Subgroups — C₃×#10618136 #14480633

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66166	C₂	1	2	yes	maximal, complemented
4	C₃×#66058	C₂	1	2	yes	maximal, complemented
5	C₃×#66049	C₂	1	2	yes	maximal, complemented
6	C₃×#66009	C₂	1	2	yes	maximal, complemented
7	C₃×#66008	C₂	1	2	yes	maximal, complemented
8	C₃×#65939	C₂	1	4	yes	maximal, complemented
9	C₃×#65931	C₂	1	4	yes	maximal, complemented
10	C₃×#65881	C₂	1	8	yes	maximal, complemented
11	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
13	#10618136	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
15	C₃×D₅×#41	—	2	16	no	—
16	C₂×C₃×#713	C₂²	1	2	yes	—
17	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	complemented
18	C₂×C₃×#711	C₂²	1	2	yes	—
19	C₂×C₃×#711	C₂²	1	4	yes	complemented
20	C₂×C₃×D₄×D₅	C₂²	1	4	yes	—
21	C₂×C₃×D₄×D₅	C₂²	1	2	yes	complemented
22	C₂×C₃×#709	C₂²	1	4	yes	—
23	C₂×C₃×#709	C₂²	1	2	yes	complemented
24	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	complemented
26	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#124	C₂²	1	2	yes	complemented
29	C₃×C₅×#121	C₂²	1	4	yes	complemented
30	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
32	C₃×#4093	C₂²	1	2	yes	complemented
33	C₃×#4090	C₂²	1	2	yes	complemented
34	C₃×#4086	C₂²	1	2	yes	complemented
35	C₃×#4085	C₂²	1	8	yes	complemented
36	C₃×#4085	C₂²	1	8	yes	complemented
37	C₃×#4083	C₂²	1	8	yes	complemented
38	C₃×#4082	C₂²	1	2	yes	complemented
39	C₃×#4076	C₂²	1	4	yes	complemented
40	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	complemented
41	C₂×C₃×#685	C₂²	1	2	yes	—
42	C₂×C₃×#683	C₂²	1	2	yes	complemented
43	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
44	C₃×#4042	C₂²	1	8	yes	complemented
45	C₃×#4040	C₂²	1	8	yes	complemented
46	C₃×#4030	C₂²	1	8	yes	complemented
47	C₃×#4029	C₂²	1	8	yes	complemented
48	C₃×#4028	C₂²	1	8	yes	complemented
49	C₃×#4024	C₂²	1	8	yes	complemented
50	C₃×#4021	C₂²	1	2	yes	complemented
51	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×D₂₀	C₂²	1	4	yes	complemented
53	C₃×#4018	C₂²	1	4	yes	complemented
54	C₃×#4018	C₂²	1	2	yes	complemented
55	C₃×#4018	C₂²	1	2	yes	complemented
56	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3449	—	5	1	no	maximal, Hall
58	C₂×D₅×#41	C₂×C₃	1	2	yes	complemented
59	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
60	#66166	C₂×C₃	1	2	yes	complemented
61	#66058	C₂×C₃	1	2	yes	complemented
62	#66049	C₂×C₃	1	2	yes	complemented
63	#66009	C₂×C₃	1	2	yes	complemented
64	#66008	C₂×C₃	1	2	yes	complemented
65	#65939	C₂×C₃	1	4	yes	complemented
66	#65931	C₂×C₃	1	4	yes	complemented
67	#65881	C₂×C₃	1	8	yes	complemented
68	#65811	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂³×C₃×D₅	C₂³	1	4	yes	—
71	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
72	C₃×C₅×#41	—	2	8	no	—
73	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
75	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
76	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
78	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
81	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
82	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
83	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
84	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
85	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
86	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
87	C₃×#713	—	2	8	no	—
88	C₃×Q₈×D₅	—	2	8	no	—
89	C₃×#711	—	2	16	no	—
90	C₃×#711	—	2	8	no	—
91	C₃×D₄×D₅	—	2	16	no	—
92	C₃×D₄×D₅	—	2	8	no	—
93	C₃×#709	—	2	8	no	—
94	C₃×#709	—	2	16	no	—
95	C₂×C₃×D₂₀	C₂³	1	2	yes	—
96	C₂×C₃×D₂₀	C₂³	1	4	yes	—
97	C₂×C₃×D₂₀	C₂³	1	4	yes	—
98	C₂×C₃×C₄×D₅	—	2	16	no	—
99	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
100	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
101	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
102	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
103	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
104	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
105	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
106	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
107	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
108	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₃×C₄²×C₅	C₂³	1	2	yes	—
111	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
113	C₃×#685	C₂³	1	4	yes	—
114	C₃×#685	C₂³	1	8	yes	—
115	C₃×#685	C₂³	1	8	yes	—
116	C₃×#685	C₂³	1	4	yes	—
117	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
118	C₃×#683	C₂³	1	4	yes	—
119	C₃×#683	C₂³	1	8	yes	—
120	C₃×#683	C₂³	1	4	yes	—
121	C₃×C₄×Dic₅	C₂³	1	2	yes	—
122	C₃×C₄×Dic₅	C₂³	1	2	yes	—
123	C₂²×C₃×#41	—	5	2	no	—
124	C₃×#537	—	5	4	no	—
125	C₃×#536	—	5	2	no	—
126	C₃×#536	—	5	2	no	—
127	C₃×#535	—	5	2	no	—
128	C₃×#535	—	5	2	no	—
129	C₃×#534	—	5	4	no	—
130	C₃×#532	—	5	2	no	—
131	C₃×#532	—	5	1	no	—
132	C₃×#532	D₅	1	1	yes	characteristic, complemented
133	C₃×#525	—	5	8	no	—
134	C₂×C₃×#117	—	5	1	no	—
135	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
136	D₅×#41	—	2	16	no	—
137	C₂×#713	C₂²×C₃	1	2	yes	—
138	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	complemented
139	C₂×#711	C₂²×C₃	1	2	yes	—
140	C₂×#711	C₂²×C₃	1	4	yes	complemented
141	C₂×D₄×D₅	C₂²×C₃	1	4	yes	—
142	C₂×D₄×D₅	C₂²×C₃	1	2	yes	complemented
143	C₂×#709	C₂²×C₃	1	4	yes	—
144	C₂×#709	C₂²×C₃	1	2	yes	complemented
145	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
146	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	complemented
147	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₅×#124	C₂²×C₃	1	2	yes	complemented
150	C₅×#121	C₂²×C₃	1	4	yes	complemented
151	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
152	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
153	#4093	C₂²×C₃	1	2	yes	complemented
154	#4090	C₂²×C₃	1	2	yes	complemented
155	#4086	C₂²×C₃	1	2	yes	complemented
156	#4085	C₂²×C₃	1	8	yes	complemented
157	#4085	C₂²×C₃	1	8	yes	complemented
158	#4083	C₂²×C₃	1	8	yes	complemented
159	#4082	C₂²×C₃	1	2	yes	complemented
160	#4076	C₂²×C₃	1	4	yes	complemented
161	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
162	C₂×#685	C₂²×C₃	1	2	yes	—
163	C₂×#683	C₂²×C₃	1	2	yes	complemented
164	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
165	#4042	C₂²×C₃	1	8	yes	complemented
166	#4040	C₂²×C₃	1	8	yes	complemented
167	#4030	C₂²×C₃	1	8	yes	complemented
168	#4029	C₂²×C₃	1	8	yes	complemented
169	#4028	C₂²×C₃	1	8	yes	complemented
170	#4024	C₂²×C₃	1	8	yes	complemented
171	#4021	C₂²×C₃	1	2	yes	complemented
172	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₄×D₂₀	C₂²×C₃	1	4	yes	complemented
174	#4018	C₂²×C₃	1	2	yes	complemented
175	#4018	C₂²×C₃	1	4	yes	complemented
176	#4018	C₂²×C₃	1	2	yes	complemented
177	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
178	#3449	—	5	1	no	Sylow
179	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
180	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
181	C₂²×C₃×D₅	—	2	8	no	—
182	C₂²×C₃×D₅	—	4	2	no	—
183	C₂²×C₃×D₅	—	4	8	no	—
184	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
185	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
186	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
187	C₃×C₅×Q₈	—	2	4	no	—
188	C₃×C₅×D₄	—	2	8	no	—
189	C₃×C₅×D₄	—	2	4	no	—
190	C₃×C₅×D₄	—	4	4	no	—
191	C₂×C₃×C₄×C₅	—	2	8	no	—
192	C₂×C₃×C₄×C₅	—	4	2	no	—
193	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
194	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
195	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
196	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
197	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
199	C₃×C₂²⋊D₅	—	2	8	no	—
200	C₃×C₂²⋊D₅	—	2	8	no	—
201	C₃×C₂²⋊D₅	—	2	8	no	—
202	C₃×C₂²⋊D₅	—	4	8	no	—
203	C₂×C₃×Dic₅	—	2	8	no	—
204	C₂×C₃×Dic₅	—	4	2	no	—
205	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
206	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
207	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
208	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
209	C₃×D₂₀	—	2	8	no	—
210	C₃×D₂₀	—	2	4	no	—
211	C₃×D₂₀	—	4	4	no	—
212	C₃×C₄×D₅	—	2	8	no	—
213	C₃×C₄×D₅	—	2	8	no	—
214	C₃×C₄×D₅	—	2	8	no	—
215	C₃×C₄×D₅	C₂×D₄	1	8	yes	—
216	C₃×C₄×D₅	C₂×D₄	1	8	yes	—
217	C₃×Dic₁₀	—	2	4	no	—
218	C₃×Dic₁₀	—	2	8	no	—
219	C₂×C₃×#41	—	5	2	no	—
220	C₂×C₃×#41	—	5	2	no	—
221	C₂×C₃×#41	—	5	4	no	—
222	C₂×C₃×#41	—	5	4	no	—
223	C₂×C₃×#41	—	5	2	no	—
224	C₂×C₃×#41	—	10	16	no	—
225	C₂×C₃×#41	C₂×D₅	1	2	yes	complemented
226	C₂²×C₃×Q₈	—	5	2	no	—
227	C₂²×C₃×D₄	—	5	4	no	—
228	C₂²×C₃×D₄	—	5	2	no	—
229	C₂³×C₃×C₄	—	5	1	no	—
230	C₂³×C₃×C₄	—	5	4	no	—
231	C₃×C₄⋊Q₈	—	5	2	no	—
232	C₃×C₄⋊Q₈	—	5	1	no	—
233	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
234	C₃×#127	—	5	2	no	—
235	C₃×#127	—	5	1	no	—
236	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
237	C₃×#124	—	5	2	no	—
238	C₃×#124	—	5	2	no	—
239	C₃×#124	—	5	2	no	—
240	C₃×#124	C₂×D₅	1	2	yes	complemented
241	C₃×#123	—	5	8	no	—
242	C₃×#123	—	5	8	no	—
243	C₃×C₂²⋊Q₈	—	5	8	no	—
244	C₃×C₂²⋊Q₈	—	5	8	no	—
245	C₃×#121	—	5	8	no	—
246	C₃×#121	—	5	8	no	—
247	C₃×#121	—	5	4	no	—
248	C₃×#121	—	5	8	no	—
249	C₃×#121	C₂×D₅	1	4	yes	complemented
250	C₃×#120	—	5	8	no	—
251	C₃×#120	—	5	8	no	—
252	C₃×C₄×D₄	—	5	8	no	—
253	C₃×C₄×D₄	—	5	4	no	—
254	C₃×C₄×D₄	C₂×D₅	1	4	yes	complemented
255	C₃×#117	—	5	4	no	—
256	C₃×#117	—	5	2	no	—
257	C₃×#117	—	5	2	no	—
258	C₂×C₃×C₄⋊C₄	—	5	2	no	—
259	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
260	C₂×C₃×C₄²	—	5	1	no	—
261	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
262	C₂³×D₅	C₂³×C₃	1	4	yes	—
263	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
264	C₅×#41	—	2	8	no	—
265	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
266	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
267	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
268	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
269	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
270	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
271	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
273	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
274	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
275	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
276	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
277	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
278	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
279	#713	—	2	8	no	—
280	Q₈×D₅	—	2	8	no	—
281	#711	—	2	16	no	—
282	#711	—	2	8	no	—
283	D₄×D₅	—	2	16	no	—
284	D₄×D₅	—	2	8	no	—
285	#709	—	2	8	no	—
286	#709	—	2	16	no	—
287	C₂×D₂₀	C₂³×C₃	1	4	yes	—
288	C₂×D₂₀	C₂³×C₃	1	2	yes	—
289	C₂×D₂₀	C₂³×C₃	1	4	yes	—
290	C₂×C₄×D₅	—	2	16	no	—
291	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
292	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
293	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
294	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
295	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
296	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
297	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
298	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
299	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
300	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
301	C₄²×C₅	C₂³×C₃	1	2	yes	—
302	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
303	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
304	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
305	#685	C₂³×C₃	1	4	yes	—
306	#685	C₂³×C₃	1	4	yes	—
307	#685	C₂³×C₃	1	8	yes	—
308	#685	C₂³×C₃	1	8	yes	—
309	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
310	#683	C₂³×C₃	1	4	yes	—
311	#683	C₂³×C₃	1	4	yes	—
312	#683	C₂³×C₃	1	8	yes	—
313	C₄×Dic₅	C₂³×C₃	1	2	yes	—
314	C₄×Dic₅	C₂³×C₃	1	2	yes	—
315	C₂²×#41	—	5	2	no	—
316	#537	—	5	4	no	—
317	#536	—	5	2	no	—
318	#536	—	5	2	no	—
319	#535	—	5	2	no	—
320	#535	—	5	2	no	—
321	#534	—	5	4	no	—
322	#532	—	5	2	no	—
323	#532	—	5	1	no	—
324	#532	C₃×D₅	1	1	yes	characteristic, complemented
325	#525	—	5	8	no	—
326	C₂×#117	—	5	1	no	—
327	C₂²×C₃×C₅	—	2	2	no	—
328	C₂²×C₃×C₅	—	2	4	no	—
329	C₂²×C₃×C₅	—	2	8	no	—
330	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
331	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
332	C₂×C₃×D₅	—	2	4	no	—
333	C₂×C₃×D₅	—	2	4	no	—
334	C₂×C₃×D₅	—	2	8	no	—
335	C₂×C₃×D₅	—	4	4	no	—
336	C₂×C₃×D₅	—	4	16	no	—
337	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
338	C₃×C₄×C₅	—	2	4	no	—
339	C₃×C₄×C₅	—	2	2	no	—
340	C₃×C₄×C₅	—	2	2	no	—
341	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
342	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
343	C₃×Dic₅	—	2	4	no	—
344	C₃×Dic₅	—	2	4	no	—
345	C₃×Dic₅	C₂²×D₄	1	4	yes	—
346	C₂⁴×C₃	—	5	1	no	—
347	C₂⁴×C₃	—	5	4	no	—
348	C₃×#41	—	2	8	no	—
349	C₃×#41	—	10	16	no	—
350	C₃×#41	—	10	16	no	—
351	C₃×#41	—	10	8	no	—
352	C₃×#41	—	10	8	no	—
353	C₃×#41	—	10	8	no	—
354	C₂×C₃×Q₈	—	5	4	no	—
355	C₂×C₃×Q₈	—	5	2	no	—
356	C₂×C₃×Q₈	—	10	8	no	—
357	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
358	C₂×C₃×D₄	—	5	4	no	—
359	C₂×C₃×D₄	—	5	4	no	—
360	C₂×C₃×D₄	—	5	4	no	—
361	C₂×C₃×D₄	—	5	8	no	—
362	C₂×C₃×D₄	—	5	4	no	—
363	C₂×C₃×D₄	—	5	2	no	—
364	C₂×C₃×D₄	—	5	4	no	—
365	C₂×C₃×D₄	—	10	8	no	—
366	C₂×C₃×D₄	—	10	16	no	—
367	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
368	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
369	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
370	C₂²×C₃×C₄	—	5	1	no	—
371	C₂²×C₃×C₄	—	5	8	no	—
372	C₂²×C₃×C₄	—	5	2	no	—
373	C₂²×C₃×C₄	—	5	2	no	—
374	C₂²×C₃×C₄	—	5	4	no	—
375	C₂²×C₃×C₄	—	5	2	no	—
376	C₂²×C₃×C₄	—	5	4	no	—
377	C₂²×C₃×C₄	—	5	4	no	—
378	C₂²×C₃×C₄	—	5	4	no	—
379	C₂²×C₃×C₄	—	10	16	no	—
380	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
381	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
382	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
383	C₃×C₄⋊C₄	—	5	4	no	—
384	C₃×C₄⋊C₄	—	5	4	no	—
385	C₃×C₄⋊C₄	—	5	8	no	—
386	C₃×C₄⋊C₄	—	5	4	no	—
387	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
388	C₃×C₂²⋊C₄	—	5	8	no	—
389	C₃×C₂²⋊C₄	—	5	4	no	—
390	C₃×C₂²⋊C₄	—	5	4	no	—
391	C₃×C₂²⋊C₄	—	5	8	no	—
392	C₃×C₂²⋊C₄	—	5	8	no	—
393	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
394	C₃×C₄²	—	5	2	no	—
395	C₃×C₄²	—	5	2	no	—
396	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
397	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
398	C₃×C₄²	C₂²×D₅	1	2	yes	—
399	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
400	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
401	C₂²×D₅	—	2	8	no	—
402	C₂²×D₅	—	4	2	no	—
403	C₂²×D₅	—	4	8	no	—
404	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
405	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
406	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
407	C₅×Q₈	—	2	4	no	—
408	C₅×D₄	—	2	8	no	—
409	C₅×D₄	—	2	4	no	—
410	C₅×D₄	—	4	4	no	—
411	C₂×C₄×C₅	—	2	8	no	—
412	C₂×C₄×C₅	—	4	2	no	—
413	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
414	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
415	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
416	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
417	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
418	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
419	C₂²⋊D₅	—	2	8	no	—
420	C₂²⋊D₅	—	2	8	no	—
421	C₂²⋊D₅	—	2	8	no	—
422	C₂²⋊D₅	—	4	8	no	—
423	C₂×Dic₅	—	2	8	no	—
424	C₂×Dic₅	—	4	2	no	—
425	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
426	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
427	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
428	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
429	D₂₀	—	2	8	no	—
430	D₂₀	—	2	4	no	—
431	D₂₀	—	4	4	no	—
432	C₄×D₅	—	2	8	no	—
433	C₄×D₅	—	2	8	no	—
434	C₄×D₅	—	2	8	no	—
435	C₄×D₅	C₂×C₃×D₄	1	8	yes	—
436	C₄×D₅	C₂×C₃×D₄	1	8	yes	—
437	Dic₁₀	—	2	4	no	—
438	Dic₁₀	—	2	8	no	—
439	C₂×#41	—	5	2	no	—
440	C₂×#41	—	5	2	no	—
441	C₂×#41	—	5	4	no	—
442	C₂×#41	—	5	4	no	—
443	C₂×#41	—	5	2	no	—
444	C₂×#41	—	10	16	no	—
445	C₂×#41	C₂×C₃×D₅	1	2	yes	complemented
446	C₂²×Q₈	—	5	2	no	—
447	C₂²×D₄	—	5	4	no	—
448	C₂²×D₄	—	5	2	no	—
449	C₂³×C₄	—	5	1	no	—
450	C₂³×C₄	—	5	4	no	—
451	C₄⋊Q₈	—	5	2	no	—
452	C₄⋊Q₈	—	5	1	no	—
453	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
454	#127	—	5	2	no	—
455	#127	—	5	1	no	—
456	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
457	#124	—	5	2	no	—
458	#124	—	5	2	no	—
459	#124	—	5	2	no	—
460	#124	C₂×C₃×D₅	1	2	yes	complemented
461	#123	—	5	8	no	—
462	#123	—	5	8	no	—
463	C₂²⋊Q₈	—	5	8	no	—
464	C₂²⋊Q₈	—	5	8	no	—
465	#121	—	5	8	no	—
466	#121	—	5	8	no	—
467	#121	—	5	4	no	—
468	#121	—	5	8	no	—
469	#121	C₂×C₃×D₅	1	4	yes	complemented
470	#120	—	5	8	no	—
471	#120	—	5	8	no	—
472	C₄×D₄	—	5	8	no	—
473	C₄×D₄	—	5	4	no	—
474	C₄×D₄	C₂×C₃×D₅	1	4	yes	complemented
475	#117	—	5	4	no	—
476	#117	—	5	2	no	—
477	#117	—	5	2	no	—
478	C₂×C₄⋊C₄	—	5	2	no	—
479	C₂×C₂²⋊C₄	—	5	2	no	—
480	C₂×C₄²	—	5	1	no	—
481	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
482	C₂×C₃×C₅	—	2	2	no	—
483	C₂×C₃×C₅	—	4	4	no	—
484	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
485	C₂×C₃×C₅	#585	1	2	yes	—
486	C₃×D₅	—	2	4	no	—
487	C₃×D₅	—	4	4	no	—
488	C₂³×C₃	—	5	2	no	—
489	C₂³×C₃	—	5	4	no	—
490	C₂³×C₃	—	5	4	no	—
491	C₂³×C₃	—	10	8	no	—
492	C₂³×C₃	—	20	2	no	—
493	C₂³×C₃	—	20	8	no	—
494	C₂³×C₃	C₂³×D₅	1	4	yes	—
495	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
496	C₃×Q₈	—	2	4	no	—
497	C₃×Q₈	—	10	8	no	—
498	C₃×Q₈	—	10	4	no	—
499	C₃×D₄	—	2	8	no	—
500	C₃×D₄	—	2	4	no	—
501	C₃×D₄	—	4	4	no	—
502	C₃×D₄	—	10	8	no	—
503	C₃×D₄	—	10	8	no	—
504	C₃×D₄	—	10	8	no	—
505	C₃×D₄	—	10	8	no	—
506	C₃×D₄	—	10	4	no	—
507	C₃×D₄	—	20	4	no	—
508	C₃×D₄	—	20	8	no	—
509	C₂×C₃×C₄	—	2	8	no	—
510	C₂×C₃×C₄	—	4	2	no	—
511	C₂×C₃×C₄	—	5	4	no	—
512	C₂×C₃×C₄	—	5	2	no	—
513	C₂×C₃×C₄	—	5	8	no	—
514	C₂×C₃×C₄	—	5	8	no	—
515	C₂×C₃×C₄	—	5	4	no	—
516	C₂×C₃×C₄	—	5	4	no	—
517	C₂×C₃×C₄	—	10	8	no	—
518	C₂×C₃×C₄	—	10	8	no	—
519	C₂×C₃×C₄	—	10	8	no	—
520	C₂×C₃×C₄	—	10	8	no	—
521	C₂×C₃×C₄	—	20	2	no	—
522	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
523	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
524	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
525	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
526	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
528	C₂²×C₅	—	2	2	no	—
529	C₂²×C₅	—	2	4	no	—
530	C₂²×C₅	—	2	8	no	—
531	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
532	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
533	C₂×D₅	—	2	4	no	—
534	C₂×D₅	—	2	4	no	—
535	C₂×D₅	—	2	8	no	—
536	C₂×D₅	—	4	4	no	—
537	C₂×D₅	—	4	16	no	—
538	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
539	C₄×C₅	—	2	4	no	—
540	C₄×C₅	—	2	2	no	—
541	C₄×C₅	—	2	2	no	—
542	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
543	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
544	Dic₅	—	2	4	no	—
545	Dic₅	—	2	4	no	—
546	Dic₅	C₂²×C₃×D₄	1	4	yes	—
547	C₂⁴	—	5	1	no	—
548	C₂⁴	—	5	4	no	—
549	#41	—	2	8	no	—
550	#41	—	10	16	no	—
551	#41	—	10	16	no	—
552	#41	—	10	8	no	—
553	#41	—	10	8	no	—
554	#41	—	10	8	no	—
555	C₂×Q₈	—	5	4	no	—
556	C₂×Q₈	—	5	2	no	—
557	C₂×Q₈	—	10	8	no	—
558	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
559	C₂×D₄	—	5	4	no	—
560	C₂×D₄	—	5	4	no	—
561	C₂×D₄	—	5	4	no	—
562	C₂×D₄	—	5	8	no	—
563	C₂×D₄	—	5	4	no	—
564	C₂×D₄	—	5	2	no	—
565	C₂×D₄	—	5	4	no	—
566	C₂×D₄	—	10	8	no	—
567	C₂×D₄	—	10	16	no	—
568	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
569	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
570	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
571	C₂²×C₄	—	5	1	no	—
572	C₂²×C₄	—	5	8	no	—
573	C₂²×C₄	—	5	2	no	—
574	C₂²×C₄	—	5	2	no	—
575	C₂²×C₄	—	5	4	no	—
576	C₂²×C₄	—	5	2	no	—
577	C₂²×C₄	—	5	4	no	—
578	C₂²×C₄	—	5	4	no	—
579	C₂²×C₄	—	5	4	no	—
580	C₂²×C₄	—	10	16	no	—
581	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
582	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
583	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
584	C₄⋊C₄	—	5	4	no	—
585	C₄⋊C₄	—	5	4	no	—
586	C₄⋊C₄	—	5	8	no	—
587	C₄⋊C₄	—	5	4	no	—
588	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
589	C₂²⋊C₄	—	5	8	no	—
590	C₂²⋊C₄	—	5	4	no	—
591	C₂²⋊C₄	—	5	4	no	—
592	C₂²⋊C₄	—	5	8	no	—
593	C₂²⋊C₄	—	5	8	no	—
594	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
595	C₄²	—	5	2	no	—
596	C₄²	—	5	2	no	—
597	C₄²	C₂²×C₃×D₅	1	2	yes	—
598	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
599	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
600	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
601	C₂²×C₃	—	2	2	no	—
602	C₂²×C₃	—	2	4	no	—
603	C₂²×C₃	—	2	8	no	—
604	C₂²×C₃	—	5	4	no	—
605	C₂²×C₃	—	10	4	no	—
606	C₂²×C₃	—	10	4	no	—
607	C₂²×C₃	—	10	8	no	—
608	C₂²×C₃	—	20	4	no	—
609	C₂²×C₃	—	20	16	no	—
610	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
611	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
612	C₃×C₄	—	2	4	no	—
613	C₃×C₄	—	2	2	no	—
614	C₃×C₄	—	2	2	no	—
615	C₃×C₄	—	5	4	no	—
616	C₃×C₄	—	10	4	no	—
617	C₃×C₄	—	10	4	no	—
618	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
619	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
620	C₂×C₅	—	2	2	no	—
621	C₂×C₅	—	4	4	no	—
622	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
623	C₂×C₅	C₃×#585	1	2	yes	—
624	D₅	—	2	4	no	—
625	D₅	—	4	4	no	—
626	C₂³	—	5	2	no	—
627	C₂³	—	5	4	no	—
628	C₂³	—	5	4	no	—
629	C₂³	—	10	8	no	—
630	C₂³	—	20	2	no	—
631	C₂³	—	20	8	no	—
632	C₂³	C₂³×C₃×D₅	1	4	yes	—
633	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
634	Q₈	—	2	4	no	—
635	Q₈	—	10	8	no	—
636	Q₈	—	10	4	no	—
637	D₄	—	2	8	no	—
638	D₄	—	2	4	no	—
639	D₄	—	4	4	no	—
640	D₄	—	10	8	no	—
641	D₄	—	10	8	no	—
642	D₄	—	10	8	no	—
643	D₄	—	10	8	no	—
644	D₄	—	10	4	no	—
645	D₄	—	20	4	no	—
646	D₄	—	20	8	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	5	4	no	—
650	C₂×C₄	—	5	2	no	—
651	C₂×C₄	—	5	8	no	—
652	C₂×C₄	—	5	8	no	—
653	C₂×C₄	—	5	4	no	—
654	C₂×C₄	—	5	4	no	—
655	C₂×C₄	—	10	8	no	—
656	C₂×C₄	—	10	8	no	—
657	C₂×C₄	—	10	8	no	—
658	C₂×C₄	—	10	8	no	—
659	C₂×C₄	—	20	2	no	—
660	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
661	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
662	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
663	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
664	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
666	C₂×C₃	—	2	2	no	—
667	C₂×C₃	—	4	4	no	—
668	C₂×C₃	—	10	4	no	—
669	C₂×C₃	—	20	4	no	—
670	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
671	C₂×C₃	#66283	1	2	yes	—
672	C₅	C₃×#3449	1	1	yes	characteristic, complemented, Sylow
673	C₂²	—	2	2	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	2	8	no	—
676	C₂²	—	5	4	no	—
677	C₂²	—	10	4	no	—
678	C₂²	—	10	4	no	—
679	C₂²	—	10	8	no	—
680	C₂²	—	20	4	no	—
681	C₂²	—	20	16	no	—
682	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
683	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
684	C₄	—	2	4	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	5	4	no	—
688	C₄	—	10	4	no	—
689	C₄	—	10	4	no	—
690	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
691	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
692	C₃	#10618136	1	1	yes	characteristic, direct product factor, Sylow
693	C₂	—	2	2	no	—
694	C₂	—	4	4	no	—
695	C₂	—	10	4	no	—
696	C₂	—	20	4	no	—
697	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
698	C₂	C₃×#66283	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#3449
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×#41	C₂	semidirect
2. C₃×C₅×#532	C₂	semidirect
3. C₃×#66166	C₂	semidirect
4. C₃×#66058	C₂	semidirect
5. C₃×#66049	C₂	semidirect
6. C₃×#66009	C₂	semidirect
7. C₃×#66008	C₂	semidirect
8. C₃×#65939	C₂	semidirect
9. C₃×#65931	C₂	semidirect
10. C₃×#65881	C₂	semidirect
11. C₃×#65811	C₂	semidirect
12. C₂×C₃×#4018	C₂	semidirect
13. #10618136	C₃	direct (N × H)
14. C₂×C₃×C₅×#41	C₂²	semidirect
17. C₂×C₃×Q₈×D₅	C₂²	semidirect
19. C₂×C₃×#711	C₂²	semidirect
21. C₂×C₃×D₄×D₅	C₂²	semidirect
23. C₂×C₃×#709	C₂²	semidirect
25. C₂²×C₃×C₄×D₅	C₂²	semidirect
26. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₃×C₅×#127	C₂²	semidirect
28. C₃×C₅×#124	C₂²	semidirect
29. C₃×C₅×#121	C₂²	semidirect
30. C₃×C₄×C₅×D₄	C₂²	semidirect
31. C₂×C₃×C₄²×C₅	C₂²	semidirect
32. C₃×#4093	C₂²	semidirect
33. C₃×#4090	C₂²	semidirect
34. C₃×#4086	C₂²	semidirect
35. C₃×#4085	C₂²	semidirect
36. C₃×#4085	C₂²	semidirect
37. C₃×#4083	C₂²	semidirect
38. C₃×#4082	C₂²	semidirect
39. C₃×#4076	C₂²	semidirect
40. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
42. C₂×C₃×#683	C₂²	semidirect
43. C₂×C₃×C₄×Dic₅	C₂²	semidirect
44. C₃×#4042	C₂²	semidirect
45. C₃×#4040	C₂²	semidirect
46. C₃×#4030	C₂²	semidirect
47. C₃×#4029	C₂²	semidirect
48. C₃×#4028	C₂²	semidirect
49. C₃×#4024	C₂²	semidirect
50. C₃×#4021	C₂²	semidirect
51. C₃×#4020	C₂²	semidirect
52. C₃×C₄×D₂₀	C₂²	semidirect
53. C₃×#4018	C₂²	semidirect
54. C₃×#4018	C₂²	semidirect
55. C₃×#4018	C₂²	semidirect
56. C₃×#4015	C₂²	semidirect
58. C₂×D₅×#41	C₂×C₃	semidirect
59. C₅×#532	C₂×C₃	semidirect
60. #66166	C₂×C₃	semidirect
61. #66058	C₂×C₃	semidirect
62. #66049	C₂×C₃	semidirect
63. #66009	C₂×C₃	semidirect
64. #66008	C₂×C₃	semidirect
65. #65939	C₂×C₃	semidirect
66. #65931	C₂×C₃	semidirect
67. #65881	C₂×C₃	semidirect
68. #65811	C₂×C₃	semidirect
69. C₂×#4018	C₂×C₃	semidirect
99. C₂×C₃×C₄×D₅	D₄	semidirect
132. C₃×#532	D₅	semidirect
135. C₂×C₅×#41	C₂²×C₃	semidirect
138. C₂×Q₈×D₅	C₂²×C₃	semidirect
140. C₂×#711	C₂²×C₃	semidirect
142. C₂×D₄×D₅	C₂²×C₃	semidirect
144. C₂×#709	C₂²×C₃	semidirect
146. C₂²×C₄×D₅	C₂²×C₃	semidirect
147. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
148. C₅×#127	C₂²×C₃	semidirect
149. C₅×#124	C₂²×C₃	semidirect
150. C₅×#121	C₂²×C₃	semidirect
151. C₄×C₅×D₄	C₂²×C₃	semidirect
152. C₂×C₄²×C₅	C₂²×C₃	semidirect
153. #4093	C₂²×C₃	semidirect
154. #4090	C₂²×C₃	semidirect
155. #4086	C₂²×C₃	semidirect
156. #4085	C₂²×C₃	semidirect
157. #4085	C₂²×C₃	semidirect
158. #4083	C₂²×C₃	semidirect
159. #4082	C₂²×C₃	semidirect
160. #4076	C₂²×C₃	semidirect
161. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
163. C₂×#683	C₂²×C₃	semidirect
164. C₂×C₄×Dic₅	C₂²×C₃	semidirect
165. #4042	C₂²×C₃	semidirect
166. #4040	C₂²×C₃	semidirect
167. #4030	C₂²×C₃	semidirect
168. #4029	C₂²×C₃	semidirect
169. #4028	C₂²×C₃	semidirect
170. #4024	C₂²×C₃	semidirect
171. #4021	C₂²×C₃	semidirect
172. #4020	C₂²×C₃	semidirect
173. C₄×D₂₀	C₂²×C₃	semidirect
174. #4018	C₂²×C₃	semidirect
175. #4018	C₂²×C₃	semidirect
176. #4018	C₂²×C₃	semidirect
177. #4015	C₂²×C₃	semidirect
225. C₂×C₃×#41	C₂×D₅	semidirect
233. C₃×C₄⋊Q₈	C₂×D₅	semidirect
236. C₃×#127	C₂×D₅	semidirect
240. C₃×#124	C₂×D₅	semidirect
249. C₃×#121	C₂×D₅	semidirect
254. C₃×C₄×D₄	C₂×D₅	semidirect
261. C₂×C₃×C₄²	C₂×D₅	semidirect
291. C₂×C₄×D₅	C₃×D₄	semidirect
324. #532	C₃×D₅	semidirect
445. C₂×#41	C₂×C₃×D₅	semidirect
453. C₄⋊Q₈	C₂×C₃×D₅	semidirect
456. #127	C₂×C₃×D₅	semidirect
460. #124	C₂×C₃×D₅	semidirect
469. #121	C₂×C₃×D₅	semidirect
474. C₄×D₄	C₂×C₃×D₅	semidirect
481. C₂×C₄²	C₂×C₃×D₅	semidirect
600. C₃×C₅	#3449	semidirect
672. C₅	C₃×#3449	semidirect
692. C₃	#10618136	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×D₅×#41	2
C₃×C₅×#532	2
C₃×#66166	2
C₃×#66058	2
C₃×#66049	2
C₃×#66009	2
C₃×#66008	2
C₃×#65939	2
C₃×#65931	2
C₃×#65881	2
C₃×#65811	2
C₂×C₃×#4018	2
#10618136	3
C₃×#3449	5

Subgroups — C3×#10618136 #14480633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618136 #14480633