Subgroups — C₁₁₃×#23512 #43291532

Order 28928.

1414 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#419×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#416×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#103×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁₃×#2043	C₂	1	4	yes	maximal, complemented
8	C₁₁₃×#2042	C₂	1	4	yes	maximal, complemented
9	C₁₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	#536×C₁₁₃	—	2	4	no	—
15	#536×C₁₁₃	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
17	C₂×#124×C₁₁₃	C₂²	1	2	yes	—
18	C₂×#123×C₁₁₃	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
20	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
23	#419×C₁₁₃	—	2	4	no	—
24	#417×C₁₁₃	—	2	4	no	—
25	#416×C₁₁₃	—	2	4	no	—
26	C₂×#103×C₁₁₃	—	2	4	no	—
27	C₂×#103×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#103×C₁₁₃	C₂²	1	4	yes	—
29	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
30	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
31	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
32	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
33	#389×C₁₁₃	—	2	2	no	—
34	#389×C₁₁₃	C₂²	1	4	yes	—
35	#380×C₁₁₃	—	2	2	no	—
36	#336×C₁₁₃	C₂²	1	4	yes	—
37	C₂×#41×C₁₁₃	—	2	2	no	—
38	C₂×#41×C₁₁₃	—	2	2	no	—
39	C₂×#41×C₁₁₃	—	2	2	no	—
40	C₂×#41×C₁₁₃	—	2	2	no	—
41	C₂×#41×C₁₁₃	—	2	2	no	—
42	C₂×#41×C₁₁₃	D₄	1	4	yes	—
43	C₂²×Q₈×C₁₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₁₃	—	2	2	no	—
45	C₂²×Q₈×C₁₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₁₃	D₄	1	4	yes	—
50	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₁₃	—	2	1	no	—
57	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₁₁₃	—	2	2	no	—
59	C₂×M₁₆×C₁₁₃	—	2	2	no	—
60	C₂×M₁₆×C₁₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₁₃	—	2	2	no	—
64	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₁₁₃	—	2	4	no	—
67	C₄⋊Q₈×C₁₁₃	—	2	4	no	—
68	#124×C₁₁₃	—	2	4	no	—
69	#124×C₁₁₃	—	2	4	no	—
70	#123×C₁₁₃	—	2	16	no	—
71	C₂²⋊Q₈×C₁₁₃	—	2	16	no	—
72	#117×C₁₁₃	—	2	2	no	—
73	#117×C₁₁₃	—	2	2	no	—
74	#117×C₁₁₃	—	2	2	no	—
75	#117×C₁₁₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₁₃	D₄	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
87	C₂×C₄²×C₁₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
89	#103×C₁₁₃	—	2	4	no	—
90	#103×C₁₁₃	—	2	8	no	—
91	#103×C₁₁₃	—	2	8	no	—
92	#103×C₁₁₃	—	2	4	no	—
93	#102×C₁₁₃	—	2	4	no	—
94	#102×C₁₁₃	—	2	4	no	—
95	#95×C₁₁₃	—	2	4	no	—
96	C₂⁴×C₁₁₃	—	2	1	no	—
97	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
98	#41×C₁₁₃	—	2	8	no	—
99	#41×C₁₁₃	—	2	8	no	—
100	#41×C₁₁₃	—	4	4	no	—
101	#41×C₁₁₃	—	4	4	no	—
102	C₂×Q₈×C₁₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₁₃	—	2	8	no	—
107	C₂×Q₈×C₁₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₁₃	—	4	2	no	—
116	C₂×Q₈×C₁₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₁₃	—	2	4	no	—
122	C₂×D₄×C₁₁₃	—	2	1	no	—
123	C₂×D₄×C₁₁₃	—	2	1	no	—
124	C₂×D₄×C₁₁₃	—	2	1	no	—
125	C₂×D₄×C₁₁₃	—	2	1	no	—
126	C₂×D₄×C₁₁₃	—	2	1	no	—
127	C₂×D₄×C₁₁₃	—	4	2	no	—
128	C₂×D₄×C₁₁₃	—	4	2	no	—
129	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₁₃	—	8	2	no	—
142	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
148	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
149	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
150	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₁₁₃	—	4	4	no	—
152	C₂×C₈×C₁₁₃	—	2	2	no	—
153	C₂×C₈×C₁₁₃	—	2	2	no	—
154	C₂×C₈×C₁₁₃	—	2	2	no	—
155	C₂×C₈×C₁₁₃	—	2	2	no	—
156	C₂×C₈×C₁₁₃	—	2	2	no	—
157	C₂×C₈×C₁₁₃	—	2	2	no	—
158	C₂×C₈×C₁₁₃	—	4	4	no	—
159	C₄⋊C₄×C₁₁₃	—	2	16	no	—
160	C₄⋊C₄×C₁₁₃	—	2	4	no	—
161	C₄⋊C₄×C₁₁₃	—	2	4	no	—
162	C₄⋊C₄×C₁₁₃	—	2	2	no	—
163	C₄⋊C₄×C₁₁₃	—	2	2	no	—
164	C₄⋊C₄×C₁₁₃	—	2	2	no	—
165	C₄⋊C₄×C₁₁₃	—	8	4	no	—
166	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
167	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
168	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
169	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
170	C₄²×C₁₁₃	—	2	2	no	—
171	C₄²×C₁₁₃	—	2	2	no	—
172	C₄²×C₁₁₃	—	4	2	no	—
173	C₂³×C₁₁₃	—	2	2	no	—
174	C₂³×C₁₁₃	—	2	2	no	—
175	C₂³×C₁₁₃	—	2	2	no	—
176	C₂³×C₁₁₃	—	4	1	no	—
177	C₂³×C₁₁₃	—	4	1	no	—
178	C₂³×C₁₁₃	—	4	2	no	—
179	C₂³×C₁₁₃	—	4	2	no	—
180	C₂³×C₁₁₃	#120	1	2	yes	—
181	C₂³×C₁₁₃	#121	1	2	yes	—
182	C₂³×C₁₁₃	#124	1	2	yes	—
183	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₁₃	—	2	4	no	—
185	Q₈×C₁₁₃	—	2	2	no	—
186	Q₈×C₁₁₃	—	2	4	no	—
187	Q₈×C₁₁₃	—	2	2	no	—
188	Q₈×C₁₁₃	—	4	2	no	—
189	Q₈×C₁₁₃	—	4	1	no	—
190	Q₈×C₁₁₃	—	4	2	no	—
191	Q₈×C₁₁₃	—	4	1	no	—
192	Q₈×C₁₁₃	—	4	8	no	—
193	D₄×C₁₁₃	—	2	2	no	—
194	D₄×C₁₁₃	—	2	2	no	—
195	D₄×C₁₁₃	—	4	8	no	—
196	D₄×C₁₁₃	—	4	1	no	—
197	D₄×C₁₁₃	—	4	1	no	—
198	C₂×C₄×C₁₁₃	—	2	4	no	—
199	C₂×C₄×C₁₁₃	—	2	4	no	—
200	C₂×C₄×C₁₁₃	—	2	2	no	—
201	C₂×C₄×C₁₁₃	—	2	4	no	—
202	C₂×C₄×C₁₁₃	—	2	4	no	—
203	C₂×C₄×C₁₁₃	—	2	4	no	—
204	C₂×C₄×C₁₁₃	—	4	1	no	—
205	C₂×C₄×C₁₁₃	—	4	2	no	—
206	C₂×C₄×C₁₁₃	—	4	1	no	—
207	C₂×C₄×C₁₁₃	—	4	2	no	—
208	C₂×C₄×C₁₁₃	—	4	4	no	—
209	C₂×C₄×C₁₁₃	—	4	8	no	—
210	C₂×C₄×C₁₁₃	—	4	8	no	—
211	C₂×C₄×C₁₁₃	—	4	2	no	—
212	C₂×C₄×C₁₁₃	—	4	2	no	—
213	C₂×C₄×C₁₁₃	—	4	2	no	—
214	C₂×C₄×C₁₁₃	—	8	4	no	—
215	C₂×C₄×C₁₁₃	#120	1	2	yes	—
216	C₂×C₄×C₁₁₃	#121	1	4	yes	—
217	C₂×C₄×C₁₁₃	#121	1	4	yes	—
218	C₂×C₄×C₁₁₃	#121	1	2	yes	—
219	C₂×C₄×C₁₁₃	#123	1	4	yes	—
220	C₂×C₄×C₁₁₃	#123	1	4	yes	—
221	C₂×C₄×C₁₁₃	#124	1	2	yes	—
222	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
228	C₈×C₁₁₃	—	4	2	no	—
229	C₈×C₁₁₃	—	4	2	no	—
230	C₂²×C₁₁₃	—	2	4	no	—
231	C₂²×C₁₁₃	—	2	4	no	—
232	C₂²×C₁₁₃	—	2	2	no	—
233	C₂²×C₁₁₃	—	2	2	no	—
234	C₂²×C₁₁₃	—	4	2	no	—
235	C₂²×C₁₁₃	—	4	4	no	—
236	C₂²×C₁₁₃	—	8	2	no	—
237	C₂²×C₁₁₃	—	8	1	no	—
238	C₂²×C₁₁₃	—	8	1	no	—
239	C₂²×C₁₁₃	#394	1	4	yes	—
240	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
241	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
242	C₂²×C₁₁₃	C₂×#124	1	1	yes	characteristic
243	C₂²×C₁₁₃	#577	1	2	yes	—
244	C₂²×C₁₁₃	#578	1	2	yes	—
245	C₄×C₁₁₃	—	4	2	no	—
246	C₄×C₁₁₃	—	4	4	no	—
247	C₄×C₁₁₃	—	4	4	no	—
248	C₄×C₁₁₃	—	4	4	no	—
249	C₄×C₁₁₃	—	8	2	no	—
250	C₄×C₁₁₃	#394	1	4	yes	—
251	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
252	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
253	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
254	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
255	#23512	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂×C₁₁₃	—	2	4	no	—
257	C₂×C₁₁₃	—	8	2	no	—
258	C₂×C₁₁₃	C₂×#394	1	1	yes	characteristic
259	C₂×C₁₁₃	#3013	1	2	yes	—
260	C₂×C₁₁₃	#3042	1	1	yes	characteristic
261	C₂×C₁₁₃	#3044	1	1	yes	characteristic
262	C₂×C₁₁₃	#3137	1	2	yes	—
263	C₂×#536	C₂×C₁₁₃	1	1	yes	characteristic
264	C₂×#417	C₂×C₁₁₃	1	1	yes	characteristic
265	C₂×#419	C₂×C₁₁₃	1	1	yes	characteristic, complemented
266	C₂×#416	C₂×C₁₁₃	1	1	yes	characteristic
267	C₂²×#103	C₂×C₁₁₃	1	1	yes	characteristic, complemented
268	#2316	C₂×C₁₁₃	1	1	yes	characteristic, complemented
269	#2043	C₂×C₁₁₃	1	4	yes	complemented
270	#2042	C₂×C₁₁₃	1	4	yes	complemented
271	#1729	C₂×C₁₁₃	1	1	yes	characteristic, complemented
272	C₁₁₃	#23512	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
274	C₂³×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
276	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
277	#536	—	2	4	no	—
278	#536	—	2	4	no	—
279	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	2	yes	—
280	C₂×#124	C₂²×C₁₁₃	1	2	yes	—
281	C₂×#123	—	2	2	no	—
282	C₂×C₂²⋊Q₈	—	2	2	no	—
283	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
284	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
286	#419	—	2	4	no	—
287	#417	—	2	4	no	—
288	#416	—	2	4	no	—
289	C₂×#103	—	2	4	no	—
290	C₂×#103	C₂²×C₁₁₃	1	4	yes	—
291	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
292	C₂×#103	C₂²×C₁₁₃	1	4	yes	—
293	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
294	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
295	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
296	#389	—	2	2	no	—
297	#389	C₂²×C₁₁₃	1	4	yes	—
298	#380	—	2	2	no	—
299	#336	C₂²×C₁₁₃	1	4	yes	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	D₄×C₁₁₃	1	4	yes	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	—	2	2	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	D₄×C₁₁₃	1	4	yes	—
313	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
314	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	2	4	no	—
331	#124	—	2	4	no	—
332	#124	—	2	4	no	—
333	#123	—	2	16	no	—
334	C₂²⋊Q₈	—	2	16	no	—
335	#117	—	2	2	no	—
336	#117	—	2	2	no	—
337	#117	—	2	2	no	—
338	#117	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	4	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
344	C₂×C₄⋊C₄	D₄×C₁₁₃	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
352	#103	—	2	4	no	—
353	#103	—	2	8	no	—
354	#103	—	2	8	no	—
355	#103	—	2	4	no	—
356	#102	—	2	4	no	—
357	#102	—	2	4	no	—
358	#95	—	2	4	no	—
359	C₂⁴	—	2	1	no	—
360	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
361	#41	—	2	8	no	—
362	#41	—	2	8	no	—
363	#41	—	4	4	no	—
364	#41	—	4	4	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	4	4	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	C₂×D₄×C₁₁₃	1	4	yes	—
383	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	8	2	no	—
405	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
406	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
410	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
411	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
412	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
414	M₁₆	—	4	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	4	4	no	—
422	C₄⋊C₄	—	2	16	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	8	4	no	—
429	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
430	C₂²⋊C₄	—	2	16	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	4	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	#120×C₁₁₃	1	2	yes	—
444	C₂³	#121×C₁₁₃	1	2	yes	—
445	C₂³	#124×C₁₁₃	1	2	yes	—
446	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
447	Q₈	—	2	4	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	2	4	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	4	1	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	4	8	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	4	8	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	1	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	#120×C₁₁₃	1	2	yes	—
479	C₂×C₄	#121×C₁₁₃	1	4	yes	—
480	C₂×C₄	#121×C₁₁₃	1	4	yes	—
481	C₂×C₄	#121×C₁₁₃	1	2	yes	—
482	C₂×C₄	#123×C₁₁₃	1	4	yes	—
483	C₂×C₄	#123×C₁₁₃	1	4	yes	—
484	C₂×C₄	#124×C₁₁₃	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
491	C₈	—	4	2	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	1	no	—
502	C₂²	#394×C₁₁₃	1	4	yes	—
503	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
504	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
505	C₂²	C₂×#124×C₁₁₃	1	1	yes	characteristic
506	C₂²	#577×C₁₁₃	1	2	yes	—
507	C₂²	#578×C₁₁₃	1	2	yes	—
508	C₄	—	4	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	8	2	no	—
513	C₄	#394×C₁₁₃	1	4	yes	—
514	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
515	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
516	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
517	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
518	C₂	—	2	4	no	—
519	C₂	—	8	2	no	—
520	C₂	C₂×#394×C₁₁₃	1	1	yes	characteristic
521	C₂	C₁₁₃×#3013	1	2	yes	—
522	C₂	C₁₁₃×#3042	1	1	yes	characteristic
523	C₂	C₁₁₃×#3044	1	1	yes	characteristic
524	C₂	C₁₁₃×#3137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂²×#41×C₁₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×#117×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#419×C₁₁₃	C₂	semidirect
5. C₂²×#103×C₁₁₃	C₂	semidirect
6. C₁₁₃×#2316	C₂	semidirect
7. C₁₁₃×#2043	C₂	semidirect
8. C₁₁₃×#2042	C₂	semidirect
9. C₁₁₃×#1729	C₂	semidirect
255. #23512	C₁₁₃	direct (N × H)
265. C₂×#419	C₂×C₁₁₃	semidirect
267. C₂²×#103	C₂×C₁₁₃	semidirect
268. #2316	C₂×C₁₁₃	semidirect
269. #2043	C₂×C₁₁₃	semidirect
270. #2042	C₂×C₁₁₃	semidirect
271. #1729	C₂×C₁₁₃	semidirect
272. C₁₁₃	#23512	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×#536×C₁₁₃	2
C₂×#417×C₁₁₃	2
C₂×#419×C₁₁₃	2
C₂×#416×C₁₁₃	2
C₂²×#103×C₁₁₃	2
C₁₁₃×#2316	2
C₁₁₃×#2043	2
C₁₁₃×#2042	2
C₁₁₃×#1729	2
#23512	113

Subgroups — C113×#23512 #43291532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#23512 #43291532