Subgroups — C₃×D₄×#713 #14483061

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#713	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66151	C₂	1	2	yes	maximal, complemented
4	C₃×#66060	C₂	1	3	yes	maximal, complemented
5	C₃×#66059	C₂	1	3	yes	maximal, complemented
6	C₃×#65964	C₂	1	6	yes	maximal, complemented
7	C₃×#65961	C₂	1	6	yes	maximal, complemented
8	C₃×#65911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₄×D₂₀	C₂	1	3	yes	maximal, complemented
11	C₃×C₄×D₄×D₅	C₂	1	3	yes	maximal, complemented
12	D₄×#713	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
14	C₂×C₃×#713	—	2	16	no	—
15	C₂×C₃×#713	C₂²	1	1	yes	characteristic
16	C₂×C₃×#713	C₂²	1	2	yes	complemented
17	C₂×C₃×#713	C₂²	1	6	yes	complemented
18	C₂×C₃×#713	C₂²	1	6	yes	complemented
19	C₂×C₃×D₄×D₅	C₂²	1	3	yes	—
20	C₂²×C₃×D₂₀	C₂²	1	6	yes	complemented
21	C₂²×C₃×C₄×D₅	C₂²	1	6	yes	complemented
22	C₃×C₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	6	yes	complemented
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₄	C₂²	1	3	yes	—
26	C₃×#4093	C₂²	1	6	yes	complemented
27	C₃×#4092	C₂²	1	6	yes	complemented
28	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
29	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
30	C₃×#4076	C₂²	1	6	yes	complemented
31	C₃×C₄×C₂²⋊D₅	C₂²	1	6	yes	complemented
32	C₃×#4041	C₂²	1	6	yes	complemented
33	C₃×#4041	C₂²	1	6	yes	complemented
34	C₃×#4041	C₂²	1	6	yes	complemented
35	C₃×#4040	C₂²	1	12	yes	complemented
36	C₃×#4039	C₂²	1	3	yes	complemented
37	C₃×#4039	C₂²	1	3	yes	complemented
38	C₃×#4039	C₂²	1	6	yes	complemented
39	C₃×#4038	C₂²	1	3	yes	complemented
40	C₃×D₅×C₄⋊C₄	C₂²	1	3	yes	complemented
41	C₃×#4028	C₂²	1	12	yes	complemented
42	C₃×#4027	C₂²	1	6	yes	complemented
43	C₃×D₅×C₂²⋊C₄	C₂²	1	6	yes	complemented
44	C₃×#4020	C₂²	1	3	yes	complemented
45	C₃×C₄×D₂₀	C₂²	1	3	yes	complemented
46	C₃×C₄×D₂₀	C₂²	1	3	yes	complemented
47	C₃×C₄²×D₅	C₂²	1	3	yes	complemented
48	C₃×D₄×#41	—	5	1	no	maximal, Hall
49	C₂²×#713	C₂×C₃	1	2	yes	complemented
50	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
51	#66151	C₂×C₃	1	2	yes	complemented
52	#66060	C₂×C₃	1	3	yes	complemented
53	#66059	C₂×C₃	1	3	yes	complemented
54	#65964	C₂×C₃	1	6	yes	complemented
55	#65961	C₂×C₃	1	6	yes	complemented
56	#65911	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×#713	C₂×C₃	1	1	yes	characteristic, complemented
58	D₄×D₂₀	C₂×C₃	1	3	yes	complemented
59	C₄×D₄×D₅	C₂×C₃	1	3	yes	complemented
60	C₂³×C₃×D₅	C₂³	1	6	yes	—
61	C₂×C₃×C₅×Q₈	—	2	8	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	—
63	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
66	C₂×C₃×C₂²⋊D₅	C₂³	1	6	yes	—
67	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
68	C₃×#713	—	2	8	no	—
69	C₃×#713	—	2	24	no	—
70	C₃×#713	—	2	24	no	—
71	C₃×#713	D₄	1	8	yes	direct product factor
72	C₃×D₄×D₅	—	2	12	no	—
73	C₂×C₃×D₂₀	—	2	24	no	—
74	C₂×C₃×D₂₀	C₂³	1	6	yes	—
75	C₂×C₃×D₂₀	C₂³	1	12	yes	—
76	C₂×C₃×D₂₀	C₂³	1	3	yes	—
77	C₂×C₃×D₂₀	C₂³	1	6	yes	—
78	C₂×C₃×D₂₀	C₂³	1	3	yes	—
79	C₂×C₃×C₄×D₅	—	2	24	no	—
80	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
81	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
82	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
83	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
84	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
85	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
89	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
90	C₃×C₄²×C₅	C₂³	1	3	yes	—
91	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
92	C₃×#685	C₂³	1	12	yes	—
93	C₃×#685	C₂³	1	6	yes	—
94	C₃×#685	C₂³	1	6	yes	—
95	C₃×#685	C₂³	1	6	yes	—
96	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
97	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
98	C₃×#683	C₂³	1	6	yes	—
99	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
100	C₃×C₄×Dic₅	C₂³	1	3	yes	—
101	C₃×C₄×Dic₅	C₂³	1	3	yes	—
102	C₂²×C₃×#41	—	5	2	no	—
103	C₃×#550	—	5	1	no	—
104	C₃×D₄×Q₈	D₅	1	1	yes	characteristic, complemented
105	C₃×#548	—	5	2	no	—
106	C₃×#547	—	5	3	no	—
107	C₃×#546	—	5	6	no	—
108	C₃×D₄²	—	5	3	no	—
109	C₃×#532	—	5	3	no	—
110	C₃×#525	—	5	6	no	—
111	C₃×C₄×#41	—	5	1	no	—
112	C₂×C₃×C₄×D₄	—	5	3	no	—
113	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
114	C₂×#713	—	2	16	no	—
115	C₂×#713	C₂²×C₃	1	1	yes	characteristic
116	C₂×#713	C₂²×C₃	1	6	yes	complemented
117	C₂×#713	C₂²×C₃	1	6	yes	complemented
118	C₂×#713	C₂²×C₃	1	2	yes	complemented
119	C₂×D₄×D₅	C₂²×C₃	1	3	yes	—
120	C₂²×D₂₀	C₂²×C₃	1	6	yes	complemented
121	C₂²×C₄×D₅	C₂²×C₃	1	6	yes	complemented
122	C₅×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
123	C₅×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
124	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₄×C₅×D₄	C₂²×C₃	1	3	yes	—
126	#4093	C₂²×C₃	1	6	yes	complemented
127	#4092	C₂²×C₃	1	6	yes	complemented
128	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
129	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
130	#4076	C₂²×C₃	1	6	yes	complemented
131	C₄×C₂²⋊D₅	C₂²×C₃	1	6	yes	complemented
132	#4041	C₂²×C₃	1	6	yes	complemented
133	#4041	C₂²×C₃	1	6	yes	complemented
134	#4041	C₂²×C₃	1	6	yes	complemented
135	#4040	C₂²×C₃	1	12	yes	complemented
136	#4039	C₂²×C₃	1	3	yes	complemented
137	#4039	C₂²×C₃	1	6	yes	complemented
138	#4039	C₂²×C₃	1	3	yes	complemented
139	#4038	C₂²×C₃	1	3	yes	complemented
140	D₅×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
141	#4028	C₂²×C₃	1	12	yes	complemented
142	#4027	C₂²×C₃	1	6	yes	complemented
143	D₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	complemented
144	#4020	C₂²×C₃	1	3	yes	complemented
145	C₄×D₂₀	C₂²×C₃	1	3	yes	complemented
146	C₄×D₂₀	C₂²×C₃	1	3	yes	complemented
147	C₄²×D₅	C₂²×C₃	1	3	yes	complemented
148	D₄×#41	—	5	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
150	C₂²×C₃×D₅	—	2	12	no	—
151	C₂²×C₃×D₅	—	2	12	no	—
152	C₂²×C₃×D₅	—	4	6	no	—
153	C₂²×C₃×D₅	C₂⁴	1	6	yes	—
154	C₂²×C₃×D₅	C₂⁴	1	3	yes	—
155	C₃×C₅×Q₈	—	2	12	no	—
156	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
157	C₃×C₅×D₄	#41	1	4	yes	complemented
158	C₂×C₃×C₄×C₅	—	2	12	no	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₂²⋊D₅	—	2	12	no	—
164	C₂×C₃×Dic₅	—	2	4	no	—
165	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
166	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
167	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
168	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
169	C₃×D₂₀	—	2	24	no	—
170	C₃×D₂₀	—	2	12	no	—
171	C₃×D₂₀	—	2	6	no	—
172	C₃×D₂₀	—	4	6	no	—
173	C₃×D₂₀	C₂×D₄	1	12	yes	complemented
174	C₃×C₄×D₅	—	2	12	no	—
175	C₃×C₄×D₅	—	2	12	no	—
176	C₃×C₄×D₅	—	2	6	no	—
177	C₃×C₄×D₅	—	2	12	no	—
178	C₃×C₄×D₅	—	4	3	no	—
179	C₃×C₄×D₅	C₂×D₄	1	12	yes	complemented
180	C₂×C₃×#41	—	5	1	no	—
181	C₂×C₃×#41	—	5	6	no	—
182	C₂×C₃×#41	—	5	6	no	—
183	C₂×C₃×#41	—	5	2	no	—
184	C₂×C₃×#41	—	10	16	no	—
185	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	complemented
186	C₂²×C₃×D₄	—	5	3	no	—
187	C₂²×C₃×D₄	—	5	6	no	—
188	C₂³×C₃×C₄	—	5	6	no	—
189	C₃×C₄⋊Q₈	C₂×D₅	1	3	yes	complemented
190	C₃×#127	—	5	3	no	—
191	C₃×#124	—	5	6	no	—
192	C₃×#123	—	5	12	no	—
193	C₃×C₂²⋊Q₈	—	5	6	no	—
194	C₃×C₂²⋊Q₈	C₂×D₅	1	6	yes	complemented
195	C₃×#121	—	5	6	no	—
196	C₃×#121	—	5	6	no	—
197	C₃×#121	—	5	6	no	—
198	C₃×#121	—	5	6	no	—
199	C₃×#120	—	5	12	no	—
200	C₃×C₄×Q₈	—	5	1	no	—
201	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
202	C₃×C₄×D₄	—	5	1	no	—
203	C₃×C₄×D₄	—	5	6	no	—
204	C₃×C₄×D₄	—	5	3	no	—
205	C₃×C₄×D₄	—	5	3	no	—
206	C₃×C₄×D₄	—	5	6	no	—
207	C₃×C₄×D₄	—	5	6	no	—
208	C₃×C₄×D₄	—	5	3	no	—
209	C₃×C₄×D₄	—	5	3	no	—
210	C₃×C₄×D₄	C₂×D₅	1	3	yes	—
211	C₃×#117	—	5	3	no	—
212	C₂×C₃×C₄⋊C₄	—	5	3	no	—
213	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
214	C₂×C₃×C₄²	—	5	3	no	—
215	C₂³×D₅	C₂³×C₃	1	6	yes	—
216	C₂×C₅×Q₈	—	2	8	no	—
217	C₂×C₅×Q₈	C₂³×C₃	1	6	yes	—
218	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
221	C₂×C₂²⋊D₅	C₂³×C₃	1	6	yes	—
222	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
223	#713	—	2	8	no	—
224	#713	—	2	24	no	—
225	#713	—	2	24	no	—
226	#713	C₃×D₄	1	8	yes	direct product factor
227	D₄×D₅	—	2	12	no	—
228	C₂×D₂₀	—	2	24	no	—
229	C₂×D₂₀	C₂³×C₃	1	6	yes	—
230	C₂×D₂₀	C₂³×C₃	1	12	yes	—
231	C₂×D₂₀	C₂³×C₃	1	3	yes	—
232	C₂×D₂₀	C₂³×C₃	1	6	yes	—
233	C₂×D₂₀	C₂³×C₃	1	3	yes	—
234	C₂×C₄×D₅	—	2	24	no	—
235	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
236	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
237	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
238	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
239	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
240	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
241	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
242	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
243	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
244	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
245	C₄²×C₅	C₂³×C₃	1	3	yes	—
246	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
247	#685	C₂³×C₃	1	6	yes	—
248	#685	C₂³×C₃	1	6	yes	—
249	#685	C₂³×C₃	1	6	yes	—
250	#685	C₂³×C₃	1	12	yes	—
251	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
252	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
253	#683	C₂³×C₃	1	6	yes	—
254	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
255	C₄×Dic₅	C₂³×C₃	1	3	yes	—
256	C₄×Dic₅	C₂³×C₃	1	3	yes	—
257	C₂²×#41	—	5	2	no	—
258	#550	—	5	1	no	—
259	D₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
260	#548	—	5	2	no	—
261	#547	—	5	3	no	—
262	#546	—	5	6	no	—
263	D₄²	—	5	3	no	—
264	#532	—	5	3	no	—
265	#525	—	5	6	no	—
266	C₄×#41	—	5	1	no	—
267	C₂×C₄×D₄	—	5	3	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	C₂×#41	1	4	yes	complemented
271	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
272	C₂×C₃×D₅	—	2	3	no	—
273	C₂×C₃×D₅	—	2	3	no	—
274	C₂×C₃×D₅	—	2	6	no	—
275	C₂×C₃×D₅	—	2	6	no	—
276	C₂×C₃×D₅	—	2	6	no	—
277	C₂×C₃×D₅	—	4	24	no	—
278	C₂×C₃×D₅	C₂²×D₄	1	6	yes	—
279	C₃×C₄×C₅	—	2	6	no	—
280	C₃×C₄×C₅	—	2	3	no	—
281	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
282	C₃×C₄×C₅	C₂×#41	1	2	yes	complemented
283	C₃×Dic₅	—	2	2	no	—
284	C₃×Dic₅	—	2	3	no	—
285	C₃×Dic₅	—	2	1	no	—
286	C₃×Dic₅	C₂²×D₄	1	2	yes	—
287	C₂⁴×C₃	—	5	6	no	—
288	C₃×#41	—	5	8	no	—
289	C₃×#41	—	10	24	no	—
290	C₃×#41	—	10	24	no	—
291	C₃×#41	—	10	8	no	—
292	C₂×C₃×Q₈	—	2	8	no	—
293	C₂×C₃×Q₈	C₂²×D₅	1	6	yes	—
294	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
295	C₂×C₃×D₄	—	5	6	no	—
296	C₂×C₃×D₄	—	5	3	no	—
297	C₂×C₃×D₄	—	5	3	no	—
298	C₂×C₃×D₄	—	5	12	no	—
299	C₂×C₃×D₄	—	5	6	no	—
300	C₂×C₃×D₄	—	5	6	no	—
301	C₂×C₃×D₄	—	10	24	no	—
302	C₂×C₃×D₄	—	10	12	no	—
303	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
304	C₂²×C₃×C₄	—	5	3	no	—
305	C₂²×C₃×C₄	—	5	2	no	—
306	C₂²×C₃×C₄	—	5	3	no	—
307	C₂²×C₃×C₄	—	5	6	no	—
308	C₂²×C₃×C₄	—	5	6	no	—
309	C₂²×C₃×C₄	—	5	6	no	—
310	C₂²×C₃×C₄	—	5	3	no	—
311	C₂²×C₃×C₄	—	10	24	no	—
312	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
313	C₃×C₄⋊C₄	—	5	6	no	—
314	C₃×C₄⋊C₄	—	5	1	no	—
315	C₃×C₄⋊C₄	—	5	3	no	—
316	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
317	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
318	C₃×C₄⋊C₄	C₂²×D₅	1	6	yes	—
319	C₃×C₂²⋊C₄	—	5	2	no	—
320	C₃×C₂²⋊C₄	—	5	6	no	—
321	C₃×C₂²⋊C₄	—	5	6	no	—
322	C₃×C₂²⋊C₄	—	5	6	no	—
323	C₃×C₂²⋊C₄	—	5	12	no	—
324	C₃×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
325	C₃×C₄²	—	5	1	no	—
326	C₃×C₄²	—	5	3	no	—
327	C₃×C₄²	—	5	3	no	—
328	C₃×C₄²	C₂²×D₅	1	3	yes	—
329	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
330	C₂²×D₅	—	2	12	no	—
331	C₂²×D₅	—	2	12	no	—
332	C₂²×D₅	—	4	6	no	—
333	C₂²×D₅	C₂⁴×C₃	1	6	yes	—
334	C₂²×D₅	C₂⁴×C₃	1	3	yes	—
335	C₅×Q₈	—	2	12	no	—
336	C₅×Q₈	C₂×C₃×D₄	1	4	yes	complemented
337	C₅×D₄	C₃×#41	1	4	yes	complemented
338	C₂×C₄×C₅	—	2	12	no	—
339	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
340	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
341	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
342	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
343	C₂²⋊D₅	—	2	12	no	—
344	C₂×Dic₅	—	2	4	no	—
345	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
346	C₂×Dic₅	C₂⁴×C₃	1	3	yes	—
347	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
348	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
349	D₂₀	—	2	24	no	—
350	D₂₀	—	2	12	no	—
351	D₂₀	—	2	6	no	—
352	D₂₀	—	4	6	no	—
353	D₂₀	C₂×C₃×D₄	1	12	yes	complemented
354	C₄×D₅	—	2	12	no	—
355	C₄×D₅	—	2	12	no	—
356	C₄×D₅	—	2	6	no	—
357	C₄×D₅	—	2	12	no	—
358	C₄×D₅	—	4	3	no	—
359	C₄×D₅	C₂×C₃×D₄	1	12	yes	complemented
360	C₂×#41	—	5	1	no	—
361	C₂×#41	—	5	6	no	—
362	C₂×#41	—	5	6	no	—
363	C₂×#41	—	5	2	no	—
364	C₂×#41	—	10	16	no	—
365	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	complemented
366	C₂²×D₄	—	5	3	no	—
367	C₂²×D₄	—	5	6	no	—
368	C₂³×C₄	—	5	6	no	—
369	C₄⋊Q₈	C₂×C₃×D₅	1	3	yes	complemented
370	#127	—	5	3	no	—
371	#124	—	5	6	no	—
372	#123	—	5	12	no	—
373	C₂²⋊Q₈	—	5	6	no	—
374	C₂²⋊Q₈	C₂×C₃×D₅	1	6	yes	complemented
375	#121	—	5	6	no	—
376	#121	—	5	6	no	—
377	#121	—	5	6	no	—
378	#121	—	5	6	no	—
379	#120	—	5	12	no	—
380	C₄×Q₈	—	5	1	no	—
381	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	6	no	—
384	C₄×D₄	—	5	3	no	—
385	C₄×D₄	—	5	3	no	—
386	C₄×D₄	—	5	6	no	—
387	C₄×D₄	—	5	6	no	—
388	C₄×D₄	—	5	3	no	—
389	C₄×D₄	—	5	3	no	—
390	C₄×D₄	C₂×C₃×D₅	1	3	yes	—
391	#117	—	5	3	no	—
392	C₂×C₄⋊C₄	—	5	3	no	—
393	C₂×C₂²⋊C₄	—	5	6	no	—
394	C₂×C₄²	—	5	3	no	—
395	C₂×C₃×C₅	—	2	4	no	—
396	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
397	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
398	C₂×C₃×C₅	#585	1	1	yes	characteristic
399	C₃×D₅	—	2	6	no	—
400	C₃×D₅	—	4	6	no	—
401	C₂³×C₃	—	5	3	no	—
402	C₂³×C₃	—	5	6	no	—
403	C₂³×C₃	—	10	12	no	—
404	C₂³×C₃	—	10	12	no	—
405	C₂³×C₃	—	20	6	no	—
406	C₂³×C₃	C₂³×D₅	1	2	yes	—
407	C₃×Q₈	—	2	12	no	—
408	C₃×Q₈	D₄×D₅	1	4	yes	complemented
409	C₃×D₄	—	5	12	no	—
410	C₃×D₄	—	10	24	no	—
411	C₃×D₄	—	10	12	no	—
412	C₃×D₄	—	10	12	no	—
413	C₃×D₄	—	10	6	no	—
414	C₃×D₄	—	20	6	no	—
415	C₃×D₄	#713	1	4	yes	direct product factor
416	C₂×C₃×C₄	—	2	12	no	—
417	C₂×C₃×C₄	—	5	1	no	—
418	C₂×C₃×C₄	—	5	12	no	—
419	C₂×C₃×C₄	—	5	1	no	—
420	C₂×C₃×C₄	—	5	3	no	—
421	C₂×C₃×C₄	—	5	2	no	—
422	C₂×C₃×C₄	—	10	12	no	—
423	C₂×C₃×C₄	—	10	12	no	—
424	C₂×C₃×C₄	—	10	4	no	—
425	C₂×C₃×C₄	—	10	12	no	—
426	C₂×C₃×C₄	—	10	6	no	—
427	C₂×C₃×C₄	—	20	3	no	—
428	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
429	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
430	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
431	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	2	2	no	—
434	C₂²×C₅	C₂×C₃×#41	1	4	yes	complemented
435	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
436	C₂×D₅	—	2	3	no	—
437	C₂×D₅	—	2	3	no	—
438	C₂×D₅	—	2	6	no	—
439	C₂×D₅	—	2	6	no	—
440	C₂×D₅	—	2	6	no	—
441	C₂×D₅	—	4	24	no	—
442	C₂×D₅	C₂²×C₃×D₄	1	6	yes	—
443	C₄×C₅	—	2	6	no	—
444	C₄×C₅	—	2	3	no	—
445	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
446	C₄×C₅	C₂×C₃×#41	1	2	yes	complemented
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	3	no	—
449	Dic₅	—	2	1	no	—
450	Dic₅	C₂²×C₃×D₄	1	2	yes	—
451	C₂⁴	—	5	6	no	—
452	#41	—	5	8	no	—
453	#41	—	10	24	no	—
454	#41	—	10	24	no	—
455	#41	—	10	8	no	—
456	C₂×Q₈	—	2	8	no	—
457	C₂×Q₈	C₂²×C₃×D₅	1	6	yes	—
458	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
459	C₂×D₄	—	5	6	no	—
460	C₂×D₄	—	5	3	no	—
461	C₂×D₄	—	5	3	no	—
462	C₂×D₄	—	5	12	no	—
463	C₂×D₄	—	5	6	no	—
464	C₂×D₄	—	5	6	no	—
465	C₂×D₄	—	10	24	no	—
466	C₂×D₄	—	10	12	no	—
467	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂²×C₄	—	5	3	no	—
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	3	no	—
471	C₂²×C₄	—	5	6	no	—
472	C₂²×C₄	—	5	6	no	—
473	C₂²×C₄	—	5	6	no	—
474	C₂²×C₄	—	5	3	no	—
475	C₂²×C₄	—	10	24	no	—
476	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
477	C₄⋊C₄	—	5	1	no	—
478	C₄⋊C₄	—	5	6	no	—
479	C₄⋊C₄	—	5	3	no	—
480	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
481	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
482	C₄⋊C₄	C₂²×C₃×D₅	1	6	yes	—
483	C₂²⋊C₄	—	5	2	no	—
484	C₂²⋊C₄	—	5	6	no	—
485	C₂²⋊C₄	—	5	6	no	—
486	C₂²⋊C₄	—	5	6	no	—
487	C₂²⋊C₄	—	5	12	no	—
488	C₂²⋊C₄	C₂²×C₃×D₅	1	6	yes	—
489	C₄²	—	5	1	no	—
490	C₄²	—	5	3	no	—
491	C₄²	—	5	3	no	—
492	C₄²	C₂²×C₃×D₅	1	3	yes	—
493	C₃×C₅	D₄×#41	1	1	yes	characteristic, complemented, Hall
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	2	no	—
496	C₂²×C₃	—	5	6	no	—
497	C₂²×C₃	—	10	3	no	—
498	C₂²×C₃	—	10	3	no	—
499	C₂²×C₃	—	10	6	no	—
500	C₂²×C₃	—	10	6	no	—
501	C₂²×C₃	—	10	6	no	—
502	C₂²×C₃	—	20	24	no	—
503	C₂²×C₃	C₂×#713	1	4	yes	complemented
504	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
505	C₃×C₄	—	2	6	no	—
506	C₃×C₄	—	2	3	no	—
507	C₃×C₄	—	5	2	no	—
508	C₃×C₄	—	10	2	no	—
509	C₃×C₄	—	10	3	no	—
510	C₃×C₄	—	10	1	no	—
511	C₃×C₄	C₂×D₄×D₅	1	6	yes	—
512	C₃×C₄	C₂×#713	1	2	yes	complemented
513	C₂×C₅	—	2	4	no	—
514	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
515	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
516	C₂×C₅	C₃×#585	1	1	yes	characteristic
517	D₅	—	2	6	no	—
518	D₅	—	4	6	no	—
519	C₂³	—	5	3	no	—
520	C₂³	—	5	6	no	—
521	C₂³	—	10	12	no	—
522	C₂³	—	10	12	no	—
523	C₂³	—	20	6	no	—
524	C₂³	C₂³×C₃×D₅	1	2	yes	—
525	Q₈	—	2	12	no	—
526	Q₈	C₃×D₄×D₅	1	4	yes	complemented
527	D₄	—	5	12	no	—
528	D₄	—	10	24	no	—
529	D₄	—	10	12	no	—
530	D₄	—	10	12	no	—
531	D₄	—	10	6	no	—
532	D₄	—	20	6	no	—
533	D₄	C₃×#713	1	4	yes	direct product factor
534	C₂×C₄	—	2	12	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	5	12	no	—
537	C₂×C₄	—	5	1	no	—
538	C₂×C₄	—	5	3	no	—
539	C₂×C₄	—	5	2	no	—
540	C₂×C₄	—	10	12	no	—
541	C₂×C₄	—	10	12	no	—
542	C₂×C₄	—	10	4	no	—
543	C₂×C₄	—	10	12	no	—
544	C₂×C₄	—	10	6	no	—
545	C₂×C₄	—	20	3	no	—
546	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
547	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
548	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
549	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
550	C₂×C₃	—	2	4	no	—
551	C₂×C₃	—	10	6	no	—
552	C₂×C₃	—	20	6	no	—
553	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
554	C₂×C₃	C₂²×#713	1	1	yes	characteristic
555	C₂×C₃	#66287	1	1	yes	characteristic
556	C₅	C₃×D₄×#41	1	1	yes	characteristic, complemented, Sylow
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	5	6	no	—
560	C₂²	—	10	3	no	—
561	C₂²	—	10	3	no	—
562	C₂²	—	10	6	no	—
563	C₂²	—	10	6	no	—
564	C₂²	—	10	6	no	—
565	C₂²	—	20	24	no	—
566	C₂²	C₂×C₃×#713	1	4	yes	complemented
567	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
568	C₄	—	2	6	no	—
569	C₄	—	2	3	no	—
570	C₄	—	5	2	no	—
571	C₄	—	10	2	no	—
572	C₄	—	10	3	no	—
573	C₄	—	10	1	no	—
574	C₄	C₂×C₃×D₄×D₅	1	6	yes	—
575	C₄	C₂×C₃×#713	1	2	yes	complemented
576	C₃	D₄×#713	1	1	yes	characteristic, direct product factor, Sylow
577	C₂	—	2	4	no	—
578	C₂	—	10	6	no	—
579	C₂	—	20	6	no	—
580	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
581	C₂	C₂²×C₃×#713	1	1	yes	characteristic
582	C₂	C₃×#66287	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×D₄×Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×D₄×Q₈	D₅
hypocenter	C₅	C₃×D₄×#41
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#713	C₂	semidirect
2. C₃×C₅×D₄×Q₈	C₂	semidirect
3. C₃×#66151	C₂	semidirect
4. C₃×#66060	C₂	semidirect
5. C₃×#66059	C₂	semidirect
6. C₃×#65964	C₂	semidirect
7. C₃×#65961	C₂	semidirect
8. C₃×#65911	C₂	semidirect
9. C₃×C₄×#713	C₂	semidirect
10. C₃×D₄×D₂₀	C₂	semidirect
11. C₃×C₄×D₄×D₅	C₂	semidirect
12. D₄×#713	C₃	direct (N × H)
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
16. C₂×C₃×#713	C₂²	semidirect
17. C₂×C₃×#713	C₂²	semidirect
18. C₂×C₃×#713	C₂²	semidirect
20. C₂²×C₃×D₂₀	C₂²	semidirect
21. C₂²×C₃×C₄×D₅	C₂²	semidirect
22. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₃×#4093	C₂²	semidirect
27. C₃×#4092	C₂²	semidirect
28. C₃×Q₈×Dic₅	C₂²	semidirect
30. C₃×#4076	C₂²	semidirect
31. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
32. C₃×#4041	C₂²	semidirect
33. C₃×#4041	C₂²	semidirect
34. C₃×#4041	C₂²	semidirect
35. C₃×#4040	C₂²	semidirect
36. C₃×#4039	C₂²	semidirect
37. C₃×#4039	C₂²	semidirect
38. C₃×#4039	C₂²	semidirect
39. C₃×#4038	C₂²	semidirect
40. C₃×D₅×C₄⋊C₄	C₂²	semidirect
41. C₃×#4028	C₂²	semidirect
42. C₃×#4027	C₂²	semidirect
43. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
44. C₃×#4020	C₂²	semidirect
45. C₃×C₄×D₂₀	C₂²	semidirect
46. C₃×C₄×D₂₀	C₂²	semidirect
47. C₃×C₄²×D₅	C₂²	semidirect
49. C₂²×#713	C₂×C₃	semidirect
50. C₅×D₄×Q₈	C₂×C₃	semidirect
51. #66151	C₂×C₃	semidirect
52. #66060	C₂×C₃	semidirect
53. #66059	C₂×C₃	semidirect
54. #65964	C₂×C₃	semidirect
55. #65961	C₂×C₃	semidirect
56. #65911	C₂×C₃	semidirect
57. C₄×#713	C₂×C₃	semidirect
58. D₄×D₂₀	C₂×C₃	semidirect
59. C₄×D₄×D₅	C₂×C₃	semidirect
71. C₃×#713	D₄	direct (N × H)
104. C₃×D₄×Q₈	D₅	semidirect
113. C₂²×C₅×Q₈	C₂²×C₃	semidirect
116. C₂×#713	C₂²×C₃	semidirect
117. C₂×#713	C₂²×C₃	semidirect
118. C₂×#713	C₂²×C₃	semidirect
120. C₂²×D₂₀	C₂²×C₃	semidirect
121. C₂²×C₄×D₅	C₂²×C₃	semidirect
122. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
123. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
124. C₄×C₅×Q₈	C₂²×C₃	semidirect
126. #4093	C₂²×C₃	semidirect
127. #4092	C₂²×C₃	semidirect
128. Q₈×Dic₅	C₂²×C₃	semidirect
130. #4076	C₂²×C₃	semidirect
131. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
132. #4041	C₂²×C₃	semidirect
133. #4041	C₂²×C₃	semidirect
134. #4041	C₂²×C₃	semidirect
135. #4040	C₂²×C₃	semidirect
136. #4039	C₂²×C₃	semidirect
137. #4039	C₂²×C₃	semidirect
138. #4039	C₂²×C₃	semidirect
139. #4038	C₂²×C₃	semidirect
140. D₅×C₄⋊C₄	C₂²×C₃	semidirect
141. #4028	C₂²×C₃	semidirect
142. #4027	C₂²×C₃	semidirect
143. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
144. #4020	C₂²×C₃	semidirect
145. C₄×D₂₀	C₂²×C₃	semidirect
146. C₄×D₂₀	C₂²×C₃	semidirect
147. C₄²×D₅	C₂²×C₃	semidirect
156. C₃×C₅×Q₈	C₂×D₄	semidirect
157. C₃×C₅×D₄	#41	semidirect
173. C₃×D₂₀	C₂×D₄	semidirect
179. C₃×C₄×D₅	C₂×D₄	semidirect
185. C₂²×C₃×Q₈	C₂×D₅	semidirect
189. C₃×C₄⋊Q₈	C₂×D₅	semidirect
194. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
201. C₃×C₄×Q₈	C₂×D₅	semidirect
226. #713	C₃×D₄	direct (N × H)
259. D₄×Q₈	C₃×D₅	semidirect
270. C₂²×C₃×C₅	C₂×#41	semidirect
282. C₃×C₄×C₅	C₂×#41	semidirect
336. C₅×Q₈	C₂×C₃×D₄	semidirect
337. C₅×D₄	C₃×#41	semidirect
353. D₂₀	C₂×C₃×D₄	semidirect
359. C₄×D₅	C₂×C₃×D₄	semidirect
365. C₂²×Q₈	C₂×C₃×D₅	semidirect
369. C₄⋊Q₈	C₂×C₃×D₅	semidirect
374. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
381. C₄×Q₈	C₂×C₃×D₅	semidirect
408. C₃×Q₈	D₄×D₅	semidirect
415. C₃×D₄	#713	direct (N × H)
434. C₂²×C₅	C₂×C₃×#41	semidirect
446. C₄×C₅	C₂×C₃×#41	semidirect
493. C₃×C₅	D₄×#41	semidirect
503. C₂²×C₃	C₂×#713	semidirect
512. C₃×C₄	C₂×#713	semidirect
526. Q₈	C₃×D₄×D₅	semidirect
533. D₄	C₃×#713	direct (N × H)
556. C₅	C₃×D₄×#41	semidirect
566. C₂²	C₂×C₃×#713	semidirect
575. C₄	C₂×C₃×#713	semidirect
576. C₃	D₄×#713	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×C₃×#713	2
C₃×C₅×D₄×Q₈	2
C₃×#66151	2
C₃×#66060	2
C₃×#66059	2
C₃×#65964	2
C₃×#65961	2
C₃×#65911	2
C₃×C₄×#713	2
C₃×D₄×D₂₀	2
C₃×C₄×D₄×D₅	2
D₄×#713	3
C₃×D₄×#41	5

Subgroups — C3×D4×#713 #14483061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#713 #14483061