Subgroups — C₁₁₃×#15218 #43283238

Order 28928.

1566 conjugacy classes of subgroups.

The subgroup lattice has 404 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
2	C₂×#389×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1444	C₂	1	4	yes	maximal
5	C₁₁₃×#1441	C₂	1	4	yes	maximal
6	C₁₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₁₁₃×C₄⋊#95	C₂	1	2	yes	maximal
8	C₂×#125×C₁₁₃	—	2	8	no	—
9	C₂×#125×C₁₁₃	—	2	4	no	—
10	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
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×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
18	#389×C₁₁₃	—	2	8	no	—
19	C₄×C₄⋊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	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
26	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
27	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
28	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
29	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
32	#125×C₁₁₃	—	2	32	no	—
33	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
34	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
35	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
36	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
45	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₁₃	D₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₁₁₃	Q₈	1	8	yes	—
48	C₂×C₄²×C₁₁₃	—	2	4	no	—
49	C₂×C₄²×C₁₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₁₃	—	2	4	no	—
53	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
54	C₂×C₄²×C₁₁₃	Q₈	1	4	yes	—
55	#95×C₁₁₃	—	2	4	no	—
56	#95×C₁₁₃	—	2	8	no	—
57	#95×C₁₁₃	—	2	8	no	—
58	#95×C₁₁₃	—	4	4	no	—
59	#95×C₁₁₃	—	4	4	no	—
60	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
61	C₂²×C₄×C₁₁₃	—	2	1	no	—
62	C₂²×C₄×C₁₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₁₃	—	2	4	no	—
74	C₂²×C₄×C₁₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₁₃	—	2	4	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	4	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	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₁₃	C₂×Q₈	1	8	yes	—
98	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
102	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
103	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
104	C₄⋊C₄×C₁₁₃	—	2	16	no	—
105	C₄⋊C₄×C₁₁₃	—	2	32	no	—
106	C₄⋊C₄×C₁₁₃	—	2	16	no	—
107	C₄⋊C₄×C₁₁₃	—	2	16	no	—
108	C₄⋊C₄×C₁₁₃	—	4	16	no	—
109	C₄²×C₁₁₃	—	2	8	no	—
110	C₄²×C₁₁₃	—	2	8	no	—
111	C₄²×C₁₁₃	—	4	4	no	—
112	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
113	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
114	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
115	C₂³×C₁₁₃	C₂²×Q₈	1	2	yes	—
116	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
117	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
118	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
119	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
120	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
121	C₂×C₄×C₁₁₃	—	2	2	no	—
122	C₂×C₄×C₁₁₃	—	2	4	no	—
123	C₂×C₄×C₁₁₃	—	2	4	no	—
124	C₂×C₄×C₁₁₃	—	2	2	no	—
125	C₂×C₄×C₁₁₃	—	2	4	no	—
126	C₂×C₄×C₁₁₃	—	2	8	no	—
127	C₂×C₄×C₁₁₃	—	2	2	no	—
128	C₂×C₄×C₁₁₃	—	2	8	no	—
129	C₂×C₄×C₁₁₃	—	2	4	no	—
130	C₂×C₄×C₁₁₃	—	2	4	no	—
131	C₂×C₄×C₁₁₃	—	2	4	no	—
132	C₂×C₄×C₁₁₃	—	2	4	no	—
133	C₂×C₄×C₁₁₃	—	2	4	no	—
134	C₂×C₄×C₁₁₃	—	2	8	no	—
135	C₂×C₄×C₁₁₃	—	2	8	no	—
136	C₂×C₄×C₁₁₃	—	2	4	no	—
137	C₂×C₄×C₁₁₃	—	2	8	no	—
138	C₂×C₄×C₁₁₃	—	2	8	no	—
139	C₂×C₄×C₁₁₃	—	4	2	no	—
140	C₂×C₄×C₁₁₃	—	4	4	no	—
141	C₂×C₄×C₁₁₃	—	4	4	no	—
142	C₂×C₄×C₁₁₃	—	4	2	no	—
143	C₂×C₄×C₁₁₃	—	4	2	no	—
144	C₂×C₄×C₁₁₃	—	4	4	no	—
145	C₂×C₄×C₁₁₃	—	4	1	no	—
146	C₂×C₄×C₁₁₃	—	4	4	no	—
147	C₂×C₄×C₁₁₃	—	4	1	no	—
148	C₂×C₄×C₁₁₃	—	4	4	no	—
149	C₂×C₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	4	2	no	—
151	C₂×C₄×C₁₁₃	—	4	2	no	—
152	C₂×C₄×C₁₁₃	—	4	2	no	—
153	C₂×C₄×C₁₁₃	—	4	4	no	—
154	C₂×C₄×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	4	4	no	—
157	C₂×C₄×C₁₁₃	—	4	4	no	—
158	C₂×C₄×C₁₁₃	#120	1	4	yes	—
159	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
160	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	8	yes	—
161	C₂×C₄×C₁₁₃	#125	1	4	yes	complemented
162	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	4	yes	—
163	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	8	yes	—
164	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
165	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
166	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
167	C₂²×C₁₁₃	#525	1	2	yes	—
168	C₂²×C₁₁₃	C₂×#125	1	1	yes	characteristic
169	C₂²×C₁₁₃	#529	1	2	yes	—
170	C₂²×C₁₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
171	C₂²×C₁₁₃	C₂×C₄⋊Q₈	1	2	yes	—
172	C₂²×C₁₁₃	#533	1	1	yes	characteristic
173	C₂²×C₁₁₃	#537	1	2	yes	—
174	C₂²×C₁₁₃	#540	1	1	yes	characteristic
175	C₂²×C₁₁₃	#541	1	1	yes	characteristic
176	C₂²×C₁₁₃	#544	1	2	yes	—
177	C₂²×C₁₁₃	#546	1	2	yes	—
178	C₂²×C₁₁₃	#547	1	2	yes	—
179	C₂²×C₁₁₃	#548	1	2	yes	—
180	C₂²×C₁₁₃	#550	1	2	yes	—
181	C₂²×C₁₁₃	#554	1	2	yes	—
182	C₂²×C₁₁₃	#554	1	2	yes	—
183	C₂²×C₁₁₃	#557	1	2	yes	—
184	C₂²×C₁₁₃	#557	1	2	yes	—
185	C₄×C₁₁₃	—	2	4	no	—
186	C₄×C₁₁₃	—	4	2	no	—
187	C₄×C₁₁₃	—	4	4	no	—
188	C₄×C₁₁₃	—	4	8	no	—
189	C₄×C₁₁₃	—	4	4	no	—
190	C₄×C₁₁₃	—	4	8	no	—
191	C₄×C₁₁₃	#395	1	8	yes	—
192	#15218	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₁₁₃	C₂×#395	1	1	yes	characteristic
194	C₂×C₁₁₃	#2407	1	2	yes	—
195	C₂×C₁₁₃	#2453	1	2	yes	—
196	C₂×C₁₁₃	#2454	1	2	yes	—
197	C₂×C₁₁₃	#2550	1	2	yes	—
198	C₂×C₁₁₃	#2552	1	2	yes	—
199	C₂×C₁₁₃	#2584	1	2	yes	—
200	C₂×C₁₁₃	#2629	1	1	yes	characteristic
201	C₂×C₁₁₃	#2851	1	1	yes	characteristic
202	C₂²×#125	C₂×C₁₁₃	1	1	yes	characteristic
203	C₂×#389	C₂×C₁₁₃	1	2	yes	—
204	C₂×C₄×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
205	#1444	C₂×C₁₁₃	1	4	yes	—
206	#1441	C₂×C₁₁₃	1	4	yes	—
207	C₄⋊#95	C₂×C₁₁₃	1	2	yes	—
208	C₄⋊#95	C₂×C₁₁₃	1	1	yes	characteristic
209	C₁₁₃	#15218	1	1	yes	characteristic, direct product factor, Sylow
210	C₂×#125	—	2	8	no	—
211	C₂×#125	—	2	4	no	—
212	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
217	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
218	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
219	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
220	#389	—	2	8	no	—
221	C₄×C₄⋊C₄	—	2	4	no	—
222	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
223	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
224	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
225	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
226	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
227	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
228	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
229	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
230	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
234	#125	—	2	32	no	—
235	C₂×C₄⋊C₄	—	2	8	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	—	4	4	no	—
248	C₂×C₄⋊C₄	D₄×C₁₁₃	1	8	yes	—
249	C₂×C₄⋊C₄	Q₈×C₁₁₃	1	8	yes	—
250	C₂×C₄²	—	2	4	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
256	C₂×C₄²	Q₈×C₁₁₃	1	4	yes	—
257	#95	—	2	4	no	—
258	#95	—	2	8	no	—
259	#95	—	2	8	no	—
260	#95	—	4	4	no	—
261	#95	—	4	4	no	—
262	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
296	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
299	C₂²×C₄	C₂×Q₈×C₁₁₃	1	8	yes	—
300	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
301	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
302	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
303	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
304	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
305	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
306	C₄⋊C₄	—	2	32	no	—
307	C₄⋊C₄	—	2	16	no	—
308	C₄⋊C₄	—	2	16	no	—
309	C₄⋊C₄	—	2	16	no	—
310	C₄⋊C₄	—	4	16	no	—
311	C₄²	—	2	8	no	—
312	C₄²	—	2	8	no	—
313	C₄²	—	4	4	no	—
314	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
315	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
316	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
317	C₂³	C₂²×Q₈×C₁₁₃	1	2	yes	—
318	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
319	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
320	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
321	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
322	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	#120×C₁₁₃	1	4	yes	—
361	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
362	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	8	yes	—
363	C₂×C₄	#125×C₁₁₃	1	4	yes	complemented
364	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	8	yes	—
365	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	4	yes	—
366	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
367	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
368	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
369	C₂²	#525×C₁₁₃	1	2	yes	—
370	C₂²	C₂×#125×C₁₁₃	1	1	yes	characteristic
371	C₂²	#529×C₁₁₃	1	2	yes	—
372	C₂²	C₂×C₄⋊Q₈×C₁₁₃	1	2	yes	—
373	C₂²	C₂×C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
374	C₂²	#533×C₁₁₃	1	1	yes	characteristic
375	C₂²	#537×C₁₁₃	1	2	yes	—
376	C₂²	#540×C₁₁₃	1	1	yes	characteristic
377	C₂²	#541×C₁₁₃	1	1	yes	characteristic
378	C₂²	#544×C₁₁₃	1	2	yes	—
379	C₂²	#546×C₁₁₃	1	2	yes	—
380	C₂²	#547×C₁₁₃	1	2	yes	—
381	C₂²	#548×C₁₁₃	1	2	yes	—
382	C₂²	#550×C₁₁₃	1	2	yes	—
383	C₂²	#554×C₁₁₃	1	2	yes	—
384	C₂²	#554×C₁₁₃	1	2	yes	—
385	C₂²	#557×C₁₁₃	1	2	yes	—
386	C₂²	#557×C₁₁₃	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	8	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	8	no	—
393	C₄	#395×C₁₁₃	1	8	yes	—
394	C₂	C₂×#395×C₁₁₃	1	1	yes	characteristic
395	C₂	C₁₁₃×#2407	1	2	yes	—
396	C₂	C₁₁₃×#2453	1	2	yes	—
397	C₂	C₁₁₃×#2454	1	2	yes	—
398	C₂	C₁₁₃×#2550	1	2	yes	—
399	C₂	C₁₁₃×#2552	1	2	yes	—
400	C₂	C₁₁₃×#2584	1	2	yes	—
401	C₂	C₁₁₃×#2629	1	1	yes	characteristic
402	C₂	C₁₁₃×#2851	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
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
161. C₂×C₄×C₁₁₃	#125	semidirect
192. #15218	C₁₁₃	direct (N × H)
209. C₁₁₃	#15218	direct (N × H)
363. C₂×C₄	#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×#389×C₁₁₃	2
C₂×C₄×C₄⋊C₄×C₁₁₃	2
C₁₁₃×#1444	2
C₁₁₃×#1441	2
C₁₁₃×C₄⋊#95	2
#15218	113

Subgroups — C113×#15218 #43283238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#15218 #43283238