Subgroups — C₁₁₃×#24649 #43292669

Order 28928.

884 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#460×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2548	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#2015	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₁₃×#1961	C₂	1	1	yes	maximal, characteristic
9	C₁₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁₃×#1926	C₂	1	2	yes	maximal, complemented
11	C₁₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₁₃	C₂²	1	2	yes	—
14	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₁₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
18	#460×C₁₁₃	—	2	4	no	—
19	#441×C₁₁₃	—	2	4	no	—
20	C₂×#106×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
23	C₂×#103×C₁₁₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₁₁₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
26	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
27	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
29	C₂×#97×C₁₁₃	C₂²	1	1	yes	characteristic
30	#394×C₁₁₃	—	2	1	no	—
31	#394×C₁₁₃	—	2	1	no	—
32	#391×C₁₁₃	C₂²	1	2	yes	—
33	#390×C₁₁₃	—	2	2	no	—
34	#390×C₁₁₃	C₂²	1	2	yes	—
35	#387×C₁₁₃	—	2	2	no	—
36	#383×C₁₁₃	—	2	1	no	—
37	#382×C₁₁₃	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
40	#376×C₁₁₃	—	2	1	no	—
41	#340×C₁₁₃	C₂²	1	2	yes	—
42	#336×C₁₁₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₁₁₃	—	2	2	no	—
49	C₂×Q₁₆×C₁₁₃	—	2	2	no	—
50	C₂×Q₁₆×C₁₁₃	—	2	2	no	—
51	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
52	C₂×SD₁₆×C₁₁₃	—	4	2	no	—
53	C₂×SD₁₆×C₁₁₃	—	4	2	no	—
54	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
57	#127×C₁₁₃	—	2	2	no	—
58	#127×C₁₁₃	—	2	2	no	—
59	#124×C₁₁₃	—	2	4	no	—
60	#124×C₁₁₃	—	4	2	no	—
61	C₄×Q₈×C₁₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₁₃	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
80	#106×C₁₁₃	—	2	2	no	—
81	C₄⋊C₈×C₁₁₃	—	2	2	no	—
82	C₄⋊C₈×C₁₁₃	—	4	2	no	—
83	#103×C₁₁₃	—	2	2	no	—
84	#103×C₁₁₃	—	2	2	no	—
85	#103×C₁₁₃	—	4	2	no	—
86	#102×C₁₁₃	—	2	4	no	—
87	#102×C₁₁₃	—	2	4	no	—
88	#102×C₁₁₃	—	4	2	no	—
89	#97×C₁₁₃	—	2	2	no	—
90	#95×C₁₁₃	—	2	1	no	—
91	#95×C₁₁₃	—	2	2	no	—
92	#95×C₁₁₃	—	2	2	no	—
93	#95×C₁₁₃	—	2	1	no	—
94	#95×C₁₁₃	—	2	2	no	—
95	#95×C₁₁₃	D₄	1	1	yes	characteristic
96	#95×C₁₁₃	D₄	1	1	yes	characteristic
97	C₂⁴×C₁₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₁₃	#41	1	2	yes	—
110	C₂×D₄×C₁₁₃	—	2	2	no	—
111	C₂×D₄×C₁₁₃	—	2	2	no	—
112	C₂×D₄×C₁₁₃	—	2	2	no	—
113	C₂×D₄×C₁₁₃	—	2	2	no	—
114	C₂×D₄×C₁₁₃	—	2	2	no	—
115	C₂×D₄×C₁₁₃	—	2	2	no	—
116	C₂×D₄×C₁₁₃	—	4	4	no	—
117	C₂×D₄×C₁₁₃	—	4	2	no	—
118	C₂×D₄×C₁₁₃	—	4	2	no	—
119	C₂×D₄×C₁₁₃	—	8	2	no	—
120	C₂²×C₄×C₁₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₁₁₃	—	2	8	no	—
131	SD₁₆×C₁₁₃	—	4	8	no	—
132	C₂×C₈×C₁₁₃	—	2	1	no	—
133	C₂×C₈×C₁₁₃	—	2	1	no	—
134	C₂×C₈×C₁₁₃	—	2	1	no	—
135	C₂×C₈×C₁₁₃	—	2	2	no	—
136	C₂×C₈×C₁₁₃	—	2	1	no	—
137	C₂×C₈×C₁₁₃	—	2	2	no	—
138	C₂×C₈×C₁₁₃	—	2	1	no	—
139	C₂×C₈×C₁₁₃	—	2	2	no	—
140	C₂×C₈×C₁₁₃	#41	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	—	2	4	no	—
142	C₄⋊C₄×C₁₁₃	—	2	1	no	—
143	C₄⋊C₄×C₁₁₃	—	2	1	no	—
144	C₄⋊C₄×C₁₁₃	—	2	2	no	—
145	C₄⋊C₄×C₁₁₃	—	2	1	no	—
146	C₄⋊C₄×C₁₁₃	—	2	2	no	—
147	C₄⋊C₄×C₁₁₃	—	4	2	no	—
148	C₄⋊C₄×C₁₁₃	—	4	2	no	—
149	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
151	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
152	C₂²⋊C₄×C₁₁₃	—	8	2	no	—
153	C₂²⋊C₄×C₁₁₃	—	8	2	no	—
154	C₄²×C₁₁₃	—	2	4	no	—
155	C₄²×C₁₁₃	—	2	2	no	—
156	C₄²×C₁₁₃	—	2	2	no	—
157	C₄²×C₁₁₃	—	4	4	no	—
158	C₄²×C₁₁₃	—	4	2	no	—
159	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₁₃	#41	1	2	yes	—
161	C₂³×C₁₁₃	—	4	2	no	—
162	C₂³×C₁₁₃	—	4	2	no	—
163	C₂³×C₁₁₃	—	4	2	no	—
164	C₂³×C₁₁₃	—	4	2	no	—
165	C₂³×C₁₁₃	—	4	2	no	—
166	C₂³×C₁₁₃	—	4	2	no	—
167	C₂³×C₁₁₃	—	4	2	no	—
168	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₁₃	—	2	2	no	—
170	Q₈×C₁₁₃	—	2	2	no	—
171	Q₈×C₁₁₃	—	2	2	no	—
172	Q₈×C₁₁₃	—	2	2	no	—
173	Q₈×C₁₁₃	—	4	1	no	—
174	Q₈×C₁₁₃	—	4	1	no	—
175	Q₈×C₁₁₃	—	4	1	no	—
176	Q₈×C₁₁₃	—	4	1	no	—
177	D₄×C₁₁₃	—	4	2	no	—
178	D₄×C₁₁₃	—	4	2	no	—
179	D₄×C₁₁₃	—	4	2	no	—
180	D₄×C₁₁₃	—	4	2	no	—
181	D₄×C₁₁₃	—	8	4	no	—
182	D₄×C₁₁₃	—	8	4	no	—
183	C₂×C₄×C₁₁₃	—	2	2	no	—
184	C₂×C₄×C₁₁₃	—	2	2	no	—
185	C₂×C₄×C₁₁₃	—	2	2	no	—
186	C₂×C₄×C₁₁₃	—	2	2	no	—
187	C₂×C₄×C₁₁₃	—	2	2	no	—
188	C₂×C₄×C₁₁₃	—	2	2	no	—
189	C₂×C₄×C₁₁₃	—	2	2	no	—
190	C₂×C₄×C₁₁₃	—	2	2	no	—
191	C₂×C₄×C₁₁₃	—	2	2	no	—
192	C₂×C₄×C₁₁₃	—	2	2	no	—
193	C₂×C₄×C₁₁₃	—	2	2	no	—
194	C₂×C₄×C₁₁₃	—	4	1	no	—
195	C₂×C₄×C₁₁₃	—	4	1	no	—
196	C₂×C₄×C₁₁₃	—	4	1	no	—
197	C₂×C₄×C₁₁₃	—	4	1	no	—
198	C₂×C₄×C₁₁₃	—	4	2	no	—
199	C₂×C₄×C₁₁₃	—	4	1	no	—
200	C₂×C₄×C₁₁₃	—	4	2	no	—
201	C₂×C₄×C₁₁₃	—	4	2	no	—
202	C₂×C₄×C₁₁₃	—	4	2	no	—
203	C₂×C₄×C₁₁₃	—	4	2	no	—
204	C₂×C₄×C₁₁₃	#121	1	2	yes	—
205	C₂×C₄×C₁₁₃	#121	1	2	yes	—
206	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₈×C₁₁₃	—	2	2	no	—
213	C₈×C₁₁₃	—	4	1	no	—
214	C₈×C₁₁₃	—	4	2	no	—
215	C₂²×C₁₁₃	—	8	2	no	—
216	C₂²×C₁₁₃	—	8	2	no	—
217	C₂²×C₁₁₃	—	8	2	no	—
218	C₂²×C₁₁₃	—	8	2	no	—
219	C₂²×C₁₁₃	—	8	2	no	—
220	C₂²×C₁₁₃	—	8	2	no	—
221	C₂²×C₁₁₃	—	8	2	no	—
222	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
223	C₂²×C₁₁₃	#546	1	1	yes	characteristic
224	C₂²×C₁₁₃	#550	1	1	yes	characteristic
225	C₂²×C₁₁₃	#575	1	2	yes	—
226	C₂²×C₁₁₃	#577	1	2	yes	—
227	C₄×C₁₁₃	—	2	2	no	—
228	C₄×C₁₁₃	—	2	2	no	—
229	C₄×C₁₁₃	—	4	2	no	—
230	C₄×C₁₁₃	—	4	2	no	—
231	C₄×C₁₁₃	—	4	2	no	—
232	C₄×C₁₁₃	—	4	2	no	—
233	C₄×C₁₁₃	—	4	2	no	—
234	C₄×C₁₁₃	—	8	2	no	—
235	C₄×C₁₁₃	—	8	1	no	—
236	C₄×C₁₁₃	#525	1	1	yes	characteristic
237	C₄×C₁₁₃	#535	1	1	yes	characteristic
238	C₄×C₁₁₃	#553	1	1	yes	characteristic
239	C₄×C₁₁₃	#555	1	1	yes	characteristic
240	#24649	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₁₁₃	—	16	2	no	—
242	C₂×C₁₁₃	#2414	1	1	yes	characteristic
243	C₂×C₁₁₃	#3040	1	1	yes	characteristic
244	C₂×C₁₁₃	#3043	1	1	yes	characteristic
245	C₂×C₁₁₃	#3317	1	2	yes	—
246	C₂×C₁₁₃	#3401	1	2	yes	—
247	C₂×#460	C₂×C₁₁₃	1	1	yes	characteristic
248	C₂×#441	C₂×C₁₁₃	1	1	yes	characteristic, complemented
249	#2548	C₂×C₁₁₃	1	1	yes	characteristic
250	#2356	C₂×C₁₁₃	1	1	yes	characteristic, complemented
251	#2055	C₂×C₁₁₃	1	2	yes	complemented
252	#2015	C₂×C₁₁₃	1	2	yes	complemented
253	#1983	C₂×C₁₁₃	1	2	yes	complemented
254	#1961	C₂×C₁₁₃	1	1	yes	characteristic
255	#1940	C₂×C₁₁₃	1	1	yes	characteristic, complemented
256	#1926	C₂×C₁₁₃	1	2	yes	complemented
257	#1805	C₂×C₁₁₃	1	1	yes	characteristic, complemented
258	C₁₁₃	#24649	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×Q₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
260	C₂²×SD₁₆	C₂²×C₁₁₃	1	2	yes	—
261	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
262	C₂×#124	C₂²×C₁₁₃	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
265	#460	—	2	4	no	—
266	#441	—	2	4	no	—
267	C₂×#106	C₂²×C₁₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
270	C₂×#103	C₂²×C₁₁₃	1	1	yes	characteristic
271	C₂×#103	C₂²×C₁₁₃	1	1	yes	characteristic
272	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
273	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
274	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
275	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
276	C₂×#97	C₂²×C₁₁₃	1	1	yes	characteristic
277	#394	—	2	1	no	—
278	#394	—	2	1	no	—
279	#391	C₂²×C₁₁₃	1	2	yes	—
280	#390	—	2	2	no	—
281	#390	C₂²×C₁₁₃	1	2	yes	—
282	#387	—	2	2	no	—
283	#383	—	2	1	no	—
284	#382	C₂²×C₁₁₃	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
287	#376	—	2	1	no	—
288	#340	C₂²×C₁₁₃	1	2	yes	—
289	#336	C₂²×C₁₁₃	1	2	yes	—
290	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×Q₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂×SD₁₆	—	4	2	no	—
301	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
304	#127	—	2	2	no	—
305	#127	—	2	2	no	—
306	#124	—	2	4	no	—
307	#124	—	4	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	D₄×C₁₁₃	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
327	#106	—	2	2	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	4	2	no	—
330	#103	—	2	2	no	—
331	#103	—	2	2	no	—
332	#103	—	4	2	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	4	2	no	—
336	#97	—	2	2	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	D₄×C₁₁₃	1	1	yes	characteristic
343	#95	D₄×C₁₁₃	1	1	yes	characteristic
344	C₂⁴	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
356	C₂×Q₈	#41×C₁₁₃	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
377	Q₁₆	—	2	8	no	—
378	SD₁₆	—	4	8	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	#41×C₁₁₃	1	2	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	8	2	no	—
400	C₂²⋊C₄	—	8	2	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	4	no	—
405	C₄²	—	4	2	no	—
406	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
407	C₄²	#41×C₁₁₃	1	2	yes	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	4	1	no	—
423	Q₈	—	4	1	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	8	4	no	—
429	D₄	—	8	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	#121×C₁₁₃	1	2	yes	—
452	C₂×C₄	#121×C₁₁₃	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
457	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
458	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	4	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
470	C₂²	#546×C₁₁₃	1	1	yes	characteristic
471	C₂²	#550×C₁₁₃	1	1	yes	characteristic
472	C₂²	#575×C₁₁₃	1	2	yes	—
473	C₂²	#577×C₁₁₃	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	1	no	—
483	C₄	#525×C₁₁₃	1	1	yes	characteristic
484	C₄	#535×C₁₁₃	1	1	yes	characteristic
485	C₄	#553×C₁₁₃	1	1	yes	characteristic
486	C₄	#555×C₁₁₃	1	1	yes	characteristic
487	C₂	—	16	2	no	—
488	C₂	C₁₁₃×#2414	1	1	yes	characteristic
489	C₂	C₁₁₃×#3040	1	1	yes	characteristic
490	C₂	C₁₁₃×#3043	1	1	yes	characteristic
491	C₂	C₁₁₃×#3317	1	2	yes	—
492	C₂	C₁₁₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#127×C₁₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₄×C₄⋊C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#441×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2356	C₂	semidirect
5. C₁₁₃×#2055	C₂	semidirect
6. C₁₁₃×#2015	C₂	semidirect
7. C₁₁₃×#1983	C₂	semidirect
9. C₁₁₃×#1940	C₂	semidirect
10. C₁₁₃×#1926	C₂	semidirect
11. C₁₁₃×#1805	C₂	semidirect
240. #24649	C₁₁₃	direct (N × H)
248. C₂×#441	C₂×C₁₁₃	semidirect
250. #2356	C₂×C₁₁₃	semidirect
251. #2055	C₂×C₁₁₃	semidirect
252. #2015	C₂×C₁₁₃	semidirect
253. #1983	C₂×C₁₁₃	semidirect
255. #1940	C₂×C₁₁₃	semidirect
256. #1926	C₂×C₁₁₃	semidirect
257. #1805	C₂×C₁₁₃	semidirect
258. C₁₁₃	#24649	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×#460×C₁₁₃	2
C₂×#441×C₁₁₃	2
C₁₁₃×#2548	2
C₁₁₃×#2356	2
C₁₁₃×#2055	2
C₁₁₃×#2015	2
C₁₁₃×#1983	2
C₁₁₃×#1961	2
C₁₁₃×#1940	2
C₁₁₃×#1926	2
C₁₁₃×#1805	2
#24649	113

Subgroups — C113×#24649 #43292669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#24649 #43292669