Subgroups — C₃×C₅×#2332 #14275366

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	2	yes	maximal
4	C₃×C₅×#388	C₂	1	2	yes	maximal
5	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₅×#2332	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2332	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
35	C₅×#391	C₂×C₃	1	2	yes	complemented
36	C₅×#388	C₂×C₃	1	2	yes	—
37	C₅×#388	C₂×C₃	1	2	yes	—
38	C₅×#387	C₂×C₃	1	2	yes	complemented
39	C₅×#387	C₂×C₃	1	2	yes	complemented
40	C₅×#381	C₂×C₃	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
42	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
43	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×Q₈	—	4	1	no	—
45	C₂×C₃×C₅×Q₈	—	4	1	no	—
46	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
47	C₂²×C₃×C₄×C₅	—	4	1	no	—
48	C₂²×C₃×C₄×C₅	—	4	1	no	—
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	—	4	2	no	—
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
64	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
66	C₃×C₄²×C₅	—	2	4	no	—
67	C₃×C₄²×C₅	—	4	1	no	—
68	C₃×C₄²×C₅	—	4	2	no	—
69	C₃×C₄²×C₅	—	4	1	no	—
70	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
71	C₃×#391	C₂×C₅	1	2	yes	complemented
72	C₃×#388	C₂×C₅	1	2	yes	—
73	C₃×#388	C₂×C₅	1	2	yes	—
74	C₃×#387	C₂×C₅	1	2	yes	complemented
75	C₃×#387	C₂×C₅	1	2	yes	complemented
76	C₃×#381	C₂×C₅	1	1	yes	characteristic
77	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
78	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
79	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	complemented
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
91	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
94	C₅×#95	C₂²×C₃	1	2	yes	—
95	C₅×#95	C₂²×C₃	1	2	yes	—
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	2	yes	—
98	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	2	yes	—
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	#2332	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	1	no	—
104	C₂³×C₃×C₅	—	2	1	no	—
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₃×C₅×Q₈	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	4	4	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	#41	1	4	yes	—
134	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
136	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	complemented
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
146	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
149	C₃×#95	C₂²×C₅	1	2	yes	—
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₃×#95	C₂²×C₅	1	2	yes	—
152	C₃×#95	C₂²×C₅	1	2	yes	—
153	C₃×#95	C₂²×C₅	1	2	yes	—
154	C₃×#95	C₂²×C₅	1	2	yes	—
155	C₃×#95	C₂²×C₅	1	2	yes	—
156	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₅×Q₈	—	4	1	no	—
158	C₂×C₅×Q₈	—	4	1	no	—
159	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
160	C₂²×C₄×C₅	—	4	1	no	—
161	C₂²×C₄×C₅	—	4	1	no	—
162	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
171	C₅×C₄⋊C₄	—	2	4	no	—
172	C₅×C₄⋊C₄	—	4	2	no	—
173	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
174	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₅×C₂²⋊C₄	—	4	1	no	—
177	C₅×C₂²⋊C₄	—	4	1	no	—
178	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
179	C₄²×C₅	—	2	4	no	—
180	C₄²×C₅	—	4	1	no	—
181	C₄²×C₅	—	4	2	no	—
182	C₄²×C₅	—	4	1	no	—
183	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
184	#391	C₂×C₃×C₅	1	2	yes	complemented
185	#388	C₂×C₃×C₅	1	2	yes	—
186	#388	C₂×C₃×C₅	1	2	yes	—
187	#387	C₂×C₃×C₅	1	2	yes	complemented
188	#387	C₂×C₃×C₅	1	2	yes	complemented
189	#381	C₂×C₃×C₅	1	1	yes	characteristic
190	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
191	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
192	C₂²×C₃×C₅	—	2	2	no	—
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	—	2	2	no	—
195	C₂²×C₃×C₅	—	4	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
202	C₃×C₄×C₅	—	2	4	no	—
203	C₃×C₄×C₅	—	2	2	no	—
204	C₃×C₄×C₅	—	2	2	no	—
205	C₃×C₄×C₅	—	2	4	no	—
206	C₃×C₄×C₅	—	2	4	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	—	4	2	no	—
210	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
211	C₂×C₃×Q₈	—	4	1	no	—
212	C₂×C₃×Q₈	—	4	1	no	—
213	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
214	C₂²×C₃×C₄	—	4	1	no	—
215	C₂²×C₃×C₄	—	4	1	no	—
216	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
218	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
219	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₃×C₄⋊C₄	—	2	4	no	—
226	C₃×C₄⋊C₄	—	4	2	no	—
227	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
228	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
229	C₃×C₂²⋊C₄	—	2	4	no	—
230	C₃×C₂²⋊C₄	—	4	1	no	—
231	C₃×C₂²⋊C₄	—	4	1	no	—
232	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
233	C₃×C₄²	—	2	4	no	—
234	C₃×C₄²	—	4	1	no	—
235	C₃×C₄²	—	4	2	no	—
236	C₃×C₄²	—	4	1	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	2	1	no	—
239	C₂³×C₅	—	2	1	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
242	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
243	C₅×Q₈	—	4	4	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	4	4	no	—
264	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
267	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
268	C₂×C₄×C₅	C₃×#41	1	4	yes	—
269	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
270	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
271	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
272	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
273	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
280	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
281	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
282	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
283	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
284	#95	C₂²×C₃×C₅	1	2	yes	—
285	#95	C₂²×C₃×C₅	1	2	yes	—
286	#95	C₂²×C₃×C₅	1	2	yes	—
287	#95	C₂²×C₃×C₅	1	2	yes	—
288	#95	C₂²×C₃×C₅	1	2	yes	—
289	#95	C₂²×C₃×C₅	1	2	yes	—
290	#95	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₃×C₅	—	4	2	no	—
292	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
293	C₂×C₃×C₅	#518	1	1	yes	characteristic
294	C₂×C₃×C₅	#519	1	1	yes	characteristic
295	C₂×C₃×C₅	#539	1	2	yes	—
296	C₂×C₃×C₅	#542	1	2	yes	—
297	C₂³×C₃	—	2	2	no	—
298	C₂³×C₃	—	2	1	no	—
299	C₂³×C₃	—	2	1	no	—
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
302	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
303	C₃×Q₈	—	4	4	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	2	1	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	4	4	no	—
324	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
325	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
326	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
327	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
328	C₂×C₃×C₄	C₅×#41	1	4	yes	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
335	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
336	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
339	C₄×C₅	—	2	4	no	—
340	C₄×C₅	—	2	2	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	4	no	—
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
348	C₂×Q₈	—	4	1	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
354	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
355	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
356	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
357	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
358	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
360	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
361	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
365	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
370	C₄²	—	2	4	no	—
371	C₄²	—	4	1	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	1	no	—
374	C₃×C₅	#2332	1	1	yes	characteristic, direct product factor, Hall
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	4	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
381	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
382	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	2	4	no	—
389	C₃×C₄	—	2	4	no	—
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	—	4	2	no	—
392	C₃×C₄	—	4	2	no	—
393	C₂×C₅	—	4	2	no	—
394	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
395	C₂×C₅	C₃×#518	1	1	yes	characteristic
396	C₂×C₅	C₃×#519	1	1	yes	characteristic
397	C₂×C₅	C₃×#539	1	2	yes	—
398	C₂×C₅	C₃×#542	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	2	no	—
403	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
404	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
405	Q₈	—	4	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
427	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
428	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
429	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
430	C₂×C₄	C₃×C₅×#41	1	4	yes	—
431	C₂×C₃	—	4	2	no	—
432	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
433	C₂×C₃	C₅×#518	1	1	yes	characteristic
434	C₂×C₃	C₅×#519	1	1	yes	characteristic
435	C₂×C₃	C₅×#539	1	2	yes	—
436	C₂×C₃	C₅×#542	1	2	yes	—
437	C₅	C₃×#2332	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
444	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
445	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₃	C₅×#2332	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	4	2	no	—
458	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
459	C₂	C₃×C₅×#518	1	1	yes	characteristic
460	C₂	C₃×C₅×#519	1	1	yes	characteristic
461	C₂	C₃×C₅×#539	1	2	yes	—
462	C₂	C₃×C₅×#542	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#387	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
8. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
10. C₅×#2332	C₃	direct (N × H)
13. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
33. C₃×#2332	C₅	direct (N × H)
35. C₅×#391	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
39. C₅×#387	C₂×C₃	semidirect
41. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
71. C₃×#391	C₂×C₅	semidirect
74. C₃×#387	C₂×C₅	semidirect
75. C₃×#387	C₂×C₅	semidirect
77. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
81. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
101. #2332	C₃×C₅	direct (N × H)
136. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
184. #391	C₂×C₃×C₅	semidirect
187. #387	C₂×C₃×C₅	semidirect
188. #387	C₂×C₃×C₅	semidirect
190. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
271. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
374. C₃×C₅	#2332	direct (N × H)
437. C₅	C₃×#2332	direct (N × H)
456. C₃	C₅×#2332	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×C₂²⋊Q₈	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#381	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2332	3
C₃×#2332	5

Subgroups — C3×C5×#2332 #14275366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2332 #14275366