Subgroups — C₃×C₅×#546 #11756635

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#120	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₅×#546	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×C₅	C₂²	1	2	yes	—
14	C₃×C₅×#41	—	2	4	no	—
15	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₄	—	2	4	no	—
17	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×D₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	complemented
25	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	complemented
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
34	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
38	C₃×#546	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂²×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#123	C₂×C₃	1	2	yes	complemented
43	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#121	C₂×C₃	1	2	yes	complemented
46	C₅×#120	C₂×C₃	1	2	yes	complemented
47	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
50	C₂³×C₃×C₅	—	2	4	no	—
51	C₂³×C₃×C₅	—	2	4	no	—
52	C₂³×C₃×C₅	—	4	2	no	—
53	C₂³×C₃×C₅	C₂³	1	2	yes	—
54	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂³×C₃×C₅	C₂³	1	2	yes	—
56	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×Q₈	—	2	2	no	—
58	C₃×C₅×D₄	—	2	4	no	—
59	C₃×C₅×D₄	—	2	4	no	—
60	C₃×C₅×D₄	—	2	2	no	—
61	C₃×C₅×D₄	—	2	2	no	—
62	C₃×C₅×D₄	—	4	2	no	—
63	C₃×C₅×D₄	D₄	1	4	yes	complemented
64	C₂×C₃×C₄×C₅	—	2	4	no	—
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	—	2	2	no	—
67	C₂×C₃×C₄×C₅	—	4	2	no	—
68	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
71	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×#123	C₂×C₅	1	2	yes	complemented
79	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#121	C₂×C₅	1	2	yes	complemented
82	C₃×#120	C₂×C₅	1	2	yes	complemented
83	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
86	C₂⁴×C₅	C₂²×C₃	1	2	yes	—
87	C₅×#41	—	2	4	no	—
88	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂×C₅×D₄	—	2	4	no	—
90	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×D₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×D₄	C₂²×C₃	1	2	yes	complemented
95	C₂×C₅×D₄	C₂²×C₃	1	2	yes	complemented
96	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	complemented
98	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	complemented
100	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
103	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
106	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
107	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
108	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
110	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
111	#546	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
112	C₂²×C₃×C₅	—	2	1	no	—
113	C₂²×C₃×C₅	—	2	2	no	—
114	C₂²×C₃×C₅	—	2	2	no	—
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	—	2	2	no	—
118	C₂²×C₃×C₅	—	2	1	no	—
119	C₂²×C₃×C₅	—	2	2	no	—
120	C₂²×C₃×C₅	—	2	1	no	—
121	C₂²×C₃×C₅	—	2	2	no	—
122	C₂²×C₃×C₅	—	4	8	no	—
123	C₂²×C₃×C₅	C₂×D₄	1	4	yes	—
124	C₂²×C₃×C₅	#41	1	2	yes	complemented
125	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
126	C₃×C₄×C₅	—	2	1	no	—
127	C₃×C₄×C₅	—	2	1	no	—
128	C₃×C₄×C₅	—	2	2	no	—
129	C₃×C₄×C₅	—	2	1	no	—
130	C₃×C₄×C₅	—	2	1	no	—
131	C₃×C₄×C₅	—	2	2	no	—
132	C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂⁴×C₃	C₂²×C₅	1	2	yes	—
134	C₃×#41	—	2	4	no	—
135	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₂×C₃×D₄	—	2	4	no	—
137	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×D₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
142	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
143	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	complemented
145	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
146	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	complemented
147	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
150	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
152	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
153	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
154	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
155	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
156	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
157	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₂³×C₅	—	2	4	no	—
159	C₂³×C₅	—	2	4	no	—
160	C₂³×C₅	—	4	2	no	—
161	C₂³×C₅	C₂³×C₃	1	2	yes	—
162	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂³×C₅	C₂³×C₃	1	2	yes	—
164	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₅×Q₈	—	2	2	no	—
166	C₅×D₄	—	2	4	no	—
167	C₅×D₄	—	2	4	no	—
168	C₅×D₄	—	2	2	no	—
169	C₅×D₄	—	2	2	no	—
170	C₅×D₄	—	4	2	no	—
171	C₅×D₄	C₃×D₄	1	4	yes	complemented
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	4	2	no	—
176	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
179	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	C₂²×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
186	#123	C₂×C₃×C₅	1	2	yes	complemented
187	C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
188	#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
189	#121	C₂×C₃×C₅	1	2	yes	complemented
190	#120	C₂×C₃×C₅	1	2	yes	complemented
191	C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
193	C₂×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
194	C₂×C₃×C₅	—	2	2	no	—
195	C₂×C₃×C₅	—	2	4	no	—
196	C₂×C₃×C₅	—	4	1	no	—
197	C₂×C₃×C₅	—	4	2	no	—
198	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
200	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂³×C₃	—	2	4	no	—
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	—	4	2	no	—
204	C₂³×C₃	C₂³×C₅	1	2	yes	—
205	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
206	C₂³×C₃	C₂³×C₅	1	2	yes	—
207	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
208	C₃×Q₈	—	2	2	no	—
209	C₃×D₄	—	2	4	no	—
210	C₃×D₄	—	2	4	no	—
211	C₃×D₄	—	2	2	no	—
212	C₃×D₄	—	2	2	no	—
213	C₃×D₄	—	4	2	no	—
214	C₃×D₄	C₅×D₄	1	4	yes	complemented
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	4	2	no	—
219	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	2	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	2	no	—
234	C₂²×C₅	—	2	1	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	4	8	no	—
237	C₂²×C₅	C₂×C₃×D₄	1	4	yes	—
238	C₂²×C₅	C₃×#41	1	2	yes	complemented
239	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	2	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	2	2	no	—
246	C₄×C₅	C₂×C₃×D₄	1	2	yes	—
247	C₂⁴	C₂²×C₃×C₅	1	2	yes	—
248	#41	—	2	4	no	—
249	C₂×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂×D₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂×D₄	C₂²×C₃×C₅	1	2	yes	complemented
256	C₂×D₄	C₂²×C₃×C₅	1	2	yes	complemented
257	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	complemented
259	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
260	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	complemented
261	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
262	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
263	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
264	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
266	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
267	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
268	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
269	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
270	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
271	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
272	C₃×C₅	#546	1	1	yes	characteristic, direct product factor, Hall
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	2	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	4	8	no	—
284	C₂²×C₃	C₂×C₅×D₄	1	4	yes	—
285	C₂²×C₃	C₅×#41	1	2	yes	complemented
286	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₅	—	2	2	no	—
295	C₂×C₅	—	2	4	no	—
296	C₂×C₅	—	4	2	no	—
297	C₂×C₅	—	4	1	no	—
298	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
299	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
300	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	2	no	—
304	C₂³	C₂³×C₃×C₅	1	2	yes	—
305	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
306	C₂³	C₂³×C₃×C₅	1	2	yes	—
307	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	2	4	no	—
311	D₄	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	4	2	no	—
314	D₄	C₃×C₅×D₄	1	4	yes	complemented
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
320	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
321	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
322	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
323	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
324	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
325	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	—	2	4	no	—
328	C₂×C₃	—	4	2	no	—
329	C₂×C₃	—	4	1	no	—
330	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
331	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
332	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
333	C₅	C₃×#546	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²	—	2	1	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	8	no	—
345	C₂²	C₂×C₃×C₅×D₄	1	4	yes	—
346	C₂²	C₃×C₅×#41	1	2	yes	complemented
347	C₂²	C₂⁴×C₃×C₅	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	C₂×C₃×C₅×D₄	1	2	yes	—
355	C₃	C₅×#546	1	1	yes	characteristic, direct product factor, Sylow
356	C₂	—	2	2	no	—
357	C₂	—	2	4	no	—
358	C₂	—	4	2	no	—
359	C₂	—	4	1	no	—
360	C₂	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
361	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
362	C₂	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₃×C₅×D₄	C₂	semidirect
3. C₃×C₅×#124	C₂	semidirect
4. C₃×C₅×#123	C₂	semidirect
5. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
6. C₃×C₅×#121	C₂	semidirect
7. C₃×C₅×#121	C₂	semidirect
8. C₃×C₅×#120	C₂	semidirect
9. C₃×C₄×C₅×D₄	C₂	semidirect
10. C₃×C₄×C₅×D₄	C₂	semidirect
11. C₂×C₃×C₅×C₂²⋊C₄	C₂	semidirect
12. C₅×#546	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₈	C₂²	semidirect
21. C₂×C₃×C₅×D₄	C₂²	semidirect
22. C₂×C₃×C₅×D₄	C₂²	semidirect
24. C₂²×C₃×C₄×C₅	C₂²	semidirect
25. C₂²×C₃×C₄×C₅	C₂²	semidirect
26. C₂²×C₃×C₄×C₅	C₂²	semidirect
27. C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₃×C₅×C₄⋊C₄	C₂²	semidirect
29. C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
37. C₃×C₄²×C₅	C₂²	semidirect
38. C₃×#546	C₅	direct (N × H)
39. C₂×C₅×#41	C₂×C₃	semidirect
40. C₂²×C₅×D₄	C₂×C₃	semidirect
41. C₅×#124	C₂×C₃	semidirect
42. C₅×#123	C₂×C₃	semidirect
43. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
44. C₅×#121	C₂×C₃	semidirect
45. C₅×#121	C₂×C₃	semidirect
46. C₅×#120	C₂×C₃	semidirect
47. C₄×C₅×D₄	C₂×C₃	semidirect
48. C₄×C₅×D₄	C₂×C₃	semidirect
49. C₂×C₅×C₂²⋊C₄	C₂×C₃	semidirect
63. C₃×C₅×D₄	D₄	semidirect
75. C₂×C₃×#41	C₂×C₅	semidirect
76. C₂²×C₃×D₄	C₂×C₅	semidirect
77. C₃×#124	C₂×C₅	semidirect
78. C₃×#123	C₂×C₅	semidirect
79. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
80. C₃×#121	C₂×C₅	semidirect
81. C₃×#121	C₂×C₅	semidirect
82. C₃×#120	C₂×C₅	semidirect
83. C₃×C₄×D₄	C₂×C₅	semidirect
84. C₃×C₄×D₄	C₂×C₅	semidirect
85. C₂×C₃×C₂²⋊C₄	C₂×C₅	semidirect
88. C₂×C₅×Q₈	C₂²×C₃	semidirect
94. C₂×C₅×D₄	C₂²×C₃	semidirect
95. C₂×C₅×D₄	C₂²×C₃	semidirect
97. C₂²×C₄×C₅	C₂²×C₃	semidirect
98. C₂²×C₄×C₅	C₂²×C₃	semidirect
99. C₂²×C₄×C₅	C₂²×C₃	semidirect
100. C₅×C₄⋊C₄	C₂²×C₃	semidirect
101. C₅×C₄⋊C₄	C₂²×C₃	semidirect
102. C₅×C₄⋊C₄	C₂²×C₃	semidirect
105. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
106. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
107. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
108. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
109. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
110. C₄²×C₅	C₂²×C₃	semidirect
111. #546	C₃×C₅	direct (N × H)
124. C₂²×C₃×C₅	#41	semidirect
135. C₂×C₃×Q₈	C₂²×C₅	semidirect
141. C₂×C₃×D₄	C₂²×C₅	semidirect
142. C₂×C₃×D₄	C₂²×C₅	semidirect
144. C₂²×C₃×C₄	C₂²×C₅	semidirect
145. C₂²×C₃×C₄	C₂²×C₅	semidirect
146. C₂²×C₃×C₄	C₂²×C₅	semidirect
147. C₃×C₄⋊C₄	C₂²×C₅	semidirect
148. C₃×C₄⋊C₄	C₂²×C₅	semidirect
149. C₃×C₄⋊C₄	C₂²×C₅	semidirect
152. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
153. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
154. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
155. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
156. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
157. C₃×C₄²	C₂²×C₅	semidirect
171. C₅×D₄	C₃×D₄	semidirect
183. C₂×#41	C₂×C₃×C₅	semidirect
184. C₂²×D₄	C₂×C₃×C₅	semidirect
185. #124	C₂×C₃×C₅	semidirect
186. #123	C₂×C₃×C₅	semidirect
187. C₂²⋊Q₈	C₂×C₃×C₅	semidirect
188. #121	C₂×C₃×C₅	semidirect
189. #121	C₂×C₃×C₅	semidirect
190. #120	C₂×C₃×C₅	semidirect
191. C₄×D₄	C₂×C₃×C₅	semidirect
192. C₄×D₄	C₂×C₃×C₅	semidirect
193. C₂×C₂²⋊C₄	C₂×C₃×C₅	semidirect
214. C₃×D₄	C₅×D₄	semidirect
238. C₂²×C₅	C₃×#41	semidirect
249. C₂×Q₈	C₂²×C₃×C₅	semidirect
255. C₂×D₄	C₂²×C₃×C₅	semidirect
256. C₂×D₄	C₂²×C₃×C₅	semidirect
258. C₂²×C₄	C₂²×C₃×C₅	semidirect
259. C₂²×C₄	C₂²×C₃×C₅	semidirect
260. C₂²×C₄	C₂²×C₃×C₅	semidirect
261. C₄⋊C₄	C₂²×C₃×C₅	semidirect
262. C₄⋊C₄	C₂²×C₃×C₅	semidirect
263. C₄⋊C₄	C₂²×C₃×C₅	semidirect
266. C₂²⋊C₄	C₂²×C₃×C₅	semidirect
267. C₂²⋊C₄	C₂²×C₃×C₅	semidirect
268. C₂²⋊C₄	C₂²×C₃×C₅	semidirect
269. C₂²⋊C₄	C₂²×C₃×C₅	semidirect
270. C₂²⋊C₄	C₂²×C₃×C₅	semidirect
271. C₄²	C₂²×C₃×C₅	semidirect
272. C₃×C₅	#546	direct (N × H)
285. C₂²×C₃	C₅×#41	semidirect
314. D₄	C₃×C₅×D₄	semidirect
333. C₅	C₃×#546	direct (N × H)
346. C₂²	C₃×C₅×#41	semidirect
355. C₃	C₅×#546	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×#41	2
C₂²×C₃×C₅×D₄	2
C₃×C₅×#124	2
C₃×C₅×#123	2
C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#121	2
C₃×C₅×#120	2
C₃×C₄×C₅×D₄	2
C₂×C₃×C₅×C₂²⋊C₄	2
C₅×#546	3
C₃×#546	5

Subgroups — C3×C5×#546 #11756635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#546 #11756635