Subgroups — C₁₁₃×#25571 #43293591

Order 28928.

1386 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#487×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2000	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁₃×#1872	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₁₃	—	2	1	no	—
11	C₂²×SD₁₆×C₁₁₃	C₂²	1	2	yes	—
12	#547×C₁₁₃	—	2	4	no	—
13	#547×C₁₁₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂×#123×C₁₁₃	—	2	2	no	—
17	C₂×C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	—
19	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
23	#487×C₁₁₃	—	2	4	no	—
24	#461×C₁₁₃	—	2	4	no	—
25	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₁₁₃	C₂²	1	4	yes	—
27	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
31	#399×C₁₁₃	—	2	2	no	—
32	#390×C₁₁₃	—	2	1	no	—
33	#384×C₁₁₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
35	#340×C₁₁₃	C₂²	1	2	yes	—
36	#340×C₁₁₃	C₂²	1	4	yes	—
37	C₂×#41×C₁₁₃	—	2	8	no	—
38	C₂×#41×C₁₁₃	—	4	4	no	—
39	C₂×#41×C₁₁₃	—	4	4	no	—
40	C₂²×Q₈×C₁₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
48	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
49	C₂×SD₁₆×C₁₁₃	—	4	4	no	—
50	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
53	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
54	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
55	C₄⋊Q₈×C₁₁₃	D₄	1	4	yes	—
56	#123×C₁₁₃	—	2	16	no	—
57	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
58	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
59	C₂²⋊Q₈×C₁₁₃	—	4	4	no	—
60	#121×C₁₁₃	—	2	4	no	—
61	#121×C₁₁₃	—	2	4	no	—
62	C₄×D₄×C₁₁₃	—	2	2	no	—
63	C₄×D₄×C₁₁₃	—	2	2	no	—
64	C₄×D₄×C₁₁₃	—	2	2	no	—
65	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
81	C₂×C₄²×C₁₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₁₃	—	2	2	no	—
84	#103×C₁₁₃	—	2	4	no	—
85	#103×C₁₁₃	—	2	8	no	—
86	#102×C₁₁₃	—	2	4	no	—
87	C₂²⋊C₈×C₁₁₃	—	4	4	no	—
88	C₄×C₈×C₁₁₃	—	2	2	no	—
89	#95×C₁₁₃	—	2	1	no	—
90	C₂⁴×C₁₁₃	—	2	1	no	—
91	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
92	#41×C₁₁₃	—	4	32	no	—
93	C₂×Q₈×C₁₁₃	—	2	4	no	—
94	C₂×Q₈×C₁₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₁₃	—	4	2	no	—
100	C₂×D₄×C₁₁₃	—	2	8	no	—
101	C₂×D₄×C₁₁₃	—	2	2	no	—
102	C₂×D₄×C₁₁₃	—	2	2	no	—
103	C₂×D₄×C₁₁₃	—	2	1	no	—
104	C₂×D₄×C₁₁₃	—	2	2	no	—
105	C₂×D₄×C₁₁₃	—	2	2	no	—
106	C₂×D₄×C₁₁₃	—	4	4	no	—
107	C₂×D₄×C₁₁₃	—	4	4	no	—
108	C₂×D₄×C₁₁₃	SD₁₆	1	4	yes	complemented
109	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₁₃	—	4	4	no	—
122	C₂²×C₄×C₁₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
128	SD₁₆×C₁₁₃	—	4	8	no	—
129	C₂×C₈×C₁₁₃	—	2	2	no	—
130	C₂×C₈×C₁₁₃	—	2	2	no	—
131	C₂×C₈×C₁₁₃	—	2	2	no	—
132	C₂×C₈×C₁₁₃	—	2	2	no	—
133	C₂×C₈×C₁₁₃	—	2	4	no	—
134	C₄⋊C₄×C₁₁₃	—	2	8	no	—
135	C₄⋊C₄×C₁₁₃	—	2	4	no	—
136	C₄⋊C₄×C₁₁₃	—	2	2	no	—
137	C₄⋊C₄×C₁₁₃	—	2	1	no	—
138	C₄⋊C₄×C₁₁₃	—	2	2	no	—
139	C₄⋊C₄×C₁₁₃	—	2	2	no	—
140	C₄⋊C₄×C₁₁₃	—	4	8	no	—
141	C₄⋊C₄×C₁₁₃	—	4	2	no	—
142	C₄⋊C₄×C₁₁₃	—	4	2	no	—
143	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
145	C₄⋊C₄×C₁₁₃	#41	1	4	yes	complemented
146	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
147	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
148	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
149	C₂²⋊C₄×C₁₁₃	—	4	8	no	—
150	C₄²×C₁₁₃	—	4	2	no	—
151	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
152	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
153	C₂³×C₁₁₃	—	2	2	no	—
154	C₂³×C₁₁₃	—	2	4	no	—
155	C₂³×C₁₁₃	—	2	2	no	—
156	C₂³×C₁₁₃	—	2	4	no	—
157	C₂³×C₁₁₃	—	2	2	no	—
158	C₂³×C₁₁₃	—	4	2	no	—
159	C₂³×C₁₁₃	—	4	1	no	—
160	C₂³×C₁₁₃	—	4	1	no	—
161	C₂³×C₁₁₃	—	4	2	no	—
162	C₂³×C₁₁₃	C₂×SD₁₆	1	4	yes	—
163	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₁₃	—	4	8	no	—
165	Q₈×C₁₁₃	—	4	2	no	—
166	Q₈×C₁₁₃	—	4	2	no	—
167	Q₈×C₁₁₃	—	4	4	no	—
168	D₄×C₁₁₃	—	2	2	no	—
169	D₄×C₁₁₃	—	2	2	no	—
170	D₄×C₁₁₃	—	2	8	no	—
171	D₄×C₁₁₃	—	4	16	no	—
172	D₄×C₁₁₃	—	4	2	no	—
173	C₂×C₄×C₁₁₃	—	2	2	no	—
174	C₂×C₄×C₁₁₃	—	2	2	no	—
175	C₂×C₄×C₁₁₃	—	2	2	no	—
176	C₂×C₄×C₁₁₃	—	2	4	no	—
177	C₂×C₄×C₁₁₃	—	2	4	no	—
178	C₂×C₄×C₁₁₃	—	2	4	no	—
179	C₂×C₄×C₁₁₃	—	4	16	no	—
180	C₂×C₄×C₁₁₃	—	4	1	no	—
181	C₂×C₄×C₁₁₃	—	4	2	no	—
182	C₂×C₄×C₁₁₃	—	4	2	no	—
183	C₂×C₄×C₁₁₃	—	4	1	no	—
184	C₂×C₄×C₁₁₃	—	4	2	no	—
185	C₂×C₄×C₁₁₃	—	4	2	no	—
186	C₂×C₄×C₁₁₃	—	4	2	no	—
187	C₂×C₄×C₁₁₃	—	4	2	no	—
188	C₂×C₄×C₁₁₃	—	4	4	no	—
189	C₂×C₄×C₁₁₃	—	4	8	no	—
190	C₂×C₄×C₁₁₃	—	4	2	no	—
191	C₂×C₄×C₁₁₃	—	4	4	no	—
192	C₂×C₄×C₁₁₃	#120	1	2	yes	—
193	C₂×C₄×C₁₁₃	#120	1	2	yes	—
194	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
199	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
200	C₈×C₁₁₃	—	4	2	no	—
201	C₈×C₁₁₃	—	4	2	no	—
202	C₂²×C₁₁₃	—	2	4	no	—
203	C₂²×C₁₁₃	—	2	8	no	—
204	C₂²×C₁₁₃	—	4	4	no	—
205	C₂²×C₁₁₃	—	4	2	no	—
206	C₂²×C₁₁₃	—	4	2	no	—
207	C₂²×C₁₁₃	—	4	2	no	—
208	C₂²×C₁₁₃	—	4	2	no	—
209	C₂²×C₁₁₃	—	4	2	no	—
210	C₂²×C₁₁₃	—	8	2	no	—
211	C₂²×C₁₁₃	—	8	2	no	—
212	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
213	C₂²×C₁₁₃	#546	1	2	yes	—
214	C₂²×C₁₁₃	C₂²×SD₁₆	1	1	yes	characteristic
215	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂²×C₁₁₃	#578	1	2	yes	—
217	C₄×C₁₁₃	—	2	2	no	—
218	C₄×C₁₁₃	—	4	4	no	—
219	C₄×C₁₁₃	—	4	2	no	—
220	C₄×C₁₁₃	—	4	2	no	—
221	C₄×C₁₁₃	—	4	4	no	—
222	C₄×C₁₁₃	—	8	2	no	—
223	C₄×C₁₁₃	#450	1	4	yes	—
224	C₄×C₁₁₃	#532	1	1	yes	characteristic
225	C₄×C₁₁₃	#535	1	1	yes	characteristic
226	C₄×C₁₁₃	#550	1	2	yes	—
227	#25571	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₁₁₃	—	4	4	no	—
229	C₂×C₁₁₃	—	8	2	no	—
230	C₂×C₁₁₃	#2431	1	1	yes	characteristic
231	C₂×C₁₁₃	C₂×#450	1	1	yes	characteristic
232	C₂×C₁₁₃	#3011	1	1	yes	characteristic
233	C₂×C₁₁₃	#3298	1	2	yes	—
234	C₂×C₁₁₃	#3330	1	2	yes	—
235	C₂×#547	C₂×C₁₁₃	1	1	yes	characteristic
236	C₂×#487	C₂×C₁₁₃	1	1	yes	characteristic, complemented
237	C₂×#461	C₂×C₁₁₃	1	1	yes	characteristic, complemented
238	#2542	C₂×C₁₁₃	1	1	yes	characteristic, complemented
239	#2000	C₂×C₁₁₃	1	4	yes	complemented
240	#1988	C₂×C₁₁₃	1	1	yes	characteristic, complemented
241	#1954	C₂×C₁₁₃	1	1	yes	characteristic, complemented
242	#1872	C₂×C₁₁₃	1	4	yes	complemented
243	C₄×#102	C₂×C₁₁₃	1	1	yes	characteristic, complemented
244	C₁₁₃	#25571	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×#41	—	2	1	no	—
246	C₂²×SD₁₆	C₂²×C₁₁₃	1	2	yes	—
247	#547	—	2	4	no	—
248	#547	—	2	4	no	—
249	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
251	C₂×#123	—	2	2	no	—
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	—
254	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
258	#487	—	2	4	no	—
259	#461	—	2	4	no	—
260	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
261	C₂×#103	C₂²×C₁₁₃	1	4	yes	—
262	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
263	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	—
265	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
266	#399	—	2	2	no	—
267	#390	—	2	1	no	—
268	#384	—	2	1	no	—
269	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
270	#340	C₂²×C₁₁₃	1	2	yes	—
271	#340	C₂²×C₁₁₃	1	4	yes	—
272	C₂×#41	—	2	8	no	—
273	C₂×#41	—	4	4	no	—
274	C₂×#41	—	4	4	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
279	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
283	C₂×SD₁₆	—	2	4	no	—
284	C₂×SD₁₆	—	4	4	no	—
285	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
286	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	D₄×C₁₁₃	1	4	yes	—
291	#123	—	2	16	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	4	4	no	—
295	#121	—	2	4	no	—
296	#121	—	2	4	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	4	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
318	C₄⋊C₈	—	2	2	no	—
319	#103	—	2	4	no	—
320	#103	—	2	8	no	—
321	#102	—	2	4	no	—
322	C₂²⋊C₈	—	4	4	no	—
323	C₄×C₈	—	2	2	no	—
324	#95	—	2	1	no	—
325	C₂⁴	—	2	1	no	—
326	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
327	#41	—	4	32	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	SD₁₆×C₁₁₃	1	4	yes	complemented
344	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
363	SD₁₆	—	4	8	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	4	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	8	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
379	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
380	C₄⋊C₄	#41×C₁₁₃	1	4	yes	complemented
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	4	8	no	—
385	C₄²	—	4	2	no	—
386	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
387	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂×SD₁₆×C₁₁₃	1	4	yes	—
398	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
399	Q₈	—	4	8	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	8	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	#120×C₁₁₃	1	2	yes	—
428	C₂×C₄	#120×C₁₁₃	1	2	yes	—
429	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	2	yes	—
430	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
434	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
448	C₂²	#546×C₁₁₃	1	2	yes	—
449	C₂²	C₂²×SD₁₆×C₁₁₃	1	1	yes	characteristic
450	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
451	C₂²	#578×C₁₁₃	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	#450×C₁₁₃	1	4	yes	—
459	C₄	#532×C₁₁₃	1	1	yes	characteristic
460	C₄	#535×C₁₁₃	1	1	yes	characteristic
461	C₄	#550×C₁₁₃	1	2	yes	—
462	C₂	—	4	4	no	—
463	C₂	—	8	2	no	—
464	C₂	C₁₁₃×#2431	1	1	yes	characteristic
465	C₂	C₂×#450×C₁₁₃	1	1	yes	characteristic
466	C₂	C₁₁₃×#3011	1	1	yes	characteristic
467	C₂	C₁₁₃×#3298	1	2	yes	—
468	C₂	C₁₁₃×#3330	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#547×C₁₁₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×C₄×D₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#487×C₁₁₃	C₂	semidirect
3. C₂×#461×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2542	C₂	semidirect
5. C₁₁₃×#2000	C₂	semidirect
6. C₁₁₃×#1988	C₂	semidirect
7. C₁₁₃×#1954	C₂	semidirect
8. C₁₁₃×#1872	C₂	semidirect
9. C₄×#102×C₁₁₃	C₂	semidirect
108. C₂×D₄×C₁₁₃	SD₁₆	semidirect
145. C₄⋊C₄×C₁₁₃	#41	semidirect
227. #25571	C₁₁₃	direct (N × H)
236. C₂×#487	C₂×C₁₁₃	semidirect
237. C₂×#461	C₂×C₁₁₃	semidirect
238. #2542	C₂×C₁₁₃	semidirect
239. #2000	C₂×C₁₁₃	semidirect
240. #1988	C₂×C₁₁₃	semidirect
241. #1954	C₂×C₁₁₃	semidirect
242. #1872	C₂×C₁₁₃	semidirect
243. C₄×#102	C₂×C₁₁₃	semidirect
244. C₁₁₃	#25571	direct (N × H)
343. C₂×D₄	SD₁₆×C₁₁₃	semidirect
380. C₄⋊C₄	#41×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₁₃	2
C₂×#487×C₁₁₃	2
C₂×#461×C₁₁₃	2
C₁₁₃×#2542	2
C₁₁₃×#2000	2
C₁₁₃×#1988	2
C₁₁₃×#1954	2
C₁₁₃×#1872	2
C₄×#102×C₁₁₃	2
#25571	113

Subgroups — C113×#25571 #43293591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#25571 #43293591