Subgroups — C₁₁₃×#25637 #43293657

Order 28928.

1446 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#463×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2014	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#2011	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁₃×#1879	C₂	1	2	yes	maximal, complemented
10	C₁₁₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₁₁₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₁₃	—	2	1	no	—
13	C₂²×SD₁₆×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂²×D₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	#550×C₁₁₃	—	2	4	no	—
18	#550×C₁₁₃	—	2	4	no	—
19	C₂×#127×C₁₁₃	C₂²	1	2	yes	—
20	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₁₃	—	2	2	no	—
23	C₂×#121×C₁₁₃	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
27	#496×C₁₁₃	—	2	4	no	—
28	#463×C₁₁₃	—	2	4	no	—
29	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₁₁₃	C₂²	1	1	yes	characteristic
31	C₂×#102×C₁₁₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
33	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
34	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
35	C₂×#97×C₁₁₃	C₂²	1	1	yes	characteristic
36	#397×C₁₁₃	—	2	1	no	—
37	#393×C₁₁₃	—	2	1	no	—
38	#391×C₁₁₃	C₂²	1	2	yes	—
39	#390×C₁₁₃	C₂²	1	2	yes	—
40	#388×C₁₁₃	—	2	2	no	—
41	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
42	#340×C₁₁₃	C₂²	1	2	yes	—
43	#336×C₁₁₃	C₂²	1	2	yes	—
44	#336×C₁₁₃	C₂²	1	2	yes	—
45	C₂×#41×C₁₁₃	—	2	8	no	—
46	C₂×#41×C₁₁₃	—	4	8	no	—
47	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₁₃	—	2	2	no	—
57	C₂³×C₄×C₁₁₃	—	2	1	no	—
58	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
59	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
60	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
61	C₂×SD₁₆×C₁₁₃	—	4	2	no	—
62	C₂×SD₁₆×C₁₁₃	—	4	2	no	—
63	C₂×D₈×C₁₁₃	—	2	2	no	—
64	C₂×D₈×C₁₁₃	—	2	4	no	—
65	C₂×D₈×C₁₁₃	—	2	4	no	—
66	C₂×D₈×C₁₁₃	—	4	2	no	—
67	C₂×D₈×C₁₁₃	—	4	2	no	—
68	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
71	#127×C₁₁₃	—	2	4	no	—
72	#127×C₁₁₃	—	2	4	no	—
73	#127×C₁₁₃	—	2	2	no	—
74	#127×C₁₁₃	D₄	1	4	yes	—
75	#124×C₁₁₃	—	2	2	no	—
76	#124×C₁₁₃	—	2	2	no	—
77	#121×C₁₁₃	—	2	8	no	—
78	#121×C₁₁₃	—	2	16	no	—
79	C₄×Q₈×C₁₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₁₃	—	2	2	no	—
81	C₄×D₄×C₁₁₃	—	2	4	no	—
82	C₄×D₄×C₁₁₃	—	2	4	no	—
83	C₄×D₄×C₁₁₃	—	2	2	no	—
84	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
95	C₂×C₄²×C₁₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₁₁₃	—	2	2	no	—
99	#103×C₁₁₃	—	2	2	no	—
100	#102×C₁₁₃	—	2	4	no	—
101	#102×C₁₁₃	—	2	2	no	—
102	#102×C₁₁₃	—	4	2	no	—
103	#102×C₁₁₃	—	4	2	no	—
104	#97×C₁₁₃	—	2	2	no	—
105	#95×C₁₁₃	—	2	1	no	—
106	#95×C₁₁₃	—	2	2	no	—
107	#95×C₁₁₃	—	2	2	no	—
108	C₂⁴×C₁₁₃	—	2	2	no	—
109	C₂⁴×C₁₁₃	—	2	1	no	—
110	C₂⁴×C₁₁₃	—	2	1	no	—
111	#41×C₁₁₃	—	4	32	no	—
112	C₂×Q₈×C₁₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₁₃	—	2	2	no	—
118	C₂×D₄×C₁₁₃	—	2	8	no	—
119	C₂×D₄×C₁₁₃	—	2	8	no	—
120	C₂×D₄×C₁₁₃	—	2	4	no	—
121	C₂×D₄×C₁₁₃	—	2	4	no	—
122	C₂×D₄×C₁₁₃	—	2	2	no	—
123	C₂×D₄×C₁₁₃	—	2	1	no	—
124	C₂×D₄×C₁₁₃	—	2	1	no	—
125	C₂×D₄×C₁₁₃	—	2	1	no	—
126	C₂×D₄×C₁₁₃	—	2	2	no	—
127	C₂×D₄×C₁₁₃	—	2	2	no	—
128	C₂×D₄×C₁₁₃	—	2	2	no	—
129	C₂×D₄×C₁₁₃	—	2	2	no	—
130	C₂×D₄×C₁₁₃	—	2	2	no	—
131	C₂×D₄×C₁₁₃	—	2	2	no	—
132	C₂×D₄×C₁₁₃	—	2	2	no	—
133	C₂×D₄×C₁₁₃	—	2	2	no	—
134	C₂×D₄×C₁₁₃	—	4	4	no	—
135	C₂×D₄×C₁₁₃	—	4	4	no	—
136	C₂×D₄×C₁₁₃	—	4	4	no	—
137	C₂×D₄×C₁₁₃	—	8	1	no	—
138	C₂×D₄×C₁₁₃	—	8	1	no	—
139	C₂×D₄×C₁₁₃	—	8	2	no	—
140	C₂×D₄×C₁₁₃	—	8	2	no	—
141	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
142	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₁₁₃	—	4	8	no	—
157	SD₁₆×C₁₁₃	—	4	4	no	—
158	D₈×C₁₁₃	—	4	8	no	—
159	D₈×C₁₁₃	—	4	4	no	—
160	C₂×C₈×C₁₁₃	—	2	2	no	—
161	C₂×C₈×C₁₁₃	—	2	2	no	—
162	C₂×C₈×C₁₁₃	—	2	1	no	—
163	C₂×C₈×C₁₁₃	—	2	1	no	—
164	C₂×C₈×C₁₁₃	—	2	2	no	—
165	C₂×C₈×C₁₁₃	—	2	2	no	—
166	C₂×C₈×C₁₁₃	#41	1	4	yes	complemented
167	C₄⋊C₄×C₁₁₃	—	2	4	no	—
168	C₄⋊C₄×C₁₁₃	—	2	2	no	—
169	C₄⋊C₄×C₁₁₃	—	2	1	no	—
170	C₄⋊C₄×C₁₁₃	—	2	2	no	—
171	C₄⋊C₄×C₁₁₃	—	2	2	no	—
172	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
174	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
175	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
176	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
177	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
178	C₂²⋊C₄×C₁₁₃	—	8	2	no	—
179	C₄²×C₁₁₃	—	2	2	no	—
180	C₄²×C₁₁₃	—	2	2	no	—
181	C₄²×C₁₁₃	—	8	1	no	—
182	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
183	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
184	C₂³×C₁₁₃	—	2	4	no	—
185	C₂³×C₁₁₃	—	2	2	no	—
186	C₂³×C₁₁₃	—	4	2	no	—
187	C₂³×C₁₁₃	—	4	2	no	—
188	C₂³×C₁₁₃	—	4	2	no	—
189	C₂³×C₁₁₃	—	4	2	no	—
190	C₂³×C₁₁₃	—	4	2	no	—
191	C₂³×C₁₁₃	—	4	2	no	—
192	C₂³×C₁₁₃	—	4	2	no	—
193	C₂³×C₁₁₃	—	4	1	no	—
194	C₂³×C₁₁₃	—	4	2	no	—
195	C₂³×C₁₁₃	—	4	1	no	—
196	C₂³×C₁₁₃	—	4	1	no	—
197	C₂³×C₁₁₃	—	4	2	no	—
198	C₂³×C₁₁₃	—	4	2	no	—
199	C₂³×C₁₁₃	—	4	1	no	—
200	C₂³×C₁₁₃	—	4	1	no	—
201	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₁₁₃	—	2	8	no	—
203	Q₈×C₁₁₃	—	4	1	no	—
204	Q₈×C₁₁₃	—	4	1	no	—
205	Q₈×C₁₁₃	—	4	2	no	—
206	D₄×C₁₁₃	—	2	2	no	—
207	D₄×C₁₁₃	—	2	2	no	—
208	D₄×C₁₁₃	—	2	4	no	—
209	D₄×C₁₁₃	—	2	4	no	—
210	D₄×C₁₁₃	—	4	8	no	—
211	D₄×C₁₁₃	—	4	16	no	—
212	D₄×C₁₁₃	—	4	2	no	—
213	D₄×C₁₁₃	—	4	1	no	—
214	D₄×C₁₁₃	—	4	2	no	—
215	D₄×C₁₁₃	—	4	1	no	—
216	D₄×C₁₁₃	—	4	2	no	—
217	D₄×C₁₁₃	—	4	2	no	—
218	D₄×C₁₁₃	—	8	4	no	—
219	D₄×C₁₁₃	—	8	8	no	—
220	C₂×C₄×C₁₁₃	—	2	2	no	—
221	C₂×C₄×C₁₁₃	—	2	2	no	—
222	C₂×C₄×C₁₁₃	—	2	2	no	—
223	C₂×C₄×C₁₁₃	—	2	1	no	—
224	C₂×C₄×C₁₁₃	—	2	1	no	—
225	C₂×C₄×C₁₁₃	—	2	2	no	—
226	C₂×C₄×C₁₁₃	—	2	2	no	—
227	C₂×C₄×C₁₁₃	—	2	2	no	—
228	C₂×C₄×C₁₁₃	—	2	2	no	—
229	C₂×C₄×C₁₁₃	—	4	8	no	—
230	C₂×C₄×C₁₁₃	—	4	16	no	—
231	C₂×C₄×C₁₁₃	—	4	2	no	—
232	C₂×C₄×C₁₁₃	—	4	1	no	—
233	C₂×C₄×C₁₁₃	—	4	2	no	—
234	C₂×C₄×C₁₁₃	—	4	2	no	—
235	C₂×C₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	—	4	2	no	—
237	C₂×C₄×C₁₁₃	#120	1	2	yes	—
238	C₂×C₄×C₁₁₃	#120	1	2	yes	—
239	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
240	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
243	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
244	C₈×C₁₁₃	—	2	4	no	—
245	C₈×C₁₁₃	—	4	1	no	—
246	C₈×C₁₁₃	—	4	1	no	—
247	C₂²×C₁₁₃	—	4	2	no	—
248	C₂²×C₁₁₃	—	4	4	no	—
249	C₂²×C₁₁₃	—	4	2	no	—
250	C₂²×C₁₁₃	—	4	4	no	—
251	C₂²×C₁₁₃	—	4	4	no	—
252	C₂²×C₁₁₃	—	4	2	no	—
253	C₂²×C₁₁₃	—	8	2	no	—
254	C₂²×C₁₁₃	—	8	2	no	—
255	C₂²×C₁₁₃	—	8	2	no	—
256	C₂²×C₁₁₃	—	8	2	no	—
257	C₂²×C₁₁₃	—	8	2	no	—
258	C₂²×C₁₁₃	—	8	2	no	—
259	C₂²×C₁₁₃	—	8	2	no	—
260	C₂²×C₁₁₃	—	8	2	no	—
261	C₂²×C₁₁₃	—	8	1	no	—
262	C₂²×C₁₁₃	—	8	1	no	—
263	C₂²×C₁₁₃	—	8	1	no	—
264	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
265	C₂²×C₁₁₃	#550	1	2	yes	—
266	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
267	C₂²×C₁₁₃	#576	1	1	yes	characteristic
268	C₂²×C₁₁₃	#577	1	1	yes	characteristic
269	C₄×C₁₁₃	—	2	2	no	—
270	C₄×C₁₁₃	—	2	4	no	—
271	C₄×C₁₁₃	—	2	2	no	—
272	C₄×C₁₁₃	—	4	2	no	—
273	C₄×C₁₁₃	—	4	2	no	—
274	C₄×C₁₁₃	—	8	2	no	—
275	C₄×C₁₁₃	—	8	1	no	—
276	C₄×C₁₁₃	#532	1	1	yes	characteristic
277	C₄×C₁₁₃	#535	1	1	yes	characteristic
278	C₄×C₁₁₃	#546	1	2	yes	—
279	#25637	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₁₁₃	—	8	2	no	—
281	C₂×C₁₁₃	—	8	4	no	—
282	C₂×C₁₁₃	—	16	1	no	—
283	C₂×C₁₁₃	#2431	1	1	yes	characteristic
284	C₂×C₁₁₃	#3003	1	1	yes	characteristic
285	C₂×C₁₁₃	#3012	1	1	yes	characteristic
286	C₂×C₁₁₃	#3397	1	2	yes	—
287	C₂×C₁₁₃	#3399	1	2	yes	—
288	C₂×#550	C₂×C₁₁₃	1	1	yes	characteristic, complemented
289	C₂×#496	C₂×C₁₁₃	1	1	yes	characteristic, complemented
290	C₂×#463	C₂×C₁₁₃	1	1	yes	characteristic, complemented
291	#2592	C₂×C₁₁₃	1	1	yes	characteristic, complemented
292	#2014	C₂×C₁₁₃	1	2	yes	complemented
293	#2011	C₂×C₁₁₃	1	2	yes	complemented
294	#1985	C₂×C₁₁₃	1	1	yes	characteristic, complemented
295	#1982	C₂×C₁₁₃	1	1	yes	characteristic, complemented
296	#1879	C₂×C₁₁₃	1	2	yes	complemented
297	#1877	C₂×C₁₁₃	1	2	yes	complemented
298	#1762	C₂×C₁₁₃	1	1	yes	characteristic, complemented
299	C₁₁₃	#25637	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×#41	—	2	1	no	—
301	C₂²×SD₁₆	C₂²×C₁₁₃	1	2	yes	—
302	C₂²×SD₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
303	C₂²×D₈	C₂²×C₁₁₃	1	2	yes	—
304	C₂²×D₈	C₂²×C₁₁₃	1	1	yes	characteristic
305	#550	—	2	4	no	—
306	#550	—	2	4	no	—
307	C₂×#127	C₂²×C₁₁₃	1	2	yes	—
308	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
309	C₂×#124	C₂²×C₁₁₃	1	1	yes	characteristic
310	C₂×#121	—	2	2	no	—
311	C₂×#121	—	2	1	no	—
312	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
314	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
315	#496	—	2	4	no	—
316	#463	—	2	4	no	—
317	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₁₃	1	1	yes	characteristic
319	C₂×#102	C₂²×C₁₁₃	1	1	yes	characteristic
320	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
321	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
322	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
323	C₂×#97	C₂²×C₁₁₃	1	1	yes	characteristic
324	#397	—	2	1	no	—
325	#393	—	2	1	no	—
326	#391	C₂²×C₁₁₃	1	2	yes	—
327	#390	C₂²×C₁₁₃	1	2	yes	—
328	#388	—	2	2	no	—
329	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₁₃	1	2	yes	—
331	#336	C₂²×C₁₁₃	1	2	yes	—
332	#336	C₂²×C₁₁₃	1	2	yes	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	—	4	8	no	—
335	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	2	1	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂×SD₁₆	—	4	2	no	—
351	C₂×D₈	—	2	2	no	—
352	C₂×D₈	—	2	4	no	—
353	C₂×D₈	—	2	4	no	—
354	C₂×D₈	—	4	2	no	—
355	C₂×D₈	—	4	2	no	—
356	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
359	#127	—	2	4	no	—
360	#127	—	2	4	no	—
361	#127	—	2	2	no	—
362	#127	D₄×C₁₁₃	1	4	yes	—
363	#124	—	2	2	no	—
364	#124	—	2	2	no	—
365	#121	—	2	8	no	—
366	#121	—	2	16	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
373	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
374	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
385	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
386	C₄⋊C₈	—	2	2	no	—
387	#103	—	2	2	no	—
388	#102	—	2	4	no	—
389	#102	—	2	2	no	—
390	#102	—	4	2	no	—
391	#102	—	4	2	no	—
392	#97	—	2	2	no	—
393	#95	—	2	1	no	—
394	#95	—	2	2	no	—
395	#95	—	2	2	no	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	—	2	1	no	—
399	#41	—	4	32	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	8	1	no	—
426	C₂×D₄	—	8	1	no	—
427	C₂×D₄	—	8	2	no	—
428	C₂×D₄	—	8	2	no	—
429	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
430	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
444	SD₁₆	—	4	8	no	—
445	SD₁₆	—	4	4	no	—
446	D₈	—	4	8	no	—
447	D₈	—	4	4	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	#41×C₁₁₃	1	4	yes	complemented
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	8	1	no	—
470	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
471	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
490	Q₈	—	2	8	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	4	no	—
498	D₄	—	4	8	no	—
499	D₄	—	4	16	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	8	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	16	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	#120×C₁₁₃	1	2	yes	—
526	C₂×C₄	#120×C₁₁₃	1	2	yes	—
527	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
528	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
531	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
532	C₈	—	2	4	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
553	C₂²	#550×C₁₁₃	1	2	yes	—
554	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
555	C₂²	#576×C₁₁₃	1	1	yes	characteristic
556	C₂²	#577×C₁₁₃	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	4	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	8	2	no	—
563	C₄	—	8	1	no	—
564	C₄	#532×C₁₁₃	1	1	yes	characteristic
565	C₄	#535×C₁₁₃	1	1	yes	characteristic
566	C₄	#546×C₁₁₃	1	2	yes	—
567	C₂	—	8	2	no	—
568	C₂	—	8	4	no	—
569	C₂	—	16	1	no	—
570	C₂	C₁₁₃×#2431	1	1	yes	characteristic
571	C₂	C₁₁₃×#3003	1	1	yes	characteristic
572	C₂	C₁₁₃×#3012	1	1	yes	characteristic
573	C₂	C₁₁₃×#3397	1	2	yes	—
574	C₂	C₁₁₃×#3399	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×C₄×Q₈×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#550×C₁₁₃	C₂	semidirect
2. C₂×#496×C₁₁₃	C₂	semidirect
3. C₂×#463×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2592	C₂	semidirect
5. C₁₁₃×#2014	C₂	semidirect
6. C₁₁₃×#2011	C₂	semidirect
7. C₁₁₃×#1985	C₂	semidirect
8. C₁₁₃×#1982	C₂	semidirect
9. C₁₁₃×#1879	C₂	semidirect
10. C₁₁₃×#1877	C₂	semidirect
11. C₁₁₃×#1762	C₂	semidirect
166. C₂×C₈×C₁₁₃	#41	semidirect
279. #25637	C₁₁₃	direct (N × H)
288. C₂×#550	C₂×C₁₁₃	semidirect
289. C₂×#496	C₂×C₁₁₃	semidirect
290. C₂×#463	C₂×C₁₁₃	semidirect
291. #2592	C₂×C₁₁₃	semidirect
292. #2014	C₂×C₁₁₃	semidirect
293. #2011	C₂×C₁₁₃	semidirect
294. #1985	C₂×C₁₁₃	semidirect
295. #1982	C₂×C₁₁₃	semidirect
296. #1879	C₂×C₁₁₃	semidirect
297. #1877	C₂×C₁₁₃	semidirect
298. #1762	C₂×C₁₁₃	semidirect
299. C₁₁₃	#25637	direct (N × H)
454. C₂×C₈	#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×#550×C₁₁₃	2
C₂×#496×C₁₁₃	2
C₂×#463×C₁₁₃	2
C₁₁₃×#2592	2
C₁₁₃×#2014	2
C₁₁₃×#2011	2
C₁₁₃×#1985	2
C₁₁₃×#1982	2
C₁₁₃×#1879	2
C₁₁₃×#1877	2
C₁₁₃×#1762	2
#25637	113

Subgroups — C113×#25637 #43293657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#25637 #43293657