Subgroups — C₃×C₅×#2697 #14275731

Order 1920.

1360 conjugacy classes of subgroups.

The subgroup lattice has 608 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	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#396	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#379	C₂	1	2	yes	maximal, complemented
10	C₅×#2697	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#123	—	2	4	no	—
16	C₃×C₅×#120	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#95	C₂²	1	2	yes	complemented
32	C₃×C₅×#95	C₂²	1	2	yes	complemented
33	C₃×C₅×#95	C₂²	1	2	yes	complemented
34	C₃×#2697	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
37	C₅×#397	C₂×C₃	1	2	yes	complemented
38	C₅×#396	C₂×C₃	1	2	yes	complemented
39	C₅×#394	C₂×C₃	1	2	yes	complemented
40	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#388	C₂×C₃	1	2	yes	complemented
42	C₅×#386	C₂×C₃	1	2	yes	complemented
43	C₅×#379	C₂×C₃	1	2	yes	complemented
44	C₂⁴×C₃×C₅	—	2	2	no	—
45	C₂⁴×C₃×C₅	—	2	4	no	—
46	C₂⁴×C₃×C₅	—	4	2	no	—
47	C₂⁴×C₃×C₅	—	4	1	no	—
48	C₂⁴×C₃×C₅	—	4	1	no	—
49	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	—	2	4	no	—
53	C₂×C₃×C₅×D₄	—	2	4	no	—
54	C₂×C₃×C₅×D₄	—	4	1	no	—
55	C₂×C₃×C₅×D₄	—	4	1	no	—
56	C₂×C₃×C₅×D₄	—	4	2	no	—
57	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	—	4	1	no	—
60	C₂²×C₃×C₄×C₅	—	4	1	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	4	no	—
68	C₃×C₅×C₄⋊C₄	—	4	1	no	—
69	C₃×C₅×C₄⋊C₄	—	4	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
79	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
80	C₃×C₄²×C₅	—	4	1	no	—
81	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
83	C₃×#397	C₂×C₅	1	2	yes	complemented
84	C₃×#396	C₂×C₅	1	2	yes	complemented
85	C₃×#394	C₂×C₅	1	2	yes	complemented
86	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#388	C₂×C₅	1	2	yes	complemented
88	C₃×#386	C₂×C₅	1	2	yes	complemented
89	C₃×#379	C₂×C₅	1	2	yes	complemented
90	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₅×#123	—	2	4	no	—
95	C₅×#120	—	2	4	no	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
99	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₅×C₂²⋊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	2	yes	—
106	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
109	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×#95	C₂²×C₃	1	2	yes	complemented
111	C₅×#95	C₂²×C₃	1	2	yes	complemented
112	C₅×#95	C₂²×C₃	1	2	yes	complemented
113	#2697	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	—	2	2	no	—
123	C₂³×C₃×C₅	—	2	1	no	—
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂³×C₃×C₅	—	4	8	no	—
129	C₂³×C₃×C₅	—	4	4	no	—
130	C₂³×C₃×C₅	—	4	4	no	—
131	C₂³×C₃×C₅	—	4	8	no	—
132	C₂³×C₃×C₅	—	4	4	no	—
133	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
134	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
135	C₂³×C₃×C₅	#41	1	4	yes	—
136	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
137	C₃×C₅×D₄	—	4	4	no	—
138	C₃×C₅×D₄	—	4	8	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	1	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	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	4	4	no	—
157	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
159	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
160	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₃×#123	—	2	4	no	—
163	C₃×#120	—	2	4	no	—
164	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
165	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
166	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
167	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
177	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₃×#95	C₂²×C₅	1	2	yes	complemented
179	C₃×#95	C₂²×C₅	1	2	yes	complemented
180	C₃×#95	C₂²×C₅	1	2	yes	complemented
181	C₂⁴×C₅	—	2	2	no	—
182	C₂⁴×C₅	—	2	4	no	—
183	C₂⁴×C₅	—	4	2	no	—
184	C₂⁴×C₅	—	4	1	no	—
185	C₂⁴×C₅	—	4	1	no	—
186	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
189	C₂×C₅×D₄	—	2	4	no	—
190	C₂×C₅×D₄	—	2	4	no	—
191	C₂×C₅×D₄	—	4	1	no	—
192	C₂×C₅×D₄	—	4	1	no	—
193	C₂×C₅×D₄	—	4	2	no	—
194	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	4	1	no	—
197	C₂²×C₄×C₅	—	4	1	no	—
198	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
200	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
201	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
202	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
203	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	—	2	4	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	—	4	2	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	4	2	no	—
213	C₅×C₂²⋊C₄	—	4	2	no	—
214	C₅×C₂²⋊C₄	—	4	2	no	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₅×C₂²⋊C₄	—	4	2	no	—
217	C₄²×C₅	—	4	1	no	—
218	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
219	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
220	#397	C₂×C₃×C₅	1	2	yes	complemented
221	#396	C₂×C₃×C₅	1	2	yes	complemented
222	#394	C₂×C₃×C₅	1	2	yes	complemented
223	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	#388	C₂×C₃×C₅	1	2	yes	complemented
225	#386	C₂×C₃×C₅	1	2	yes	complemented
226	#379	C₂×C₃×C₅	1	2	yes	complemented
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	—	2	2	no	—
229	C₂²×C₃×C₅	—	2	4	no	—
230	C₂²×C₃×C₅	—	2	4	no	—
231	C₂²×C₃×C₅	—	2	4	no	—
232	C₂²×C₃×C₅	—	2	4	no	—
233	C₂²×C₃×C₅	—	2	4	no	—
234	C₂²×C₃×C₅	—	4	16	no	—
235	C₂²×C₃×C₅	—	4	2	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	2	no	—
239	C₂²×C₃×C₅	—	4	2	no	—
240	C₂²×C₃×C₅	—	4	1	no	—
241	C₂²×C₃×C₅	—	4	1	no	—
242	C₂²×C₃×C₅	—	4	1	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	2	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
247	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	—	4	2	no	—
254	C₃×C₄×C₅	—	4	2	no	—
255	C₃×C₄×C₅	—	4	2	no	—
256	C₂⁴×C₃	—	2	2	no	—
257	C₂⁴×C₃	—	2	4	no	—
258	C₂⁴×C₃	—	4	2	no	—
259	C₂⁴×C₃	—	4	1	no	—
260	C₂⁴×C₃	—	4	1	no	—
261	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
262	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
263	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
264	C₂×C₃×D₄	—	2	4	no	—
265	C₂×C₃×D₄	—	2	4	no	—
266	C₂×C₃×D₄	—	4	1	no	—
267	C₂×C₃×D₄	—	4	1	no	—
268	C₂×C₃×D₄	—	4	2	no	—
269	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
270	C₂²×C₃×C₄	—	2	2	no	—
271	C₂²×C₃×C₄	—	4	1	no	—
272	C₂²×C₃×C₄	—	4	1	no	—
273	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
274	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
278	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₄⋊C₄	—	2	4	no	—
280	C₃×C₄⋊C₄	—	4	1	no	—
281	C₃×C₄⋊C₄	—	4	2	no	—
282	C₃×C₂²⋊C₄	—	2	2	no	—
283	C₃×C₂²⋊C₄	—	2	4	no	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₂²⋊C₄	—	2	4	no	—
286	C₃×C₂²⋊C₄	—	2	4	no	—
287	C₃×C₂²⋊C₄	—	4	2	no	—
288	C₃×C₂²⋊C₄	—	4	2	no	—
289	C₃×C₂²⋊C₄	—	4	2	no	—
290	C₃×C₂²⋊C₄	—	4	2	no	—
291	C₃×C₂²⋊C₄	—	4	2	no	—
292	C₃×C₄²	—	4	1	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	2	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	4	8	no	—
308	C₂³×C₅	—	4	4	no	—
309	C₂³×C₅	—	4	4	no	—
310	C₂³×C₅	—	4	8	no	—
311	C₂³×C₅	—	4	4	no	—
312	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
313	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
314	C₂³×C₅	C₃×#41	1	4	yes	—
315	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
316	C₅×D₄	—	4	4	no	—
317	C₅×D₄	—	4	8	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	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	4	4	no	—
336	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
337	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
338	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
339	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
340	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
341	#123	—	2	4	no	—
342	#120	—	2	4	no	—
343	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
344	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
345	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
346	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
355	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
356	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
357	#95	C₂²×C₃×C₅	1	2	yes	complemented
358	#95	C₂²×C₃×C₅	1	2	yes	complemented
359	#95	C₂²×C₃×C₅	1	2	yes	complemented
360	C₂×C₃×C₅	—	4	2	no	—
361	C₂×C₃×C₅	—	4	2	no	—
362	C₂×C₃×C₅	—	4	4	no	—
363	C₂×C₃×C₅	#534	1	1	yes	characteristic
364	C₂×C₃×C₅	#538	1	2	yes	—
365	C₂×C₃×C₅	#546	1	2	yes	—
366	C₂×C₃×C₅	#551	1	1	yes	characteristic
367	C₂×C₃×C₅	#560	1	1	yes	characteristic
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	—	2	2	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	2	2	no	—
376	C₂³×C₃	—	2	2	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	—	2	2	no	—
382	C₂³×C₃	—	4	8	no	—
383	C₂³×C₃	—	4	4	no	—
384	C₂³×C₃	—	4	4	no	—
385	C₂³×C₃	—	4	8	no	—
386	C₂³×C₃	—	4	4	no	—
387	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
388	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
389	C₂³×C₃	C₅×#41	1	4	yes	—
390	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
391	C₃×D₄	—	4	4	no	—
392	C₃×D₄	—	4	8	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	4	4	no	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	4	no	—
415	C₂²×C₅	—	2	4	no	—
416	C₂²×C₅	—	2	4	no	—
417	C₂²×C₅	—	2	4	no	—
418	C₂²×C₅	—	2	4	no	—
419	C₂²×C₅	—	4	16	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	2	no	—
423	C₂²×C₅	—	4	2	no	—
424	C₂²×C₅	—	4	2	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	—	4	2	no	—
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
431	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
432	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	4	2	no	—
440	C₄×C₅	—	4	2	no	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	4	2	no	—
444	C₂⁴	—	4	1	no	—
445	C₂⁴	—	4	1	no	—
446	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
447	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
448	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
459	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
460	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
461	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
462	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
463	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₄²	—	4	1	no	—
478	C₃×C₅	#2697	1	1	yes	characteristic, direct product factor, Hall
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	4	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	4	no	—
484	C₂²×C₃	—	2	4	no	—
485	C₂²×C₃	—	2	4	no	—
486	C₂²×C₃	—	4	16	no	—
487	C₂²×C₃	—	4	2	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	4	2	no	—
490	C₂²×C₃	—	4	2	no	—
491	C₂²×C₃	—	4	2	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	1	no	—
496	C₂²×C₃	—	4	2	no	—
497	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
499	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	4	2	no	—
504	C₃×C₄	—	4	2	no	—
505	C₃×C₄	—	4	2	no	—
506	C₃×C₄	—	4	2	no	—
507	C₃×C₄	—	4	2	no	—
508	C₂×C₅	—	4	2	no	—
509	C₂×C₅	—	4	4	no	—
510	C₂×C₅	—	4	2	no	—
511	C₂×C₅	C₃×#534	1	1	yes	characteristic
512	C₂×C₅	C₃×#538	1	2	yes	—
513	C₂×C₅	C₃×#546	1	2	yes	—
514	C₂×C₅	C₃×#551	1	1	yes	characteristic
515	C₂×C₅	C₃×#560	1	1	yes	characteristic
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	4	8	no	—
531	C₂³	—	4	4	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	4	8	no	—
534	C₂³	—	4	4	no	—
535	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
536	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
537	C₂³	C₃×C₅×#41	1	4	yes	—
538	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
539	D₄	—	4	4	no	—
540	D₄	—	4	8	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
560	C₂×C₃	—	4	2	no	—
561	C₂×C₃	—	4	4	no	—
562	C₂×C₃	—	4	2	no	—
563	C₂×C₃	C₅×#534	1	1	yes	characteristic
564	C₂×C₃	C₅×#538	1	2	yes	—
565	C₂×C₃	C₅×#546	1	2	yes	—
566	C₂×C₃	C₅×#551	1	1	yes	characteristic
567	C₂×C₃	C₅×#560	1	1	yes	characteristic
568	C₅	C₃×#2697	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	4	16	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
588	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
589	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
592	C₄	—	2	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₃	C₅×#2697	1	1	yes	characteristic, direct product factor, Sylow
599	C₂	—	4	2	no	—
600	C₂	—	4	4	no	—
601	C₂	—	4	2	no	—
602	C₂	C₃×C₅×#534	1	1	yes	characteristic
603	C₂	C₃×C₅×#538	1	2	yes	—
604	C₂	C₃×C₅×#546	1	2	yes	—
605	C₂	C₃×C₅×#551	1	1	yes	characteristic
606	C₂	C₃×C₅×#560	1	1	yes	characteristic

	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. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#396	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#379	C₂	semidirect
10. C₅×#2697	C₃	direct (N × H)
14. C₂³×C₃×C₄×C₅	C₂²	semidirect
17. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
30. C₂×C₃×C₄²×C₅	C₂²	semidirect
31. C₃×C₅×#95	C₂²	semidirect
32. C₃×C₅×#95	C₂²	semidirect
33. C₃×C₅×#95	C₂²	semidirect
34. C₃×#2697	C₅	direct (N × H)
35. C₂×C₅×#123	C₂×C₃	semidirect
37. C₅×#397	C₂×C₃	semidirect
38. C₅×#396	C₂×C₃	semidirect
39. C₅×#394	C₂×C₃	semidirect
40. C₅×#390	C₂×C₃	semidirect
41. C₅×#388	C₂×C₃	semidirect
42. C₅×#386	C₂×C₃	semidirect
43. C₅×#379	C₂×C₃	semidirect
81. C₂×C₃×#123	C₂×C₅	semidirect
83. C₃×#397	C₂×C₅	semidirect
84. C₃×#396	C₂×C₅	semidirect
85. C₃×#394	C₂×C₅	semidirect
86. C₃×#390	C₂×C₅	semidirect
87. C₃×#388	C₂×C₅	semidirect
88. C₃×#386	C₂×C₅	semidirect
89. C₃×#379	C₂×C₅	semidirect
93. C₂³×C₄×C₅	C₂²×C₃	semidirect
96. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
97. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
98. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
107. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
108. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
109. C₂×C₄²×C₅	C₂²×C₃	semidirect
110. C₅×#95	C₂²×C₃	semidirect
111. C₅×#95	C₂²×C₃	semidirect
112. C₅×#95	C₂²×C₃	semidirect
113. #2697	C₃×C₅	direct (N × H)
161. C₂³×C₃×C₄	C₂²×C₅	semidirect
164. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
165. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
166. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
175. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
176. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
177. C₂×C₃×C₄²	C₂²×C₅	semidirect
178. C₃×#95	C₂²×C₅	semidirect
179. C₃×#95	C₂²×C₅	semidirect
180. C₃×#95	C₂²×C₅	semidirect
218. C₂×#123	C₂×C₃×C₅	semidirect
220. #397	C₂×C₃×C₅	semidirect
221. #396	C₂×C₃×C₅	semidirect
222. #394	C₂×C₃×C₅	semidirect
223. #390	C₂×C₃×C₅	semidirect
224. #388	C₂×C₃×C₅	semidirect
225. #386	C₂×C₃×C₅	semidirect
226. #379	C₂×C₃×C₅	semidirect
340. C₂³×C₄	C₂²×C₃×C₅	semidirect
343. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
344. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
345. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
354. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
355. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
356. C₂×C₄²	C₂²×C₃×C₅	semidirect
357. #95	C₂²×C₃×C₅	semidirect
358. #95	C₂²×C₃×C₅	semidirect
359. #95	C₂²×C₃×C₅	semidirect
478. C₃×C₅	#2697	direct (N × H)
568. C₅	C₃×#2697	direct (N × H)
598. C₃	C₅×#2697	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
C₃×C₅×#397	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#379	2
C₅×#2697	3
C₃×#2697	5

Subgroups — C3×C5×#2697 #14275731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2697 #14275731