Subgroups — C₃×C₅×#2684 #14275718

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	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×#394	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#393	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×#379	C₂	1	2	yes	maximal, complemented
10	C₅×#2684	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#124	—	2	4	no	—
17	C₃×C₅×#120	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×#95	C₂²	1	2	yes	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×#2684	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#124	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×#394	C₂×C₃	1	2	yes	complemented
39	C₅×#393	C₂×C₃	1	2	yes	complemented
40	C₅×#388	C₂×C₃	1	2	yes	complemented
41	C₅×#386	C₂×C₃	1	2	yes	complemented
42	C₅×#386	C₂×C₃	1	1	yes	characteristic, 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×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	4	1	no	—
54	C₂×C₃×C₅×Q₈	—	4	1	no	—
55	C₂×C₃×C₅×D₄	—	2	4	no	—
56	C₂×C₃×C₅×D₄	—	2	4	no	—
57	C₂×C₃×C₅×D₄	—	4	1	no	—
58	C₂×C₃×C₅×D₄	—	4	1	no	—
59	C₂×C₃×C₅×D₄	—	4	2	no	—
60	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
61	C₂²×C₃×C₄×C₅	—	4	1	no	—
62	C₂²×C₃×C₄×C₅	—	4	2	no	—
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	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	4	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	1	no	—
80	C₃×C₄²×C₅	—	2	2	no	—
81	C₂×C₃×#124	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×#394	C₂×C₅	1	2	yes	complemented
85	C₃×#393	C₂×C₅	1	2	yes	complemented
86	C₃×#388	C₂×C₅	1	2	yes	complemented
87	C₃×#386	C₂×C₅	1	1	yes	characteristic, 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×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
93	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₅×#124	—	2	4	no	—
96	C₅×#120	—	2	4	no	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
98	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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	complemented
107	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₅×#95	C₂²×C₃	1	2	yes	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	#2684	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	1	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	2	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×Q₈	—	4	4	no	—
138	C₃×C₅×D₄	—	4	4	no	—
139	C₃×C₅×D₄	—	4	8	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	1	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	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	4	4	no	—
158	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
161	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
162	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₃×#124	—	2	4	no	—
165	C₃×#120	—	2	4	no	—
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	2	yes	complemented
176	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, 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	C₃×#95	C₂²×C₅	1	2	yes	complemented
182	C₂⁴×C₅	—	2	2	no	—
183	C₂⁴×C₅	—	2	4	no	—
184	C₂⁴×C₅	—	4	2	no	—
185	C₂⁴×C₅	—	4	1	no	—
186	C₂⁴×C₅	—	4	1	no	—
187	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
190	C₂×C₅×Q₈	—	2	2	no	—
191	C₂×C₅×Q₈	—	4	1	no	—
192	C₂×C₅×Q₈	—	4	1	no	—
193	C₂×C₅×D₄	—	2	4	no	—
194	C₂×C₅×D₄	—	2	4	no	—
195	C₂×C₅×D₄	—	4	1	no	—
196	C₂×C₅×D₄	—	4	1	no	—
197	C₂×C₅×D₄	—	4	2	no	—
198	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
199	C₂²×C₄×C₅	—	4	1	no	—
200	C₂²×C₄×C₅	—	4	2	no	—
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	2	yes	—
204	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
205	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₅×C₄⋊C₄	—	4	2	no	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	2	4	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	C₅×C₂²⋊C₄	—	4	1	no	—
218	C₄²×C₅	—	2	2	no	—
219	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
220	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
221	#397	C₂×C₃×C₅	1	2	yes	complemented
222	#394	C₂×C₃×C₅	1	2	yes	complemented
223	#393	C₂×C₃×C₅	1	2	yes	complemented
224	#388	C₂×C₃×C₅	1	2	yes	complemented
225	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#386	C₂×C₃×C₅	1	2	yes	complemented
227	#379	C₂×C₃×C₅	1	2	yes	complemented
228	C₂²×C₃×C₅	—	2	2	no	—
229	C₂²×C₃×C₅	—	2	2	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	—	2	4	no	—
235	C₂²×C₃×C₅	—	4	16	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	2	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	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
248	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
251	C₃×C₄×C₅	—	2	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	C₃×C₄×C₅	—	4	2	no	—
257	C₂⁴×C₃	—	2	2	no	—
258	C₂⁴×C₃	—	2	4	no	—
259	C₂⁴×C₃	—	4	2	no	—
260	C₂⁴×C₃	—	4	1	no	—
261	C₂⁴×C₃	—	4	1	no	—
262	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
263	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
264	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
265	C₂×C₃×Q₈	—	2	2	no	—
266	C₂×C₃×Q₈	—	4	1	no	—
267	C₂×C₃×Q₈	—	4	1	no	—
268	C₂×C₃×D₄	—	2	4	no	—
269	C₂×C₃×D₄	—	2	4	no	—
270	C₂×C₃×D₄	—	4	1	no	—
271	C₂×C₃×D₄	—	4	1	no	—
272	C₂×C₃×D₄	—	4	2	no	—
273	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
274	C₂²×C₃×C₄	—	4	1	no	—
275	C₂²×C₃×C₄	—	4	2	no	—
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	2	yes	—
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	—	4	2	no	—
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	2	4	no	—
285	C₃×C₂²⋊C₄	—	2	4	no	—
286	C₃×C₂²⋊C₄	—	2	4	no	—
287	C₃×C₂²⋊C₄	—	2	4	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×C₂²⋊C₄	—	4	1	no	—
293	C₃×C₄²	—	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	1	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	2	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	—	2	2	no	—
308	C₂³×C₅	—	4	8	no	—
309	C₂³×C₅	—	4	4	no	—
310	C₂³×C₅	—	4	4	no	—
311	C₂³×C₅	—	4	8	no	—
312	C₂³×C₅	—	4	4	no	—
313	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
314	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
315	C₂³×C₅	C₃×#41	1	4	yes	—
316	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
317	C₅×Q₈	—	4	4	no	—
318	C₅×D₄	—	4	4	no	—
319	C₅×D₄	—	4	8	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	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	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	4	4	no	—
338	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
339	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
340	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
341	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
342	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
344	#124	—	2	4	no	—
345	#120	—	2	4	no	—
346	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
347	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
355	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
356	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
357	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
358	#95	C₂²×C₃×C₅	1	2	yes	complemented
359	#95	C₂²×C₃×C₅	1	2	yes	complemented
360	#95	C₂²×C₃×C₅	1	2	yes	complemented
361	#95	C₂²×C₃×C₅	1	2	yes	complemented
362	C₂×C₃×C₅	—	4	2	no	—
363	C₂×C₃×C₅	—	4	2	no	—
364	C₂×C₃×C₅	—	4	4	no	—
365	C₂×C₃×C₅	#534	1	1	yes	characteristic
366	C₂×C₃×C₅	#538	1	2	yes	—
367	C₂×C₃×C₅	#546	1	2	yes	—
368	C₂×C₃×C₅	#551	1	1	yes	characteristic
369	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
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	1	no	—
375	C₂³×C₃	—	2	2	no	—
376	C₂³×C₃	—	2	2	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	2	1	no	—
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	4	8	no	—
385	C₂³×C₃	—	4	4	no	—
386	C₂³×C₃	—	4	4	no	—
387	C₂³×C₃	—	4	8	no	—
388	C₂³×C₃	—	4	4	no	—
389	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
390	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
391	C₂³×C₃	C₅×#41	1	4	yes	—
392	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
393	C₃×Q₈	—	4	4	no	—
394	C₃×D₄	—	4	4	no	—
395	C₃×D₄	—	4	8	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	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	—	2	2	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	4	4	no	—
414	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	4	no	—
418	C₂²×C₅	—	2	4	no	—
419	C₂²×C₅	—	2	4	no	—
420	C₂²×C₅	—	2	4	no	—
421	C₂²×C₅	—	2	4	no	—
422	C₂²×C₅	—	4	16	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	—	4	2	no	—
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	—	4	2	no	—
429	C₂²×C₅	—	4	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
434	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
435	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
437	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	4	2	no	—
440	C₄×C₅	—	4	2	no	—
441	C₄×C₅	—	4	2	no	—
442	C₄×C₅	—	4	2	no	—
443	C₄×C₅	—	4	2	no	—
444	C₂⁴	—	2	2	no	—
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	4	2	no	—
447	C₂⁴	—	4	1	no	—
448	C₂⁴	—	4	1	no	—
449	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
450	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	4	1	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
464	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
465	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
466	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
467	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
468	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
469	C₄⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₄²	—	2	2	no	—
481	C₃×C₅	#2684	1	1	yes	characteristic, direct product factor, Hall
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	4	no	—
485	C₂²×C₃	—	2	4	no	—
486	C₂²×C₃	—	2	4	no	—
487	C₂²×C₃	—	2	4	no	—
488	C₂²×C₃	—	2	4	no	—
489	C₂²×C₃	—	4	16	no	—
490	C₂²×C₃	—	4	2	no	—
491	C₂²×C₃	—	4	2	no	—
492	C₂²×C₃	—	4	2	no	—
493	C₂²×C₃	—	4	2	no	—
494	C₂²×C₃	—	4	2	no	—
495	C₂²×C₃	—	4	1	no	—
496	C₂²×C₃	—	4	1	no	—
497	C₂²×C₃	—	4	1	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	4	2	no	—
500	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
501	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
502	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	4	2	no	—
507	C₃×C₄	—	4	2	no	—
508	C₃×C₄	—	4	2	no	—
509	C₃×C₄	—	4	2	no	—
510	C₃×C₄	—	4	2	no	—
511	C₂×C₅	—	4	2	no	—
512	C₂×C₅	—	4	4	no	—
513	C₂×C₅	—	4	2	no	—
514	C₂×C₅	C₃×#534	1	1	yes	characteristic
515	C₂×C₅	C₃×#538	1	2	yes	—
516	C₂×C₅	C₃×#546	1	2	yes	—
517	C₂×C₅	C₃×#551	1	1	yes	characteristic
518	C₂×C₅	C₃×H(3,𝔽₄)	1	1	yes	characteristic
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	8	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	4	8	no	—
537	C₂³	—	4	4	no	—
538	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
539	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
540	C₂³	C₃×C₅×#41	1	4	yes	—
541	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
542	Q₈	—	4	4	no	—
543	D₄	—	4	4	no	—
544	D₄	—	4	8	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	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	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
564	C₂×C₃	—	4	2	no	—
565	C₂×C₃	—	4	4	no	—
566	C₂×C₃	—	4	2	no	—
567	C₂×C₃	C₅×#534	1	1	yes	characteristic
568	C₂×C₃	C₅×#538	1	2	yes	—
569	C₂×C₃	C₅×#546	1	2	yes	—
570	C₂×C₃	C₅×#551	1	1	yes	characteristic
571	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
572	C₅	C₃×#2684	1	1	yes	characteristic, direct product factor, Sylow
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	2	no	—
591	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
592	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
593	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
596	C₄	—	2	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₃	C₅×#2684	1	1	yes	characteristic, direct product factor, Sylow
603	C₂	—	4	2	no	—
604	C₂	—	4	4	no	—
605	C₂	—	4	2	no	—
606	C₂	C₃×C₅×#534	1	1	yes	characteristic
607	C₂	C₃×C₅×#538	1	2	yes	—
608	C₂	C₃×C₅×#546	1	2	yes	—
609	C₂	C₃×C₅×#551	1	1	yes	characteristic
610	C₂	C₃×C₅×H(3,𝔽₄)	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×#124	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#393	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#386	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#379	C₂	semidirect
10. C₅×#2684	C₃	direct (N × H)
12. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂³×C₃×C₄×C₅	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
27. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₄²×C₅	C₂²	semidirect
30. C₃×C₅×#95	C₂²	semidirect
31. C₃×C₅×#95	C₂²	semidirect
32. C₃×C₅×#95	C₂²	semidirect
33. C₃×C₅×#95	C₂²	semidirect
34. C₃×#2684	C₅	direct (N × H)
35. C₂×C₅×#124	C₂×C₃	semidirect
37. C₅×#397	C₂×C₃	semidirect
38. C₅×#394	C₂×C₃	semidirect
39. C₅×#393	C₂×C₃	semidirect
40. C₅×#388	C₂×C₃	semidirect
41. C₅×#386	C₂×C₃	semidirect
42. C₅×#386	C₂×C₃	semidirect
43. C₅×#379	C₂×C₃	semidirect
81. C₂×C₃×#124	C₂×C₅	semidirect
83. C₃×#397	C₂×C₅	semidirect
84. C₃×#394	C₂×C₅	semidirect
85. C₃×#393	C₂×C₅	semidirect
86. C₃×#388	C₂×C₅	semidirect
87. C₃×#386	C₂×C₅	semidirect
88. C₃×#386	C₂×C₅	semidirect
89. C₃×#379	C₂×C₅	semidirect
91. C₂²×C₅×Q₈	C₂²×C₃	semidirect
94. C₂³×C₄×C₅	C₂²×C₃	semidirect
97. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
106. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
107. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
108. C₂×C₄²×C₅	C₂²×C₃	semidirect
109. C₅×#95	C₂²×C₃	semidirect
110. C₅×#95	C₂²×C₃	semidirect
111. C₅×#95	C₂²×C₃	semidirect
112. C₅×#95	C₂²×C₃	semidirect
113. #2684	C₃×C₅	direct (N × H)
160. C₂²×C₃×Q₈	C₂²×C₅	semidirect
163. C₂³×C₃×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
181. C₃×#95	C₂²×C₅	semidirect
219. C₂×#124	C₂×C₃×C₅	semidirect
221. #397	C₂×C₃×C₅	semidirect
222. #394	C₂×C₃×C₅	semidirect
223. #393	C₂×C₃×C₅	semidirect
224. #388	C₂×C₃×C₅	semidirect
225. #386	C₂×C₃×C₅	semidirect
226. #386	C₂×C₃×C₅	semidirect
227. #379	C₂×C₃×C₅	semidirect
340. C₂²×Q₈	C₂²×C₃×C₅	semidirect
343. C₂³×C₄	C₂²×C₃×C₅	semidirect
346. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
355. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
356. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
357. C₂×C₄²	C₂²×C₃×C₅	semidirect
358. #95	C₂²×C₃×C₅	semidirect
359. #95	C₂²×C₃×C₅	semidirect
360. #95	C₂²×C₃×C₅	semidirect
361. #95	C₂²×C₃×C₅	semidirect
481. C₃×C₅	#2684	direct (N × H)
572. C₅	C₃×#2684	direct (N × H)
602. C₃	C₅×#2684	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×#124	2
C₂×C₃×C₅×#120	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#379	2
C₅×#2684	3
C₃×#2684	5

Subgroups — C3×C5×#2684 #14275718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2684 #14275718