Subgroups — C₁₁₃×#13905 #43281925

Order 28928.

2430 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#382×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#380×C₁₁₃	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1445	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1438	C₂	1	2	yes	maximal
7	C₁₁₃×#1437	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₁₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
11	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
12	C₂×C₄×D₄×C₁₁₃	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	8	yes	—
17	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
20	#382×C₁₁₃	—	2	4	no	—
21	#380×C₁₁₃	—	2	16	no	—
22	C₄×C₄⋊C₄×C₁₁₃	—	2	4	no	—
23	C₂×#95×C₁₁₃	C₂²	1	8	yes	—
24	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
25	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
26	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
27	C₂⁵×C₁₁₃	C₂³	1	2	yes	—
28	C₂²×D₄×C₁₁₃	—	2	8	no	—
29	C₂²×D₄×C₁₁₃	—	2	2	no	—
30	C₂²×D₄×C₁₁₃	—	2	2	no	—
31	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₁₃	—	2	4	no	—
33	C₂³×C₄×C₁₁₃	—	2	4	no	—
34	C₂³×C₄×C₁₁₃	—	2	8	no	—
35	C₂³×C₄×C₁₁₃	—	2	8	no	—
36	C₂³×C₄×C₁₁₃	C₂×C₄	1	8	yes	—
37	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₁₁₃	—	2	32	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₁₃	D₄	1	8	yes	complemented
52	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₁₃	—	2	16	no	—
55	C₂×C₂²⋊C₄×C₁₁₃	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₁₁₃	—	4	8	no	—
57	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	8	yes	—
58	C₂×C₄²×C₁₁₃	—	2	4	no	—
59	C₂×C₄²×C₁₁₃	—	4	4	no	—
60	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
62	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
63	#95×C₁₁₃	—	2	4	no	—
64	#95×C₁₁₃	—	2	16	no	—
65	#95×C₁₁₃	—	2	4	no	—
66	#95×C₁₁₃	—	2	4	no	—
67	C₂⁴×C₁₁₃	—	2	4	no	—
68	C₂⁴×C₁₁₃	—	2	2	no	—
69	C₂⁴×C₁₁₃	—	2	2	no	—
70	C₂⁴×C₁₁₃	—	2	4	no	—
71	C₂⁴×C₁₁₃	—	2	4	no	—
72	C₂⁴×C₁₁₃	—	2	4	no	—
73	C₂⁴×C₁₁₃	—	2	4	no	—
74	C₂⁴×C₁₁₃	C₂²×C₄	1	4	yes	—
75	C₂⁴×C₁₁₃	#41	1	8	yes	—
76	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
77	C₂×D₄×C₁₁₃	—	2	16	no	—
78	C₂×D₄×C₁₁₃	—	2	16	no	—
79	C₂×D₄×C₁₁₃	—	2	16	no	—
80	C₂×D₄×C₁₁₃	—	2	8	no	—
81	C₂²×C₄×C₁₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₁₃	—	2	16	no	—
93	C₂²×C₄×C₁₁₃	—	2	32	no	—
94	C₂²×C₄×C₁₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₁₃	—	2	8	no	—
96	C₂²×C₄×C₁₁₃	—	2	8	no	—
97	C₂²×C₄×C₁₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	4	16	no	—
100	C₂²×C₄×C₁₁₃	—	4	8	no	—
101	C₂²×C₄×C₁₁₃	—	4	8	no	—
102	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
115	C₄⋊C₄×C₁₁₃	—	2	8	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	32	no	—
120	C₄²×C₁₁₃	—	4	8	no	—
121	C₄²×C₁₁₃	C₂²⋊C₄	1	16	yes	complemented
122	C₂³×C₁₁₃	—	2	4	no	—
123	C₂³×C₁₁₃	—	2	4	no	—
124	C₂³×C₁₁₃	—	2	8	no	—
125	C₂³×C₁₁₃	—	2	8	no	—
126	C₂³×C₁₁₃	—	2	8	no	—
127	C₂³×C₁₁₃	—	2	8	no	—
128	C₂³×C₁₁₃	—	2	8	no	—
129	C₂³×C₁₁₃	—	2	8	no	—
130	C₂³×C₁₁₃	—	2	8	no	—
131	C₂³×C₁₁₃	—	2	8	no	—
132	C₂³×C₁₁₃	—	4	4	no	—
133	C₂³×C₁₁₃	—	4	2	no	—
134	C₂³×C₁₁₃	—	4	2	no	—
135	C₂³×C₁₁₃	—	4	2	no	—
136	C₂³×C₁₁₃	—	4	2	no	—
137	C₂³×C₁₁₃	—	4	4	no	—
138	C₂³×C₁₁₃	—	4	4	no	—
139	C₂³×C₁₁₃	—	4	4	no	—
140	C₂³×C₁₁₃	—	4	4	no	—
141	C₂³×C₁₁₃	—	4	4	no	—
142	C₂³×C₁₁₃	#117	1	8	yes	—
143	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
144	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
145	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
147	C₂³×C₁₁₃	C₂×#41	1	4	yes	—
148	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
149	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
150	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
151	D₄×C₁₁₃	—	2	32	no	—
152	C₂×C₄×C₁₁₃	—	2	4	no	—
153	C₂×C₄×C₁₁₃	—	2	4	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	4	no	—
159	C₂×C₄×C₁₁₃	—	2	4	no	—
160	C₂×C₄×C₁₁₃	—	2	8	no	—
161	C₂×C₄×C₁₁₃	—	2	8	no	—
162	C₂×C₄×C₁₁₃	—	2	16	no	—
163	C₂×C₄×C₁₁₃	—	4	4	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	2	no	—
166	C₂×C₄×C₁₁₃	—	4	2	no	—
167	C₂×C₄×C₁₁₃	—	4	4	no	—
168	C₂×C₄×C₁₁₃	—	4	8	no	—
169	C₂×C₄×C₁₁₃	—	4	32	no	—
170	C₂×C₄×C₁₁₃	—	4	4	no	—
171	C₂×C₄×C₁₁₃	—	4	4	no	—
172	C₂×C₄×C₁₁₃	—	4	4	no	—
173	C₂×C₄×C₁₁₃	—	4	8	no	—
174	C₂×C₄×C₁₁₃	—	4	8	no	—
175	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₄×C₁₁₃	C₄×D₄	1	8	yes	—
179	C₂×C₄×C₁₁₃	#121	1	8	yes	—
180	C₂×C₄×C₁₁₃	#124	1	4	yes	—
181	C₂×C₄×C₁₁₃	#127	1	4	yes	—
182	C₂²×C₁₁₃	—	2	16	no	—
183	C₂²×C₁₁₃	—	2	8	no	—
184	C₂²×C₁₁₃	—	4	8	no	—
185	C₂²×C₁₁₃	—	4	4	no	—
186	C₂²×C₁₁₃	—	4	8	no	—
187	C₂²×C₁₁₃	—	4	8	no	—
188	C₂²×C₁₁₃	—	4	8	no	—
189	C₂²×C₁₁₃	—	4	8	no	—
190	C₂²×C₁₁₃	—	4	4	no	—
191	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₁₃	C₂×#117	1	2	yes	—
193	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
194	C₂²×C₁₁₃	#520	1	2	yes	—
195	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
196	C₂²×C₁₁₃	#525	1	2	yes	—
197	C₂²×C₁₁₃	#525	1	2	yes	—
198	C₂²×C₁₁₃	C₂×#124	1	1	yes	characteristic
199	C₂²×C₁₁₃	C₂×#127	1	1	yes	characteristic
200	C₂²×C₁₁₃	#535	1	1	yes	characteristic
201	C₂²×C₁₁₃	#536	1	1	yes	characteristic
202	C₂²×C₁₁₃	#537	1	2	yes	—
203	C₂²×C₁₁₃	#546	1	4	yes	—
204	C₂²×C₁₁₃	#548	1	4	yes	—
205	C₂²×C₁₁₃	#552	1	4	yes	—
206	C₂²×C₁₁₃	#553	1	4	yes	—
207	C₄×C₁₁₃	—	2	4	no	—
208	C₄×C₁₁₃	—	2	4	no	—
209	C₄×C₁₁₃	—	4	8	no	—
210	C₄×C₁₁₃	—	4	4	no	—
211	C₄×C₁₁₃	—	8	4	no	—
212	C₄×C₁₁₃	#390	1	8	yes	—
213	#13905	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₁₁₃	—	4	8	no	—
215	C₂×C₁₁₃	#2280	1	1	yes	characteristic
216	C₂×C₁₁₃	C₂×#390	1	1	yes	characteristic
217	C₂×C₁₁₃	#2311	1	1	yes	characteristic
218	C₂×C₁₁₃	#2352	1	4	yes	—
219	C₂×C₁₁₃	#2535	1	2	yes	—
220	C₂×C₁₁₃	#2536	1	2	yes	—
221	C₂×C₁₁₃	#2540	1	2	yes	—
222	C₂×C₁₁₃	#2562	1	2	yes	—
223	C₂²×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic
224	C₂×#382	C₂×C₁₁₃	1	1	yes	characteristic, complemented
225	C₂×#380	C₂×C₁₁₃	1	4	yes	complemented
226	C₂×C₄×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic, complemented
227	#1445	C₂×C₁₁₃	1	2	yes	complemented
228	#1438	C₂×C₁₁₃	1	2	yes	—
229	#1437	C₂×C₁₁₃	1	4	yes	complemented
230	C₁₁₃	#13905	1	1	yes	characteristic, direct product factor, Sylow
231	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
232	C₂⁴×C₄	C₂²×C₁₁₃	1	2	yes	—
233	C₂×C₄×D₄	—	2	4	no	—
234	C₂×C₄×D₄	—	2	4	no	—
235	C₂×C₄×D₄	C₄×C₁₁₃	1	8	yes	complemented
236	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
237	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
239	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	8	yes	—
240	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
241	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
242	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
243	#382	—	2	4	no	—
244	#380	—	2	16	no	—
245	C₄×C₄⋊C₄	—	2	4	no	—
246	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
247	C₂×#95	C₂²×C₁₁₃	1	8	yes	—
248	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
249	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
250	C₂⁵	C₂³×C₁₁₃	1	2	yes	—
251	C₂²×D₄	—	2	8	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
255	C₂³×C₄	—	2	4	no	—
256	C₂³×C₄	—	2	4	no	—
257	C₂³×C₄	—	2	8	no	—
258	C₂³×C₄	—	2	8	no	—
259	C₂³×C₄	C₂×C₄×C₁₁₃	1	8	yes	—
260	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
261	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
262	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
263	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
265	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
266	C₄×D₄	—	2	32	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	8	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
274	C₂×C₄⋊C₄	D₄×C₁₁₃	1	8	yes	complemented
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	16	no	—
278	C₂×C₂²⋊C₄	—	2	16	no	—
279	C₂×C₂²⋊C₄	—	4	8	no	—
280	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	8	yes	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	—	4	4	no	—
283	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
284	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
285	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
286	#95	—	2	4	no	—
287	#95	—	2	16	no	—
288	#95	—	2	4	no	—
289	#95	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	2	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	4	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	C₂²×C₄×C₁₁₃	1	4	yes	—
298	C₂⁴	#41×C₁₁₃	1	8	yes	—
299	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
300	C₂×D₄	—	2	16	no	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	16	no	—
316	C₂²×C₄	—	2	32	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	16	no	—
323	C₂²×C₄	—	4	8	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
327	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
330	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
337	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	16	no	—
340	C₄⋊C₄	—	4	8	no	—
341	C₂²⋊C₄	—	2	16	no	—
342	C₂²⋊C₄	—	4	32	no	—
343	C₄²	—	4	8	no	—
344	C₄²	C₂²⋊C₄×C₁₁₃	1	16	yes	complemented
345	C₂³	—	2	4	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	8	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	8	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	4	no	—
365	C₂³	#117×C₁₁₃	1	8	yes	—
366	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
367	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
368	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
369	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
370	C₂³	C₂×#41×C₁₁₃	1	4	yes	—
371	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
372	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
373	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
374	D₄	—	2	32	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	16	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	32	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
399	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
401	C₂×C₄	C₄×D₄×C₁₁₃	1	8	yes	—
402	C₂×C₄	#121×C₁₁₃	1	8	yes	—
403	C₂×C₄	#124×C₁₁₃	1	4	yes	—
404	C₂×C₄	#127×C₁₁₃	1	4	yes	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	16	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	4	8	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	8	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	8	no	—
414	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
415	C₂²	C₂×#117×C₁₁₃	1	2	yes	—
416	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
417	C₂²	#520×C₁₁₃	1	2	yes	—
418	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
419	C₂²	#525×C₁₁₃	1	2	yes	—
420	C₂²	#525×C₁₁₃	1	2	yes	—
421	C₂²	C₂×#124×C₁₁₃	1	1	yes	characteristic
422	C₂²	C₂×#127×C₁₁₃	1	1	yes	characteristic
423	C₂²	#535×C₁₁₃	1	1	yes	characteristic
424	C₂²	#536×C₁₁₃	1	1	yes	characteristic
425	C₂²	#537×C₁₁₃	1	2	yes	—
426	C₂²	#546×C₁₁₃	1	4	yes	—
427	C₂²	#548×C₁₁₃	1	4	yes	—
428	C₂²	#552×C₁₁₃	1	4	yes	—
429	C₂²	#553×C₁₁₃	1	4	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	8	no	—
433	C₄	—	4	4	no	—
434	C₄	—	8	4	no	—
435	C₄	#390×C₁₁₃	1	8	yes	—
436	C₂	—	4	8	no	—
437	C₂	C₁₁₃×#2280	1	1	yes	characteristic
438	C₂	C₂×#390×C₁₁₃	1	1	yes	characteristic
439	C₂	C₁₁₃×#2311	1	1	yes	characteristic
440	C₂	C₁₁₃×#2352	1	4	yes	—
441	C₂	C₁₁₃×#2535	1	2	yes	—
442	C₂	C₁₁₃×#2536	1	2	yes	—
443	C₂	C₁₁₃×#2540	1	2	yes	—
444	C₂	C₁₁₃×#2562	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#382×C₁₁₃	C₂	semidirect
3. C₂×#380×C₁₁₃	C₂	semidirect
4. C₂×C₄×C₄⋊C₄×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1445	C₂	semidirect
7. C₁₁₃×#1437	C₂	semidirect
12. C₂×C₄×D₄×C₁₁₃	C₄	semidirect
51. C₂×C₄⋊C₄×C₁₁₃	D₄	semidirect
121. C₄²×C₁₁₃	C₂²⋊C₄	semidirect
213. #13905	C₁₁₃	direct (N × H)
224. C₂×#382	C₂×C₁₁₃	semidirect
225. C₂×#380	C₂×C₁₁₃	semidirect
226. C₂×C₄×C₄⋊C₄	C₂×C₁₁₃	semidirect
227. #1445	C₂×C₁₁₃	semidirect
229. #1437	C₂×C₁₁₃	semidirect
230. C₁₁₃	#13905	direct (N × H)
235. C₂×C₄×D₄	C₄×C₁₁₃	semidirect
274. C₂×C₄⋊C₄	D₄×C₁₁₃	semidirect
344. C₄²	C₂²⋊C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₁₃	2
C₂×#382×C₁₁₃	2
C₂×#380×C₁₁₃	2
C₂×C₄×C₄⋊C₄×C₁₁₃	2
C₁₁₃×#1445	2
C₁₁₃×#1438	2
C₁₁₃×#1437	2
#13905	113

Subgroups — C113×#13905 #43281925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#13905 #43281925