Subgroups — C₅×#78663 #14411806

Order 1920.

1548 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	C₂×C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5234	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5126	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4727	C₂	1	2	yes	maximal, complemented
9	C₅×#4727	C₂	1	2	yes	maximal, complemented
10	C₅×#4726	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
12	C₅×#2880	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×D₃×#41	—	2	4	no	—
15	C₅×D₃×#41	—	2	4	no	—
16	C₂×C₅×#239	C₄	1	1	yes	characteristic
17	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic
18	C₂×C₅×#237	C₄	1	2	yes	—
19	C₂×C₅×#237	C₄	1	1	yes	characteristic
20	C₂×C₅×D₃×D₄	C₄	1	2	yes	—
21	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
22	C₂×C₅×#235	C₂²	1	2	yes	—
23	C₂×C₅×#235	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₅×#907	—	2	4	no	—
31	C₅×#901	—	2	4	no	—
32	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
33	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
34	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
35	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
36	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
37	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
38	C₅×#830	C₂²	1	2	yes	complemented
39	C₅×#830	C₂²	1	2	yes	complemented
40	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
42	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
46	#78663	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₂²×C₅×#41	—	3	1	no	—
48	C₂×C₅×#131	—	3	1	no	—
49	C₂×C₅×#131	—	3	1	no	—
50	C₅×#408	—	3	2	no	—
51	C₅×#408	—	3	2	no	—
52	C₅×#408	—	3	1	no	—
53	C₅×#408	D₃	1	1	yes	characteristic, complemented
54	C₅×#407	—	3	2	no	—
55	C₅×#407	—	3	1	no	—
56	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
57	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
58	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
60	C₃×C₅×#41	—	2	2	no	—
61	C₃×C₅×#41	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
64	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×#67	C₂×C₄	1	2	yes	—
68	C₂×C₅×#67	C₂×C₄	1	2	yes	—
69	C₂×C₅×#67	C₂×C₄	1	2	yes	—
70	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
72	C₅×#239	—	2	4	no	—
73	C₅×D₃×Q₈	—	2	4	no	—
74	C₅×#237	—	2	8	no	—
75	C₅×#237	—	2	4	no	—
76	C₅×D₃×D₄	—	2	8	no	—
77	C₅×D₃×D₄	—	2	4	no	—
78	C₅×#235	—	2	4	no	—
79	C₅×#235	—	2	4	no	—
80	C₅×#235	D₄	1	4	yes	—
81	C₅×#235	D₄	1	4	yes	—
82	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
83	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	—	2	2	no	—
85	C₂×C₄×C₅×D₃	—	2	2	no	—
86	C₂×C₄×C₅×D₃	—	2	4	no	—
87	C₂×C₄×C₅×D₃	—	2	4	no	—
88	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
90	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
91	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
95	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
96	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
97	C₃×C₅×M₁₆	—	2	2	no	—
98	C₂×C₃×C₅×C₈	—	2	2	no	—
99	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₅×#208	—	2	2	no	—
103	C₂×C₅×C₃⋊C₈	—	2	2	no	—
104	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
106	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
107	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
108	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
109	C₅×D₃×C₈	—	2	4	no	—
110	C₅×D₃×C₈	—	2	4	no	—
111	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic
112	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#901	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
115	#5234	C₂×C₅	1	1	yes	characteristic, complemented
116	#5126	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
118	#4727	C₂×C₅	1	2	yes	complemented
119	#4727	C₂×C₅	1	2	yes	complemented
120	#4726	C₂×C₅	1	2	yes	complemented
121	D₃×C₂²⋊C₈	C₂×C₅	1	2	yes	complemented
122	C₂×C₅×#41	—	3	1	no	—
123	C₂×C₅×#41	—	3	2	no	—
124	C₂×C₅×#41	—	3	1	no	—
125	C₂×C₅×#41	—	3	1	no	—
126	C₂×C₅×#41	—	3	2	no	—
127	C₂×C₅×#41	—	6	4	no	—
128	C₂×C₅×#41	—	6	4	no	—
129	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₅×Q₈	—	3	1	no	—
131	C₂²×C₅×D₄	—	3	2	no	—
132	C₂²×C₅×D₄	—	3	1	no	—
133	C₂³×C₄×C₅	—	3	2	no	—
134	C₂³×C₄×C₅	—	3	1	no	—
135	C₅×#131	—	6	4	no	—
136	C₅×#131	—	6	4	no	—
137	C₂×C₅×M₁₆	—	3	1	no	—
138	C₂×C₅×M₁₆	—	3	2	no	—
139	C₂×C₅×M₁₆	—	3	2	no	—
140	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
141	C₂²×C₅×C₈	—	3	1	no	—
142	C₂²×C₅×C₈	—	3	2	no	—
143	C₂²×C₅×C₈	—	3	2	no	—
144	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
145	C₅×C₂²⋊C₈	—	3	2	no	—
146	C₅×C₂²⋊C₈	—	3	2	no	—
147	C₅×C₂²⋊C₈	—	3	1	no	—
148	C₅×C₂²⋊C₈	—	3	2	no	—
149	C₅×C₂²⋊C₈	—	3	1	no	—
150	C₅×C₂²⋊C₈	—	3	1	no	—
151	C₅×C₂²⋊C₈	—	3	1	no	—
152	C₅×C₂²⋊C₈	—	3	2	no	—
153	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
154	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
155	#2880	—	3	1	no	Sylow
156	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
157	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₅×D₃	—	2	2	no	—
159	C₂²×C₅×D₃	—	2	4	no	—
160	C₂²×C₅×D₃	—	2	4	no	—
161	C₂²×C₅×D₃	—	2	2	no	—
162	C₂²×C₅×D₃	—	4	2	no	—
163	C₂²×C₅×D₃	—	4	1	no	—
164	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
166	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
167	C₃×C₅×Q₈	—	2	2	no	—
168	C₃×C₅×D₄	—	2	4	no	—
169	C₃×C₅×D₄	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	2	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
175	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
177	C₅×#67	—	2	4	no	—
178	C₅×#67	—	2	4	no	—
179	C₅×#67	C₂²⋊C₄	1	8	yes	—
180	C₂×C₅×Dic₃	—	2	2	no	—
181	C₂×C₅×Dic₃	—	2	4	no	—
182	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
185	C₅×D₁₂	—	2	4	no	—
186	C₅×D₁₂	C₂²⋊C₄	1	4	yes	—
187	C₄×C₅×D₃	—	2	4	no	—
188	C₄×C₅×D₃	—	2	2	no	—
189	C₄×C₅×D₃	—	2	2	no	—
190	C₄×C₅×D₃	—	2	1	no	—
191	C₄×C₅×D₃	—	2	1	no	—
192	C₄×C₅×D₃	—	2	1	no	—
193	C₄×C₅×D₃	—	2	1	no	—
194	C₄×C₅×D₃	—	2	4	no	—
195	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
196	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
197	C₅×Dic₆	—	2	4	no	—
198	C₅×Dic₆	C₂²⋊C₄	1	4	yes	—
199	C₃×C₅×C₈	—	2	1	no	—
200	C₃×C₅×C₈	—	2	2	no	—
201	C₃×C₅×C₈	—	2	1	no	—
202	C₅×C₃⋊C₈	—	2	1	no	—
203	C₅×C₃⋊C₈	—	2	2	no	—
204	C₅×C₃⋊C₈	—	2	1	no	—
205	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
206	D₃×#41	—	2	4	no	—
207	D₃×#41	—	2	4	no	—
208	C₂×#239	C₄×C₅	1	1	yes	characteristic
209	C₂×D₃×Q₈	C₄×C₅	1	1	yes	characteristic
210	C₂×#237	C₄×C₅	1	2	yes	—
211	C₂×#237	C₄×C₅	1	1	yes	characteristic
212	C₂×D₃×D₄	C₄×C₅	1	2	yes	—
213	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
214	C₂×#235	C₂²×C₅	1	2	yes	—
215	C₂×#235	C₂²×C₅	1	1	yes	characteristic
216	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
217	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
218	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
219	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
220	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
221	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
222	#907	—	2	4	no	—
223	#901	—	2	4	no	—
224	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
225	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
226	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
227	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
228	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
229	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
230	#830	C₂²×C₅	1	2	yes	complemented
231	#830	C₂²×C₅	1	2	yes	complemented
232	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
233	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
234	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
235	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	complemented
236	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
237	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₂⁴×C₅	—	3	2	no	—
239	C₂⁴×C₅	—	3	1	no	—
240	C₅×#41	—	2	2	no	—
241	C₅×#41	—	2	2	no	—
242	C₅×#41	—	3	4	no	—
243	C₅×#41	—	3	4	no	—
244	C₅×#41	—	6	4	no	—
245	C₅×#41	—	6	4	no	—
246	C₅×#41	—	6	8	no	—
247	C₅×#41	—	6	4	no	—
248	C₅×#41	—	6	4	no	—
249	C₂×C₅×Q₈	—	3	1	no	—
250	C₂×C₅×Q₈	—	3	2	no	—
251	C₂×C₅×Q₈	—	6	4	no	—
252	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
253	C₂×C₅×D₄	—	3	2	no	—
254	C₂×C₅×D₄	—	3	2	no	—
255	C₂×C₅×D₄	—	3	2	no	—
256	C₂×C₅×D₄	—	3	1	no	—
257	C₂×C₅×D₄	—	3	2	no	—
258	C₂×C₅×D₄	—	6	8	no	—
259	C₂×C₅×D₄	—	6	4	no	—
260	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
261	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	—	3	2	no	—
263	C₂²×C₄×C₅	—	3	2	no	—
264	C₂²×C₄×C₅	—	3	1	no	—
265	C₂²×C₄×C₅	—	3	2	no	—
266	C₂²×C₄×C₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	2	no	—
268	C₂²×C₄×C₅	—	3	1	no	—
269	C₂²×C₄×C₅	—	3	1	no	—
270	C₂²×C₄×C₅	—	3	1	no	—
271	C₂²×C₄×C₅	—	6	4	no	—
272	C₂²×C₄×C₅	—	6	4	no	—
273	C₂²×C₄×C₅	—	6	2	no	—
274	C₂²×C₄×C₅	—	6	2	no	—
275	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
276	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
277	C₅×M₁₆	—	2	2	no	—
278	C₅×M₁₆	—	6	4	no	—
279	C₅×M₁₆	—	6	4	no	—
280	C₅×M₁₆	—	6	2	no	—
281	C₂×C₅×C₈	—	2	2	no	—
282	C₂×C₅×C₈	—	3	1	no	—
283	C₂×C₅×C₈	—	3	1	no	—
284	C₂×C₅×C₈	—	3	2	no	—
285	C₂×C₅×C₈	—	6	4	no	—
286	C₂×C₅×C₈	—	6	4	no	—
287	C₂×C₅×C₈	—	6	2	no	—
288	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
289	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
290	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
291	C₂²×#41	—	3	1	no	—
292	C₂×#131	—	3	1	no	—
293	C₂×#131	—	3	1	no	—
294	#408	—	3	1	no	—
295	#408	—	3	2	no	—
296	#408	—	3	2	no	—
297	#408	C₅×D₃	1	1	yes	characteristic, complemented
298	#407	—	3	1	no	—
299	#407	—	3	2	no	—
300	C₂×C₂²⋊C₈	—	3	1	no	—
301	C₂×C₂²⋊C₈	—	3	2	no	—
302	C₂²×C₃×C₅	—	2	1	no	—
303	C₂²×C₃×C₅	—	2	1	no	—
304	C₂²×C₃×C₅	—	2	2	no	—
305	C₂²×C₃×C₅	—	2	2	no	—
306	C₂²×C₃×C₅	—	2	2	no	—
307	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₅×D₃	—	2	1	no	—
310	C₂×C₅×D₃	—	2	2	no	—
311	C₂×C₅×D₃	—	2	1	no	—
312	C₂×C₅×D₃	—	2	2	no	—
313	C₂×C₅×D₃	—	2	1	no	—
314	C₂×C₅×D₃	—	2	1	no	—
315	C₂×C₅×D₃	—	2	1	no	—
316	C₂×C₅×D₃	—	4	8	no	—
317	C₂×C₅×D₃	—	4	4	no	—
318	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
319	C₂×C₅×D₃	#131	1	2	yes	complemented
320	C₃×C₄×C₅	—	2	2	no	—
321	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
322	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
324	C₅×Dic₃	—	2	1	no	—
325	C₅×Dic₃	—	2	1	no	—
326	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
327	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
329	C₃×#41	—	2	2	no	—
330	C₃×#41	—	2	2	no	—
331	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
332	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
333	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂×#67	C₂×C₄×C₅	1	2	yes	—
337	C₂×#67	C₂×C₄×C₅	1	2	yes	—
338	C₂×#67	C₂×C₄×C₅	1	2	yes	—
339	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
341	#239	—	2	4	no	—
342	D₃×Q₈	—	2	4	no	—
343	#237	—	2	8	no	—
344	#237	—	2	4	no	—
345	D₃×D₄	—	2	8	no	—
346	D₃×D₄	—	2	4	no	—
347	#235	—	2	4	no	—
348	#235	—	2	4	no	—
349	#235	C₅×D₄	1	4	yes	—
350	#235	C₅×D₄	1	4	yes	—
351	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
352	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄×D₃	—	2	2	no	—
354	C₂×C₄×D₃	—	2	2	no	—
355	C₂×C₄×D₃	—	2	4	no	—
356	C₂×C₄×D₃	—	2	4	no	—
357	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
358	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
359	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
360	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
364	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
365	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
366	C₃×M₁₆	—	2	2	no	—
367	C₂×C₃×C₈	—	2	2	no	—
368	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
370	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
371	#208	—	2	2	no	—
372	C₂×C₃⋊C₈	—	2	2	no	—
373	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
375	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
376	ΓL(1,𝔽₂₅)	—	2	4	no	—
377	ΓL(1,𝔽₂₅)	—	2	4	no	—
378	D₃×C₈	—	2	4	no	—
379	D₃×C₈	—	2	4	no	—
380	C₂³×C₅	—	3	1	no	—
381	C₂³×C₅	—	3	2	no	—
382	C₂³×C₅	—	3	1	no	—
383	C₂³×C₅	—	6	4	no	—
384	C₂³×C₅	—	6	2	no	—
385	C₂³×C₅	—	6	4	no	—
386	C₂³×C₅	—	6	2	no	—
387	C₂³×C₅	—	12	1	no	—
388	C₂³×C₅	—	12	2	no	—
389	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
390	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
391	C₅×Q₈	—	2	2	no	—
392	C₅×Q₈	—	3	4	no	—
393	C₅×Q₈	—	6	4	no	—
394	C₅×D₄	—	2	4	no	—
395	C₅×D₄	—	2	2	no	—
396	C₅×D₄	—	3	8	no	—
397	C₅×D₄	—	3	4	no	—
398	C₅×D₄	—	6	4	no	—
399	C₅×D₄	—	6	4	no	—
400	C₅×D₄	—	6	4	no	—
401	C₂×C₄×C₅	—	2	2	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	—	3	2	no	—
404	C₂×C₄×C₅	—	3	4	no	—
405	C₂×C₄×C₅	—	3	4	no	—
406	C₂×C₄×C₅	—	3	1	no	—
407	C₂×C₄×C₅	—	3	1	no	—
408	C₂×C₄×C₅	—	6	4	no	—
409	C₂×C₄×C₅	—	6	4	no	—
410	C₂×C₄×C₅	—	6	4	no	—
411	C₂×C₄×C₅	—	6	2	no	—
412	C₂×C₄×C₅	—	6	2	no	—
413	C₂×C₄×C₅	—	6	2	no	—
414	C₂×C₄×C₅	—	6	1	no	—
415	C₂×C₄×C₅	—	6	1	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	6	1	no	—
418	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
419	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
420	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
421	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
422	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
423	C₅×C₈	—	2	1	no	—
424	C₅×C₈	—	2	1	no	—
425	C₅×C₈	—	2	2	no	—
426	C₅×C₈	—	6	1	no	—
427	C₅×C₈	—	6	2	no	—
428	C₅×C₈	—	6	1	no	—
429	C₂×#41	—	3	1	no	—
430	C₂×#41	—	3	2	no	—
431	C₂×#41	—	3	1	no	—
432	C₂×#41	—	3	1	no	—
433	C₂×#41	—	3	2	no	—
434	C₂×#41	—	6	4	no	—
435	C₂×#41	—	6	4	no	—
436	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
437	C₂²×Q₈	—	3	1	no	—
438	C₂²×D₄	—	3	2	no	—
439	C₂²×D₄	—	3	1	no	—
440	C₂³×C₄	—	3	2	no	—
441	C₂³×C₄	—	3	1	no	—
442	#131	—	6	4	no	—
443	#131	—	6	4	no	—
444	C₂×M₁₆	—	3	1	no	—
445	C₂×M₁₆	—	3	2	no	—
446	C₂×M₁₆	—	3	2	no	—
447	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
448	C₂²×C₈	—	3	1	no	—
449	C₂²×C₈	—	3	2	no	—
450	C₂²×C₈	—	3	2	no	—
451	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
452	C₂²⋊C₈	—	3	2	no	—
453	C₂²⋊C₈	—	3	2	no	—
454	C₂²⋊C₈	—	3	1	no	—
455	C₂²⋊C₈	—	3	2	no	—
456	C₂²⋊C₈	—	3	1	no	—
457	C₂²⋊C₈	—	3	1	no	—
458	C₂²⋊C₈	—	3	1	no	—
459	C₂²⋊C₈	—	3	2	no	—
460	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
461	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
462	C₂×C₃×C₅	—	2	2	no	—
463	C₂×C₃×C₅	—	4	2	no	—
464	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
466	C₂×C₃×C₅	#568	1	1	yes	characteristic
467	C₅×D₃	—	2	2	no	—
468	C₅×D₃	—	2	4	no	—
469	C₅×D₃	—	4	1	no	—
470	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
471	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
472	C₂²×D₃	—	2	2	no	—
473	C₂²×D₃	—	2	4	no	—
474	C₂²×D₃	—	2	4	no	—
475	C₂²×D₃	—	2	2	no	—
476	C₂²×D₃	—	4	2	no	—
477	C₂²×D₃	—	4	1	no	—
478	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
479	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
480	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
481	C₃×Q₈	—	2	2	no	—
482	C₃×D₄	—	2	4	no	—
483	C₃×D₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	—	2	2	no	—
486	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
487	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
489	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
490	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
491	#67	—	2	4	no	—
492	#67	—	2	4	no	—
493	#67	C₅×C₂²⋊C₄	1	8	yes	—
494	C₂×Dic₃	—	2	2	no	—
495	C₂×Dic₃	—	2	4	no	—
496	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
498	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
499	D₁₂	—	2	4	no	—
500	D₁₂	C₅×C₂²⋊C₄	1	4	yes	—
501	C₄×D₃	—	2	4	no	—
502	C₄×D₃	—	2	2	no	—
503	C₄×D₃	—	2	2	no	—
504	C₄×D₃	—	2	1	no	—
505	C₄×D₃	—	2	1	no	—
506	C₄×D₃	—	2	1	no	—
507	C₄×D₃	—	2	1	no	—
508	C₄×D₃	—	2	4	no	—
509	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
510	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
511	Dic₆	—	2	4	no	—
512	Dic₆	C₅×C₂²⋊C₄	1	4	yes	—
513	C₃×C₈	—	2	1	no	—
514	C₃×C₈	—	2	2	no	—
515	C₃×C₈	—	2	1	no	—
516	C₃⋊C₈	—	2	1	no	—
517	C₃⋊C₈	—	2	2	no	—
518	C₃⋊C₈	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	2	2	no	—
522	C₂²×C₅	—	2	2	no	—
523	C₂²×C₅	—	2	2	no	—
524	C₂²×C₅	—	3	4	no	—
525	C₂²×C₅	—	3	2	no	—
526	C₂²×C₅	—	6	1	no	—
527	C₂²×C₅	—	6	2	no	—
528	C₂²×C₅	—	6	2	no	—
529	C₂²×C₅	—	6	1	no	—
530	C₂²×C₅	—	6	1	no	—
531	C₂²×C₅	—	6	1	no	—
532	C₂²×C₅	—	6	1	no	—
533	C₂²×C₅	—	12	4	no	—
534	C₂²×C₅	—	12	8	no	—
535	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
536	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
537	C₄×C₅	—	2	2	no	—
538	C₄×C₅	—	3	4	no	—
539	C₄×C₅	—	6	1	no	—
540	C₄×C₅	—	6	1	no	—
541	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
542	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
543	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
544	C₂⁴	—	3	2	no	—
545	C₂⁴	—	3	1	no	—
546	#41	—	2	2	no	—
547	#41	—	2	2	no	—
548	#41	—	3	4	no	—
549	#41	—	3	4	no	—
550	#41	—	6	4	no	—
551	#41	—	6	4	no	—
552	#41	—	6	8	no	—
553	#41	—	6	4	no	—
554	#41	—	6	4	no	—
555	C₂×Q₈	—	3	1	no	—
556	C₂×Q₈	—	3	2	no	—
557	C₂×Q₈	—	6	4	no	—
558	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
559	C₂×D₄	—	3	2	no	—
560	C₂×D₄	—	3	2	no	—
561	C₂×D₄	—	3	2	no	—
562	C₂×D₄	—	3	1	no	—
563	C₂×D₄	—	3	2	no	—
564	C₂×D₄	—	6	8	no	—
565	C₂×D₄	—	6	4	no	—
566	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
567	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
568	C₂²×C₄	—	3	2	no	—
569	C₂²×C₄	—	3	2	no	—
570	C₂²×C₄	—	3	1	no	—
571	C₂²×C₄	—	3	2	no	—
572	C₂²×C₄	—	3	1	no	—
573	C₂²×C₄	—	3	2	no	—
574	C₂²×C₄	—	3	1	no	—
575	C₂²×C₄	—	3	1	no	—
576	C₂²×C₄	—	3	1	no	—
577	C₂²×C₄	—	6	4	no	—
578	C₂²×C₄	—	6	4	no	—
579	C₂²×C₄	—	6	2	no	—
580	C₂²×C₄	—	6	2	no	—
581	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
582	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
583	M₁₆	—	2	2	no	—
584	M₁₆	—	6	4	no	—
585	M₁₆	—	6	4	no	—
586	M₁₆	—	6	2	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	—	3	1	no	—
589	C₂×C₈	—	3	2	no	—
590	C₂×C₈	—	3	1	no	—
591	C₂×C₈	—	6	4	no	—
592	C₂×C₈	—	6	4	no	—
593	C₂×C₈	—	6	2	no	—
594	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
595	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
596	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
597	C₃×C₅	#2880	1	1	yes	characteristic, complemented, Hall
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	2	2	no	—
602	C₂²×C₃	—	2	2	no	—
603	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
604	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
605	C₂×D₃	—	2	1	no	—
606	C₂×D₃	—	2	2	no	—
607	C₂×D₃	—	2	1	no	—
608	C₂×D₃	—	2	2	no	—
609	C₂×D₃	—	2	1	no	—
610	C₂×D₃	—	2	1	no	—
611	C₂×D₃	—	2	1	no	—
612	C₂×D₃	—	4	8	no	—
613	C₂×D₃	—	4	4	no	—
614	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
615	C₂×D₃	C₅×#131	1	2	yes	complemented
616	C₃×C₄	—	2	2	no	—
617	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
618	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
619	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
620	Dic₃	—	2	1	no	—
621	Dic₃	—	2	1	no	—
622	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
623	C₂×C₅	—	2	2	no	—
624	C₂×C₅	—	4	2	no	—
625	C₂×C₅	—	6	2	no	—
626	C₂×C₅	—	6	4	no	—
627	C₂×C₅	—	12	1	no	—
628	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
629	C₂×C₅	D₃×#131	1	1	yes	characteristic
630	C₂×C₅	#5750	1	1	yes	characteristic
631	C₂³	—	3	1	no	—
632	C₂³	—	3	2	no	—
633	C₂³	—	3	1	no	—
634	C₂³	—	6	4	no	—
635	C₂³	—	6	2	no	—
636	C₂³	—	6	4	no	—
637	C₂³	—	6	2	no	—
638	C₂³	—	12	1	no	—
639	C₂³	—	12	2	no	—
640	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
641	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
642	Q₈	—	2	2	no	—
643	Q₈	—	3	4	no	—
644	Q₈	—	6	4	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	2	no	—
647	D₄	—	3	8	no	—
648	D₄	—	3	4	no	—
649	D₄	—	6	4	no	—
650	D₄	—	6	4	no	—
651	D₄	—	6	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	3	2	no	—
655	C₂×C₄	—	3	4	no	—
656	C₂×C₄	—	3	4	no	—
657	C₂×C₄	—	3	1	no	—
658	C₂×C₄	—	3	1	no	—
659	C₂×C₄	—	6	4	no	—
660	C₂×C₄	—	6	4	no	—
661	C₂×C₄	—	6	4	no	—
662	C₂×C₄	—	6	2	no	—
663	C₂×C₄	—	6	2	no	—
664	C₂×C₄	—	6	2	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	6	1	no	—
668	C₂×C₄	—	6	1	no	—
669	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
670	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
671	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
672	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
673	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
674	C₈	—	2	1	no	—
675	C₈	—	2	1	no	—
676	C₈	—	2	2	no	—
677	C₈	—	6	1	no	—
678	C₈	—	6	2	no	—
679	C₈	—	6	1	no	—
680	C₂×C₃	—	2	2	no	—
681	C₂×C₃	—	4	2	no	—
682	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
683	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
684	C₂×C₃	C₅×#568	1	1	yes	characteristic
685	D₃	—	2	2	no	—
686	D₃	—	2	4	no	—
687	D₃	—	4	1	no	—
688	C₅	#78663	1	1	yes	characteristic, direct product factor, Sylow
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	3	4	no	—
695	C₂²	—	3	2	no	—
696	C₂²	—	6	1	no	—
697	C₂²	—	6	2	no	—
698	C₂²	—	6	1	no	—
699	C₂²	—	6	2	no	—
700	C₂²	—	6	1	no	—
701	C₂²	—	6	1	no	—
702	C₂²	—	6	1	no	—
703	C₂²	—	12	4	no	—
704	C₂²	—	12	8	no	—
705	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
706	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
707	C₄	—	2	2	no	—
708	C₄	—	3	4	no	—
709	C₄	—	6	1	no	—
710	C₄	—	6	1	no	—
711	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
712	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
713	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
714	C₃	C₅×#2880	1	1	yes	characteristic, complemented, Sylow
715	C₂	—	2	2	no	—
716	C₂	—	4	2	no	—
717	C₂	—	6	2	no	—
718	C₂	—	6	4	no	—
719	C₂	—	12	1	no	—
720	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
721	C₂	C₅×D₃×#131	1	1	yes	characteristic
722	C₂	C₅×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#408	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×D₃×#41	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#408	D₃
hypocenter	C₃	C₅×#2880
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#907	C₂	semidirect
3. C₂×C₅×#901	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₅×#5234	C₂	semidirect
6. C₅×#5126	C₂	semidirect
7. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
8. C₅×#4727	C₂	semidirect
9. C₅×#4727	C₂	semidirect
10. C₅×#4726	C₂	semidirect
11. C₅×D₃×C₂²⋊C₈	C₂	semidirect
26. C₂×C₃×C₅×M₁₆	C₂²	semidirect
27. C₂²×C₃×C₅×C₈	C₂²	semidirect
28. C₂×C₅×#208	C₂²	semidirect
29. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
32. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
33. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
34. C₂×C₅×D₃×C₈	C₂²	semidirect
35. C₂×C₅×D₃×C₈	C₂²	semidirect
36. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
37. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
38. C₅×#830	C₂²	semidirect
39. C₅×#830	C₂²	semidirect
43. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
44. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
45. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
46. #78663	C₅	direct (N × H)
53. C₅×#408	D₃	semidirect
112. C₂×#907	C₂×C₅	semidirect
113. C₂×#901	C₂×C₅	semidirect
114. C₃×#408	C₂×C₅	semidirect
115. #5234	C₂×C₅	semidirect
116. #5126	C₂×C₅	semidirect
117. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
118. #4727	C₂×C₅	semidirect
119. #4727	C₂×C₅	semidirect
120. #4726	C₂×C₅	semidirect
121. D₃×C₂²⋊C₈	C₂×C₅	semidirect
140. C₂×C₅×M₁₆	C₂×D₃	semidirect
144. C₂²×C₅×C₈	C₂×D₃	semidirect
153. C₅×C₂²⋊C₈	C₂×D₃	semidirect
154. C₅×C₂²⋊C₈	C₂×D₃	semidirect
218. C₂×C₃×M₁₆	C₂²×C₅	semidirect
219. C₂²×C₃×C₈	C₂²×C₅	semidirect
220. C₂×#208	C₂²×C₅	semidirect
221. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
224. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
225. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
226. C₂×D₃×C₈	C₂²×C₅	semidirect
227. C₂×D₃×C₈	C₂²×C₅	semidirect
228. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
229. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
230. #830	C₂²×C₅	semidirect
231. #830	C₂²×C₅	semidirect
235. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
236. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
237. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
297. #408	C₅×D₃	semidirect
319. C₂×C₅×D₃	#131	semidirect
447. C₂×M₁₆	C₂×C₅×D₃	semidirect
451. C₂²×C₈	C₂×C₅×D₃	semidirect
460. C₂²⋊C₈	C₂×C₅×D₃	semidirect
461. C₂²⋊C₈	C₂×C₅×D₃	semidirect
597. C₃×C₅	#2880	semidirect
615. C₂×D₃	C₅×#131	semidirect
688. C₅	#78663	direct (N × H)
714. C₃	C₅×#2880	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₂×C₅×#907	2
C₂×C₅×#901	2
C₃×C₅×#408	2
C₅×#5234	2
C₅×#5126	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₅×#4727	2
C₅×#4726	2
C₅×D₃×C₂²⋊C₈	2
C₅×#2880	3
#78663	5

Subgroups — C5×#78663 #14411806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78663 #14411806