Subgroups — C₃×C₅×#2396 #14275430

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#396	C₂	1	2	yes	maximal
7	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
12	C₅×#2396	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	—	2	4	no	—
16	C₃×C₅×#117	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
30	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	1	yes	characteristic
36	C₃×C₅×#95	C₂²	1	1	yes	characteristic
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×#2396	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
41	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#399	C₂×C₃	1	1	yes	characteristic
43	C₅×#398	C₂×C₃	1	2	yes	complemented
44	C₅×#396	C₂×C₃	1	2	yes	—
45	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#393	C₂×C₃	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
50	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×Q₈	—	2	2	no	—
52	C₂×C₃×C₅×Q₈	—	2	4	no	—
53	C₂²×C₃×C₄×C₅	—	2	2	no	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	—	2	4	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	4	no	—
71	C₃×C₅×C₄⋊C₄	—	2	4	no	—
72	C₃×C₅×C₄⋊C₄	—	2	4	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₄²×C₅	—	2	2	no	—
78	C₃×C₄²×C₅	—	2	4	no	—
79	C₃×C₄²×C₅	—	2	4	no	—
80	C₃×C₄²×C₅	D₄	1	4	yes	—
81	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
83	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#399	C₂×C₅	1	1	yes	characteristic
85	C₃×#398	C₂×C₅	1	2	yes	complemented
86	C₃×#396	C₂×C₅	1	2	yes	—
87	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#393	C₂×C₅	1	1	yes	characteristic
89	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
90	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
92	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₄×C₅×Q₈	—	2	4	no	—
95	C₅×#117	—	2	4	no	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
108	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
109	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₅×#95	C₂²×C₃	1	2	yes	—
112	C₅×#95	C₂²×C₃	1	2	yes	—
113	C₅×#95	C₂²×C₃	1	2	yes	—
114	C₅×#95	C₂²×C₃	1	1	yes	characteristic
115	C₅×#95	C₂²×C₃	1	1	yes	characteristic
116	C₅×#95	C₂²×C₃	1	2	yes	—
117	#2396	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
118	C₂³×C₃×C₅	—	2	1	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	1	no	—
122	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
123	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	8	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	1	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	8	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
149	C₂×C₃×C₄×C₅	#41	1	4	yes	—
150	C₂×C₃×C₄×C₅	#41	1	4	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₄×Q₈	—	2	4	no	—
155	C₃×#117	—	2	4	no	—
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
168	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
169	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
171	C₃×#95	C₂²×C₅	1	2	yes	—
172	C₃×#95	C₂²×C₅	1	2	yes	—
173	C₃×#95	C₂²×C₅	1	2	yes	—
174	C₃×#95	C₂²×C₅	1	1	yes	characteristic
175	C₃×#95	C₂²×C₅	1	1	yes	characteristic
176	C₃×#95	C₂²×C₅	1	2	yes	—
177	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₅×Q₈	—	2	2	no	—
179	C₂×C₅×Q₈	—	2	4	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	—	2	2	no	—
182	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
186	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
191	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
192	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	4	no	—
198	C₅×C₄⋊C₄	—	2	4	no	—
199	C₅×C₄⋊C₄	—	2	4	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	2	4	no	—
203	C₅×C₂²⋊C₄	—	2	4	no	—
204	C₄²×C₅	—	2	2	no	—
205	C₄²×C₅	—	2	4	no	—
206	C₄²×C₅	—	2	4	no	—
207	C₄²×C₅	C₃×D₄	1	4	yes	—
208	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
210	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
211	#399	C₂×C₃×C₅	1	1	yes	characteristic
212	#398	C₂×C₃×C₅	1	2	yes	complemented
213	#396	C₂×C₃×C₅	1	2	yes	—
214	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#393	C₂×C₃×C₅	1	1	yes	characteristic
216	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
217	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	—	2	4	no	—
221	C₂²×C₃×C₅	—	4	1	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	—	4	1	no	—
224	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
226	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
227	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
228	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	2	4	no	—
232	C₃×C₄×C₅	—	2	4	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	—	4	1	no	—
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
239	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₃×Q₈	—	2	2	no	—
241	C₂×C₃×Q₈	—	2	4	no	—
242	C₂²×C₃×C₄	—	2	2	no	—
243	C₂²×C₃×C₄	—	2	2	no	—
244	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
245	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
249	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
253	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
254	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	4	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	2	4	no	—
260	C₃×C₄⋊C₄	—	2	4	no	—
261	C₃×C₄⋊C₄	—	2	4	no	—
262	C₃×C₂²⋊C₄	—	2	2	no	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	2	4	no	—
265	C₃×C₂²⋊C₄	—	2	4	no	—
266	C₃×C₄²	—	2	2	no	—
267	C₃×C₄²	—	2	4	no	—
268	C₃×C₄²	—	2	4	no	—
269	C₃×C₄²	C₅×D₄	1	4	yes	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	2	no	—
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
275	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
276	C₅×Q₈	—	2	8	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	8	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
300	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
301	C₂×C₄×C₅	C₃×#41	1	4	yes	—
302	C₂×C₄×C₅	C₃×#41	1	4	yes	—
303	C₂×C₄×C₅	C₃×#41	1	2	yes	—
304	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
306	C₄×Q₈	—	2	4	no	—
307	#117	—	2	4	no	—
308	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
313	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
314	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
319	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
320	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
321	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
322	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
323	#95	C₂²×C₃×C₅	1	2	yes	—
324	#95	C₂²×C₃×C₅	1	2	yes	—
325	#95	C₂²×C₃×C₅	1	2	yes	—
326	#95	C₂²×C₃×C₅	1	1	yes	characteristic
327	#95	C₂²×C₃×C₅	1	1	yes	characteristic
328	#95	C₂²×C₃×C₅	1	2	yes	—
329	C₂×C₃×C₅	—	4	2	no	—
330	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
331	C₂×C₃×C₅	#525	1	1	yes	characteristic
332	C₂×C₃×C₅	#529	1	2	yes	—
333	C₂×C₃×C₅	#532	1	1	yes	characteristic
334	C₂×C₃×C₅	#533	1	2	yes	—
335	C₂³×C₃	—	2	1	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	2	2	no	—
338	C₂³×C₃	—	2	1	no	—
339	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
340	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
341	C₃×Q₈	—	2	8	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	8	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
362	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
363	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
365	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
366	C₂×C₃×C₄	C₅×#41	1	4	yes	—
367	C₂×C₃×C₄	C₅×#41	1	4	yes	—
368	C₂×C₃×C₄	C₅×#41	1	2	yes	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	2	4	no	—
371	C₂²×C₅	—	4	1	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
375	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
376	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
377	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
378	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	2	4	no	—
382	C₄×C₅	—	2	4	no	—
383	C₄×C₅	—	2	2	no	—
384	C₄×C₅	—	4	1	no	—
385	C₄×C₅	—	4	2	no	—
386	C₄×C₅	—	4	1	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
389	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
395	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
396	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
399	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
402	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
403	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
404	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	4	no	—
419	C₄²	C₃×C₅×D₄	1	4	yes	—
420	C₃×C₅	#2396	1	1	yes	characteristic, direct product factor, Hall
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	2	4	no	—
423	C₂²×C₃	—	4	1	no	—
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	4	1	no	—
426	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
427	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
428	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
429	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
430	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	4	no	—
434	C₃×C₄	—	2	4	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	4	2	no	—
440	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
441	C₂×C₅	—	4	2	no	—
442	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
443	C₂×C₅	C₃×#525	1	1	yes	characteristic
444	C₂×C₅	C₃×#529	1	2	yes	—
445	C₂×C₅	C₃×#532	1	1	yes	characteristic
446	C₂×C₅	C₃×#533	1	2	yes	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	1	no	—
451	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
452	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
453	Q₈	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
474	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
475	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
476	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
477	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
478	C₂×C₄	C₃×C₅×#41	1	4	yes	—
479	C₂×C₄	C₃×C₅×#41	1	4	yes	—
480	C₂×C₄	C₃×C₅×#41	1	2	yes	—
481	C₂×C₃	—	4	2	no	—
482	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
483	C₂×C₃	C₅×#525	1	1	yes	characteristic
484	C₂×C₃	C₅×#529	1	2	yes	—
485	C₂×C₃	C₅×#532	1	1	yes	characteristic
486	C₂×C₃	C₅×#533	1	2	yes	—
487	C₅	C₃×#2396	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
494	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
495	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
496	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
497	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	4	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	2	no	—
507	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
508	C₃	C₅×#2396	1	1	yes	characteristic, direct product factor, Sylow
509	C₂	—	4	2	no	—
510	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂	C₃×C₅×#525	1	1	yes	characteristic
512	C₂	C₃×C₅×#529	1	2	yes	—
513	C₂	C₃×C₅×#532	1	1	yes	characteristic
514	C₂	C₃×C₅×#533	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
5. C₃×C₅×#398	C₂	semidirect
7. C₃×C₅×#395	C₂	semidirect
9. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#2396	C₃	direct (N × H)
38. C₃×#2396	C₅	direct (N × H)
39. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
41. C₅×#400	C₂×C₃	semidirect
43. C₅×#398	C₂×C₃	semidirect
45. C₅×#395	C₂×C₃	semidirect
47. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
48. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
55. C₂²×C₃×C₄×C₅	Q₈	semidirect
81. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
83. C₃×#400	C₂×C₅	semidirect
85. C₃×#398	C₂×C₅	semidirect
87. C₃×#395	C₂×C₅	semidirect
89. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
90. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
117. #2396	C₃×C₅	direct (N × H)
182. C₂²×C₄×C₅	C₃×Q₈	semidirect
208. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
210. #400	C₂×C₃×C₅	semidirect
212. #398	C₂×C₃×C₅	semidirect
214. #395	C₂×C₃×C₅	semidirect
216. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
217. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
244. C₂²×C₃×C₄	C₅×Q₈	semidirect
394. C₂²×C₄	C₃×C₅×Q₈	semidirect
420. C₃×C₅	#2396	direct (N × H)
487. C₅	C₃×#2396	direct (N × H)
508. C₃	C₅×#2396	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×C₃×C₄×C₅×Q₈	2
C₂×C₃×C₅×#117	2
C₃×C₅×#400	2
C₃×C₅×#399	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#395	2
C₃×C₅×#393	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2396	3
C₃×#2396	5

Subgroups — C3×C5×#2396 #14275430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2396 #14275430