Subgroups — C₁₁₃×#20964 #43288984

Order 28928.

1700 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₂×#413×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2879	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1891	C₂	1	8	yes	maximal, complemented
6	C₂×#344×C₁₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
9	#568×C₁₁₃	—	2	2	no	—
10	#568×C₁₁₃	—	2	4	no	—
11	#568×C₁₁₃	C₂²	1	4	yes	—
12	C₂×#131×C₁₁₃	—	2	4	no	—
13	C₂²×M₁₆×C₁₁₃	—	2	2	no	—
14	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
16	#537×C₁₁₃	—	2	2	no	—
17	#536×C₁₁₃	—	2	1	no	—
18	#536×C₁₁₃	C₄	1	2	yes	—
19	#535×C₁₁₃	—	2	1	no	—
20	#535×C₁₁₃	C₄	1	2	yes	—
21	#534×C₁₁₃	C₄	1	4	yes	—
22	#532×C₁₁₃	—	2	2	no	—
23	#525×C₁₁₃	—	2	2	no	—
24	#525×C₁₁₃	C₂²	1	4	yes	—
25	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
26	#413×C₁₁₃	—	2	2	no	—
27	#413×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#101×C₁₁₃	—	2	1	no	—
29	C₂×#100×C₁₁₃	—	2	1	no	—
30	#408×C₁₁₃	—	2	4	no	—
31	#408×C₁₁₃	—	2	4	no	—
32	#407×C₁₁₃	C₂²	1	8	yes	complemented
33	#344×C₁₁₃	C₂²	1	8	yes	complemented
34	C₂×#41×C₁₁₃	—	2	2	no	—
35	C₂×#41×C₁₁₃	—	2	2	no	—
36	C₂×#41×C₁₁₃	—	2	1	no	—
37	C₂×#41×C₁₁₃	—	2	1	no	—
38	C₂×#41×C₁₁₃	—	2	1	no	—
39	C₂×#41×C₁₁₃	—	2	1	no	—
40	C₂×#41×C₁₁₃	—	2	2	no	—
41	C₂×#41×C₁₁₃	—	2	2	no	—
42	C₂×#41×C₁₁₃	—	2	2	no	—
43	C₂×#41×C₁₁₃	—	2	2	no	—
44	C₂×#41×C₁₁₃	—	2	2	no	—
45	C₂×#41×C₁₁₃	—	2	2	no	—
46	C₂×#41×C₁₁₃	C₂×C₄	1	2	yes	—
47	C₂×#41×C₁₁₃	D₄	1	2	yes	—
48	C₂×#41×C₁₁₃	D₄	1	2	yes	—
49	C₂×#41×C₁₁₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
54	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
57	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
59	#131×C₁₁₃	—	2	16	no	—
60	#131×C₁₁₃	—	2	16	no	—
61	C₂×M₁₆×C₁₁₃	—	2	4	no	—
62	C₂×M₁₆×C₁₁₃	—	2	8	no	—
63	C₂×M₁₆×C₁₁₃	—	2	2	no	—
64	C₂×M₁₆×C₁₁₃	—	2	8	no	—
65	C₂×M₁₆×C₁₁₃	—	2	2	no	—
66	C₂×M₁₆×C₁₁₃	—	2	2	no	—
67	C₂×M₁₆×C₁₁₃	—	2	2	no	—
68	C₂×M₁₆×C₁₁₃	—	2	2	no	—
69	C₂×M₁₆×C₁₁₃	—	2	2	no	—
70	C₂×M₁₆×C₁₁₃	—	2	2	no	—
71	C₂×M₁₆×C₁₁₃	—	2	2	no	—
72	C₂×M₁₆×C₁₁₃	—	2	2	no	—
73	C₂×M₁₆×C₁₁₃	D₄	1	4	yes	complemented
74	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
75	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
76	C₂²×C₈×C₁₁₃	—	2	4	no	—
77	C₂²×C₈×C₁₁₃	—	2	2	no	—
78	C₂²×C₈×C₁₁₃	D₄	1	4	yes	complemented
79	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
80	#127×C₁₁₃	—	2	2	no	—
81	#124×C₁₁₃	—	2	2	no	—
82	#124×C₁₁₃	—	2	2	no	—
83	#123×C₁₁₃	—	2	4	no	—
84	#123×C₁₁₃	C₂×C₄	1	8	yes	—
85	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
86	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
87	#121×C₁₁₃	—	2	8	no	—
88	#121×C₁₁₃	—	2	4	no	—
89	#121×C₁₁₃	—	2	4	no	—
90	#120×C₁₁₃	—	2	4	no	—
91	#120×C₁₁₃	C₂×C₄	1	8	yes	—
92	C₄×D₄×C₁₁₃	—	2	8	no	—
93	#117×C₁₁₃	—	2	1	no	—
94	#117×C₁₁₃	—	2	1	no	—
95	#117×C₁₁₃	C₂×C₄	1	2	yes	—
96	#117×C₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
99	C₂×C₄²×C₁₁₃	—	2	1	no	—
100	#101×C₁₁₃	—	2	4	no	—
101	#100×C₁₁₃	—	2	4	no	—
102	C₂²⋊C₈×C₁₁₃	—	2	16	no	—
103	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
104	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
105	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
106	#41×C₁₁₃	—	2	4	no	—
107	#41×C₁₁₃	—	2	4	no	—
108	#41×C₁₁₃	—	2	4	no	—
109	#41×C₁₁₃	—	2	4	no	—
110	#41×C₁₁₃	—	2	4	no	—
111	#41×C₁₁₃	—	2	4	no	—
112	#41×C₁₁₃	—	2	4	no	—
113	#41×C₁₁₃	—	2	4	no	—
114	#41×C₁₁₃	—	4	1	no	—
115	#41×C₁₁₃	—	4	2	no	—
116	#41×C₁₁₃	—	4	1	no	—
117	#41×C₁₁₃	—	4	2	no	—
118	#41×C₁₁₃	—	4	2	no	—
119	#41×C₁₁₃	—	4	2	no	—
120	#41×C₁₁₃	—	4	2	no	—
121	#41×C₁₁₃	—	4	1	no	—
122	#41×C₁₁₃	—	4	1	no	—
123	#41×C₁₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
131	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₁₁₃	—	2	4	no	—
133	C₂×D₄×C₁₁₃	—	2	4	no	—
134	C₂×D₄×C₁₁₃	—	2	2	no	—
135	C₂×D₄×C₁₁₃	—	2	2	no	—
136	C₂×D₄×C₁₁₃	—	2	4	no	—
137	C₂×D₄×C₁₁₃	—	2	4	no	—
138	C₂×D₄×C₁₁₃	—	2	8	no	—
139	C₂×D₄×C₁₁₃	—	2	1	no	—
140	C₂×D₄×C₁₁₃	—	2	1	no	—
141	C₂×D₄×C₁₁₃	—	2	2	no	—
142	C₂×D₄×C₁₁₃	—	2	2	no	—
143	C₂×D₄×C₁₁₃	—	2	2	no	—
144	C₂×D₄×C₁₁₃	—	2	2	no	—
145	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
146	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
148	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
159	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
160	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
170	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
171	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₁₁₃	—	2	16	no	—
173	M₁₆×C₁₁₃	—	2	4	no	—
174	M₁₆×C₁₁₃	—	2	4	no	—
175	M₁₆×C₁₁₃	—	2	4	no	—
176	M₁₆×C₁₁₃	—	2	4	no	—
177	M₁₆×C₁₁₃	—	2	4	no	—
178	M₁₆×C₁₁₃	—	2	4	no	—
179	M₁₆×C₁₁₃	—	4	2	no	—
180	M₁₆×C₁₁₃	—	4	2	no	—
181	C₂×C₈×C₁₁₃	—	2	16	no	—
182	C₂×C₈×C₁₁₃	—	2	4	no	—
183	C₂×C₈×C₁₁₃	—	2	4	no	—
184	C₂×C₈×C₁₁₃	—	2	4	no	—
185	C₂×C₈×C₁₁₃	—	4	2	no	—
186	C₂×C₈×C₁₁₃	—	4	2	no	—
187	C₂×C₈×C₁₁₃	C₂×D₄	1	8	yes	—
188	C₄⋊C₄×C₁₁₃	—	2	2	no	—
189	C₄⋊C₄×C₁₁₃	—	2	8	no	—
190	C₄⋊C₄×C₁₁₃	—	2	2	no	—
191	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
192	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
193	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
194	C₂²⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
195	C₄²×C₁₁₃	—	2	2	no	—
196	C₄²×C₁₁₃	—	2	2	no	—
197	C₂³×C₁₁₃	—	2	2	no	—
198	C₂³×C₁₁₃	—	2	2	no	—
199	C₂³×C₁₁₃	—	2	2	no	—
200	C₂³×C₁₁₃	—	2	4	no	—
201	C₂³×C₁₁₃	—	8	1	no	—
202	C₂³×C₁₁₃	—	8	2	no	—
203	C₂³×C₁₁₃	—	8	2	no	—
204	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
205	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₁₁₃	C₄×D₄	1	2	yes	—
208	C₂³×C₁₁₃	C₄×D₄	1	2	yes	—
209	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
210	Q₈×C₁₁₃	—	2	4	no	—
211	Q₈×C₁₁₃	—	2	4	no	—
212	Q₈×C₁₁₃	—	4	1	no	—
213	Q₈×C₁₁₃	—	4	1	no	—
214	Q₈×C₁₁₃	—	4	2	no	—
215	D₄×C₁₁₃	—	2	8	no	—
216	D₄×C₁₁₃	—	2	8	no	—
217	D₄×C₁₁₃	—	2	4	no	—
218	D₄×C₁₁₃	—	2	4	no	—
219	D₄×C₁₁₃	—	4	2	no	—
220	D₄×C₁₁₃	—	4	2	no	—
221	D₄×C₁₁₃	—	4	4	no	—
222	D₄×C₁₁₃	—	4	1	no	—
223	D₄×C₁₁₃	—	4	1	no	—
224	D₄×C₁₁₃	—	4	2	no	—
225	D₄×C₁₁₃	—	8	8	no	—
226	C₂×C₄×C₁₁₃	—	2	2	no	—
227	C₂×C₄×C₁₁₃	—	2	2	no	—
228	C₂×C₄×C₁₁₃	—	2	4	no	—
229	C₂×C₄×C₁₁₃	—	2	4	no	—
230	C₂×C₄×C₁₁₃	—	2	4	no	—
231	C₂×C₄×C₁₁₃	—	2	4	no	—
232	C₂×C₄×C₁₁₃	—	2	4	no	—
233	C₂×C₄×C₁₁₃	—	2	2	no	—
234	C₂×C₄×C₁₁₃	—	2	4	no	—
235	C₂×C₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	—	4	4	no	—
237	C₂×C₄×C₁₁₃	—	4	2	no	—
238	C₂×C₄×C₁₁₃	—	8	2	no	—
239	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
240	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₁₃	#120	1	2	yes	—
246	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₁₃	#121	1	2	yes	—
248	C₂×C₄×C₁₁₃	#121	1	2	yes	—
249	C₂×C₄×C₁₁₃	#121	1	2	yes	—
250	C₂×C₄×C₁₁₃	#121	1	2	yes	—
251	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
252	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
253	C₂×C₄×C₁₁₃	#123	1	2	yes	—
254	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
258	C₈×C₁₁₃	—	2	8	no	—
259	C₈×C₁₁₃	—	4	4	no	—
260	C₂²×C₁₁₃	—	2	4	no	—
261	C₂²×C₁₁₃	—	4	1	no	—
262	C₂²×C₁₁₃	—	4	1	no	—
263	C₂²×C₁₁₃	—	4	1	no	—
264	C₂²×C₁₁₃	—	4	2	no	—
265	C₂²×C₁₁₃	—	4	2	no	—
266	C₂²×C₁₁₃	—	4	4	no	—
267	C₂²×C₁₁₃	—	4	4	no	—
268	C₂²×C₁₁₃	—	4	4	no	—
269	C₂²×C₁₁₃	—	4	8	no	—
270	C₂²×C₁₁₃	—	4	2	no	—
271	C₂²×C₁₁₃	—	8	2	no	—
272	C₂²×C₁₁₃	#386	1	1	yes	characteristic
273	C₂²×C₁₁₃	#386	1	1	yes	characteristic
274	C₂²×C₁₁₃	#386	1	2	yes	—
275	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
277	C₄×C₁₁₃	—	2	4	no	—
278	C₄×C₁₁₃	—	4	4	no	—
279	C₄×C₁₁₃	—	4	2	no	—
280	C₄×C₁₁₃	#386	1	1	yes	characteristic
281	C₄×C₁₁₃	#386	1	1	yes	characteristic
282	C₄×C₁₁₃	#386	1	2	yes	—
283	C₄×C₁₁₃	C₂×#120	1	1	yes	characteristic
284	C₄×C₁₁₃	C₂×#121	1	2	yes	—
285	C₄×C₁₁₃	C₂×#123	1	1	yes	characteristic
286	#20964	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₁₁₃	—	2	1	no	—
288	C₂×C₁₁₃	—	2	2	no	—
289	C₂×C₁₁₃	—	2	1	no	—
290	C₂×C₁₁₃	—	2	1	no	—
291	C₂×C₁₁₃	—	2	2	no	—
292	C₂×C₁₁₃	—	4	4	no	—
293	C₂×C₁₁₃	—	8	2	no	—
294	C₂×C₁₁₃	C₂×#386	1	1	yes	characteristic
295	C₂×#568	C₂×C₁₁₃	1	1	yes	characteristic, complemented
296	#3449	C₂×C₁₁₃	1	1	yes	characteristic
297	C₂×#413	C₂×C₁₁₃	1	1	yes	characteristic, complemented
298	#2879	C₂×C₁₁₃	1	2	yes	complemented
299	#1891	C₂×C₁₁₃	1	8	yes	complemented
300	C₂×#344	C₂×C₁₁₃	1	2	yes	complemented
301	C₁₁₃	#20964	1	1	yes	characteristic, direct product factor, Sylow
302	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
303	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
304	#568	—	2	2	no	—
305	#568	—	2	4	no	—
306	#568	C₂²×C₁₁₃	1	4	yes	—
307	C₂×#131	—	2	4	no	—
308	C₂²×M₁₆	—	2	2	no	—
309	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
310	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
311	#537	—	2	2	no	—
312	#536	—	2	1	no	—
313	#536	C₄×C₁₁₃	1	2	yes	—
314	#535	—	2	1	no	—
315	#535	C₄×C₁₁₃	1	2	yes	—
316	#534	C₄×C₁₁₃	1	4	yes	—
317	#532	—	2	2	no	—
318	#525	—	2	2	no	—
319	#525	C₂²×C₁₁₃	1	4	yes	—
320	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
321	#413	—	2	2	no	—
322	#413	C₂²×C₁₁₃	1	4	yes	—
323	C₂×#101	—	2	1	no	—
324	C₂×#100	—	2	1	no	—
325	#408	—	2	4	no	—
326	#408	—	2	4	no	—
327	#407	C₂²×C₁₁₃	1	8	yes	complemented
328	#344	C₂²×C₁₁₃	1	8	yes	complemented
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	C₂×C₄×C₁₁₃	1	2	yes	—
342	C₂×#41	D₄×C₁₁₃	1	2	yes	—
343	C₂×#41	D₄×C₁₁₃	1	2	yes	—
344	C₂×#41	C₂³×C₁₁₃	1	2	yes	—
345	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
346	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
347	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
348	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
349	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
350	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
351	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
354	#131	—	2	16	no	—
355	#131	—	2	16	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	—	2	8	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	8	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	2	2	no	—
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	—	2	2	no	—
368	C₂×M₁₆	D₄×C₁₁₃	1	4	yes	complemented
369	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
370	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
371	C₂²×C₈	—	2	4	no	—
372	C₂²×C₈	—	2	2	no	—
373	C₂²×C₈	D₄×C₁₁₃	1	4	yes	complemented
374	C₄⋊Q₈	—	2	2	no	—
375	#127	—	2	2	no	—
376	#124	—	2	2	no	—
377	#124	—	2	2	no	—
378	#123	—	2	4	no	—
379	#123	C₂×C₄×C₁₁₃	1	8	yes	—
380	C₂²⋊Q₈	—	2	4	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	#121	—	2	8	no	—
383	#121	—	2	4	no	—
384	#121	—	2	4	no	—
385	#120	—	2	4	no	—
386	#120	C₂×C₄×C₁₁₃	1	8	yes	—
387	C₄×D₄	—	2	8	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	C₂×C₄×C₁₁₃	1	2	yes	—
391	#117	C₂³×C₁₁₃	1	2	yes	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
394	C₂×C₄²	—	2	1	no	—
395	#101	—	2	4	no	—
396	#100	—	2	4	no	—
397	C₂²⋊C₈	—	2	16	no	—
398	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
399	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
400	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	2	4	no	—
405	#41	—	2	4	no	—
406	#41	—	2	4	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	4	1	no	—
410	#41	—	4	2	no	—
411	#41	—	4	1	no	—
412	#41	—	4	2	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	#41	—	4	2	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	2	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
426	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
441	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
442	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
443	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
454	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
455	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
456	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
458	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
464	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
465	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
467	M₁₆	—	2	16	no	—
468	M₁₆	—	2	4	no	—
469	M₁₆	—	2	4	no	—
470	M₁₆	—	2	4	no	—
471	M₁₆	—	2	4	no	—
472	M₁₆	—	2	4	no	—
473	M₁₆	—	2	4	no	—
474	M₁₆	—	4	2	no	—
475	M₁₆	—	4	2	no	—
476	C₂×C₈	—	2	16	no	—
477	C₂×C₈	—	2	4	no	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	—	2	4	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	C₂×D₄×C₁₁₃	1	8	yes	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	8	1	no	—
497	C₂³	—	8	2	no	—
498	C₂³	—	8	2	no	—
499	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
500	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
501	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
502	C₂³	C₄×D₄×C₁₁₃	1	2	yes	—
503	C₂³	C₄×D₄×C₁₁₃	1	2	yes	—
504	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
505	Q₈	—	2	4	no	—
506	Q₈	—	2	4	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	2	no	—
510	D₄	—	2	8	no	—
511	D₄	—	2	8	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	2	no	—
520	D₄	—	8	8	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
535	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
537	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
538	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
539	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
540	C₂×C₄	#120×C₁₁₃	1	2	yes	—
541	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
542	C₂×C₄	#121×C₁₁₃	1	2	yes	—
543	C₂×C₄	#121×C₁₁₃	1	2	yes	—
544	C₂×C₄	#121×C₁₁₃	1	2	yes	—
545	C₂×C₄	#121×C₁₁₃	1	2	yes	—
546	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
547	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
548	C₂×C₄	#123×C₁₁₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
553	C₈	—	2	8	no	—
554	C₈	—	4	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	8	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	#386×C₁₁₃	1	1	yes	characteristic
568	C₂²	#386×C₁₁₃	1	1	yes	characteristic
569	C₂²	#386×C₁₁₃	1	2	yes	—
570	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
571	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
572	C₄	—	2	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	#386×C₁₁₃	1	1	yes	characteristic
576	C₄	#386×C₁₁₃	1	1	yes	characteristic
577	C₄	#386×C₁₁₃	1	2	yes	—
578	C₄	C₂×#120×C₁₁₃	1	1	yes	characteristic
579	C₄	C₂×#121×C₁₁₃	1	2	yes	—
580	C₄	C₂×#123×C₁₁₃	1	1	yes	characteristic
581	C₂	—	2	1	no	—
582	C₂	—	2	2	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	2	no	—
586	C₂	—	4	4	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂×#386×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁₃	C₂×#120
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂×C₁₁₃	C₂×#386
prime radical	C₁₁₃×#3449	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁₃ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#568×C₁₁₃	C₂	semidirect
3. C₂×#413×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2879	C₂	semidirect
5. C₁₁₃×#1891	C₂	semidirect
6. C₂×#344×C₁₁₃	C₂	semidirect
32. #407×C₁₁₃	C₂²	semidirect
33. #344×C₁₁₃	C₂²	semidirect
73. C₂×M₁₆×C₁₁₃	D₄	semidirect
78. C₂²×C₈×C₁₁₃	D₄	semidirect
286. #20964	C₁₁₃	direct (N × H)
295. C₂×#568	C₂×C₁₁₃	semidirect
297. C₂×#413	C₂×C₁₁₃	semidirect
298. #2879	C₂×C₁₁₃	semidirect
299. #1891	C₂×C₁₁₃	semidirect
300. C₂×#344	C₂×C₁₁₃	semidirect
301. C₁₁₃	#20964	direct (N × H)
327. #407	C₂²×C₁₁₃	semidirect
328. #344	C₂²×C₁₁₃	semidirect
368. C₂×M₁₆	D₄×C₁₁₃	semidirect
373. C₂²×C₈	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#568×C₁₁₃	2
C₁₁₃×#3449	2
C₂×#413×C₁₁₃	2
C₁₁₃×#2879	2
C₁₁₃×#1891	2
C₂×#344×C₁₁₃	2
#20964	113

Subgroups — C113×#20964 #43288984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20964 #43288984