Subgroups — C₃×C₅×#2429 #14275463

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#396	C₂	1	2	yes	maximal
7	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#388	C₂	1	2	yes	maximal
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2429	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
17	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
18	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
19	C₃×C₄×C₅×Q₈	—	2	4	no	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
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×C₅×#95	C₂²	1	2	yes	—
39	C₃×C₅×#95	C₂²	1	2	yes	—
40	C₃×#2429	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
43	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
44	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#398	C₂×C₃	1	2	yes	complemented
46	C₅×#396	C₂×C₃	1	2	yes	—
47	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#389	C₂×C₃	1	2	yes	complemented
50	C₅×#388	C₂×C₃	1	2	yes	—
51	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
52	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
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	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	—	2	4	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	4	no	—
75	C₃×C₅×C₄⋊C₄	—	2	4	no	—
76	C₃×C₅×C₄⋊C₄	—	2	4	no	—
77	C₃×C₅×C₄⋊C₄	—	2	4	no	—
78	C₃×C₅×C₄⋊C₄	—	2	4	no	—
79	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
84	C₃×C₄²×C₅	—	2	4	no	—
85	C₃×C₄²×C₅	—	2	2	no	—
86	C₃×C₄²×C₅	—	2	2	no	—
87	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
89	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
90	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#398	C₂×C₅	1	2	yes	complemented
92	C₃×#396	C₂×C₅	1	2	yes	—
93	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#389	C₂×C₅	1	2	yes	complemented
95	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#388	C₂×C₅	1	2	yes	—
97	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
98	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
101	C₅×C₄⋊Q₈	—	2	4	no	—
102	C₅×C₂²⋊Q₈	—	2	4	no	—
103	C₅×C₂²⋊Q₈	—	2	4	no	—
104	C₄×C₅×Q₈	—	2	4	no	—
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
120	C₅×#95	C₂²×C₃	1	1	yes	characteristic
121	C₅×#95	C₂²×C₃	1	1	yes	characteristic
122	C₅×#95	C₂²×C₃	1	2	yes	—
123	C₅×#95	C₂²×C₃	1	2	yes	—
124	C₅×#95	C₂²×C₃	1	2	yes	—
125	#2429	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	—	2	1	no	—
129	C₂³×C₃×C₅	—	2	1	no	—
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
133	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
134	C₃×C₅×Q₈	—	2	8	no	—
135	C₃×C₅×Q₈	—	4	4	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	4	4	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
165	C₂×C₃×C₄×C₅	#41	1	2	yes	—
166	C₂×C₃×C₄×C₅	#41	1	2	yes	—
167	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄⋊Q₈	—	2	4	no	—
171	C₃×C₂²⋊Q₈	—	2	4	no	—
172	C₃×C₂²⋊Q₈	—	2	4	no	—
173	C₃×C₄×Q₈	—	2	4	no	—
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
189	C₃×#95	C₂²×C₅	1	1	yes	characteristic
190	C₃×#95	C₂²×C₅	1	1	yes	characteristic
191	C₃×#95	C₂²×C₅	1	2	yes	—
192	C₃×#95	C₂²×C₅	1	2	yes	—
193	C₃×#95	C₂²×C₅	1	2	yes	—
194	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×Q₈	—	2	2	no	—
196	C₂×C₅×Q₈	—	2	2	no	—
197	C₂×C₅×Q₈	—	2	2	no	—
198	C₂×C₅×Q₈	—	2	2	no	—
199	C₂×C₅×Q₈	—	2	2	no	—
200	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
201	C₂²×C₄×C₅	—	2	2	no	—
202	C₂²×C₄×C₅	—	2	2	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	—	2	4	no	—
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	4	no	—
217	C₅×C₄⋊C₄	—	2	4	no	—
218	C₅×C₄⋊C₄	—	2	4	no	—
219	C₅×C₄⋊C₄	—	2	4	no	—
220	C₅×C₄⋊C₄	—	2	4	no	—
221	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
222	C₅×C₂²⋊C₄	—	2	4	no	—
223	C₅×C₂²⋊C₄	—	2	4	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
226	C₄²×C₅	—	2	4	no	—
227	C₄²×C₅	—	2	2	no	—
228	C₄²×C₅	—	2	2	no	—
229	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#398	C₂×C₃×C₅	1	2	yes	complemented
234	#396	C₂×C₃×C₅	1	2	yes	—
235	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#389	C₂×C₃×C₅	1	2	yes	complemented
237	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#388	C₂×C₃×C₅	1	2	yes	—
239	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
250	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
251	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
252	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
253	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
254	C₃×C₄×C₅	—	2	4	no	—
255	C₃×C₄×C₅	—	2	4	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	—	4	1	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	—	4	1	no	—
262	C₃×C₄×C₅	—	4	2	no	—
263	C₃×C₄×C₅	#121	1	4	yes	—
264	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₃×Q₈	—	2	2	no	—
266	C₂×C₃×Q₈	—	2	2	no	—
267	C₂×C₃×Q₈	—	2	2	no	—
268	C₂×C₃×Q₈	—	2	2	no	—
269	C₂×C₃×Q₈	—	2	2	no	—
270	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	—	2	2	no	—
274	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
276	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₃×C₄⋊C₄	—	2	4	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	2	4	no	—
287	C₃×C₄⋊C₄	—	2	4	no	—
288	C₃×C₄⋊C₄	—	2	4	no	—
289	C₃×C₄⋊C₄	—	2	4	no	—
290	C₃×C₄⋊C₄	—	2	4	no	—
291	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
292	C₃×C₂²⋊C₄	—	2	4	no	—
293	C₃×C₂²⋊C₄	—	2	4	no	—
294	C₃×C₂²⋊C₄	—	2	2	no	—
295	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
296	C₃×C₄²	—	2	4	no	—
297	C₃×C₄²	—	2	2	no	—
298	C₃×C₄²	—	2	2	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	1	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
306	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
307	C₅×Q₈	—	2	8	no	—
308	C₅×Q₈	—	4	4	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	4	4	no	—
332	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
333	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
334	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
335	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
336	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
337	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
338	C₂×C₄×C₅	C₃×#41	1	2	yes	—
339	C₂×C₄×C₅	C₃×#41	1	2	yes	—
340	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
341	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₄⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₄×Q₈	—	2	4	no	—
347	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
348	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
350	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
351	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
352	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
353	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
354	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
359	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
360	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
361	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
362	#95	C₂²×C₃×C₅	1	1	yes	characteristic
363	#95	C₂²×C₃×C₅	1	1	yes	characteristic
364	#95	C₂²×C₃×C₅	1	2	yes	—
365	#95	C₂²×C₃×C₅	1	2	yes	—
366	#95	C₂²×C₃×C₅	1	2	yes	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
369	C₂×C₃×C₅	#533	1	1	yes	characteristic
370	C₂×C₃×C₅	#541	1	1	yes	characteristic
371	C₂×C₃×C₅	#547	1	1	yes	characteristic
372	C₂×C₃×C₅	#548	1	1	yes	characteristic
373	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
374	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
375	C₂³×C₃	—	2	1	no	—
376	C₂³×C₃	—	2	1	no	—
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	—	2	1	no	—
379	C₂³×C₃	—	2	1	no	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
382	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
383	C₃×Q₈	—	2	8	no	—
384	C₃×Q₈	—	4	4	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	4	4	no	—
408	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
409	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
413	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
414	C₂×C₃×C₄	C₅×#41	1	2	yes	—
415	C₂×C₃×C₄	C₅×#41	1	2	yes	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
424	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
425	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
426	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
427	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
428	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
429	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
430	C₄×C₅	—	2	4	no	—
431	C₄×C₅	—	2	4	no	—
432	C₄×C₅	—	2	2	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	C₃×#121	1	4	yes	—
440	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
452	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
453	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
454	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
455	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
456	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
458	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
472	C₄²	—	2	4	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₃×C₅	#2429	1	1	yes	characteristic, direct product factor, Hall
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	2	no	—
479	C₂²×C₃	—	4	1	no	—
480	C₂²×C₃	—	4	1	no	—
481	C₂²×C₃	—	4	1	no	—
482	C₂²×C₃	—	4	1	no	—
483	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
485	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
486	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
487	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
488	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
490	C₃×C₄	—	2	4	no	—
491	C₃×C₄	—	2	4	no	—
492	C₃×C₄	—	2	2	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	4	1	no	—
496	C₃×C₄	—	4	2	no	—
497	C₃×C₄	—	4	1	no	—
498	C₃×C₄	—	4	2	no	—
499	C₃×C₄	C₅×#121	1	4	yes	—
500	C₂×C₅	—	4	2	no	—
501	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
502	C₂×C₅	C₃×#533	1	1	yes	characteristic
503	C₂×C₅	C₃×#541	1	1	yes	characteristic
504	C₂×C₅	C₃×#547	1	1	yes	characteristic
505	C₂×C₅	C₃×#548	1	1	yes	characteristic
506	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
507	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
515	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
516	Q₈	—	2	8	no	—
517	Q₈	—	4	4	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
542	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
543	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
544	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
545	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
546	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
547	C₂×C₄	C₃×C₅×#41	1	2	yes	—
548	C₂×C₄	C₃×C₅×#41	1	2	yes	—
549	C₂×C₃	—	4	2	no	—
550	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
551	C₂×C₃	C₅×#533	1	1	yes	characteristic
552	C₂×C₃	C₅×#541	1	1	yes	characteristic
553	C₂×C₃	C₅×#547	1	1	yes	characteristic
554	C₂×C₃	C₅×#548	1	1	yes	characteristic
555	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
556	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
557	C₅	C₃×#2429	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
566	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
567	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
568	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
569	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
570	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
571	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
572	C₄	—	2	4	no	—
573	C₄	—	2	4	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	2	no	—
581	C₄	C₃×C₅×#121	1	4	yes	—
582	C₃	C₅×#2429	1	1	yes	characteristic, direct product factor, Sylow
583	C₂	—	4	2	no	—
584	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
585	C₂	C₃×C₅×#533	1	1	yes	characteristic
586	C₂	C₃×C₅×#541	1	1	yes	characteristic
587	C₂	C₃×C₅×#547	1	1	yes	characteristic
588	C₂	C₃×C₅×#548	1	1	yes	characteristic
589	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
590	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
5. C₃×C₅×#398	C₂	semidirect
7. C₃×C₅×#391	C₂	semidirect
8. C₃×C₅×#389	C₂	semidirect
9. C₃×C₅×#389	C₂	semidirect
12. C₅×#2429	C₃	direct (N × H)
40. C₃×#2429	C₅	direct (N × H)
41. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
44. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
45. C₅×#398	C₂×C₃	semidirect
47. C₅×#391	C₂×C₃	semidirect
48. C₅×#389	C₂×C₃	semidirect
49. C₅×#389	C₂×C₃	semidirect
83. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
87. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
90. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
91. C₃×#398	C₂×C₅	semidirect
93. C₃×#391	C₂×C₅	semidirect
94. C₃×#389	C₂×C₅	semidirect
95. C₃×#389	C₂×C₅	semidirect
125. #2429	C₃×C₅	direct (N × H)
225. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
229. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
232. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
233. #398	C₂×C₃×C₅	semidirect
235. #391	C₂×C₃×C₅	semidirect
236. #389	C₂×C₃×C₅	semidirect
237. #389	C₂×C₃×C₅	semidirect
295. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
471. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
475. C₃×C₅	#2429	direct (N × H)
557. C₅	C₃×#2429	direct (N × H)
582. C₃	C₅×#2429	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×C₅×C₄⋊Q₈	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2429	3
C₃×#2429	5

Subgroups — C3×C5×#2429 #14275463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2429 #14275463