Subgroups — C₄×#386×C₁₁₃ #43281782

Order 28928.

3366 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄²×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#386×C₁₁₃	C₂	1	2	yes	maximal
4	C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1437	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1436	C₂	1	2	yes	maximal, complemented
8	C₁₁₃×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
9	C₄×#95×C₁₁₃	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₁₃	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
15	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
16	C₂×C₄×D₄×C₁₁₃	C₄	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
21	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₁₃	—	2	4	no	—
23	C₂²×C₄²×C₁₁₃	—	2	8	no	—
24	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
28	#386×C₁₁₃	C₄	1	16	yes	direct product factor
29	C₄×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
30	C₄×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
31	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
32	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
33	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
34	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
35	C₂⁵×C₁₁₃	C₂³	1	1	yes	characteristic
36	C₂⁵×C₁₁₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₁₃	—	2	4	no	—
40	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
41	C₂²×D₄×C₁₁₃	C₂×C₄	1	8	yes	—
42	C₂³×C₄×C₁₁₃	—	2	4	no	—
43	C₂³×C₄×C₁₁₃	—	2	4	no	—
44	C₂³×C₄×C₁₁₃	—	2	8	no	—
45	C₂³×C₄×C₁₁₃	—	2	4	no	—
46	C₂³×C₄×C₁₁₃	—	2	8	no	—
47	C₂³×C₄×C₁₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₁₃	—	2	2	no	—
49	C₂³×C₄×C₁₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₁₃	—	2	4	no	—
51	C₂³×C₄×C₁₁₃	—	2	4	no	—
52	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
53	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	complemented
54	C₂³×C₄×C₁₁₃	C₂×C₄	1	8	yes	complemented
55	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
56	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
57	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₁₃	—	2	32	no	—
65	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	complemented
68	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	complemented
78	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	8	yes	complemented
79	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	16	yes	complemented
80	C₂×C₄²×C₁₁₃	—	2	32	no	—
81	C₂×C₄²×C₁₁₃	—	2	4	no	—
82	C₂×C₄²×C₁₁₃	—	2	8	no	—
83	C₂×C₄²×C₁₁₃	—	2	4	no	—
84	C₂×C₄²×C₁₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₁₃	—	2	2	no	—
86	C₂×C₄²×C₁₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₁₃	—	2	4	no	—
88	C₂×C₄²×C₁₁₃	—	2	4	no	—
89	C₂×C₄²×C₁₁₃	—	2	4	no	—
90	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	complemented
91	C₂×C₄²×C₁₁₃	D₄	1	8	yes	complemented
92	#95×C₁₁₃	—	2	8	no	—
93	#95×C₁₁₃	—	2	4	no	—
94	#95×C₁₁₃	—	2	8	no	—
95	#95×C₁₁₃	C₂×C₄	1	16	yes	complemented
96	C₂⁴×C₁₁₃	—	2	2	no	—
97	C₂⁴×C₁₁₃	—	2	2	no	—
98	C₂⁴×C₁₁₃	—	2	4	no	—
99	C₂⁴×C₁₁₃	—	2	2	no	—
100	C₂⁴×C₁₁₃	—	2	1	no	—
101	C₂⁴×C₁₁₃	—	2	1	no	—
102	C₂⁴×C₁₁₃	—	2	4	no	—
103	C₂⁴×C₁₁₃	—	2	2	no	—
104	C₂⁴×C₁₁₃	—	2	2	no	—
105	C₂⁴×C₁₁₃	C₂²×C₄	1	4	yes	—
106	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
107	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₁₁₃	C₂²×C₄	1	4	yes	—
109	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
110	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
111	C₂⁴×C₁₁₃	#41	1	4	yes	—
112	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
113	C₂×D₄×C₁₁₃	—	2	8	no	—
114	C₂×D₄×C₁₁₃	—	2	8	no	—
115	C₂×D₄×C₁₁₃	—	2	16	no	—
116	C₂×D₄×C₁₁₃	—	2	16	no	—
117	C₂×D₄×C₁₁₃	C₄²	1	16	yes	complemented
118	C₂²×C₄×C₁₁₃	—	2	16	no	—
119	C₂²×C₄×C₁₁₃	—	2	32	no	—
120	C₂²×C₄×C₁₁₃	—	2	16	no	—
121	C₂²×C₄×C₁₁₃	—	2	16	no	—
122	C₂²×C₄×C₁₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₁₃	—	2	16	no	—
132	C₂²×C₄×C₁₁₃	—	2	32	no	—
133	C₂²×C₄×C₁₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₁₃	—	2	16	no	—
135	C₂²×C₄×C₁₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₁₃	—	2	16	no	—
151	C₂²×C₄×C₁₁₃	—	4	4	no	—
152	C₂²×C₄×C₁₁₃	—	4	8	no	—
153	C₂²×C₄×C₁₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	16	yes	complemented
155	C₂²×C₄×C₁₁₃	C₂²×C₄	1	8	yes	—
156	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
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	8	yes	—
162	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
166	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₁₃	#41	1	8	yes	—
170	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
171	C₄⋊C₄×C₁₁₃	—	2	8	no	—
172	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
173	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
174	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
175	C₂²⋊C₄×C₁₁₃	—	2	32	no	—
176	C₄²×C₁₁₃	—	2	16	no	—
177	C₄²×C₁₁₃	—	2	8	no	—
178	C₄²×C₁₁₃	—	2	16	no	—
179	C₄²×C₁₁₃	—	4	8	no	—
180	C₂³×C₁₁₃	—	2	4	no	—
181	C₂³×C₁₁₃	—	2	8	no	—
182	C₂³×C₁₁₃	—	2	4	no	—
183	C₂³×C₁₁₃	—	2	8	no	—
184	C₂³×C₁₁₃	—	2	2	no	—
185	C₂³×C₁₁₃	—	2	4	no	—
186	C₂³×C₁₁₃	—	2	2	no	—
187	C₂³×C₁₁₃	—	2	4	no	—
188	C₂³×C₁₁₃	—	2	8	no	—
189	C₂³×C₁₁₃	—	2	8	no	—
190	C₂³×C₁₁₃	—	2	4	no	—
191	C₂³×C₁₁₃	—	2	2	no	—
192	C₂³×C₁₁₃	—	2	2	no	—
193	C₂³×C₁₁₃	—	2	8	no	—
194	C₂³×C₁₁₃	—	2	4	no	—
195	C₂³×C₁₁₃	—	2	4	no	—
196	C₂³×C₁₁₃	—	2	4	no	—
197	C₂³×C₁₁₃	—	2	4	no	—
198	C₂³×C₁₁₃	—	2	8	no	—
199	C₂³×C₁₁₃	—	4	1	no	—
200	C₂³×C₁₁₃	—	4	2	no	—
201	C₂³×C₁₁₃	—	4	1	no	—
202	C₂³×C₁₁₃	—	4	4	no	—
203	C₂³×C₁₁₃	—	4	2	no	—
204	C₂³×C₁₁₃	—	4	4	no	—
205	C₂³×C₁₁₃	—	4	2	no	—
206	C₂³×C₁₁₃	C₂×C₄²	1	4	yes	—
207	C₂³×C₁₁₃	C₂×C₄²	1	4	yes	complemented
208	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
209	C₂³×C₁₁₃	#117	1	4	yes	—
210	C₂³×C₁₁₃	C₄×D₄	1	8	yes	—
211	C₂³×C₁₁₃	C₄×D₄	1	8	yes	—
212	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₂³×C₁₁₃	C₂³×C₄	1	2	yes	—
214	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
217	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
218	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
219	C₂³×C₁₁₃	C₂×#41	1	4	yes	—
220	D₄×C₁₁₃	—	2	32	no	—
221	C₂×C₄×C₁₁₃	—	2	64	no	—
222	C₂×C₄×C₁₁₃	—	2	2	no	—
223	C₂×C₄×C₁₁₃	—	2	2	no	—
224	C₂×C₄×C₁₁₃	—	2	4	no	—
225	C₂×C₄×C₁₁₃	—	2	8	no	—
226	C₂×C₄×C₁₁₃	—	2	8	no	—
227	C₂×C₄×C₁₁₃	—	2	4	no	—
228	C₂×C₄×C₁₁₃	—	2	4	no	—
229	C₂×C₄×C₁₁₃	—	2	2	no	—
230	C₂×C₄×C₁₁₃	—	2	8	no	—
231	C₂×C₄×C₁₁₃	—	2	4	no	—
232	C₂×C₄×C₁₁₃	—	2	2	no	—
233	C₂×C₄×C₁₁₃	—	2	8	no	—
234	C₂×C₄×C₁₁₃	—	2	8	no	—
235	C₂×C₄×C₁₁₃	—	2	8	no	—
236	C₂×C₄×C₁₁₃	—	2	32	no	—
237	C₂×C₄×C₁₁₃	—	2	2	no	—
238	C₂×C₄×C₁₁₃	—	2	2	no	—
239	C₂×C₄×C₁₁₃	—	2	8	no	—
240	C₂×C₄×C₁₁₃	—	2	8	no	—
241	C₂×C₄×C₁₁₃	—	2	4	no	—
242	C₂×C₄×C₁₁₃	—	2	4	no	—
243	C₂×C₄×C₁₁₃	—	2	8	no	—
244	C₂×C₄×C₁₁₃	—	4	1	no	—
245	C₂×C₄×C₁₁₃	—	4	4	no	—
246	C₂×C₄×C₁₁₃	—	4	2	no	—
247	C₂×C₄×C₁₁₃	—	4	1	no	—
248	C₂×C₄×C₁₁₃	—	4	2	no	—
249	C₂×C₄×C₁₁₃	—	4	4	no	—
250	C₂×C₄×C₁₁₃	—	4	4	no	—
251	C₂×C₄×C₁₁₃	—	4	2	no	—
252	C₂×C₄×C₁₁₃	—	4	4	no	—
253	C₂×C₄×C₁₁₃	—	4	16	no	—
254	C₂×C₄×C₁₁₃	C₂×C₄²	1	4	yes	complemented
255	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
256	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
257	C₂×C₄×C₁₁₃	C₄×D₄	1	8	yes	—
258	C₂×C₄×C₁₁₃	C₄×D₄	1	16	yes	complemented
259	C₂×C₄×C₁₁₃	#120	1	4	yes	—
260	C₂×C₄×C₁₁₃	#121	1	8	yes	—
261	C₂×C₄×C₁₁₃	#123	1	4	yes	—
262	C₂²×C₁₁₃	—	2	8	no	—
263	C₂²×C₁₁₃	—	2	4	no	—
264	C₂²×C₁₁₃	—	2	8	no	—
265	C₂²×C₁₁₃	—	2	4	no	—
266	C₂²×C₁₁₃	—	2	8	no	—
267	C₂²×C₁₁₃	—	2	16	no	—
268	C₂²×C₁₁₃	—	2	8	no	—
269	C₂²×C₁₁₃	—	2	4	no	—
270	C₂²×C₁₁₃	—	2	8	no	—
271	C₂²×C₁₁₃	—	4	2	no	—
272	C₂²×C₁₁₃	—	4	4	no	—
273	C₂²×C₁₁₃	—	4	2	no	—
274	C₂²×C₁₁₃	—	4	4	no	—
275	C₂²×C₁₁₃	—	4	8	no	—
276	C₂²×C₁₁₃	—	4	4	no	—
277	C₂²×C₁₁₃	C₄×C₂²⋊C₄	1	8	yes	complemented
278	C₂²×C₁₁₃	C₂²×C₄²	1	1	yes	characteristic
279	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
281	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
282	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
283	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
284	C₂²×C₁₁₃	C₂×C₄×D₄	1	4	yes	—
285	C₂²×C₁₁₃	C₄×#41	1	2	yes	—
286	C₂²×C₁₁₃	C₄×#41	1	4	yes	—
287	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
288	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
289	C₂²×C₁₁₃	C₂×#123	1	1	yes	characteristic
290	C₂²×C₁₁₃	#525	1	4	yes	—
291	C₂²×C₁₁₃	#525	1	2	yes	—
292	C₂²×C₁₁₃	#529	1	4	yes	—
293	C₂²×C₁₁₃	#532	1	2	yes	—
294	C₄×C₁₁₃	—	2	4	no	—
295	C₄×C₁₁₃	—	2	4	no	—
296	C₄×C₁₁₃	—	2	16	no	—
297	C₄×C₁₁₃	—	4	2	no	—
298	C₄×C₁₁₃	—	4	2	no	—
299	C₄×C₁₁₃	—	4	8	no	—
300	C₄×C₁₁₃	#386	1	8	yes	direct product factor
301	C₄×#386	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂×C₁₁₃	—	2	8	no	—
303	C₂×C₁₁₃	—	4	4	no	—
304	C₂×C₁₁₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₁₁₃	C₄²×D₄	1	2	yes	—
306	C₂×C₁₁₃	C₂×#386	1	1	yes	characteristic
307	C₂×C₁₁₃	#2290	1	2	yes	—
308	C₂×C₁₁₃	#2297	1	1	yes	characteristic
309	C₂×C₁₁₃	C₄×#120	1	2	yes	—
310	C₂×C₁₁₃	C₄×#121	1	4	yes	—
311	C₂×C₁₁₃	C₄×#123	1	2	yes	—
312	C₂²×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic
313	C₂³×C₄²	C₂×C₁₁₃	1	1	yes	characteristic, complemented
314	C₂×#386	C₂×C₁₁₃	1	2	yes	—
315	C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic, complemented
316	C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	1	2	yes	complemented
317	#1437	C₂×C₁₁₃	1	2	yes	complemented
318	#1436	C₂×C₁₁₃	1	2	yes	complemented
319	C₂²⋊#95	C₂×C₁₁₃	1	2	yes	complemented
320	C₄×#95	C₂×C₁₁₃	1	2	yes	complemented
321	C₁₁₃	C₄×#386	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×C₁₁₃	1	2	yes	—
324	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
326	C₂×C₄×D₄	—	2	4	no	—
327	C₂×C₄×D₄	—	2	4	no	—
328	C₂×C₄×D₄	C₄×C₁₁₃	1	8	yes	complemented
329	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
333	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
334	C₂²×C₄²	—	2	4	no	—
335	C₂²×C₄²	—	2	8	no	—
336	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
337	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
338	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
339	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
340	#386	C₄×C₁₁₃	1	16	yes	direct product factor
341	C₄×C₂²⋊C₄	—	2	4	no	—
342	C₄×C₂²⋊C₄	—	2	8	no	—
343	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
344	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
345	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
346	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
347	C₂⁵	C₂³×C₁₁₃	1	1	yes	characteristic
348	C₂⁵	C₂³×C₁₁₃	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	4	no	—
352	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
353	C₂²×D₄	C₂×C₄×C₁₁₃	1	8	yes	—
354	C₂³×C₄	—	2	4	no	—
355	C₂³×C₄	—	2	4	no	—
356	C₂³×C₄	—	2	8	no	—
357	C₂³×C₄	—	2	4	no	—
358	C₂³×C₄	—	2	8	no	—
359	C₂³×C₄	—	2	4	no	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	—	2	2	no	—
362	C₂³×C₄	—	2	4	no	—
363	C₂³×C₄	—	2	4	no	—
364	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
365	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	complemented
366	C₂³×C₄	C₂×C₄×C₁₁₃	1	8	yes	complemented
367	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
368	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
369	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
370	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
375	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
376	C₄×D₄	—	2	32	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	complemented
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₂²⋊C₄	—	2	4	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	8	no	—
387	C₂×C₂²⋊C₄	—	2	8	no	—
388	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	complemented
390	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	8	yes	complemented
391	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	16	yes	complemented
392	C₂×C₄²	—	2	32	no	—
393	C₂×C₄²	—	2	2	no	—
394	C₂×C₄²	—	2	2	no	—
395	C₂×C₄²	—	2	4	no	—
396	C₂×C₄²	—	2	8	no	—
397	C₂×C₄²	—	2	4	no	—
398	C₂×C₄²	—	2	4	no	—
399	C₂×C₄²	—	2	4	no	—
400	C₂×C₄²	—	2	4	no	—
401	C₂×C₄²	—	2	4	no	—
402	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	complemented
403	C₂×C₄²	D₄×C₁₁₃	1	8	yes	complemented
404	#95	—	2	8	no	—
405	#95	—	2	4	no	—
406	#95	—	2	8	no	—
407	#95	C₂×C₄×C₁₁₃	1	16	yes	complemented
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	—	2	1	no	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	C₂²×C₄×C₁₁₃	1	4	yes	—
418	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
419	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
420	C₂⁴	C₂²×C₄×C₁₁₃	1	4	yes	—
421	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
422	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
423	C₂⁴	#41×C₁₁₃	1	4	yes	—
424	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	16	no	—
428	C₂×D₄	—	2	16	no	—
429	C₂×D₄	C₄²×C₁₁₃	1	16	yes	complemented
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	2	32	no	—
432	C₂²×C₄	—	2	16	no	—
433	C₂²×C₄	—	2	16	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	16	no	—
444	C₂²×C₄	—	2	32	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	2	16	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	4	8	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	16	yes	complemented
467	C₂²×C₄	C₂²×C₄×C₁₁₃	1	8	yes	—
468	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
469	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
470	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
471	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
472	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
473	C₂²×C₄	C₂²×C₄×C₁₁₃	1	8	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
478	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
480	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
481	C₂²×C₄	#41×C₁₁₃	1	8	yes	—
482	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
483	C₄⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	16	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	32	no	—
488	C₄²	—	2	16	no	—
489	C₄²	—	2	8	no	—
490	C₄²	—	2	16	no	—
491	C₄²	—	4	8	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	8	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	8	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	4	2	no	—
518	C₂³	C₂×C₄²×C₁₁₃	1	4	yes	—
519	C₂³	C₂×C₄²×C₁₁₃	1	4	yes	complemented
520	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
521	C₂³	#117×C₁₁₃	1	4	yes	—
522	C₂³	C₄×D₄×C₁₁₃	1	8	yes	—
523	C₂³	C₄×D₄×C₁₁₃	1	8	yes	—
524	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
525	C₂³	C₂³×C₄×C₁₁₃	1	2	yes	—
526	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
527	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
528	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
529	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
530	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
531	C₂³	C₂×#41×C₁₁₃	1	4	yes	—
532	D₄	—	2	32	no	—
533	C₂×C₄	—	2	64	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	32	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	16	no	—
566	C₂×C₄	C₂×C₄²×C₁₁₃	1	4	yes	complemented
567	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
568	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
569	C₂×C₄	C₄×D₄×C₁₁₃	1	8	yes	—
570	C₂×C₄	C₄×D₄×C₁₁₃	1	16	yes	complemented
571	C₂×C₄	#120×C₁₁₃	1	4	yes	—
572	C₂×C₄	#121×C₁₁₃	1	8	yes	—
573	C₂×C₄	#123×C₁₁₃	1	4	yes	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	8	no	—
588	C₂²	—	4	4	no	—
589	C₂²	C₄×C₂²⋊C₄×C₁₁₃	1	8	yes	complemented
590	C₂²	C₂²×C₄²×C₁₁₃	1	1	yes	characteristic
591	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
592	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
593	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
594	C₂²	C₂×C₄×D₄×C₁₁₃	1	4	yes	—
595	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
596	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
597	C₂²	C₄×#41×C₁₁₃	1	2	yes	—
598	C₂²	C₄×#41×C₁₁₃	1	4	yes	—
599	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
600	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
601	C₂²	C₂×#123×C₁₁₃	1	1	yes	characteristic
602	C₂²	#525×C₁₁₃	1	4	yes	—
603	C₂²	#525×C₁₁₃	1	2	yes	—
604	C₂²	#529×C₁₁₃	1	4	yes	—
605	C₂²	#532×C₁₁₃	1	2	yes	—
606	C₄	—	2	4	no	—
607	C₄	—	2	16	no	—
608	C₄	—	2	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	8	no	—
612	C₄	#386×C₁₁₃	1	8	yes	direct product factor
613	C₂	—	2	8	no	—
614	C₂	—	4	4	no	—
615	C₂	C₂×C₄×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
616	C₂	C₄²×D₄×C₁₁₃	1	2	yes	—
617	C₂	C₂×#386×C₁₁₃	1	1	yes	characteristic
618	C₂	C₁₁₃×#2290	1	2	yes	—
619	C₂	C₁₁₃×#2297	1	1	yes	characteristic
620	C₂	C₄×#120×C₁₁₃	1	2	yes	—
621	C₂	C₄×#121×C₁₁₃	1	4	yes	—
622	C₂	C₄×#123×C₁₁₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₁₃	C₂³
commutator	C₂²	C₂²×C₄²×C₁₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
socle	C₂⁴×C₁₁₃	C₂⁴
prime radical	C₂³×D₄×C₁₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄²×C₁₁₃	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	semidirect
5. C₂×C₄×C₂²⋊C₄×C₁₁₃	C₂	semidirect
6. C₁₁₃×#1437	C₂	semidirect
7. C₁₁₃×#1436	C₂	semidirect
8. C₁₁₃×C₂²⋊#95	C₂	semidirect
9. C₄×#95×C₁₁₃	C₂	semidirect
16. C₂×C₄×D₄×C₁₁₃	C₄	semidirect
28. #386×C₁₁₃	C₄	direct (N × H)
53. C₂³×C₄×C₁₁₃	C₂×C₄	semidirect
54. C₂³×C₄×C₁₁₃	C₂×C₄	semidirect
67. C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	semidirect
77. C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	semidirect
78. C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	semidirect
79. C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	semidirect
90. C₂×C₄²×C₁₁₃	C₂×C₄	semidirect
91. C₂×C₄²×C₁₁₃	D₄	semidirect
95. #95×C₁₁₃	C₂×C₄	semidirect
117. C₂×D₄×C₁₁₃	C₄²	semidirect
154. C₂²×C₄×C₁₁₃	C₂²⋊C₄	semidirect
207. C₂³×C₁₁₃	C₂×C₄²	semidirect
254. C₂×C₄×C₁₁₃	C₂×C₄²	semidirect
258. C₂×C₄×C₁₁₃	C₄×D₄	semidirect
277. C₂²×C₁₁₃	C₄×C₂²⋊C₄	semidirect
300. C₄×C₁₁₃	#386	direct (N × H)
301. C₄×#386	C₁₁₃	direct (N × H)
313. C₂³×C₄²	C₂×C₁₁₃	semidirect
315. C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	semidirect
316. C₂×C₄×C₂²⋊C₄	C₂×C₁₁₃	semidirect
317. #1437	C₂×C₁₁₃	semidirect
318. #1436	C₂×C₁₁₃	semidirect
319. C₂²⋊#95	C₂×C₁₁₃	semidirect
320. C₄×#95	C₂×C₁₁₃	semidirect
321. C₁₁₃	C₄×#386	direct (N × H)
328. C₂×C₄×D₄	C₄×C₁₁₃	semidirect
340. #386	C₄×C₁₁₃	direct (N × H)
365. C₂³×C₄	C₂×C₄×C₁₁₃	semidirect
366. C₂³×C₄	C₂×C₄×C₁₁₃	semidirect
379. C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	semidirect
389. C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	semidirect
390. C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	semidirect
391. C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	semidirect
402. C₂×C₄²	C₂×C₄×C₁₁₃	semidirect
403. C₂×C₄²	D₄×C₁₁₃	semidirect
407. #95	C₂×C₄×C₁₁₃	semidirect
429. C₂×D₄	C₄²×C₁₁₃	semidirect
466. C₂²×C₄	C₂²⋊C₄×C₁₁₃	semidirect
519. C₂³	C₂×C₄²×C₁₁₃	semidirect
566. C₂×C₄	C₂×C₄²×C₁₁₃	semidirect
570. C₂×C₄	C₄×D₄×C₁₁₃	semidirect
589. C₂²	C₄×C₂²⋊C₄×C₁₁₃	semidirect
612. C₄	#386×C₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₁₃	2
C₂³×C₄²×C₁₁₃	2
C₂×#386×C₁₁₃	2
C₂×C₄×C₂²⋊C₄×C₁₁₃	2
C₁₁₃×#1437	2
C₁₁₃×#1436	2
C₁₁₃×C₂²⋊#95	2
C₄×#95×C₁₁₃	2
C₄×#386	113

Subgroups — C4×#386×C113 #43281782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#386×C₁₁₃ #43281782