Subgroups — C₃×C₅×#2411 #14275445

Order 1920.

1572 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#396	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2411	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	C₃×C₅×#123	—	2	4	no	—
19	C₃×C₅×#120	—	2	4	no	—
20	C₃×C₅×#117	—	2	4	no	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
38	C₃×C₅×#95	C₂²	1	2	yes	complemented
39	C₃×C₅×#95	C₂²	1	2	yes	complemented
40	C₃×#2411	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
43	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#396	C₂×C₃	1	2	yes	complemented
46	C₅×#394	C₂×C₃	1	2	yes	complemented
47	C₅×#390	C₂×C₃	1	2	yes	complemented
48	C₅×#388	C₂×C₃	1	2	yes	complemented
49	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃×C₅	—	2	2	no	—
53	C₂⁴×C₃×C₅	—	2	4	no	—
54	C₂⁴×C₃×C₅	—	2	2	no	—
55	C₂⁴×C₃×C₅	—	2	2	no	—
56	C₂⁴×C₃×C₅	—	4	2	no	—
57	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
58	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
59	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	4	no	—
65	C₂×C₃×C₅×D₄	—	4	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	—	2	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	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	—	2	4	no	—
80	C₃×C₅×C₄⋊C₄	—	2	2	no	—
81	C₃×C₅×C₄⋊C₄	—	2	2	no	—
82	C₃×C₅×C₄⋊C₄	—	4	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
92	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
93	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
94	C₃×C₄²×C₅	—	2	4	no	—
95	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
97	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#396	C₂×C₅	1	2	yes	complemented
100	C₃×#394	C₂×C₅	1	2	yes	complemented
101	C₃×#390	C₂×C₅	1	2	yes	complemented
102	C₃×#388	C₂×C₅	1	2	yes	complemented
103	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
109	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
110	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₅×#123	—	2	4	no	—
112	C₅×#120	—	2	4	no	—
113	C₅×#117	—	2	4	no	—
114	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
118	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
130	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
131	C₅×#95	C₂²×C₃	1	2	yes	complemented
132	C₅×#95	C₂²×C₃	1	2	yes	complemented
133	#2411	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	—	2	8	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	1	no	—
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	4	8	no	—
149	C₂³×C₃×C₅	—	4	8	no	—
150	C₂³×C₃×C₅	—	4	4	no	—
151	C₂³×C₃×C₅	—	4	4	no	—
152	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
153	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
154	C₂³×C₃×C₅	#41	1	4	yes	—
155	C₂³×C₃×C₅	#41	1	2	yes	—
156	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
157	C₃×C₅×D₄	—	4	8	no	—
158	C₃×C₅×D₄	—	4	4	no	—
159	C₂×C₃×C₄×C₅	—	2	8	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	—	2	1	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	1	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	2	no	—
178	C₂×C₃×C₄×C₅	—	2	2	no	—
179	C₂×C₃×C₄×C₅	—	4	4	no	—
180	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
181	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
182	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
183	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
185	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
186	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
188	C₃×#123	—	2	4	no	—
189	C₃×#120	—	2	4	no	—
190	C₃×#117	—	2	4	no	—
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
193	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
194	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
195	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
205	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
206	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
207	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
208	C₃×#95	C₂²×C₅	1	2	yes	complemented
209	C₃×#95	C₂²×C₅	1	2	yes	complemented
210	C₂⁴×C₅	—	2	2	no	—
211	C₂⁴×C₅	—	2	4	no	—
212	C₂⁴×C₅	—	2	2	no	—
213	C₂⁴×C₅	—	2	2	no	—
214	C₂⁴×C₅	—	4	2	no	—
215	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
217	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	2	no	—
220	C₂×C₅×D₄	—	2	4	no	—
221	C₂×C₅×D₄	—	2	2	no	—
222	C₂×C₅×D₄	—	2	4	no	—
223	C₂×C₅×D₄	—	4	2	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	2	2	no	—
226	C₂²×C₄×C₅	—	2	2	no	—
227	C₂²×C₄×C₅	—	4	2	no	—
228	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
229	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
233	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
236	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
237	C₅×C₄⋊C₄	—	2	4	no	—
238	C₅×C₄⋊C₄	—	2	2	no	—
239	C₅×C₄⋊C₄	—	2	2	no	—
240	C₅×C₄⋊C₄	—	4	2	no	—
241	C₅×C₂²⋊C₄	—	2	2	no	—
242	C₅×C₂²⋊C₄	—	2	2	no	—
243	C₅×C₂²⋊C₄	—	2	4	no	—
244	C₅×C₂²⋊C₄	—	2	4	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	4	2	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
252	C₄²×C₅	—	2	4	no	—
253	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
254	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
255	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
257	#396	C₂×C₃×C₅	1	2	yes	complemented
258	#394	C₂×C₃×C₅	1	2	yes	complemented
259	#390	C₂×C₃×C₅	1	2	yes	complemented
260	#388	C₂×C₃×C₅	1	2	yes	complemented
261	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
263	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	4	no	—
267	C₂²×C₃×C₅	—	2	4	no	—
268	C₂²×C₃×C₅	—	2	4	no	—
269	C₂²×C₃×C₅	—	2	4	no	—
270	C₂²×C₃×C₅	—	2	4	no	—
271	C₂²×C₃×C₅	—	4	16	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	—	4	2	no	—
276	C₂²×C₃×C₅	—	4	1	no	—
277	C₂²×C₃×C₅	—	4	1	no	—
278	C₂²×C₃×C₅	—	4	1	no	—
279	C₂²×C₃×C₅	—	4	2	no	—
280	C₂²×C₃×C₅	—	4	2	no	—
281	C₂²×C₃×C₅	#121	1	4	yes	—
282	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
285	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
286	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	—	2	2	no	—
289	C₃×C₄×C₅	—	2	4	no	—
290	C₃×C₄×C₅	—	4	1	no	—
291	C₃×C₄×C₅	—	4	1	no	—
292	C₃×C₄×C₅	—	4	1	no	—
293	C₃×C₄×C₅	—	4	2	no	—
294	C₃×C₄×C₅	—	4	2	no	—
295	C₂⁴×C₃	—	2	2	no	—
296	C₂⁴×C₃	—	2	4	no	—
297	C₂⁴×C₃	—	2	2	no	—
298	C₂⁴×C₃	—	2	2	no	—
299	C₂⁴×C₃	—	4	2	no	—
300	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
301	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
302	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₃×D₄	—	2	2	no	—
304	C₂×C₃×D₄	—	2	2	no	—
305	C₂×C₃×D₄	—	2	4	no	—
306	C₂×C₃×D₄	—	2	2	no	—
307	C₂×C₃×D₄	—	2	4	no	—
308	C₂×C₃×D₄	—	4	2	no	—
309	C₂²×C₃×C₄	—	2	2	no	—
310	C₂²×C₃×C₄	—	2	2	no	—
311	C₂²×C₃×C₄	—	2	2	no	—
312	C₂²×C₃×C₄	—	4	2	no	—
313	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
314	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
316	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
318	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
320	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	4	2	no	—
326	C₃×C₂²⋊C₄	—	2	2	no	—
327	C₃×C₂²⋊C₄	—	2	2	no	—
328	C₃×C₂²⋊C₄	—	2	4	no	—
329	C₃×C₂²⋊C₄	—	2	4	no	—
330	C₃×C₂²⋊C₄	—	2	4	no	—
331	C₃×C₂²⋊C₄	—	2	4	no	—
332	C₃×C₂²⋊C₄	—	2	2	no	—
333	C₃×C₂²⋊C₄	—	2	2	no	—
334	C₃×C₂²⋊C₄	—	4	2	no	—
335	C₃×C₂²⋊C₄	—	4	2	no	—
336	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
337	C₃×C₄²	—	2	4	no	—
338	C₂³×C₅	—	2	2	no	—
339	C₂³×C₅	—	2	2	no	—
340	C₂³×C₅	—	2	8	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	2	2	no	—
346	C₂³×C₅	—	2	2	no	—
347	C₂³×C₅	—	2	1	no	—
348	C₂³×C₅	—	2	1	no	—
349	C₂³×C₅	—	2	1	no	—
350	C₂³×C₅	—	2	2	no	—
351	C₂³×C₅	—	2	2	no	—
352	C₂³×C₅	—	4	8	no	—
353	C₂³×C₅	—	4	8	no	—
354	C₂³×C₅	—	4	4	no	—
355	C₂³×C₅	—	4	4	no	—
356	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
357	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
358	C₂³×C₅	C₃×#41	1	4	yes	—
359	C₂³×C₅	C₃×#41	1	2	yes	—
360	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
361	C₅×D₄	—	4	8	no	—
362	C₅×D₄	—	4	4	no	—
363	C₂×C₄×C₅	—	2	8	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	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	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	2	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	4	4	no	—
384	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
385	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
386	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
387	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
388	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
389	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
390	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
391	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
392	#123	—	2	4	no	—
393	#120	—	2	4	no	—
394	#117	—	2	4	no	—
395	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
396	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
397	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
398	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
399	C₂×C₂²⋊C₄	—	2	4	no	—
400	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
404	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
409	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
410	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
411	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
412	#95	C₂²×C₃×C₅	1	2	yes	complemented
413	#95	C₂²×C₃×C₅	1	2	yes	complemented
414	C₂×C₃×C₅	—	2	4	no	—
415	C₂×C₃×C₅	—	4	4	no	—
416	C₂×C₃×C₅	—	8	1	no	—
417	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
418	C₂×C₃×C₅	#525	1	1	yes	characteristic
419	C₂×C₃×C₅	#535	1	1	yes	characteristic
420	C₂×C₃×C₅	#546	1	2	yes	—
421	C₂×C₃×C₅	#551	1	2	yes	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	8	no	—
425	C₂³×C₃	—	2	2	no	—
426	C₂³×C₃	—	2	2	no	—
427	C₂³×C₃	—	2	2	no	—
428	C₂³×C₃	—	2	2	no	—
429	C₂³×C₃	—	2	2	no	—
430	C₂³×C₃	—	2	2	no	—
431	C₂³×C₃	—	2	1	no	—
432	C₂³×C₃	—	2	1	no	—
433	C₂³×C₃	—	2	1	no	—
434	C₂³×C₃	—	2	2	no	—
435	C₂³×C₃	—	2	2	no	—
436	C₂³×C₃	—	4	8	no	—
437	C₂³×C₃	—	4	8	no	—
438	C₂³×C₃	—	4	4	no	—
439	C₂³×C₃	—	4	4	no	—
440	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
441	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
442	C₂³×C₃	C₅×#41	1	4	yes	—
443	C₂³×C₃	C₅×#41	1	2	yes	—
444	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
445	C₃×D₄	—	4	8	no	—
446	C₃×D₄	—	4	4	no	—
447	C₂×C₃×C₄	—	2	8	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	2	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	2	2	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	2	no	—
465	C₂×C₃×C₄	—	2	2	no	—
466	C₂×C₃×C₄	—	2	2	no	—
467	C₂×C₃×C₄	—	4	4	no	—
468	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
469	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
470	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
471	C₂²×C₅	—	2	2	no	—
472	C₂²×C₅	—	2	2	no	—
473	C₂²×C₅	—	2	4	no	—
474	C₂²×C₅	—	2	4	no	—
475	C₂²×C₅	—	2	4	no	—
476	C₂²×C₅	—	2	4	no	—
477	C₂²×C₅	—	2	4	no	—
478	C₂²×C₅	—	4	16	no	—
479	C₂²×C₅	—	4	2	no	—
480	C₂²×C₅	—	4	2	no	—
481	C₂²×C₅	—	4	2	no	—
482	C₂²×C₅	—	4	2	no	—
483	C₂²×C₅	—	4	1	no	—
484	C₂²×C₅	—	4	1	no	—
485	C₂²×C₅	—	4	1	no	—
486	C₂²×C₅	—	4	2	no	—
487	C₂²×C₅	—	4	2	no	—
488	C₂²×C₅	C₃×#121	1	4	yes	—
489	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
490	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
491	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
492	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
493	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
494	C₄×C₅	—	2	2	no	—
495	C₄×C₅	—	2	2	no	—
496	C₄×C₅	—	2	4	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	2	no	—
501	C₄×C₅	—	4	2	no	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	4	2	no	—
507	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
508	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
509	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
521	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
522	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
523	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
524	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
525	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
527	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
528	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
544	C₄²	—	2	4	no	—
545	C₃×C₅	#2411	1	1	yes	characteristic, direct product factor, Hall
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	4	no	—
549	C₂²×C₃	—	2	4	no	—
550	C₂²×C₃	—	2	4	no	—
551	C₂²×C₃	—	2	4	no	—
552	C₂²×C₃	—	2	4	no	—
553	C₂²×C₃	—	4	16	no	—
554	C₂²×C₃	—	4	2	no	—
555	C₂²×C₃	—	4	2	no	—
556	C₂²×C₃	—	4	2	no	—
557	C₂²×C₃	—	4	2	no	—
558	C₂²×C₃	—	4	1	no	—
559	C₂²×C₃	—	4	1	no	—
560	C₂²×C₃	—	4	1	no	—
561	C₂²×C₃	—	4	2	no	—
562	C₂²×C₃	—	4	2	no	—
563	C₂²×C₃	C₅×#121	1	4	yes	—
564	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
565	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
566	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
567	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
568	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
569	C₃×C₄	—	2	2	no	—
570	C₃×C₄	—	2	2	no	—
571	C₃×C₄	—	2	4	no	—
572	C₃×C₄	—	4	1	no	—
573	C₃×C₄	—	4	1	no	—
574	C₃×C₄	—	4	1	no	—
575	C₃×C₄	—	4	2	no	—
576	C₃×C₄	—	4	2	no	—
577	C₂×C₅	—	2	4	no	—
578	C₂×C₅	—	4	4	no	—
579	C₂×C₅	—	8	1	no	—
580	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
581	C₂×C₅	C₃×#525	1	1	yes	characteristic
582	C₂×C₅	C₃×#535	1	1	yes	characteristic
583	C₂×C₅	C₃×#546	1	2	yes	—
584	C₂×C₅	C₃×#551	1	2	yes	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	8	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	4	8	no	—
600	C₂³	—	4	8	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
604	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
605	C₂³	C₃×C₅×#41	1	4	yes	—
606	C₂³	C₃×C₅×#41	1	2	yes	—
607	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
608	D₄	—	4	8	no	—
609	D₄	—	4	4	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
632	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
633	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
634	C₂×C₃	—	2	4	no	—
635	C₂×C₃	—	4	4	no	—
636	C₂×C₃	—	8	1	no	—
637	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
638	C₂×C₃	C₅×#525	1	1	yes	characteristic
639	C₂×C₃	C₅×#535	1	1	yes	characteristic
640	C₂×C₃	C₅×#546	1	2	yes	—
641	C₂×C₃	C₅×#551	1	2	yes	—
642	C₅	C₃×#2411	1	1	yes	characteristic, direct product factor, Sylow
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	4	16	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	C₃×C₅×#121	1	4	yes	—
661	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
662	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
663	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
664	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
665	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₃	C₅×#2411	1	1	yes	characteristic, direct product factor, Sylow
675	C₂	—	2	4	no	—
676	C₂	—	4	4	no	—
677	C₂	—	8	1	no	—
678	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
679	C₂	C₃×C₅×#525	1	1	yes	characteristic
680	C₂	C₃×C₅×#535	1	1	yes	characteristic
681	C₂	C₃×C₅×#546	1	2	yes	—
682	C₂	C₃×C₅×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#120	C₂
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×#123	C₂	semidirect
3. C₂×C₃×C₅×#117	C₂	semidirect
4. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
5. C₃×C₅×#396	C₂	semidirect
6. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₅×#388	C₂	semidirect
9. C₃×C₅×#386	C₂	semidirect
10. C₃×C₅×#385	C₂	semidirect
11. C₃×C₅×#379	C₂	semidirect
12. C₅×#2411	C₃	direct (N × H)
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
37. C₂×C₃×C₄²×C₅	C₂²	semidirect
38. C₃×C₅×#95	C₂²	semidirect
39. C₃×C₅×#95	C₂²	semidirect
40. C₃×#2411	C₅	direct (N × H)
41. C₂×C₅×#123	C₂×C₃	semidirect
43. C₂×C₅×#117	C₂×C₃	semidirect
44. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
45. C₅×#396	C₂×C₃	semidirect
46. C₅×#394	C₂×C₃	semidirect
47. C₅×#390	C₂×C₃	semidirect
48. C₅×#388	C₂×C₃	semidirect
49. C₅×#386	C₂×C₃	semidirect
50. C₅×#385	C₂×C₃	semidirect
51. C₅×#379	C₂×C₃	semidirect
70. C₂²×C₃×C₄×C₅	D₄	semidirect
95. C₂×C₃×#123	C₂×C₅	semidirect
97. C₂×C₃×#117	C₂×C₅	semidirect
98. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
99. C₃×#396	C₂×C₅	semidirect
100. C₃×#394	C₂×C₅	semidirect
101. C₃×#390	C₂×C₅	semidirect
102. C₃×#388	C₂×C₅	semidirect
103. C₃×#386	C₂×C₅	semidirect
104. C₃×#385	C₂×C₅	semidirect
105. C₃×#379	C₂×C₅	semidirect
114. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
115. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
116. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
117. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
127. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
128. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
129. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
130. C₂×C₄²×C₅	C₂²×C₃	semidirect
131. C₅×#95	C₂²×C₃	semidirect
132. C₅×#95	C₂²×C₃	semidirect
133. #2411	C₃×C₅	direct (N × H)
191. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
192. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
193. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
194. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
204. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
205. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
206. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
207. C₂×C₃×C₄²	C₂²×C₅	semidirect
208. C₃×#95	C₂²×C₅	semidirect
209. C₃×#95	C₂²×C₅	semidirect
228. C₂²×C₄×C₅	C₃×D₄	semidirect
253. C₂×#123	C₂×C₃×C₅	semidirect
255. C₂×#117	C₂×C₃×C₅	semidirect
256. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
257. #396	C₂×C₃×C₅	semidirect
258. #394	C₂×C₃×C₅	semidirect
259. #390	C₂×C₃×C₅	semidirect
260. #388	C₂×C₃×C₅	semidirect
261. #386	C₂×C₃×C₅	semidirect
262. #385	C₂×C₃×C₅	semidirect
263. #379	C₂×C₃×C₅	semidirect
313. C₂²×C₃×C₄	C₅×D₄	semidirect
395. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
396. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
397. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
398. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
408. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
409. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
410. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
411. C₂×C₄²	C₂²×C₃×C₅	semidirect
412. #95	C₂²×C₃×C₅	semidirect
413. #95	C₂²×C₃×C₅	semidirect
520. C₂²×C₄	C₃×C₅×D₄	semidirect
545. C₃×C₅	#2411	direct (N × H)
642. C₅	C₃×#2411	direct (N × H)
674. C₃	C₅×#2411	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×#123	2
C₂×C₃×C₅×#120	2
C₂×C₃×C₅×#117	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#379	2
C₅×#2411	3
C₃×#2411	5

Subgroups — C3×C5×#2411 #14275445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2411 #14275445