Subgroups — C₁₁₃×#15216 #43283236

Order 28928.

1782 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#380×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1442	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1439	C₂	1	4	yes	maximal
6	C₁₁₃×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂×#125×C₁₁₃	—	2	8	no	—
10	C₂×#125×C₁₁₃	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
16	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
18	#380×C₁₁₃	—	2	8	no	—
19	C₄×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
20	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
21	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
22	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
23	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
24	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
25	C₂⁵×C₁₁₃	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₁₁₃	—	2	2	no	—
27	C₂³×C₄×C₁₁₃	—	2	4	no	—
28	C₂³×C₄×C₁₁₃	—	2	4	no	—
29	C₂³×C₄×C₁₁₃	—	2	2	no	—
30	C₂³×C₄×C₁₁₃	Q₈	1	4	yes	—
31	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
32	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
37	#125×C₁₁₃	—	2	32	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₁₃	D₄	1	8	yes	—
47	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
53	C₂×C₄²×C₁₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₁₃	—	2	2	no	—
55	C₂×C₄²×C₁₁₃	—	2	4	no	—
56	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
57	#95×C₁₁₃	—	2	4	no	—
58	#95×C₁₁₃	—	2	8	no	—
59	#95×C₁₁₃	—	2	8	no	—
60	#95×C₁₁₃	—	4	4	no	—
61	#95×C₁₁₃	—	4	4	no	—
62	C₂⁴×C₁₁₃	—	2	1	no	—
63	C₂⁴×C₁₁₃	—	2	2	no	—
64	C₂⁴×C₁₁₃	—	2	2	no	—
65	C₂⁴×C₁₁₃	—	2	1	no	—
66	C₂⁴×C₁₁₃	—	2	2	no	—
67	C₂⁴×C₁₁₃	—	2	2	no	—
68	C₂⁴×C₁₁₃	—	2	2	no	—
69	C₂⁴×C₁₁₃	C₂×Q₈	1	2	yes	—
70	C₂⁴×C₁₁₃	#41	1	4	yes	—
71	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
72	C₂²×C₄×C₁₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₁₃	—	2	4	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	2	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₁₃	—	2	1	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₁₃	—	2	8	no	—
95	C₂²×C₄×C₁₁₃	—	2	16	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₁₃	—	4	4	no	—
104	C₂²×C₄×C₁₁₃	—	4	4	no	—
105	C₂²×C₄×C₁₁₃	—	4	8	no	—
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
113	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
114	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
115	C₄⋊C₄×C₁₁₃	—	2	32	no	—
116	C₄⋊C₄×C₁₁₃	—	2	16	no	—
117	C₄⋊C₄×C₁₁₃	—	4	8	no	—
118	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
119	C₂²⋊C₄×C₁₁₃	—	4	16	no	—
120	C₄²×C₁₁₃	—	2	8	no	—
121	C₄²×C₁₁₃	—	4	4	no	—
122	C₂³×C₁₁₃	—	2	2	no	—
123	C₂³×C₁₁₃	—	2	4	no	—
124	C₂³×C₁₁₃	—	2	4	no	—
125	C₂³×C₁₁₃	—	2	4	no	—
126	C₂³×C₁₁₃	—	2	2	no	—
127	C₂³×C₁₁₃	—	2	4	no	—
128	C₂³×C₁₁₃	—	2	4	no	—
129	C₂³×C₁₁₃	—	2	4	no	—
130	C₂³×C₁₁₃	—	2	4	no	—
131	C₂³×C₁₁₃	—	2	4	no	—
132	C₂³×C₁₁₃	—	4	1	no	—
133	C₂³×C₁₁₃	—	4	1	no	—
134	C₂³×C₁₁₃	—	4	2	no	—
135	C₂³×C₁₁₃	—	4	2	no	—
136	C₂³×C₁₁₃	—	4	1	no	—
137	C₂³×C₁₁₃	—	4	1	no	—
138	C₂³×C₁₁₃	—	4	2	no	—
139	C₂³×C₁₁₃	—	4	2	no	—
140	C₂³×C₁₁₃	—	4	2	no	—
141	C₂³×C₁₁₃	—	4	2	no	—
142	C₂³×C₁₁₃	#125	1	4	yes	complemented
143	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
144	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
145	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
146	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
147	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
148	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
149	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
150	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
151	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
152	C₂×C₄×C₁₁₃	—	2	4	no	—
153	C₂×C₄×C₁₁₃	—	2	8	no	—
154	C₂×C₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	2	4	no	—
156	C₂×C₄×C₁₁₃	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	2	4	no	—
158	C₂×C₄×C₁₁₃	—	2	4	no	—
159	C₂×C₄×C₁₁₃	—	2	8	no	—
160	C₂×C₄×C₁₁₃	—	2	8	no	—
161	C₂×C₄×C₁₁₃	—	2	4	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	4	1	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	2	no	—
166	C₂×C₄×C₁₁₃	—	4	1	no	—
167	C₂×C₄×C₁₁₃	—	4	2	no	—
168	C₂×C₄×C₁₁₃	—	4	2	no	—
169	C₂×C₄×C₁₁₃	—	4	4	no	—
170	C₂×C₄×C₁₁₃	—	4	2	no	—
171	C₂×C₄×C₁₁₃	—	4	2	no	—
172	C₂×C₄×C₁₁₃	—	4	2	no	—
173	C₂×C₄×C₁₁₃	—	4	4	no	—
174	C₂×C₄×C₁₁₃	—	4	2	no	—
175	C₂×C₄×C₁₁₃	—	4	4	no	—
176	C₂×C₄×C₁₁₃	—	4	2	no	—
177	C₂×C₄×C₁₁₃	—	4	2	no	—
178	C₂×C₄×C₁₁₃	—	4	16	no	—
179	C₂×C₄×C₁₁₃	—	4	4	no	—
180	C₂×C₄×C₁₁₃	—	4	4	no	—
181	C₂×C₄×C₁₁₃	—	4	4	no	—
182	C₂×C₄×C₁₁₃	—	4	4	no	—
183	C₂×C₄×C₁₁₃	—	4	4	no	—
184	C₂×C₄×C₁₁₃	—	4	4	no	—
185	C₂×C₄×C₁₁₃	—	4	4	no	—
186	C₂×C₄×C₁₁₃	#120	1	4	yes	—
187	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
188	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	8	yes	—
189	C₂×C₄×C₁₁₃	#124	1	4	yes	—
190	C₂×C₄×C₁₁₃	#124	1	8	yes	—
191	C₂²×C₁₁₃	—	2	4	no	—
192	C₂²×C₁₁₃	—	2	8	no	—
193	C₂²×C₁₁₃	—	4	4	no	—
194	C₂²×C₁₁₃	—	4	2	no	—
195	C₂²×C₁₁₃	—	4	2	no	—
196	C₂²×C₁₁₃	—	4	4	no	—
197	C₂²×C₁₁₃	—	4	4	no	—
198	C₂²×C₁₁₃	—	4	4	no	—
199	C₂²×C₁₁₃	—	4	4	no	—
200	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
201	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
203	C₂²×C₁₁₃	#525	1	2	yes	—
204	C₂²×C₁₁₃	C₂×#124	1	1	yes	characteristic
205	C₂²×C₁₁₃	C₂×#124	1	2	yes	—
206	C₂²×C₁₁₃	C₂×#125	1	1	yes	characteristic
207	C₂²×C₁₁₃	#529	1	2	yes	—
208	C₂²×C₁₁₃	#533	1	1	yes	characteristic
209	C₂²×C₁₁₃	#537	1	2	yes	—
210	C₂²×C₁₁₃	#540	1	1	yes	characteristic
211	C₂²×C₁₁₃	#541	1	1	yes	characteristic
212	C₂²×C₁₁₃	#544	1	2	yes	—
213	C₂²×C₁₁₃	#546	1	2	yes	—
214	C₂²×C₁₁₃	#547	1	2	yes	—
215	C₂²×C₁₁₃	#548	1	2	yes	—
216	C₂²×C₁₁₃	#550	1	2	yes	—
217	C₂²×C₁₁₃	#552	1	2	yes	—
218	C₂²×C₁₁₃	#552	1	2	yes	—
219	C₂²×C₁₁₃	#553	1	2	yes	—
220	C₂²×C₁₁₃	#553	1	2	yes	—
221	C₄×C₁₁₃	—	4	4	no	—
222	C₄×C₁₁₃	—	4	2	no	—
223	C₄×C₁₁₃	—	4	4	no	—
224	C₄×C₁₁₃	—	4	8	no	—
225	C₄×C₁₁₃	—	8	4	no	—
226	C₄×C₁₁₃	#393	1	8	yes	—
227	#15216	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₁₁₃	—	4	4	no	—
229	C₂×C₁₁₃	C₂×#393	1	1	yes	characteristic
230	C₂×C₁₁₃	#2407	1	2	yes	—
231	C₂×C₁₁₃	#2441	1	2	yes	—
232	C₂×C₁₁₃	#2442	1	2	yes	—
233	C₂×C₁₁₃	#2489	1	2	yes	—
234	C₂×C₁₁₃	#2490	1	2	yes	—
235	C₂×C₁₁₃	#2562	1	2	yes	—
236	C₂×C₁₁₃	#2629	1	1	yes	characteristic
237	C₂×C₁₁₃	#2851	1	1	yes	characteristic
238	C₂²×#125	C₂×C₁₁₃	1	1	yes	characteristic, complemented
239	C₂×#380	C₂×C₁₁₃	1	2	yes	—
240	C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
241	#1442	C₂×C₁₁₃	1	4	yes	complemented
242	#1439	C₂×C₁₁₃	1	4	yes	—
243	C₄⋊#95	C₂×C₁₁₃	1	1	yes	characteristic, complemented
244	C₄⋊#95	C₂×C₁₁₃	1	2	yes	complemented
245	C₁₁₃	#15216	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
247	C₂×#125	—	2	8	no	—
248	C₂×#125	—	2	4	no	—
249	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
250	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
254	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
255	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
256	#380	—	2	8	no	—
257	C₄×C₂²⋊C₄	—	2	4	no	—
258	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
259	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
260	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
261	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
262	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
263	C₂⁵	C₂³×C₁₁₃	1	1	yes	characteristic
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	—	2	4	no	—
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	Q₈×C₁₁₃	1	4	yes	—
269	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
270	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
271	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
275	#125	—	2	32	no	—
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	2	8	no	—
278	C₂×C₄⋊C₄	—	2	8	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	D₄×C₁₁₃	1	8	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	8	no	—
290	C₂×C₂²⋊C₄	—	4	4	no	—
291	C₂×C₄²	—	2	4	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
295	#95	—	2	4	no	—
296	#95	—	2	8	no	—
297	#95	—	2	8	no	—
298	#95	—	4	4	no	—
299	#95	—	4	4	no	—
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	2	no	—
307	C₂⁴	C₂×Q₈×C₁₁₃	1	2	yes	—
308	C₂⁴	#41×C₁₁₃	1	4	yes	—
309	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	16	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	8	no	—
344	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
345	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
346	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
348	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
349	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
350	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
351	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
352	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
353	C₄⋊C₄	—	2	32	no	—
354	C₄⋊C₄	—	2	16	no	—
355	C₄⋊C₄	—	4	8	no	—
356	C₂²⋊C₄	—	2	16	no	—
357	C₂²⋊C₄	—	4	16	no	—
358	C₄²	—	2	8	no	—
359	C₄²	—	4	4	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	#125×C₁₁₃	1	4	yes	complemented
381	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
382	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
383	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
384	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
385	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
386	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
387	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
388	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
389	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	16	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	#120×C₁₁₃	1	4	yes	—
425	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
426	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	8	yes	—
427	C₂×C₄	#124×C₁₁₃	1	4	yes	—
428	C₂×C₄	#124×C₁₁₃	1	8	yes	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	8	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
439	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
440	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
441	C₂²	#525×C₁₁₃	1	2	yes	—
442	C₂²	C₂×#124×C₁₁₃	1	1	yes	characteristic
443	C₂²	C₂×#124×C₁₁₃	1	2	yes	—
444	C₂²	C₂×#125×C₁₁₃	1	1	yes	characteristic
445	C₂²	#529×C₁₁₃	1	2	yes	—
446	C₂²	#533×C₁₁₃	1	1	yes	characteristic
447	C₂²	#537×C₁₁₃	1	2	yes	—
448	C₂²	#540×C₁₁₃	1	1	yes	characteristic
449	C₂²	#541×C₁₁₃	1	1	yes	characteristic
450	C₂²	#544×C₁₁₃	1	2	yes	—
451	C₂²	#546×C₁₁₃	1	2	yes	—
452	C₂²	#547×C₁₁₃	1	2	yes	—
453	C₂²	#548×C₁₁₃	1	2	yes	—
454	C₂²	#550×C₁₁₃	1	2	yes	—
455	C₂²	#552×C₁₁₃	1	2	yes	—
456	C₂²	#552×C₁₁₃	1	2	yes	—
457	C₂²	#553×C₁₁₃	1	2	yes	—
458	C₂²	#553×C₁₁₃	1	2	yes	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	8	no	—
463	C₄	—	8	4	no	—
464	C₄	#393×C₁₁₃	1	8	yes	—
465	C₂	—	4	4	no	—
466	C₂	C₂×#393×C₁₁₃	1	1	yes	characteristic
467	C₂	C₁₁₃×#2407	1	2	yes	—
468	C₂	C₁₁₃×#2441	1	2	yes	—
469	C₂	C₁₁₃×#2442	1	2	yes	—
470	C₂	C₁₁₃×#2489	1	2	yes	—
471	C₂	C₁₁₃×#2490	1	2	yes	—
472	C₂	C₁₁₃×#2562	1	2	yes	—
473	C₂	C₁₁₃×#2629	1	1	yes	characteristic
474	C₂	C₁₁₃×#2851	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#125×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1442	C₂	semidirect
6. C₁₁₃×C₄⋊#95	C₂	semidirect
7. C₁₁₃×C₄⋊#95	C₂	semidirect
142. C₂³×C₁₁₃	#125	semidirect
227. #15216	C₁₁₃	direct (N × H)
238. C₂²×#125	C₂×C₁₁₃	semidirect
241. #1442	C₂×C₁₁₃	semidirect
243. C₄⋊#95	C₂×C₁₁₃	semidirect
244. C₄⋊#95	C₂×C₁₁₃	semidirect
245. C₁₁₃	#15216	direct (N × H)
380. C₂³	#125×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₁₁₃	2
C₂×#380×C₁₁₃	2
C₂×C₄×C₂²⋊C₄×C₁₁₃	2
C₁₁₃×#1442	2
C₁₁₃×#1439	2
C₁₁₃×C₄⋊#95	2
#15216	113

Subgroups — C113×#15216 #43283236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#15216 #43283236