Subgroups — C₁₁₃×#10732 #43278752

Order 28928.

1510 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₁₃	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	—	2	2	no	—
7	C₂²×M₁₆×C₁₁₃	—	2	1	no	—
8	C₂²×M₁₆×C₁₁₃	—	2	8	no	—
9	C₂²×M₁₆×C₁₁₃	C₄	1	4	yes	complemented
10	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₁₃	—	2	1	no	—
12	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
14	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
15	#381×C₁₁₃	—	2	1	no	—
16	#380×C₁₁₃	C₄	1	2	yes	complemented
17	#380×C₁₁₃	C₄	1	2	yes	complemented
18	#379×C₁₁₃	—	2	1	no	—
19	C₄×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
21	C₄×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
22	C₄×C₂²⋊C₄×C₁₁₃	C₄	1	4	yes	complemented
23	C₂×#95×C₁₁₃	—	2	1	no	—
24	#339×C₁₁₃	—	2	8	no	—
25	C₂⁵×C₁₁₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₁₃	—	2	4	no	—
27	C₂³×C₄×C₁₁₃	—	2	4	no	—
28	C₂³×C₄×C₁₁₃	—	2	2	no	—
29	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
35	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₁₃	Q₈	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₁₃	—	2	16	no	—
40	C₂×M₁₆×C₁₁₃	—	2	8	no	—
41	C₂×M₁₆×C₁₁₃	—	2	4	no	—
42	C₂×M₁₆×C₁₁₃	—	2	2	no	—
43	C₂×M₁₆×C₁₁₃	—	2	4	no	—
44	C₂×M₁₆×C₁₁₃	—	2	16	no	—
45	C₂×M₁₆×C₁₁₃	C₂×C₄	1	4	yes	—
46	C₂×M₁₆×C₁₁₃	D₄	1	8	yes	—
47	C₂²×C₈×C₁₁₃	—	2	8	no	—
48	C₂²×C₈×C₁₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₁₃	—	2	2	no	—
50	#117×C₁₁₃	—	2	4	no	—
51	#117×C₁₁₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₁₃	—	2	4	no	—
59	C₂×C₄²×C₁₁₃	—	2	4	no	—
60	C₂×C₄²×C₁₁₃	—	2	2	no	—
61	C₂×C₄²×C₁₁₃	—	2	2	no	—
62	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
63	#95×C₁₁₃	—	2	4	no	—
64	#95×C₁₁₃	—	2	2	no	—
65	#95×C₁₁₃	—	2	2	no	—
66	C₂⁴×C₁₁₃	—	2	4	no	—
67	C₂⁴×C₁₁₃	—	2	4	no	—
68	C₂⁴×C₁₁₃	—	4	2	no	—
69	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
71	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₁₁₃	C₄⋊C₄	1	2	yes	—
73	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₁₃	—	2	8	no	—
78	C₂²×C₄×C₁₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₁₃	—	2	4	no	—
80	C₂²×C₄×C₁₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	4	4	no	—
91	C₂²×C₄×C₁₁₃	—	4	4	no	—
92	C₂²×C₄×C₁₁₃	C₄²	1	2	yes	—
93	C₂²×C₄×C₁₁₃	C₄²	1	2	yes	—
94	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
112	M₁₆×C₁₁₃	—	2	16	no	—
113	M₁₆×C₁₁₃	—	2	4	no	—
114	M₁₆×C₁₁₃	—	2	8	no	—
115	M₁₆×C₁₁₃	C₂²⋊C₄	1	8	yes	complemented
116	C₂×C₈×C₁₁₃	—	2	16	no	—
117	C₂×C₈×C₁₁₃	—	2	4	no	—
118	C₂×C₈×C₁₁₃	—	2	8	no	—
119	C₄⋊C₄×C₁₁₃	—	2	8	no	—
120	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
121	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
122	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
123	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
124	C₄²×C₁₁₃	—	2	8	no	—
125	C₄²×C₁₁₃	—	4	2	no	—
126	C₄²×C₁₁₃	—	4	2	no	—
127	C₄²×C₁₁₃	—	4	2	no	—
128	C₄²×C₁₁₃	—	4	2	no	—
129	C₂³×C₁₁₃	—	2	2	no	—
130	C₂³×C₁₁₃	—	2	2	no	—
131	C₂³×C₁₁₃	—	2	2	no	—
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	2	4	no	—
134	C₂³×C₁₁₃	—	2	4	no	—
135	C₂³×C₁₁₃	—	2	4	no	—
136	C₂³×C₁₁₃	—	2	4	no	—
137	C₂³×C₁₁₃	—	2	2	no	—
138	C₂³×C₁₁₃	—	2	2	no	—
139	C₂³×C₁₁₃	—	2	2	no	—
140	C₂³×C₁₁₃	—	4	2	no	—
141	C₂³×C₁₁₃	—	4	2	no	—
142	C₂³×C₁₁₃	—	4	16	no	—
143	C₂³×C₁₁₃	#95	1	2	yes	—
144	C₂³×C₁₁₃	#95	1	2	yes	—
145	C₂³×C₁₁₃	#104	1	4	yes	—
146	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂³×C₁₁₃	#121	1	4	yes	—
150	C₂×C₄×C₁₁₃	—	2	4	no	—
151	C₂×C₄×C₁₁₃	—	2	4	no	—
152	C₂×C₄×C₁₁₃	—	2	2	no	—
153	C₂×C₄×C₁₁₃	—	2	2	no	—
154	C₂×C₄×C₁₁₃	—	2	4	no	—
155	C₂×C₄×C₁₁₃	—	2	4	no	—
156	C₂×C₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	2	2	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	2	4	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	2	4	no	—
164	C₂×C₄×C₁₁₃	—	2	8	no	—
165	C₂×C₄×C₁₁₃	—	4	16	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	4	4	no	—
168	C₂×C₄×C₁₁₃	—	4	4	no	—
169	C₂×C₄×C₁₁₃	—	4	4	no	—
170	C₂×C₄×C₁₁₃	—	4	4	no	—
171	C₂×C₄×C₁₁₃	#95	1	2	yes	—
172	C₂×C₄×C₁₁₃	#95	1	2	yes	—
173	C₂×C₄×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁₃	#117	1	2	yes	—
179	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₁₁₃	#120	1	2	yes	—
182	C₂×C₄×C₁₁₃	#120	1	2	yes	—
183	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₁₁₃	#123	1	2	yes	—
185	C₂×C₄×C₁₁₃	#123	1	2	yes	—
186	C₈×C₁₁₃	—	2	8	no	—
187	C₂²×C₁₁₃	—	2	8	no	—
188	C₂²×C₁₁₃	—	2	8	no	—
189	C₂²×C₁₁₃	—	2	2	no	—
190	C₂²×C₁₁₃	—	2	1	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	—	2	1	no	—
193	C₂²×C₁₁₃	—	2	2	no	—
194	C₂²×C₁₁₃	—	2	1	no	—
195	C₂²×C₁₁₃	—	2	2	no	—
196	C₂²×C₁₁₃	—	2	2	no	—
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	—	4	8	no	—
199	C₂²×C₁₁₃	—	4	8	no	—
200	C₂²×C₁₁₃	—	4	4	no	—
201	C₂²×C₁₁₃	#339	1	4	yes	complemented
202	C₂²×C₁₁₃	C₂×#95	1	1	yes	characteristic
203	C₂²×C₁₁₃	#380	1	2	yes	—
204	C₂²×C₁₁₃	#386	1	2	yes	—
205	C₂²×C₁₁₃	#386	1	2	yes	—
206	C₂²×C₁₁₃	C₂×#104	1	2	yes	—
207	C₂²×C₁₁₃	#421	1	2	yes	—
208	C₄×C₁₁₃	—	2	2	no	—
209	C₄×C₁₁₃	—	2	2	no	—
210	C₄×C₁₁₃	—	4	8	no	—
211	C₄×C₁₁₃	—	8	4	no	—
212	C₄×C₁₁₃	C₄×C₂²⋊C₄	1	2	yes	—
213	C₄×C₁₁₃	#379	1	1	yes	characteristic
214	C₄×C₁₁₃	#381	1	1	yes	characteristic
215	C₄×C₁₁₃	#385	1	2	yes	—
216	C₄×C₁₁₃	#385	1	2	yes	—
217	#10732	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂×C₁₁₃	—	2	2	no	—
219	C₂×C₁₁₃	—	2	4	no	—
220	C₂×C₁₁₃	—	2	2	no	—
221	C₂×C₁₁₃	—	4	2	no	—
222	C₂×C₁₁₃	C₂²⋊#95	1	1	yes	characteristic
223	C₂×C₁₁₃	C₂×#339	1	1	yes	characteristic
224	C₂×C₁₁₃	#1733	1	1	yes	characteristic
225	C₂×C₁₁₃	#1871	1	4	yes	—
226	C₂³×M₁₆	C₂×C₁₁₃	1	1	yes	characteristic
227	#2280	C₂×C₁₁₃	1	1	yes	characteristic
228	C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
229	C₂×#339	C₂×C₁₁₃	1	4	yes	complemented
230	C₁₁₃	#10732	1	1	yes	characteristic, direct product factor, Sylow
231	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
232	C₂²×M₁₆	—	2	2	no	—
233	C₂²×M₁₆	—	2	1	no	—
234	C₂²×M₁₆	—	2	8	no	—
235	C₂²×M₁₆	C₄×C₁₁₃	1	4	yes	complemented
236	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
237	C₂³×C₈	—	2	1	no	—
238	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
239	C₂²×C₂²⋊C₄	—	2	1	no	—
240	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
241	#381	—	2	1	no	—
242	#380	C₄×C₁₁₃	1	2	yes	complemented
243	#380	C₄×C₁₁₃	1	2	yes	complemented
244	#379	—	2	1	no	—
245	C₄×C₂²⋊C₄	—	2	2	no	—
246	C₄×C₂²⋊C₄	—	2	1	no	—
247	C₄×C₂²⋊C₄	—	2	1	no	—
248	C₄×C₂²⋊C₄	C₄×C₁₁₃	1	4	yes	complemented
249	C₂×#95	—	2	1	no	—
250	#339	—	2	8	no	—
251	C₂⁵	D₄×C₁₁₃	1	1	yes	characteristic
252	C₂³×C₄	—	2	4	no	—
253	C₂³×C₄	—	2	4	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
256	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
257	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
259	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
260	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
262	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
263	C₂³×C₄	Q₈×C₁₁₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
265	C₂×M₁₆	—	2	16	no	—
266	C₂×M₁₆	—	2	8	no	—
267	C₂×M₁₆	—	2	4	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	4	no	—
270	C₂×M₁₆	—	2	16	no	—
271	C₂×M₁₆	C₂×C₄×C₁₁₃	1	4	yes	—
272	C₂×M₁₆	D₄×C₁₁₃	1	8	yes	—
273	C₂²×C₈	—	2	8	no	—
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	—	2	2	no	—
276	#117	—	2	4	no	—
277	#117	—	2	4	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
289	#95	—	2	4	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	4	2	no	—
295	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
296	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
297	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
298	C₂⁴	C₄⋊C₄×C₁₁₃	1	2	yes	—
299	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	C₄²×C₁₁₃	1	2	yes	—
319	C₂²×C₄	C₄²×C₁₁₃	1	2	yes	—
320	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
321	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
324	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
325	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
326	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
327	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
328	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
329	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
336	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
337	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
338	M₁₆	—	2	16	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	8	no	—
341	M₁₆	C₂²⋊C₄×C₁₁₃	1	8	yes	complemented
342	C₂×C₈	—	2	16	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	16	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₄²	—	2	8	no	—
351	C₄²	—	4	2	no	—
352	C₄²	—	4	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	—	4	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	16	no	—
369	C₂³	#95×C₁₁₃	1	2	yes	—
370	C₂³	#95×C₁₁₃	1	2	yes	—
371	C₂³	#104×C₁₁₃	1	4	yes	—
372	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
373	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
374	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
375	C₂³	#121×C₁₁₃	1	4	yes	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	4	16	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	#95×C₁₁₃	1	2	yes	—
398	C₂×C₄	#95×C₁₁₃	1	2	yes	—
399	C₂×C₄	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
404	C₂×C₄	#117×C₁₁₃	1	2	yes	—
405	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
406	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
407	C₂×C₄	#120×C₁₁₃	1	2	yes	—
408	C₂×C₄	#120×C₁₁₃	1	2	yes	—
409	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
410	C₂×C₄	#123×C₁₁₃	1	2	yes	—
411	C₂×C₄	#123×C₁₁₃	1	2	yes	—
412	C₈	—	2	8	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	4	8	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	4	4	no	—
427	C₂²	#339×C₁₁₃	1	4	yes	complemented
428	C₂²	C₂×#95×C₁₁₃	1	1	yes	characteristic
429	C₂²	#380×C₁₁₃	1	2	yes	—
430	C₂²	#386×C₁₁₃	1	2	yes	—
431	C₂²	#386×C₁₁₃	1	2	yes	—
432	C₂²	C₂×#104×C₁₁₃	1	2	yes	—
433	C₂²	#421×C₁₁₃	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	8	no	—
437	C₄	—	8	4	no	—
438	C₄	C₄×C₂²⋊C₄×C₁₁₃	1	2	yes	—
439	C₄	#379×C₁₁₃	1	1	yes	characteristic
440	C₄	#381×C₁₁₃	1	1	yes	characteristic
441	C₄	#385×C₁₁₃	1	2	yes	—
442	C₄	#385×C₁₁₃	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	2	4	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	2	no	—
447	C₂	C₁₁₃×C₂²⋊#95	1	1	yes	characteristic
448	C₂	C₂×#339×C₁₁₃	1	1	yes	characteristic
449	C₂	C₁₁₃×#1733	1	1	yes	characteristic
450	C₂	C₁₁₃×#1871	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. C₂²×M₁₆×C₁₁₃	C₄	semidirect
16. #380×C₁₁₃	C₄	semidirect
17. #380×C₁₁₃	C₄	semidirect
22. C₄×C₂²⋊C₄×C₁₁₃	C₄	semidirect
115. M₁₆×C₁₁₃	C₂²⋊C₄	semidirect
201. C₂²×C₁₁₃	#339	semidirect
217. #10732	C₁₁₃	direct (N × H)
229. C₂×#339	C₂×C₁₁₃	semidirect
230. C₁₁₃	#10732	direct (N × H)
235. C₂²×M₁₆	C₄×C₁₁₃	semidirect
242. #380	C₄×C₁₁₃	semidirect
243. #380	C₄×C₁₁₃	semidirect
248. C₄×C₂²⋊C₄	C₄×C₁₁₃	semidirect
341. M₁₆	C₂²⋊C₄×C₁₁₃	semidirect
427. C₂²	#339×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₁₃	2
C₁₁₃×#2280	2
C₂×C₄×C₂²⋊C₄×C₁₁₃	2
C₂×#339×C₁₁₃	2
#10732	113

Subgroups — C113×#10732 #43278752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#10732 #43278752