Subgroups — C₃×#10619169 #14480639

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66167	C₂	1	4	yes	maximal, complemented
4	C₃×#66166	C₂	1	4	yes	maximal, complemented
5	C₃×#66164	C₂	1	2	yes	maximal, complemented
6	C₃×#66162	C₂	1	4	yes	maximal, complemented
7	C₃×#66159	C₂	1	2	yes	maximal, complemented
8	C₃×#66150	C₂	1	2	yes	maximal, complemented
9	C₃×#66139	C₂	1	2	yes	maximal, complemented
10	C₃×#66138	C₂	1	4	yes	maximal, complemented
11	C₃×#66125	C₂	1	4	yes	maximal, complemented
12	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
13	#10619169	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅×#41	—	2	8	no	—
15	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
24	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
25	C₂×C₃×#709	—	2	8	no	—
26	C₂×C₃×#709	C₂²	1	2	yes	—
27	C₂×C₃×#709	C₂²	1	2	yes	—
28	C₂×C₃×#709	C₂²	1	2	yes	complemented
29	C₂×C₃×#709	C₂²	1	2	yes	complemented
30	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
32	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
33	C₃×#4099	C₂²	1	8	yes	complemented
34	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
35	C₃×#4093	C₂²	1	4	yes	complemented
36	C₃×#4092	C₂²	1	8	yes	complemented
37	C₃×#4090	C₂²	1	4	yes	complemented
38	C₃×#4086	C₂²	1	4	yes	complemented
39	C₃×#4085	C₂²	1	16	yes	complemented
40	C₃×#4084	C₂²	1	8	yes	complemented
41	C₃×#4083	C₂²	1	8	yes	complemented
42	C₃×#4082	C₂²	1	4	yes	complemented
43	C₃×#4081	C₂²	1	8	yes	complemented
44	C₃×#4076	C₂²	1	8	yes	complemented
45	C₃×#4075	C₂²	1	8	yes	complemented
46	C₃×C₄×C₂²⋊D₅	C₂²	1	16	yes	complemented
47	C₃×#4072	C₂²	1	2	yes	complemented
48	C₃×#4072	C₂²	1	2	yes	complemented
49	C₃×#4072	C₂²	1	2	yes	complemented
50	C₃×#4072	C₂²	1	2	yes	complemented
51	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
52	C₃×#4070	C₂²	1	8	yes	complemented
53	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
54	C₃×#3449	—	5	1	no	maximal, Hall
55	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×#709	C₂×C₃	1	1	yes	characteristic, complemented
57	#66167	C₂×C₃	1	4	yes	complemented
58	#66166	C₂×C₃	1	4	yes	complemented
59	#66164	C₂×C₃	1	2	yes	complemented
60	#66162	C₂×C₃	1	4	yes	complemented
61	#66159	C₂×C₃	1	2	yes	complemented
62	#66150	C₂×C₃	1	2	yes	complemented
63	#66139	C₂×C₃	1	2	yes	complemented
64	#66138	C₂×C₃	1	4	yes	complemented
65	#66125	C₂×C₃	1	4	yes	complemented
66	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂³×C₃×D₅	C₂³	1	2	yes	—
70	C₃×C₅×#41	—	2	8	no	—
71	C₃×C₅×#41	—	2	8	no	—
72	C₃×C₅×#41	—	2	8	no	—
73	C₃×C₅×#41	—	2	8	no	—
74	C₂×C₃×C₅×Q₈	—	2	4	no	—
75	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
76	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
77	C₂×C₃×C₅×D₄	—	2	8	no	—
78	C₂×C₃×C₅×D₄	—	2	4	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
80	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
81	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
82	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
83	C₂²×C₃×C₄×C₅	—	2	8	no	—
84	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
85	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
86	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
87	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
95	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
96	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
97	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
98	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
99	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
100	C₃×#709	—	2	8	no	—
101	C₃×#709	—	2	8	no	—
102	C₃×#709	—	2	8	no	—
103	C₃×#709	—	2	8	no	—
104	C₂×C₃×D₂₀	—	2	4	no	—
105	C₂×C₃×D₂₀	C₂³	1	2	yes	—
106	C₂×C₃×D₂₀	C₂³	1	2	yes	—
107	C₂×C₃×C₄×D₅	—	2	8	no	—
108	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
109	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
110	C₂×C₃×Dic₁₀	—	2	4	no	—
111	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
112	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
113	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
114	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	—
115	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
116	C₃×#685	C₂³	1	16	yes	—
117	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
118	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
119	C₃×#683	C₂³	1	16	yes	—
120	C₃×C₄×Dic₅	C₂³	1	4	yes	—
121	C₃×C₄×Dic₅	C₂³	1	4	yes	—
122	C₂²×C₃×#41	—	5	1	no	—
123	C₂²×C₃×#41	D₅	1	1	yes	characteristic, complemented
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	4	no	—
131	C₃×#525	—	5	4	no	—
132	C₃×#525	—	5	4	no	—
133	C₂×C₃×#117	—	5	1	no	—
134	C₂×C₅×#41	—	2	8	no	—
135	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
136	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
137	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
138	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
139	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
141	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
143	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	complemented
144	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
145	C₂×#709	—	2	8	no	—
146	C₂×#709	C₂²×C₃	1	2	yes	—
147	C₂×#709	C₂²×C₃	1	2	yes	—
148	C₂×#709	C₂²×C₃	1	2	yes	complemented
149	C₂×#709	C₂²×C₃	1	2	yes	complemented
150	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
152	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
153	#4099	C₂²×C₃	1	8	yes	complemented
154	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
155	#4093	C₂²×C₃	1	4	yes	complemented
156	#4092	C₂²×C₃	1	8	yes	complemented
157	#4090	C₂²×C₃	1	4	yes	complemented
158	#4086	C₂²×C₃	1	4	yes	complemented
159	#4085	C₂²×C₃	1	16	yes	complemented
160	#4084	C₂²×C₃	1	8	yes	complemented
161	#4083	C₂²×C₃	1	8	yes	complemented
162	#4082	C₂²×C₃	1	4	yes	complemented
163	#4081	C₂²×C₃	1	8	yes	complemented
164	#4076	C₂²×C₃	1	8	yes	complemented
165	#4075	C₂²×C₃	1	8	yes	complemented
166	C₄×C₂²⋊D₅	C₂²×C₃	1	16	yes	complemented
167	#4072	C₂²×C₃	1	2	yes	complemented
168	#4072	C₂²×C₃	1	2	yes	complemented
169	#4072	C₂²×C₃	1	2	yes	complemented
170	#4072	C₂²×C₃	1	2	yes	complemented
171	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
172	#4070	C₂²×C₃	1	8	yes	complemented
173	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
174	#3449	—	5	1	no	Sylow
175	C₂³×C₃×C₅	—	2	4	no	—
176	C₂³×C₃×C₅	—	4	2	no	—
177	C₂³×C₃×C₅	—	4	4	no	—
178	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
179	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
180	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
181	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
182	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
183	C₂²×C₃×D₅	—	2	4	no	—
184	C₂²×C₃×D₅	—	4	4	no	—
185	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
186	C₃×C₅×Q₈	—	2	4	no	—
187	C₃×C₅×Q₈	—	2	4	no	—
188	C₃×C₅×D₄	—	2	8	no	—
189	C₃×C₅×D₄	—	2	8	no	—
190	C₃×C₅×D₄	—	2	4	no	—
191	C₃×C₅×D₄	—	2	4	no	—
192	C₂×C₃×C₄×C₅	—	2	4	no	—
193	C₂×C₃×C₄×C₅	—	2	8	no	—
194	C₂×C₃×C₄×C₅	—	2	8	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
196	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
197	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
198	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
199	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
200	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
201	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
202	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
204	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
206	C₃×C₂²⋊D₅	—	2	8	no	—
207	C₃×C₂²⋊D₅	—	2	8	no	—
208	C₃×C₂²⋊D₅	—	4	16	no	—
209	C₂×C₃×Dic₅	—	2	4	no	—
210	C₂×C₃×Dic₅	—	4	4	no	—
211	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
212	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
213	C₃×D₂₀	—	2	4	no	—
214	C₃×D₂₀	—	2	4	no	—
215	C₃×C₄×D₅	—	2	8	no	—
216	C₃×C₄×D₅	—	2	8	no	—
217	C₃×Dic₁₀	—	2	4	no	—
218	C₃×Dic₁₀	—	2	4	no	—
219	C₂×C₃×#41	—	2	8	no	—
220	C₂×C₃×#41	—	5	2	no	—
221	C₂×C₃×#41	—	5	2	no	—
222	C₂×C₃×#41	—	5	2	no	—
223	C₂×C₃×#41	—	5	2	no	—
224	C₂×C₃×#41	—	10	8	no	—
225	C₂×C₃×#41	C₂×D₅	1	2	yes	—
226	C₂×C₃×#41	C₂×D₅	1	2	yes	—
227	C₂×C₃×#41	C₂×D₅	1	2	yes	complemented
228	C₂×C₃×#41	C₂×D₅	1	2	yes	complemented
229	C₂²×C₃×Q₈	—	5	1	no	—
230	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
231	C₂²×C₃×D₄	—	5	2	no	—
232	C₂²×C₃×D₄	—	5	1	no	—
233	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
234	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
235	C₂³×C₃×C₄	—	5	2	no	—
236	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
237	C₂³×C₃×C₄	C₂×D₅	1	2	yes	complemented
238	C₃×C₄⋊Q₈	—	5	4	no	—
239	C₃×#127	—	5	4	no	—
240	C₃×#124	—	5	4	no	—
241	C₃×#124	—	5	4	no	—
242	C₃×#123	—	5	8	no	—
243	C₃×#123	—	5	8	no	—
244	C₃×C₂²⋊Q₈	—	5	8	no	—
245	C₃×C₂²⋊Q₈	—	5	8	no	—
246	C₃×#121	—	5	8	no	—
247	C₃×#121	—	5	16	no	—
248	C₃×#121	—	5	8	no	—
249	C₃×#120	—	5	8	no	—
250	C₃×#120	—	5	8	no	—
251	C₃×C₄×D₄	—	5	16	no	—
252	C₃×#117	—	5	2	no	—
253	C₃×#117	—	5	2	no	—
254	C₃×#117	—	5	2	no	—
255	C₃×#117	—	5	2	no	—
256	C₂×C₃×C₄⋊C₄	—	5	2	no	—
257	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
258	C₂×C₃×C₄²	—	5	2	no	—
259	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
260	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
261	C₂³×D₅	C₂³×C₃	1	2	yes	—
262	C₅×#41	—	2	8	no	—
263	C₅×#41	—	2	8	no	—
264	C₅×#41	—	2	8	no	—
265	C₅×#41	—	2	8	no	—
266	C₂×C₅×Q₈	—	2	4	no	—
267	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
268	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
269	C₂×C₅×D₄	—	2	8	no	—
270	C₂×C₅×D₄	—	2	4	no	—
271	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
272	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
273	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
274	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
275	C₂²×C₄×C₅	—	2	8	no	—
276	C₂²×C₄×C₅	C₃×D₄	1	8	yes	complemented
277	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
278	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
279	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
280	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₂²⋊D₅	—	2	8	no	—
287	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
288	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
289	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
290	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
291	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
292	#709	—	2	8	no	—
293	#709	—	2	8	no	—
294	#709	—	2	8	no	—
295	#709	—	2	8	no	—
296	C₂×D₂₀	—	2	4	no	—
297	C₂×D₂₀	C₂³×C₃	1	2	yes	—
298	C₂×D₂₀	C₂³×C₃	1	2	yes	—
299	C₂×C₄×D₅	—	2	8	no	—
300	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
301	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
302	C₂×Dic₁₀	—	2	4	no	—
303	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
304	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
305	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
306	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
307	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	—
308	#685	C₂³×C₃	1	16	yes	—
309	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
310	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
311	#683	C₂³×C₃	1	16	yes	—
312	C₄×Dic₅	C₂³×C₃	1	4	yes	—
313	C₄×Dic₅	C₂³×C₃	1	4	yes	—
314	C₂²×#41	—	5	1	no	—
315	C₂²×#41	C₃×D₅	1	1	yes	characteristic, complemented
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	4	no	—
323	#525	—	5	4	no	—
324	#525	—	5	4	no	—
325	C₂×#117	—	5	1	no	—
326	C₂²×C₃×C₅	—	2	2	no	—
327	C₂²×C₃×C₅	—	2	2	no	—
328	C₂²×C₃×C₅	—	2	2	no	—
329	C₂²×C₃×C₅	—	2	4	no	—
330	C₂²×C₃×C₅	—	2	8	no	—
331	C₂²×C₃×C₅	—	4	4	no	—
332	C₂²×C₃×C₅	—	4	8	no	—
333	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
334	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
335	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
336	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
337	C₂×C₃×D₅	—	2	4	no	—
338	C₂×C₃×D₅	—	2	8	no	—
339	C₂×C₃×D₅	—	4	8	no	—
340	C₃×C₄×C₅	—	2	4	no	—
341	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
342	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
343	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
344	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
345	C₃×Dic₅	—	2	4	no	—
346	C₃×Dic₅	—	2	8	no	—
347	C₂⁴×C₃	—	5	2	no	—
348	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
349	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
350	C₃×#41	—	2	8	no	—
351	C₃×#41	—	2	8	no	—
352	C₃×#41	—	2	8	no	—
353	C₃×#41	—	2	8	no	—
354	C₃×#41	—	10	8	no	—
355	C₃×#41	—	10	8	no	—
356	C₃×#41	—	10	8	no	—
357	C₃×#41	—	10	8	no	—
358	C₂×C₃×Q₈	—	2	4	no	—
359	C₂×C₃×Q₈	—	5	2	no	—
360	C₂×C₃×Q₈	—	5	2	no	—
361	C₂×C₃×Q₈	—	10	4	no	—
362	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
363	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
364	C₂×C₃×D₄	—	2	8	no	—
365	C₂×C₃×D₄	—	2	4	no	—
366	C₂×C₃×D₄	—	5	4	no	—
367	C₂×C₃×D₄	—	5	4	no	—
368	C₂×C₃×D₄	—	5	16	no	—
369	C₂×C₃×D₄	—	5	2	no	—
370	C₂×C₃×D₄	—	5	2	no	—
371	C₂×C₃×D₄	—	10	8	no	—
372	C₂×C₃×D₄	—	10	4	no	—
373	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
374	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
375	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
376	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
377	C₂²×C₃×C₄	—	2	8	no	—
378	C₂²×C₃×C₄	—	5	2	no	—
379	C₂²×C₃×C₄	—	5	4	no	—
380	C₂²×C₃×C₄	—	5	4	no	—
381	C₂²×C₃×C₄	—	5	4	no	—
382	C₂²×C₃×C₄	—	10	8	no	—
383	C₂²×C₃×C₄	C₂²⋊D₅	1	8	yes	complemented
384	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
385	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
386	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
387	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
393	C₃×C₄⋊C₄	—	5	16	no	—
394	C₃×C₄⋊C₄	—	5	4	no	—
395	C₃×C₄⋊C₄	—	5	4	no	—
396	C₃×C₂²⋊C₄	—	5	4	no	—
397	C₃×C₂²⋊C₄	—	5	4	no	—
398	C₃×C₂²⋊C₄	—	5	16	no	—
399	C₃×C₂²⋊C₄	—	5	16	no	—
400	C₃×C₄²	—	5	4	no	—
401	C₃×C₄²	—	5	4	no	—
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	4	2	no	—
404	C₂³×C₅	—	4	4	no	—
405	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
406	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
407	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
408	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
409	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
410	C₂²×D₅	—	2	4	no	—
411	C₂²×D₅	—	4	4	no	—
412	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
413	C₅×Q₈	—	2	4	no	—
414	C₅×Q₈	—	2	4	no	—
415	C₅×D₄	—	2	8	no	—
416	C₅×D₄	—	2	8	no	—
417	C₅×D₄	—	2	4	no	—
418	C₅×D₄	—	2	4	no	—
419	C₂×C₄×C₅	—	2	4	no	—
420	C₂×C₄×C₅	—	2	8	no	—
421	C₂×C₄×C₅	—	2	8	no	—
422	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
423	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
424	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
425	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
426	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
427	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
428	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
429	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
430	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
431	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
432	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
433	C₂²⋊D₅	—	2	8	no	—
434	C₂²⋊D₅	—	2	8	no	—
435	C₂²⋊D₅	—	4	16	no	—
436	C₂×Dic₅	—	2	4	no	—
437	C₂×Dic₅	—	4	4	no	—
438	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
439	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
440	D₂₀	—	2	4	no	—
441	D₂₀	—	2	4	no	—
442	C₄×D₅	—	2	8	no	—
443	C₄×D₅	—	2	8	no	—
444	Dic₁₀	—	2	4	no	—
445	Dic₁₀	—	2	4	no	—
446	C₂×#41	—	2	8	no	—
447	C₂×#41	—	5	2	no	—
448	C₂×#41	—	5	2	no	—
449	C₂×#41	—	5	2	no	—
450	C₂×#41	—	5	2	no	—
451	C₂×#41	—	10	8	no	—
452	C₂×#41	C₂×C₃×D₅	1	2	yes	—
453	C₂×#41	C₂×C₃×D₅	1	2	yes	—
454	C₂×#41	C₂×C₃×D₅	1	2	yes	complemented
455	C₂×#41	C₂×C₃×D₅	1	2	yes	complemented
456	C₂²×Q₈	—	5	1	no	—
457	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
458	C₂²×D₄	—	5	2	no	—
459	C₂²×D₄	—	5	1	no	—
460	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
461	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
462	C₂³×C₄	—	5	2	no	—
463	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
464	C₂³×C₄	C₂×C₃×D₅	1	2	yes	complemented
465	C₄⋊Q₈	—	5	4	no	—
466	#127	—	5	4	no	—
467	#124	—	5	4	no	—
468	#124	—	5	4	no	—
469	#123	—	5	8	no	—
470	#123	—	5	8	no	—
471	C₂²⋊Q₈	—	5	8	no	—
472	C₂²⋊Q₈	—	5	8	no	—
473	#121	—	5	8	no	—
474	#121	—	5	16	no	—
475	#121	—	5	8	no	—
476	#120	—	5	8	no	—
477	#120	—	5	8	no	—
478	C₄×D₄	—	5	16	no	—
479	#117	—	5	2	no	—
480	#117	—	5	2	no	—
481	#117	—	5	2	no	—
482	#117	—	5	2	no	—
483	C₂×C₄⋊C₄	—	5	2	no	—
484	C₂×C₂²⋊C₄	—	5	2	no	—
485	C₂×C₄²	—	5	2	no	—
486	C₂×C₃×C₅	—	2	2	no	—
487	C₂×C₃×C₅	—	2	2	no	—
488	C₂×C₃×C₅	—	2	2	no	—
489	C₂×C₃×C₅	—	4	4	no	—
490	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
491	C₂×C₃×C₅	#585	1	2	yes	—
492	C₃×D₅	—	4	4	no	—
493	C₂³×C₃	—	2	4	no	—
494	C₂³×C₃	—	4	2	no	—
495	C₂³×C₃	—	4	4	no	—
496	C₂³×C₃	—	5	4	no	—
497	C₂³×C₃	—	10	4	no	—
498	C₂³×C₃	—	20	4	no	—
499	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
500	C₂³×C₃	C₂³×D₅	1	4	yes	—
501	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
502	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
503	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
504	C₃×Q₈	—	2	4	no	—
505	C₃×Q₈	—	2	4	no	—
506	C₃×Q₈	—	10	4	no	—
507	C₃×Q₈	—	10	4	no	—
508	C₃×D₄	—	2	8	no	—
509	C₃×D₄	—	2	8	no	—
510	C₃×D₄	—	2	4	no	—
511	C₃×D₄	—	2	4	no	—
512	C₃×D₄	—	10	8	no	—
513	C₃×D₄	—	10	8	no	—
514	C₃×D₄	—	10	4	no	—
515	C₃×D₄	—	10	4	no	—
516	C₃×D₄	—	20	16	no	—
517	C₂×C₃×C₄	—	2	4	no	—
518	C₂×C₃×C₄	—	2	8	no	—
519	C₂×C₃×C₄	—	2	8	no	—
520	C₂×C₃×C₄	—	5	8	no	—
521	C₂×C₃×C₄	—	5	4	no	—
522	C₂×C₃×C₄	—	10	4	no	—
523	C₂×C₃×C₄	—	10	8	no	—
524	C₂×C₃×C₄	—	10	8	no	—
525	C₂×C₃×C₄	—	20	4	no	—
526	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
527	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
528	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
529	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
530	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
531	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
532	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
533	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
537	C₂²×C₅	—	2	2	no	—
538	C₂²×C₅	—	2	2	no	—
539	C₂²×C₅	—	2	2	no	—
540	C₂²×C₅	—	2	4	no	—
541	C₂²×C₅	—	2	8	no	—
542	C₂²×C₅	—	4	4	no	—
543	C₂²×C₅	—	4	8	no	—
544	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
545	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
546	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
547	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
548	C₂×D₅	—	2	4	no	—
549	C₂×D₅	—	2	8	no	—
550	C₂×D₅	—	4	8	no	—
551	C₄×C₅	—	2	4	no	—
552	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
553	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
554	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
555	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
556	Dic₅	—	2	4	no	—
557	Dic₅	—	2	8	no	—
558	C₂⁴	—	5	2	no	—
559	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
560	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
561	#41	—	2	8	no	—
562	#41	—	2	8	no	—
563	#41	—	2	8	no	—
564	#41	—	2	8	no	—
565	#41	—	10	8	no	—
566	#41	—	10	8	no	—
567	#41	—	10	8	no	—
568	#41	—	10	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	5	2	no	—
571	C₂×Q₈	—	5	2	no	—
572	C₂×Q₈	—	10	4	no	—
573	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
574	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	5	4	no	—
578	C₂×D₄	—	5	4	no	—
579	C₂×D₄	—	5	16	no	—
580	C₂×D₄	—	5	2	no	—
581	C₂×D₄	—	5	2	no	—
582	C₂×D₄	—	10	8	no	—
583	C₂×D₄	—	10	4	no	—
584	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
585	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
586	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
587	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
588	C₂²×C₄	—	2	8	no	—
589	C₂²×C₄	—	5	2	no	—
590	C₂²×C₄	—	5	4	no	—
591	C₂²×C₄	—	5	4	no	—
592	C₂²×C₄	—	5	4	no	—
593	C₂²×C₄	—	10	8	no	—
594	C₂²×C₄	C₃×C₂²⋊D₅	1	8	yes	complemented
595	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
596	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
597	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
598	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
600	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
602	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
603	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
604	C₄⋊C₄	—	5	4	no	—
605	C₄⋊C₄	—	5	4	no	—
606	C₄⋊C₄	—	5	16	no	—
607	C₂²⋊C₄	—	5	4	no	—
608	C₂²⋊C₄	—	5	4	no	—
609	C₂²⋊C₄	—	5	16	no	—
610	C₂²⋊C₄	—	5	16	no	—
611	C₄²	—	5	4	no	—
612	C₄²	—	5	4	no	—
613	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	2	no	—
616	C₂²×C₃	—	2	2	no	—
617	C₂²×C₃	—	2	8	no	—
618	C₂²×C₃	—	2	4	no	—
619	C₂²×C₃	—	4	4	no	—
620	C₂²×C₃	—	4	8	no	—
621	C₂²×C₃	—	10	8	no	—
622	C₂²×C₃	—	10	4	no	—
623	C₂²×C₃	—	20	8	no	—
624	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
625	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
626	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
627	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
628	C₃×C₄	—	2	4	no	—
629	C₃×C₄	—	10	8	no	—
630	C₃×C₄	—	10	4	no	—
631	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
632	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
633	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
634	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
635	C₂×C₅	—	2	2	no	—
636	C₂×C₅	—	2	2	no	—
637	C₂×C₅	—	2	2	no	—
638	C₂×C₅	—	4	4	no	—
639	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
640	C₂×C₅	C₃×#585	1	2	yes	—
641	D₅	—	4	4	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	5	4	no	—
646	C₂³	—	10	4	no	—
647	C₂³	—	20	4	no	—
648	C₂³	C₂×C₃×C₂²⋊D₅	1	4	yes	—
649	C₂³	C₂³×C₃×D₅	1	4	yes	—
650	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
651	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
652	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
653	Q₈	—	2	4	no	—
654	Q₈	—	2	4	no	—
655	Q₈	—	10	4	no	—
656	Q₈	—	10	4	no	—
657	D₄	—	2	8	no	—
658	D₄	—	2	8	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	4	no	—
661	D₄	—	10	8	no	—
662	D₄	—	10	8	no	—
663	D₄	—	10	4	no	—
664	D₄	—	10	4	no	—
665	D₄	—	20	16	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	8	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	5	8	no	—
670	C₂×C₄	—	5	4	no	—
671	C₂×C₄	—	10	4	no	—
672	C₂×C₄	—	10	8	no	—
673	C₂×C₄	—	10	8	no	—
674	C₂×C₄	—	20	4	no	—
675	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
676	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
677	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
678	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
679	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
680	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
681	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
682	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
683	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
684	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
685	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
686	C₂×C₃	—	2	2	no	—
687	C₂×C₃	—	2	2	no	—
688	C₂×C₃	—	2	2	no	—
689	C₂×C₃	—	4	4	no	—
690	C₂×C₃	—	20	4	no	—
691	C₂×C₃	#66283	1	2	yes	—
692	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
693	C₅	C₃×#3449	1	1	yes	characteristic, complemented, Sylow
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	8	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	8	no	—
701	C₂²	—	10	8	no	—
702	C₂²	—	10	4	no	—
703	C₂²	—	20	8	no	—
704	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
705	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
706	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
707	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
708	C₄	—	2	4	no	—
709	C₄	—	10	8	no	—
710	C₄	—	10	4	no	—
711	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
712	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
713	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
714	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
715	C₃	#10619169	1	1	yes	characteristic, direct product factor, Sylow
716	C₂	—	2	2	no	—
717	C₂	—	2	2	no	—
718	C₂	—	2	2	no	—
719	C₂	—	4	4	no	—
720	C₂	—	20	4	no	—
721	C₂	C₃×#66283	1	2	yes	—
722	C₂	C₂³×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂²×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂²×C₃×#41	D₅
hypocenter	C₅	C₃×#3449
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₃×#709	C₂	semidirect
3. C₃×#66167	C₂	semidirect
4. C₃×#66166	C₂	semidirect
5. C₃×#66164	C₂	semidirect
6. C₃×#66162	C₂	semidirect
7. C₃×#66159	C₂	semidirect
8. C₃×#66150	C₂	semidirect
9. C₃×#66139	C₂	semidirect
10. C₃×#66138	C₂	semidirect
11. C₃×#66125	C₂	semidirect
12. C₂×C₃×#4072	C₂	semidirect
13. #10619169	C₃	direct (N × H)
17. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₂²×C₃×C₅×Q₈	C₂²	semidirect
21. C₂²×C₃×C₅×D₄	C₂²	semidirect
23. C₂³×C₃×C₄×C₅	C₂²	semidirect
28. C₂×C₃×#709	C₂²	semidirect
29. C₂×C₃×#709	C₂²	semidirect
30. C₂²×C₃×D₂₀	C₂²	semidirect
31. C₂²×C₃×C₄×D₅	C₂²	semidirect
32. C₂²×C₃×Dic₁₀	C₂²	semidirect
33. C₃×#4099	C₂²	semidirect
35. C₃×#4093	C₂²	semidirect
36. C₃×#4092	C₂²	semidirect
37. C₃×#4090	C₂²	semidirect
38. C₃×#4086	C₂²	semidirect
39. C₃×#4085	C₂²	semidirect
40. C₃×#4084	C₂²	semidirect
41. C₃×#4083	C₂²	semidirect
42. C₃×#4082	C₂²	semidirect
43. C₃×#4081	C₂²	semidirect
44. C₃×#4076	C₂²	semidirect
45. C₃×#4075	C₂²	semidirect
46. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
47. C₃×#4072	C₂²	semidirect
48. C₃×#4072	C₂²	semidirect
49. C₃×#4072	C₂²	semidirect
50. C₃×#4072	C₂²	semidirect
51. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
52. C₃×#4070	C₂²	semidirect
53. C₂×C₃×C₄×Dic₅	C₂²	semidirect
55. C₂²×C₅×#41	C₂×C₃	semidirect
56. C₂²×#709	C₂×C₃	semidirect
57. #66167	C₂×C₃	semidirect
58. #66166	C₂×C₃	semidirect
59. #66164	C₂×C₃	semidirect
60. #66162	C₂×C₃	semidirect
61. #66159	C₂×C₃	semidirect
62. #66150	C₂×C₃	semidirect
63. #66139	C₂×C₃	semidirect
64. #66138	C₂×C₃	semidirect
65. #66125	C₂×C₃	semidirect
66. C₂×#4072	C₂×C₃	semidirect
84. C₂²×C₃×C₄×C₅	D₄	semidirect
123. C₂²×C₃×#41	D₅	semidirect
137. C₂×C₅×#41	C₂²×C₃	semidirect
138. C₂×C₅×#41	C₂²×C₃	semidirect
139. C₂²×C₅×Q₈	C₂²×C₃	semidirect
141. C₂²×C₅×D₄	C₂²×C₃	semidirect
143. C₂³×C₄×C₅	C₂²×C₃	semidirect
148. C₂×#709	C₂²×C₃	semidirect
149. C₂×#709	C₂²×C₃	semidirect
150. C₂²×D₂₀	C₂²×C₃	semidirect
151. C₂²×C₄×D₅	C₂²×C₃	semidirect
152. C₂²×Dic₁₀	C₂²×C₃	semidirect
153. #4099	C₂²×C₃	semidirect
155. #4093	C₂²×C₃	semidirect
156. #4092	C₂²×C₃	semidirect
157. #4090	C₂²×C₃	semidirect
158. #4086	C₂²×C₃	semidirect
159. #4085	C₂²×C₃	semidirect
160. #4084	C₂²×C₃	semidirect
161. #4083	C₂²×C₃	semidirect
162. #4082	C₂²×C₃	semidirect
163. #4081	C₂²×C₃	semidirect
164. #4076	C₂²×C₃	semidirect
165. #4075	C₂²×C₃	semidirect
166. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
167. #4072	C₂²×C₃	semidirect
168. #4072	C₂²×C₃	semidirect
169. #4072	C₂²×C₃	semidirect
170. #4072	C₂²×C₃	semidirect
171. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
172. #4070	C₂²×C₃	semidirect
173. C₂×C₄×Dic₅	C₂²×C₃	semidirect
227. C₂×C₃×#41	C₂×D₅	semidirect
228. C₂×C₃×#41	C₂×D₅	semidirect
230. C₂²×C₃×Q₈	C₂×D₅	semidirect
234. C₂²×C₃×D₄	C₂×D₅	semidirect
237. C₂³×C₃×C₄	C₂×D₅	semidirect
276. C₂²×C₄×C₅	C₃×D₄	semidirect
315. C₂²×#41	C₃×D₅	semidirect
383. C₂²×C₃×C₄	C₂²⋊D₅	semidirect
454. C₂×#41	C₂×C₃×D₅	semidirect
455. C₂×#41	C₂×C₃×D₅	semidirect
457. C₂²×Q₈	C₂×C₃×D₅	semidirect
461. C₂²×D₄	C₂×C₃×D₅	semidirect
464. C₂³×C₄	C₂×C₃×D₅	semidirect
594. C₂²×C₄	C₃×C₂²⋊D₅	semidirect
613. C₃×C₅	#3449	semidirect
693. C₅	C₃×#3449	semidirect
715. C₃	#10619169	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×#41	2
C₂²×C₃×#709	2
C₃×#66167	2
C₃×#66166	2
C₃×#66164	2
C₃×#66162	2
C₃×#66159	2
C₃×#66150	2
C₃×#66139	2
C₃×#66138	2
C₃×#66125	2
C₂×C₃×#4072	2
#10619169	3
C₃×#3449	5

Subgroups — C3×#10619169 #14480639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10619169 #14480639