Subgroups — C₃×C₅×#2321 #14275355

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2321	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#120	C₄	1	8	yes	complemented
20	C₃×C₄×C₅×D₄	—	2	4	no	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊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	2	yes	—
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
36	C₃×C₅×#95	C₂²	1	2	yes	complemented
37	C₃×C₅×#95	C₂²	1	2	yes	complemented
38	C₃×C₅×#95	C₂²	1	2	yes	complemented
39	C₃×#2321	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
41	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#390	C₂×C₃	1	2	yes	complemented
44	C₅×#388	C₂×C₃	1	2	yes	complemented
45	C₅×#388	C₂×C₃	1	2	yes	complemented
46	C₅×#386	C₂×C₃	1	2	yes	complemented
47	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
50	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂⁴×C₃×C₅	—	2	2	no	—
52	C₂⁴×C₃×C₅	—	2	2	no	—
53	C₂⁴×C₃×C₅	—	4	2	no	—
54	C₂⁴×C₃×C₅	—	4	2	no	—
55	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
56	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
57	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
58	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	4	2	no	—
62	C₂×C₃×C₅×D₄	—	4	2	no	—
63	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
64	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	4	2	no	—
68	C₂²×C₃×C₄×C₅	—	4	2	no	—
69	C₂²×C₃×C₄×C₅	—	4	2	no	—
70	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	—	2	2	no	—
80	C₃×C₅×C₄⋊C₄	—	4	2	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
88	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
89	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
90	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
91	C₃×C₄²×C₅	—	2	2	no	—
92	C₃×C₄²×C₅	—	4	2	no	—
93	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
94	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#390	C₂×C₅	1	2	yes	complemented
97	C₃×#388	C₂×C₅	1	2	yes	complemented
98	C₃×#388	C₂×C₅	1	2	yes	complemented
99	C₃×#386	C₂×C₅	1	2	yes	complemented
100	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
105	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
107	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
108	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×#120	C₃×C₄	1	8	yes	complemented
111	C₄×C₅×D₄	—	2	4	no	—
112	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
114	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
115	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
125	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
127	C₅×#95	C₂²×C₃	1	2	yes	complemented
128	C₅×#95	C₂²×C₃	1	2	yes	complemented
129	C₅×#95	C₂²×C₃	1	2	yes	complemented
130	#2321	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	—	2	8	no	—
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	—	2	2	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	2	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	4	8	no	—
145	C₂³×C₃×C₅	—	4	4	no	—
146	C₂³×C₃×C₅	—	4	4	no	—
147	C₂³×C₃×C₅	—	4	8	no	—
148	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
149	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
150	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
151	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
152	C₂³×C₃×C₅	#41	1	2	yes	—
153	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₅×D₄	—	2	8	no	—
155	C₃×C₅×D₄	—	4	8	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	2	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	1	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	2	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	4	4	no	—
173	C₂×C₃×C₄×C₅	—	4	4	no	—
174	C₂×C₃×C₄×C₅	—	4	4	no	—
175	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
177	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
178	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
179	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
180	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
182	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
183	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₃×#120	C₄×C₅	1	8	yes	complemented
186	C₃×C₄×D₄	—	2	4	no	—
187	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
189	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
190	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
199	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
200	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
201	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
202	C₃×#95	C₂²×C₅	1	2	yes	complemented
203	C₃×#95	C₂²×C₅	1	2	yes	complemented
204	C₃×#95	C₂²×C₅	1	2	yes	complemented
205	C₂⁴×C₅	—	2	2	no	—
206	C₂⁴×C₅	—	2	2	no	—
207	C₂⁴×C₅	—	4	2	no	—
208	C₂⁴×C₅	—	4	2	no	—
209	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	complemented
210	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
211	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₅×D₄	—	2	2	no	—
214	C₂×C₅×D₄	—	2	2	no	—
215	C₂×C₅×D₄	—	4	2	no	—
216	C₂×C₅×D₄	—	4	2	no	—
217	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
218	C₂×C₅×D₄	C₂×C₃×C₄	1	8	yes	complemented
219	C₂²×C₄×C₅	—	2	2	no	—
220	C₂²×C₄×C₅	—	2	2	no	—
221	C₂²×C₄×C₅	—	4	2	no	—
222	C₂²×C₄×C₅	—	4	2	no	—
223	C₂²×C₄×C₅	—	4	2	no	—
224	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
225	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
227	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
229	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
231	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₂²⋊C₄	—	2	2	no	—
236	C₅×C₂²⋊C₄	—	2	2	no	—
237	C₅×C₂²⋊C₄	—	2	4	no	—
238	C₅×C₂²⋊C₄	—	2	4	no	—
239	C₅×C₂²⋊C₄	—	2	2	no	—
240	C₅×C₂²⋊C₄	—	4	2	no	—
241	C₅×C₂²⋊C₄	—	4	2	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
244	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
245	C₄²×C₅	—	2	2	no	—
246	C₄²×C₅	—	4	2	no	—
247	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	#390	C₂×C₃×C₅	1	2	yes	complemented
251	#388	C₂×C₃×C₅	1	2	yes	complemented
252	#388	C₂×C₃×C₅	1	2	yes	complemented
253	#386	C₂×C₃×C₅	1	2	yes	complemented
254	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
257	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂²×C₃×C₅	—	2	4	no	—
259	C₂²×C₃×C₅	—	2	2	no	—
260	C₂²×C₃×C₅	—	2	2	no	—
261	C₂²×C₃×C₅	—	2	4	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	—	2	4	no	—
264	C₂²×C₃×C₅	—	2	4	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	2	4	no	—
267	C₂²×C₃×C₅	—	4	16	no	—
268	C₂²×C₃×C₅	—	4	1	no	—
269	C₂²×C₃×C₅	—	4	2	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	2	no	—
275	C₂²×C₃×C₅	C₄×D₄	1	4	yes	—
276	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
277	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
279	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
280	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
281	C₃×C₄×C₅	—	2	2	no	—
282	C₃×C₄×C₅	—	2	4	no	—
283	C₃×C₄×C₅	—	2	2	no	—
284	C₃×C₄×C₅	—	2	2	no	—
285	C₃×C₄×C₅	—	4	1	no	—
286	C₃×C₄×C₅	—	4	1	no	—
287	C₃×C₄×C₅	—	4	2	no	—
288	C₃×C₄×C₅	—	4	2	no	—
289	C₂⁴×C₃	—	2	2	no	—
290	C₂⁴×C₃	—	2	2	no	—
291	C₂⁴×C₃	—	4	2	no	—
292	C₂⁴×C₃	—	4	2	no	—
293	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
294	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
295	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
296	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	4	2	no	—
300	C₂×C₃×D₄	—	4	2	no	—
301	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
302	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
303	C₂²×C₃×C₄	—	2	2	no	—
304	C₂²×C₃×C₄	—	2	2	no	—
305	C₂²×C₃×C₄	—	4	2	no	—
306	C₂²×C₃×C₄	—	4	2	no	—
307	C₂²×C₃×C₄	—	4	2	no	—
308	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
309	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
310	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
312	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
315	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
317	C₃×C₄⋊C₄	—	2	2	no	—
318	C₃×C₄⋊C₄	—	4	2	no	—
319	C₃×C₂²⋊C₄	—	2	2	no	—
320	C₃×C₂²⋊C₄	—	2	2	no	—
321	C₃×C₂²⋊C₄	—	2	4	no	—
322	C₃×C₂²⋊C₄	—	2	4	no	—
323	C₃×C₂²⋊C₄	—	2	2	no	—
324	C₃×C₂²⋊C₄	—	4	2	no	—
325	C₃×C₂²⋊C₄	—	4	2	no	—
326	C₃×C₂²⋊C₄	—	4	2	no	—
327	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
328	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
329	C₃×C₄²	—	2	2	no	—
330	C₃×C₄²	—	4	2	no	—
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	8	no	—
334	C₂³×C₅	—	2	2	no	—
335	C₂³×C₅	—	2	1	no	—
336	C₂³×C₅	—	2	1	no	—
337	C₂³×C₅	—	2	2	no	—
338	C₂³×C₅	—	2	2	no	—
339	C₂³×C₅	—	2	2	no	—
340	C₂³×C₅	—	2	2	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	4	8	no	—
345	C₂³×C₅	—	4	4	no	—
346	C₂³×C₅	—	4	4	no	—
347	C₂³×C₅	—	4	8	no	—
348	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
349	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
350	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
351	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
352	C₂³×C₅	C₃×#41	1	2	yes	—
353	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
354	C₅×D₄	—	2	8	no	—
355	C₅×D₄	—	4	8	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	4	4	no	—
373	C₂×C₄×C₅	—	4	4	no	—
374	C₂×C₄×C₅	—	4	4	no	—
375	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
376	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
377	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
378	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
379	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
380	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
381	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
382	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
383	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
384	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
385	#120	C₃×C₄×C₅	1	8	yes	complemented
386	C₄×D₄	—	2	4	no	—
387	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
388	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
399	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
400	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
401	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
402	#95	C₂²×C₃×C₅	1	2	yes	complemented
403	#95	C₂²×C₃×C₅	1	2	yes	complemented
404	#95	C₂²×C₃×C₅	1	2	yes	complemented
405	C₂×C₃×C₅	—	2	4	no	—
406	C₂×C₃×C₅	—	4	2	no	—
407	C₂×C₃×C₅	—	4	4	no	—
408	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
409	C₂×C₃×C₅	#518	1	2	yes	—
410	C₂×C₃×C₅	#534	1	1	yes	characteristic
411	C₂×C₃×C₅	#535	1	1	yes	characteristic
412	C₂×C₃×C₅	#538	1	2	yes	—
413	C₂³×C₃	—	2	2	no	—
414	C₂³×C₃	—	2	2	no	—
415	C₂³×C₃	—	2	8	no	—
416	C₂³×C₃	—	2	2	no	—
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	—	2	1	no	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	2	no	—
425	C₂³×C₃	—	2	2	no	—
426	C₂³×C₃	—	4	8	no	—
427	C₂³×C₃	—	4	4	no	—
428	C₂³×C₃	—	4	4	no	—
429	C₂³×C₃	—	4	8	no	—
430	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
431	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
432	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
433	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
434	C₂³×C₃	C₅×#41	1	2	yes	—
435	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
436	C₃×D₄	—	2	8	no	—
437	C₃×D₄	—	4	8	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	2	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	2	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	4	4	no	—
455	C₂×C₃×C₄	—	4	4	no	—
456	C₂×C₃×C₄	—	4	4	no	—
457	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
458	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
459	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
460	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
461	C₂²×C₅	—	2	4	no	—
462	C₂²×C₅	—	2	2	no	—
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	2	4	no	—
465	C₂²×C₅	—	2	2	no	—
466	C₂²×C₅	—	2	4	no	—
467	C₂²×C₅	—	2	4	no	—
468	C₂²×C₅	—	2	4	no	—
469	C₂²×C₅	—	2	4	no	—
470	C₂²×C₅	—	4	16	no	—
471	C₂²×C₅	—	4	1	no	—
472	C₂²×C₅	—	4	2	no	—
473	C₂²×C₅	—	4	1	no	—
474	C₂²×C₅	—	4	2	no	—
475	C₂²×C₅	—	4	2	no	—
476	C₂²×C₅	—	4	2	no	—
477	C₂²×C₅	—	4	2	no	—
478	C₂²×C₅	C₃×C₄×D₄	1	4	yes	—
479	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
480	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
481	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
482	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
483	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
484	C₄×C₅	—	2	2	no	—
485	C₄×C₅	—	2	4	no	—
486	C₄×C₅	—	2	2	no	—
487	C₄×C₅	—	2	2	no	—
488	C₄×C₅	—	4	1	no	—
489	C₄×C₅	—	4	1	no	—
490	C₄×C₅	—	4	2	no	—
491	C₄×C₅	—	4	2	no	—
492	C₂⁴	—	2	2	no	—
493	C₂⁴	—	2	2	no	—
494	C₂⁴	—	4	2	no	—
495	C₂⁴	—	4	2	no	—
496	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	complemented
497	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
498	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
499	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
505	C₂×D₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
512	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
513	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
514	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
515	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
516	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
518	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
519	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
531	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
532	C₄²	—	2	2	no	—
533	C₄²	—	4	2	no	—
534	C₃×C₅	#2321	1	1	yes	characteristic, direct product factor, Hall
535	C₂²×C₃	—	2	4	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	4	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	—	2	4	no	—
541	C₂²×C₃	—	2	4	no	—
542	C₂²×C₃	—	2	4	no	—
543	C₂²×C₃	—	2	4	no	—
544	C₂²×C₃	—	4	16	no	—
545	C₂²×C₃	—	4	1	no	—
546	C₂²×C₃	—	4	2	no	—
547	C₂²×C₃	—	4	1	no	—
548	C₂²×C₃	—	4	2	no	—
549	C₂²×C₃	—	4	2	no	—
550	C₂²×C₃	—	4	2	no	—
551	C₂²×C₃	—	4	2	no	—
552	C₂²×C₃	C₄×C₅×D₄	1	4	yes	—
553	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
554	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
555	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
556	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
557	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
558	C₃×C₄	—	2	2	no	—
559	C₃×C₄	—	2	4	no	—
560	C₃×C₄	—	2	2	no	—
561	C₃×C₄	—	2	2	no	—
562	C₃×C₄	—	4	1	no	—
563	C₃×C₄	—	4	1	no	—
564	C₃×C₄	—	4	2	no	—
565	C₃×C₄	—	4	2	no	—
566	C₂×C₅	—	2	4	no	—
567	C₂×C₅	—	4	4	no	—
568	C₂×C₅	—	4	2	no	—
569	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
570	C₂×C₅	C₃×#518	1	2	yes	—
571	C₂×C₅	C₃×#534	1	1	yes	characteristic
572	C₂×C₅	C₃×#535	1	1	yes	characteristic
573	C₂×C₅	C₃×#538	1	2	yes	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	8	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	4	8	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	4	no	—
590	C₂³	—	4	8	no	—
591	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
592	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
593	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
594	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
595	C₂³	C₃×C₅×#41	1	2	yes	—
596	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
597	D₄	—	2	8	no	—
598	D₄	—	4	8	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
619	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
620	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
621	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
622	C₂×C₃	—	2	4	no	—
623	C₂×C₃	—	4	4	no	—
624	C₂×C₃	—	4	2	no	—
625	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
626	C₂×C₃	C₅×#518	1	2	yes	—
627	C₂×C₃	C₅×#534	1	1	yes	characteristic
628	C₂×C₃	C₅×#535	1	1	yes	characteristic
629	C₂×C₃	C₅×#538	1	2	yes	—
630	C₅	C₃×#2321	1	1	yes	characteristic, direct product factor, Sylow
631	C₂²	—	2	4	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	4	16	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	C₃×C₄×C₅×D₄	1	4	yes	—
649	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
650	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
651	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
652	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
653	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
654	C₄	—	2	2	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₃	C₅×#2321	1	1	yes	characteristic, direct product factor, Sylow
663	C₂	—	2	4	no	—
664	C₂	—	4	4	no	—
665	C₂	—	4	2	no	—
666	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
667	C₂	C₃×C₅×#518	1	2	yes	—
668	C₂	C₃×C₅×#534	1	1	yes	characteristic
669	C₂	C₃×C₅×#535	1	1	yes	characteristic
670	C₂	C₃×C₅×#538	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	C₂×C₃×C₅×#120	C₂
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. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#388	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#386	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#385	C₂	semidirect
10. C₃×C₅×#379	C₂	semidirect
11. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
12. C₅×#2321	C₃	direct (N × H)
18. C₂³×C₃×C₄×C₅	C₂²	semidirect
19. C₃×C₅×#120	C₄	semidirect
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₂×C₃×C₄²×C₅	C₂²	semidirect
35. C₂×C₃×C₄²×C₅	C₂²	semidirect
36. C₃×C₅×#95	C₂²	semidirect
37. C₃×C₅×#95	C₂²	semidirect
38. C₃×C₅×#95	C₂²	semidirect
39. C₃×#2321	C₅	direct (N × H)
41. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
42. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
43. C₅×#390	C₂×C₃	semidirect
44. C₅×#388	C₂×C₃	semidirect
45. C₅×#388	C₂×C₃	semidirect
46. C₅×#386	C₂×C₃	semidirect
47. C₅×#386	C₂×C₃	semidirect
48. C₅×#385	C₂×C₃	semidirect
49. C₅×#379	C₂×C₃	semidirect
50. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
55. C₂⁴×C₃×C₅	C₂×C₄	semidirect
64. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
70. C₂²×C₃×C₄×C₅	D₄	semidirect
89. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
90. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
94. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
95. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
96. C₃×#390	C₂×C₅	semidirect
97. C₃×#388	C₂×C₅	semidirect
98. C₃×#388	C₂×C₅	semidirect
99. C₃×#386	C₂×C₅	semidirect
100. C₃×#386	C₂×C₅	semidirect
101. C₃×#385	C₂×C₅	semidirect
102. C₃×#379	C₂×C₅	semidirect
103. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
109. C₂³×C₄×C₅	C₂²×C₃	semidirect
110. C₅×#120	C₃×C₄	semidirect
112. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
113. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
123. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
124. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
125. C₂×C₄²×C₅	C₂²×C₃	semidirect
126. C₂×C₄²×C₅	C₂²×C₃	semidirect
127. C₅×#95	C₂²×C₃	semidirect
128. C₅×#95	C₂²×C₃	semidirect
129. C₅×#95	C₂²×C₃	semidirect
130. #2321	C₃×C₅	direct (N × H)
184. C₂³×C₃×C₄	C₂²×C₅	semidirect
185. C₃×#120	C₄×C₅	semidirect
187. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
188. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
198. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
199. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
200. C₂×C₃×C₄²	C₂²×C₅	semidirect
201. C₂×C₃×C₄²	C₂²×C₅	semidirect
202. C₃×#95	C₂²×C₅	semidirect
203. C₃×#95	C₂²×C₅	semidirect
204. C₃×#95	C₂²×C₅	semidirect
209. C₂⁴×C₅	C₂×C₃×C₄	semidirect
218. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
224. C₂²×C₄×C₅	C₃×D₄	semidirect
243. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
244. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
248. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
249. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
250. #390	C₂×C₃×C₅	semidirect
251. #388	C₂×C₃×C₅	semidirect
252. #388	C₂×C₃×C₅	semidirect
253. #386	C₂×C₃×C₅	semidirect
254. #386	C₂×C₃×C₅	semidirect
255. #385	C₂×C₃×C₅	semidirect
256. #379	C₂×C₃×C₅	semidirect
257. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
293. C₂⁴×C₃	C₂×C₄×C₅	semidirect
302. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
308. C₂²×C₃×C₄	C₅×D₄	semidirect
327. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
328. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
384. C₂³×C₄	C₂²×C₃×C₅	semidirect
385. #120	C₃×C₄×C₅	semidirect
387. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
388. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
398. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
399. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
400. C₂×C₄²	C₂²×C₃×C₅	semidirect
401. C₂×C₄²	C₂²×C₃×C₅	semidirect
402. #95	C₂²×C₃×C₅	semidirect
403. #95	C₂²×C₃×C₅	semidirect
404. #95	C₂²×C₃×C₅	semidirect
496. C₂⁴	C₂×C₃×C₄×C₅	semidirect
505. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
511. C₂²×C₄	C₃×C₅×D₄	semidirect
530. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
531. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
534. C₃×C₅	#2321	direct (N × H)
630. C₅	C₃×#2321	direct (N × H)
662. C₃	C₅×#2321	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×#120	2
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2321	3
C₃×#2321	5

Subgroups — C3×C5×#2321 #14275355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2321 #14275355