
223	#343	C₂²×C₁₁₃	1	4	yes	—
224	#343	C₂²×C₁₁₃	1	4	yes	—
225	C₂×#41	—	2	4	no	—
226	C₂×#41	—	2	4	no	—
227	C₂×#41	—	2	4	no	—
228	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
229	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
230	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
232	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
233	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
234	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
236	C₂×M₁₆	C₂³×C₁₁₃	1	8	yes	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×D₄	—	2	8	no	—
240	C₄×D₄	—	2	8	no	—
241	C₄×D₄	—	2	4	no	—
242	C₄×D₄	—	2	4	no	—
243	#117	—	2	8	no	—
244	#117	D₄×C₁₁₃	1	8	yes	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
259	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
262	C₄⋊C₈	—	2	8	no	—
263	#101	—	2	8	no	—
264	#100	—	2	8	no	—
265	C₂²⋊C₈	—	2	8	no	—
266	#97	—	2	4	no	—
267	C₄×C₈	—	2	4	no	—
268	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
269	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
270	#41	—	2	32	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	#41×C₁₁₃	1	4	yes	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	#41×C₁₁₃	1	4	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	8	2	no	—
289	C₂²×C₄	—	8	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
301	M₁₆	—	2	8	no	—
302	M₁₆	—	2	8	no	—
303	C₂×C₈	—	2	8	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
310	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
314	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
318	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
328	C₂³	#117×C₁₁₃	1	4	yes	—
329	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
330	Q₈	—	2	8	no	—
331	D₄	—	2	16	no	—
332	D₄	—	2	8	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	—	8	4	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
355	C₂×C₄	#117×C₁₁₃	1	4	yes	—
356	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
357	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
358	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
359	C₈	—	4	8	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
373	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
374	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	#525×C₁₁₃	1	4	yes	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	4	2	no	—
387	C₂	—	4	4	no	—
388	C₂	C₁₁₃×#2280	1	1	yes	characteristic
389	C₂	C₁₁₃×#2888	1	1	yes	characteristic
390	C₂	C₁₁₃×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂²×#41×C₁₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂×#117×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₃×#2921	C₂	semidirect
3. C₁₁₃×#1821	C₂	semidirect
4. C₁₁₃×#1801	C₂	semidirect
5. C₁₁₃×#1800	C₂	semidirect
7. C₄×#101×C₁₁₃	C₂	semidirect
8. C₄×#100×C₁₁₃	C₂	semidirect
188. #20731	C₁₁₃	direct (N × H)
197. #2921	C₂×C₁₁₃	semidirect
198. #1821	C₂×C₁₁₃	semidirect
199. #1801	C₂×C₁₁₃	semidirect
200. #1800	C₂×C₁₁₃	semidirect
202. C₄×#101	C₂×C₁₁₃	semidirect
203. C₄×#100	C₂×C₁₁₃	semidirect
204. C₁₁₃	#20731	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#520×C₁₁₃	2
C₁₁₃×#2921	2
C₁₁₃×#1821	2
C₁₁₃×#1801	2
C₁₁₃×#1800	2
C₁₁₃×#1785	2
C₄×#101×C₁₁₃	2
C₄×#100×C₁₁₃	2
#20731	113

Subgroups — C113×#20731 #43288751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20731 #43288751