Subgroups — C₅×#78992 #14412908

Order 1920.

1476 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5964	C₂	1	1	yes	maximal, characteristic
2	C₅×#5745	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5522	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#825	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5005	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4821	C₂	1	4	yes	maximal, complemented
9	C₅×D₃×#104	C₂	1	4	yes	maximal, complemented
10	C₅×#2901	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₅×#1010	—	2	1	no	—
13	C₅×#1010	C₄	1	2	yes	complemented
14	C₅×#1009	—	2	1	no	—
15	C₅×#1009	C₄	1	2	yes	complemented
16	C₅×D₃×#41	—	2	2	no	—
17	C₅×D₃×#41	C₂²	1	4	yes	—
18	C₅×#1007	C₄	1	2	yes	complemented
19	C₅×#1004	—	2	2	no	—
20	C₅×#1004	C₄	1	2	yes	complemented
21	C₂×C₅×#235	—	2	2	no	—
22	C₂×C₅×#235	C₂²	1	1	yes	characteristic
23	C₂×C₅×#235	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
28	C₅×#907	—	2	2	no	—
29	C₅×D₃×M₁₆	C₂²	1	4	yes	complemented
30	C₅×#901	—	2	2	no	—
31	C₅×#893	—	2	1	no	—
32	C₅×#887	—	2	1	no	—
33	C₅×#67⋊C₄	—	2	2	no	—
34	C₅×#872	C₂²	1	2	yes	complemented
35	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
36	C₃×C₅×#104	C₂²	1	4	yes	complemented
37	C₅×#837	C₂²	1	2	yes	complemented
38	C₅×#837	C₂²	1	2	yes	complemented
39	C₅×#825	C₂²	1	2	yes	complemented
40	C₅×#825	C₂²	1	2	yes	complemented
41	C₅×#805	C₂²	1	4	yes	complemented
42	#78992	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#585	—	3	1	no	—
44	C₅×#568	—	3	1	no	—
45	C₄×C₅×#41	—	3	1	no	—
46	C₅×#421	—	3	4	no	—
47	C₅×#421	—	3	1	no	—
48	C₅×#421	D₃	1	1	yes	characteristic, complemented
49	C₂×C₅×#104	—	3	4	no	—
50	C₂×C₅×#104	—	3	1	no	—
51	C₂×C₅×#104	—	3	1	no	—
52	C₃×C₅×#41	—	2	1	no	—
53	C₃×C₅×#41	—	2	1	no	—
54	C₃×C₅×#41	C₂×C₄	1	2	yes	complemented
55	C₃×C₅×#41	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₅×#67	—	2	1	no	—
62	C₂×C₅×#67	—	2	4	no	—
63	C₂×C₅×#67	D₄	1	2	yes	—
64	C₂²×C₅×Dic₃	—	2	1	no	—
65	C₅×#239	—	2	2	no	—
66	C₅×#239	C₂×C₄	1	4	yes	complemented
67	C₅×D₃×Q₈	—	2	2	no	—
68	C₅×D₃×Q₈	C₂×C₄	1	4	yes	complemented
69	C₅×#237	—	2	4	no	—
70	C₅×#237	—	2	4	no	—
71	C₅×#237	—	2	2	no	—
72	C₅×#237	C₂×C₄	1	4	yes	complemented
73	C₅×D₃×D₄	—	2	4	no	—
74	C₅×D₃×D₄	—	2	4	no	—
75	C₅×D₃×D₄	—	2	2	no	—
76	C₅×D₃×D₄	C₂×C₄	1	4	yes	complemented
77	C₅×#235	—	2	1	no	—
78	C₅×#235	—	2	1	no	—
79	C₅×#235	—	2	4	no	—
80	C₅×#235	—	2	2	no	—
81	C₅×#235	—	2	4	no	—
82	C₅×#235	—	2	2	no	—
83	C₅×#235	C₂×C₄	1	2	yes	—
84	C₅×#235	C₂×C₄	1	2	yes	—
85	C₅×#235	C₂×C₄	1	2	yes	complemented
86	C₅×#235	D₄	1	2	yes	—
87	C₅×#235	D₄	1	2	yes	—
88	C₅×#235	C₂³	1	2	yes	—
89	C₂×C₅×D₁₂	—	2	2	no	—
90	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₄×C₅×D₃	—	2	4	no	—
94	C₂×C₄×C₅×D₃	—	2	2	no	—
95	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
96	C₂×C₅×Dic₆	—	2	2	no	—
97	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
99	C₃×C₅×M₁₆	—	2	1	no	—
100	C₃×C₅×M₁₆	C₂³	1	2	yes	—
101	C₂×C₃×C₅×C₈	—	2	1	no	—
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₃×C₄²×C₅	C₂³	1	2	yes	—
105	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
106	C₅×Dic₃⋊C₄	—	2	2	no	—
107	C₄×C₅×Dic₃	—	2	1	no	—
108	C₄×C₅×Dic₃	—	2	2	no	—
109	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
110	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
111	C₅×#208	—	2	1	no	—
112	C₅×#208	C₂³	1	2	yes	—
113	C₂×C₅×C₃⋊C₈	—	2	1	no	—
114	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
115	C₅×D₃×C₈	—	2	4	no	—
116	#5964	C₂×C₅	1	1	yes	characteristic
117	#5745	C₂×C₅	1	1	yes	characteristic, complemented
118	#5522	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#421	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#837	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×#825	C₂×C₅	1	1	yes	characteristic, complemented
122	#5005	C₂×C₅	1	1	yes	characteristic, complemented
123	#4821	C₂×C₅	1	4	yes	complemented
124	D₃×#104	C₂×C₅	1	4	yes	complemented
125	C₅×2₋¹⁺⁴	—	3	2	no	—
126	C₅×2₋¹⁺⁴	—	3	2	no	—
127	C₅×2₋¹⁺⁴	—	6	1	no	—
128	C₅×H(5,𝔽₂)	—	3	2	no	—
129	C₅×H(5,𝔽₂)	—	3	2	no	—
130	C₅×H(5,𝔽₂)	—	6	2	no	—
131	C₅×H(5,𝔽₂)	—	6	1	no	—
132	C₂×C₅×#41	—	3	1	no	—
133	C₂×C₅×#41	—	3	4	no	—
134	C₂×C₅×#41	—	3	1	no	—
135	C₂×C₅×#41	—	6	2	no	—
136	C₂×C₅×#41	—	6	2	no	—
137	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
138	C₅×#131	—	6	2	no	—
139	C₅×#131	—	6	2	no	—
140	C₂×C₅×M₁₆	—	3	1	no	—
141	C₂×C₅×M₁₆	—	3	4	no	—
142	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
143	C₄×C₅×Q₈	—	6	1	no	—
144	C₄×C₅×D₄	—	6	2	no	—
145	C₄×C₅×D₄	—	6	1	no	—
146	C₅×#117	—	3	2	no	—
147	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
148	C₂×C₄²×C₅	—	3	1	no	—
149	C₂×C₄²×C₅	—	3	2	no	—
150	C₅×#104	—	3	2	no	—
151	C₅×#104	—	3	2	no	—
152	C₅×#104	—	3	2	no	—
153	C₅×#104	—	3	2	no	—
154	C₅×#104	—	3	4	no	—
155	C₅×#104	C₂×D₃	1	4	yes	complemented
156	#2901	—	3	1	no	Sylow
157	C₂³×C₃×C₅	—	2	1	no	—
158	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₅×D₃	—	2	1	no	—
160	C₂²×C₅×D₃	—	2	4	no	—
161	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
162	C₃×C₅×Q₈	—	2	1	no	—
163	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
164	C₃×C₅×D₄	—	2	2	no	—
165	C₃×C₅×D₄	—	2	2	no	—
166	C₃×C₅×D₄	—	2	1	no	—
167	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	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	1	yes	characteristic
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₅×#67	—	2	2	no	—
179	C₅×#67	—	2	2	no	—
180	C₅×#67	—	2	4	no	—
181	C₅×#67	—	2	4	no	—
182	C₅×#67	C₂²⋊C₄	1	4	yes	—
183	C₅×#67	C₂²⋊C₄	1	4	yes	—
184	C₂×C₅×Dic₃	—	2	1	no	—
185	C₂×C₅×Dic₃	—	2	1	no	—
186	C₂×C₅×Dic₃	—	2	4	no	—
187	C₂×C₅×Dic₃	—	2	1	no	—
188	C₂×C₅×Dic₃	—	4	2	no	—
189	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
190	C₅×D₁₂	—	2	4	no	—
191	C₅×D₁₂	—	2	1	no	—
192	C₅×D₁₂	C₂²⋊C₄	1	2	yes	—
193	C₅×D₁₂	C₂²⋊C₄	1	2	yes	—
194	C₅×D₁₂	C₂²×C₄	1	2	yes	—
195	C₄×C₅×D₃	—	2	4	no	—
196	C₄×C₅×D₃	—	2	2	no	—
197	C₄×C₅×D₃	—	2	2	no	—
198	C₄×C₅×D₃	—	2	4	no	—
199	C₄×C₅×D₃	—	4	4	no	—
200	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
201	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
202	C₅×Dic₆	—	2	1	no	—
203	C₅×Dic₆	—	2	4	no	—
204	C₅×Dic₆	C₂²⋊C₄	1	2	yes	—
205	C₅×Dic₆	C₂²⋊C₄	1	2	yes	—
206	C₅×Dic₆	C₂²×C₄	1	2	yes	—
207	C₃×C₅×C₈	—	2	2	no	—
208	C₅×C₃⋊C₈	—	2	2	no	—
209	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
210	#1010	—	2	1	no	—
211	#1010	C₄×C₅	1	2	yes	complemented
212	#1009	—	2	1	no	—
213	#1009	C₄×C₅	1	2	yes	complemented
214	D₃×#41	—	2	2	no	—
215	D₃×#41	C₂²×C₅	1	4	yes	—
216	#1007	C₄×C₅	1	2	yes	complemented
217	#1004	—	2	2	no	—
218	#1004	C₄×C₅	1	2	yes	complemented
219	C₂×#235	—	2	2	no	—
220	C₂×#235	C₂²×C₅	1	1	yes	characteristic
221	C₂×#235	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
223	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
224	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
225	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
226	#907	—	2	2	no	—
227	D₃×M₁₆	C₂²×C₅	1	4	yes	complemented
228	#901	—	2	2	no	—
229	#893	—	2	1	no	—
230	#887	—	2	1	no	—
231	#67⋊C₄	—	2	2	no	—
232	#872	C₂²×C₅	1	2	yes	complemented
233	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
234	C₃×#104	C₂²×C₅	1	4	yes	complemented
235	#837	C₂²×C₅	1	2	yes	complemented
236	#837	C₂²×C₅	1	2	yes	complemented
237	#825	C₂²×C₅	1	2	yes	complemented
238	#825	C₂²×C₅	1	2	yes	complemented
239	#805	C₂²×C₅	1	4	yes	complemented
240	C₅×#41	—	2	1	no	—
241	C₅×#41	—	2	1	no	—
242	C₅×#41	—	3	2	no	—
243	C₅×#41	—	3	2	no	—
244	C₅×#41	—	3	2	no	—
245	C₅×#41	—	3	2	no	—
246	C₅×#41	—	3	4	no	—
247	C₅×#41	—	3	4	no	—
248	C₅×#41	—	3	2	no	—
249	C₅×#41	—	3	2	no	—
250	C₅×#41	—	6	4	no	—
251	C₅×#41	—	6	4	no	—
252	C₅×#41	—	6	2	no	—
253	C₅×#41	—	6	2	no	—
254	C₅×#41	—	6	4	no	—
255	C₅×#41	—	6	4	no	—
256	C₅×#41	—	6	2	no	—
257	C₅×#41	—	6	2	no	—
258	C₅×#41	—	6	1	no	—
259	C₅×#41	—	6	1	no	—
260	C₅×#41	C₄×D₃	1	2	yes	complemented
261	C₅×#41	C₂²×D₃	1	2	yes	—
262	C₂×C₅×Q₈	—	3	1	no	—
263	C₂×C₅×Q₈	—	3	4	no	—
264	C₂×C₅×Q₈	—	3	1	no	—
265	C₂×C₅×Q₈	—	6	2	no	—
266	C₂×C₅×Q₈	—	6	2	no	—
267	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic, complemented
268	C₂×C₅×D₄	—	2	1	no	—
269	C₂×C₅×D₄	—	3	2	no	—
270	C₂×C₅×D₄	—	3	4	no	—
271	C₂×C₅×D₄	—	3	1	no	—
272	C₂×C₅×D₄	—	3	1	no	—
273	C₂×C₅×D₄	—	6	2	no	—
274	C₂×C₅×D₄	—	6	4	no	—
275	C₂×C₅×D₄	—	6	2	no	—
276	C₂×C₅×D₄	—	6	4	no	—
277	C₂×C₅×D₄	—	6	4	no	—
278	C₂×C₅×D₄	—	6	1	no	—
279	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic, complemented
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	3	2	no	—
282	C₂²×C₄×C₅	—	6	4	no	—
283	C₂²×C₄×C₅	—	6	2	no	—
284	C₂²×C₄×C₅	—	6	1	no	—
285	C₂²×C₄×C₅	—	6	1	no	—
286	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
287	C₅×M₁₆	—	2	1	no	—
288	C₅×M₁₆	—	3	2	no	—
289	C₅×M₁₆	—	6	4	no	—
290	C₅×M₁₆	—	6	1	no	—
291	C₅×M₁₆	C₂²×D₃	1	2	yes	—
292	C₂×C₅×C₈	—	2	1	no	—
293	C₂×C₅×C₈	—	6	4	no	—
294	C₂×C₅×C₈	—	6	1	no	—
295	C₅×C₄⋊C₄	—	2	1	no	—
296	C₅×C₄⋊C₄	—	6	2	no	—
297	C₅×C₂²⋊C₄	—	2	1	no	—
298	C₅×C₂²⋊C₄	—	6	2	no	—
299	C₄²×C₅	—	3	1	no	—
300	C₄²×C₅	—	3	1	no	—
301	C₄²×C₅	—	6	2	no	—
302	C₄²×C₅	—	6	1	no	—
303	C₄²×C₅	C₂²×D₃	1	2	yes	—
304	#585	—	3	1	no	—
305	#568	—	3	1	no	—
306	C₄×#41	—	3	1	no	—
307	#421	—	3	1	no	—
308	#421	—	3	4	no	—
309	#421	C₅×D₃	1	1	yes	characteristic, complemented
310	C₂×#104	—	3	1	no	—
311	C₂×#104	—	3	1	no	—
312	C₂×#104	—	3	4	no	—
313	C₂²×C₃×C₅	—	2	2	no	—
314	C₂²×C₃×C₅	—	4	1	no	—
315	C₂²×C₃×C₅	—	8	1	no	—
316	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₅×D₃	—	2	2	no	—
320	C₂×C₅×D₃	—	4	2	no	—
321	C₂×C₅×D₃	—	8	4	no	—
322	C₂×C₅×D₃	—	8	1	no	—
323	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
324	C₃×C₄×C₅	—	2	2	no	—
325	C₃×C₄×C₅	—	4	2	no	—
326	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
329	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₅×Dic₃	—	2	2	no	—
331	C₅×Dic₃	—	2	2	no	—
332	C₅×Dic₃	—	4	1	no	—
333	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
334	C₃×#41	—	2	1	no	—
335	C₃×#41	—	2	1	no	—
336	C₃×#41	C₂×C₄×C₅	1	2	yes	complemented
337	C₃×#41	C₂³×C₅	1	2	yes	—
338	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
339	C₂×C₃×D₄	—	2	1	no	—
340	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
341	C₂²×C₃×C₄	—	2	1	no	—
342	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂×#67	—	2	1	no	—
344	C₂×#67	—	2	4	no	—
345	C₂×#67	C₅×D₄	1	2	yes	—
346	C₂²×Dic₃	—	2	1	no	—
347	#239	—	2	2	no	—
348	#239	C₂×C₄×C₅	1	4	yes	complemented
349	D₃×Q₈	—	2	2	no	—
350	D₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
351	#237	—	2	4	no	—
352	#237	—	2	4	no	—
353	#237	—	2	2	no	—
354	#237	C₂×C₄×C₅	1	4	yes	complemented
355	D₃×D₄	—	2	4	no	—
356	D₃×D₄	—	2	4	no	—
357	D₃×D₄	—	2	2	no	—
358	D₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
359	#235	—	2	1	no	—
360	#235	—	2	1	no	—
361	#235	—	2	4	no	—
362	#235	—	2	2	no	—
363	#235	—	2	4	no	—
364	#235	—	2	2	no	—
365	#235	C₂×C₄×C₅	1	2	yes	—
366	#235	C₂×C₄×C₅	1	2	yes	—
367	#235	C₂×C₄×C₅	1	2	yes	complemented
368	#235	C₅×D₄	1	2	yes	—
369	#235	C₅×D₄	1	2	yes	—
370	#235	C₂³×C₅	1	2	yes	—
371	C₂×D₁₂	—	2	2	no	—
372	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic, complemented
373	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
374	C₂×C₄×D₃	—	2	1	no	—
375	C₂×C₄×D₃	—	2	4	no	—
376	C₂×C₄×D₃	—	2	2	no	—
377	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
378	C₂×Dic₆	—	2	2	no	—
379	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
380	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
381	C₃×M₁₆	—	2	1	no	—
382	C₃×M₁₆	C₂³×C₅	1	2	yes	—
383	C₂×C₃×C₈	—	2	1	no	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₂²⋊C₄	—	2	1	no	—
386	C₃×C₄²	C₂³×C₅	1	2	yes	—
387	(C₂×D₃)⋊C₄	—	2	2	no	—
388	Dic₃⋊C₄	—	2	2	no	—
389	C₄×Dic₃	—	2	1	no	—
390	C₄×Dic₃	—	2	2	no	—
391	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
392	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
393	#208	—	2	1	no	—
394	#208	C₂³×C₅	1	2	yes	—
395	C₂×C₃⋊C₈	—	2	1	no	—
396	ΓL(1,𝔽₂₅)	—	2	4	no	—
397	D₃×C₈	—	2	4	no	—
398	C₂³×C₅	—	2	1	no	—
399	C₂³×C₅	—	3	2	no	—
400	C₂³×C₅	—	6	4	no	—
401	C₂³×C₅	—	6	1	no	—
402	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
403	C₅×Q₈	—	2	1	no	—
404	C₅×Q₈	—	3	2	no	—
405	C₅×Q₈	—	3	2	no	—
406	C₅×Q₈	—	3	2	no	—
407	C₅×Q₈	—	6	4	no	—
408	C₅×Q₈	—	6	1	no	—
409	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
410	C₅×D₄	—	2	2	no	—
411	C₅×D₄	—	2	2	no	—
412	C₅×D₄	—	2	1	no	—
413	C₅×D₄	—	3	4	no	—
414	C₅×D₄	—	3	4	no	—
415	C₅×D₄	—	3	2	no	—
416	C₅×D₄	—	3	2	no	—
417	C₅×D₄	—	3	2	no	—
418	C₅×D₄	—	6	4	no	—
419	C₅×D₄	—	6	4	no	—
420	C₅×D₄	—	6	4	no	—
421	C₅×D₄	—	6	2	no	—
422	C₅×D₄	—	6	2	no	—
423	C₅×D₄	—	6	1	no	—
424	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	2	no	—
427	C₂×C₄×C₅	—	2	2	no	—
428	C₂×C₄×C₅	—	2	2	no	—
429	C₂×C₄×C₅	—	3	2	no	—
430	C₂×C₄×C₅	—	3	4	no	—
431	C₂×C₄×C₅	—	3	4	no	—
432	C₂×C₄×C₅	—	6	4	no	—
433	C₂×C₄×C₅	—	6	4	no	—
434	C₂×C₄×C₅	—	6	4	no	—
435	C₂×C₄×C₅	—	6	1	no	—
436	C₂×C₄×C₅	—	6	1	no	—
437	C₂×C₄×C₅	—	6	2	no	—
438	C₂×C₄×C₅	—	6	2	no	—
439	C₂×C₄×C₅	—	6	1	no	—
440	C₂×C₄×C₅	—	12	4	no	—
441	C₂×C₄×C₅	—	12	2	no	—
442	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
443	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
444	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
445	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
446	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
448	C₅×C₈	—	2	2	no	—
449	C₅×C₈	—	6	2	no	—
450	2₋¹⁺⁴	—	3	2	no	—
451	2₋¹⁺⁴	—	3	2	no	—
452	2₋¹⁺⁴	—	6	1	no	—
453	H(5,𝔽₂)	—	3	2	no	—
454	H(5,𝔽₂)	—	3	2	no	—
455	H(5,𝔽₂)	—	6	2	no	—
456	H(5,𝔽₂)	—	6	1	no	—
457	C₂×#41	—	3	1	no	—
458	C₂×#41	—	3	4	no	—
459	C₂×#41	—	3	1	no	—
460	C₂×#41	—	6	2	no	—
461	C₂×#41	—	6	2	no	—
462	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
463	#131	—	6	2	no	—
464	#131	—	6	2	no	—
465	C₂×M₁₆	—	3	1	no	—
466	C₂×M₁₆	—	3	4	no	—
467	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
468	C₄×Q₈	—	6	1	no	—
469	C₄×D₄	—	6	2	no	—
470	C₄×D₄	—	6	1	no	—
471	#117	—	3	2	no	—
472	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
473	C₂×C₄²	—	3	1	no	—
474	C₂×C₄²	—	3	2	no	—
475	#104	—	3	2	no	—
476	#104	—	3	2	no	—
477	#104	—	3	2	no	—
478	#104	—	3	2	no	—
479	#104	—	3	4	no	—
480	#104	C₂×C₅×D₃	1	4	yes	complemented
481	C₂×C₃×C₅	—	2	1	no	—
482	C₂×C₃×C₅	—	2	1	no	—
483	C₂×C₃×C₅	—	2	1	no	—
484	C₂×C₃×C₅	—	4	2	no	—
485	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
486	C₅×D₃	—	2	4	no	—
487	C₅×D₃	—	4	2	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂²×D₃	—	2	1	no	—
491	C₂²×D₃	—	2	4	no	—
492	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
493	C₃×Q₈	—	2	1	no	—
494	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
495	C₃×D₄	—	2	2	no	—
496	C₃×D₄	—	2	2	no	—
497	C₃×D₄	—	2	1	no	—
498	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
509	#67	—	2	2	no	—
510	#67	—	2	2	no	—
511	#67	—	2	4	no	—
512	#67	—	2	4	no	—
513	#67	C₅×C₂²⋊C₄	1	4	yes	—
514	#67	C₅×C₂²⋊C₄	1	4	yes	—
515	C₂×Dic₃	—	2	1	no	—
516	C₂×Dic₃	—	2	1	no	—
517	C₂×Dic₃	—	2	4	no	—
518	C₂×Dic₃	—	2	1	no	—
519	C₂×Dic₃	—	4	2	no	—
520	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
521	D₁₂	—	2	4	no	—
522	D₁₂	—	2	1	no	—
523	D₁₂	C₅×C₂²⋊C₄	1	2	yes	—
524	D₁₂	C₅×C₂²⋊C₄	1	2	yes	—
525	D₁₂	C₂²×C₄×C₅	1	2	yes	—
526	C₄×D₃	—	2	4	no	—
527	C₄×D₃	—	2	2	no	—
528	C₄×D₃	—	2	2	no	—
529	C₄×D₃	—	2	4	no	—
530	C₄×D₃	—	4	4	no	—
531	C₄×D₃	C₂²×C₄×C₅	1	4	yes	—
532	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
533	Dic₆	—	2	1	no	—
534	Dic₆	—	2	4	no	—
535	Dic₆	C₅×C₂²⋊C₄	1	2	yes	—
536	Dic₆	C₅×C₂²⋊C₄	1	2	yes	—
537	Dic₆	C₂²×C₄×C₅	1	2	yes	—
538	C₃×C₈	—	2	2	no	—
539	C₃⋊C₈	—	2	2	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	3	4	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	—	6	2	no	—
544	C₂²×C₅	—	8	1	no	—
545	C₂²×C₅	—	12	2	no	—
546	C₂²×C₅	—	24	1	no	—
547	C₂²×C₅	—	24	4	no	—
548	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
549	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
550	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
551	C₄×C₅	—	2	2	no	—
552	C₄×C₅	—	3	4	no	—
553	C₄×C₅	—	4	2	no	—
554	C₄×C₅	—	6	2	no	—
555	C₄×C₅	—	6	2	no	—
556	C₄×C₅	—	12	1	no	—
557	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
558	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
559	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
560	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
561	#41	—	2	1	no	—
562	#41	—	2	1	no	—
563	#41	—	3	2	no	—
564	#41	—	3	2	no	—
565	#41	—	3	2	no	—
566	#41	—	3	2	no	—
567	#41	—	3	4	no	—
568	#41	—	3	4	no	—
569	#41	—	3	2	no	—
570	#41	—	3	2	no	—
571	#41	—	6	4	no	—
572	#41	—	6	4	no	—
573	#41	—	6	2	no	—
574	#41	—	6	2	no	—
575	#41	—	6	4	no	—
576	#41	—	6	4	no	—
577	#41	—	6	2	no	—
578	#41	—	6	2	no	—
579	#41	—	6	1	no	—
580	#41	—	6	1	no	—
581	#41	C₄×C₅×D₃	1	2	yes	complemented
582	#41	C₂²×C₅×D₃	1	2	yes	—
583	C₂×Q₈	—	3	1	no	—
584	C₂×Q₈	—	3	4	no	—
585	C₂×Q₈	—	3	1	no	—
586	C₂×Q₈	—	6	2	no	—
587	C₂×Q₈	—	6	2	no	—
588	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic, complemented
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	3	2	no	—
591	C₂×D₄	—	3	4	no	—
592	C₂×D₄	—	3	1	no	—
593	C₂×D₄	—	3	1	no	—
594	C₂×D₄	—	6	2	no	—
595	C₂×D₄	—	6	4	no	—
596	C₂×D₄	—	6	2	no	—
597	C₂×D₄	—	6	4	no	—
598	C₂×D₄	—	6	4	no	—
599	C₂×D₄	—	6	1	no	—
600	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic, complemented
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	3	2	no	—
603	C₂²×C₄	—	6	4	no	—
604	C₂²×C₄	—	6	2	no	—
605	C₂²×C₄	—	6	1	no	—
606	C₂²×C₄	—	6	1	no	—
607	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
608	M₁₆	—	2	1	no	—
609	M₁₆	—	3	2	no	—
610	M₁₆	—	6	4	no	—
611	M₁₆	—	6	1	no	—
612	M₁₆	C₂²×C₅×D₃	1	2	yes	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	6	4	no	—
615	C₂×C₈	—	6	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	6	2	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	6	2	no	—
620	C₄²	—	3	1	no	—
621	C₄²	—	3	1	no	—
622	C₄²	—	6	2	no	—
623	C₄²	—	6	1	no	—
624	C₄²	C₂²×C₅×D₃	1	2	yes	—
625	C₃×C₅	#2901	1	1	yes	characteristic, complemented, Hall
626	C₂²×C₃	—	2	2	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	8	1	no	—
629	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
630	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
631	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
632	C₂×D₃	—	2	2	no	—
633	C₂×D₃	—	4	2	no	—
634	C₂×D₃	—	8	4	no	—
635	C₂×D₃	—	8	1	no	—
636	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	4	2	no	—
639	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
640	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
641	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
642	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
643	Dic₃	—	2	2	no	—
644	Dic₃	—	2	2	no	—
645	Dic₃	—	4	1	no	—
646	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
647	C₂×C₅	—	2	1	no	—
648	C₂×C₅	—	2	1	no	—
649	C₂×C₅	—	2	1	no	—
650	C₂×C₅	—	4	2	no	—
651	C₂×C₅	—	6	4	no	—
652	C₂×C₅	—	12	2	no	—
653	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
654	C₂³	—	2	1	no	—
655	C₂³	—	3	2	no	—
656	C₂³	—	6	4	no	—
657	C₂³	—	6	1	no	—
658	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
659	Q₈	—	2	1	no	—
660	Q₈	—	3	2	no	—
661	Q₈	—	3	2	no	—
662	Q₈	—	3	2	no	—
663	Q₈	—	6	4	no	—
664	Q₈	—	6	1	no	—
665	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	1	no	—
669	D₄	—	3	4	no	—
670	D₄	—	3	4	no	—
671	D₄	—	3	2	no	—
672	D₄	—	3	2	no	—
673	D₄	—	3	2	no	—
674	D₄	—	6	4	no	—
675	D₄	—	6	4	no	—
676	D₄	—	6	4	no	—
677	D₄	—	6	2	no	—
678	D₄	—	6	2	no	—
679	D₄	—	6	1	no	—
680	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	3	2	no	—
686	C₂×C₄	—	3	4	no	—
687	C₂×C₄	—	3	4	no	—
688	C₂×C₄	—	6	4	no	—
689	C₂×C₄	—	6	4	no	—
690	C₂×C₄	—	6	4	no	—
691	C₂×C₄	—	6	1	no	—
692	C₂×C₄	—	6	1	no	—
693	C₂×C₄	—	6	2	no	—
694	C₂×C₄	—	6	2	no	—
695	C₂×C₄	—	6	1	no	—
696	C₂×C₄	—	12	4	no	—
697	C₂×C₄	—	12	2	no	—
698	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
699	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
700	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
701	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
702	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
703	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
704	C₈	—	2	2	no	—
705	C₈	—	6	2	no	—
706	C₂×C₃	—	2	1	no	—
707	C₂×C₃	—	2	1	no	—
708	C₂×C₃	—	2	1	no	—
709	C₂×C₃	—	4	2	no	—
710	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
711	D₃	—	2	4	no	—
712	D₃	—	4	2	no	—
713	C₅	#78992	1	1	yes	characteristic, direct product factor, Sylow
714	C₂²	—	2	2	no	—
715	C₂²	—	3	4	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	6	2	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	12	2	no	—
720	C₂²	—	24	1	no	—
721	C₂²	—	24	4	no	—
722	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
723	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
724	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
725	C₄	—	2	2	no	—
726	C₄	—	3	4	no	—
727	C₄	—	4	2	no	—
728	C₄	—	6	2	no	—
729	C₄	—	6	2	no	—
730	C₄	—	12	1	no	—
731	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
732	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
733	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
734	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
735	C₃	C₅×#2901	1	1	yes	characteristic, complemented, Sylow
736	C₂	—	2	1	no	—
737	C₂	—	2	1	no	—
738	C₂	—	2	1	no	—
739	C₂	—	4	2	no	—
740	C₂	—	6	4	no	—
741	C₂	—	12	2	no	—
742	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#421	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₅×#5964	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#421	D₃
hypocenter	C₃	C₅×#2901
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#421

Complements

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

N	H ≅ G/N	type
2. C₅×#5745	C₂	semidirect
3. C₅×#5522	C₂	semidirect
4. C₃×C₅×#421	C₂	semidirect
5. C₂×C₅×#837	C₂	semidirect
6. C₂×C₅×#825	C₂	semidirect
7. C₅×#5005	C₂	semidirect
8. C₅×#4821	C₂	semidirect
9. C₅×D₃×#104	C₂	semidirect
13. C₅×#1010	C₄	semidirect
15. C₅×#1009	C₄	semidirect
18. C₅×#1007	C₄	semidirect
20. C₅×#1004	C₄	semidirect
24. C₂×C₃×C₅×M₁₆	C₂²	semidirect
25. C₃×C₅×#117	C₂²	semidirect
26. C₂×C₄×C₅×Dic₃	C₂²	semidirect
27. C₂×C₅×#208	C₂²	semidirect
29. C₅×D₃×M₁₆	C₂²	semidirect
34. C₅×#872	C₂²	semidirect
35. C₄²×C₅×D₃	C₂²	semidirect
36. C₃×C₅×#104	C₂²	semidirect
37. C₅×#837	C₂²	semidirect
38. C₅×#837	C₂²	semidirect
39. C₅×#825	C₂²	semidirect
40. C₅×#825	C₂²	semidirect
41. C₅×#805	C₂²	semidirect
42. #78992	C₅	direct (N × H)
48. C₅×#421	D₃	semidirect
54. C₃×C₅×#41	C₂×C₄	semidirect
56. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
58. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
66. C₅×#239	C₂×C₄	semidirect
68. C₅×D₃×Q₈	C₂×C₄	semidirect
72. C₅×#237	C₂×C₄	semidirect
76. C₅×D₃×D₄	C₂×C₄	semidirect
85. C₅×#235	C₂×C₄	semidirect
90. C₂×C₅×D₁₂	C₂×C₄	semidirect
97. C₂×C₅×Dic₆	C₂×C₄	semidirect
117. #5745	C₂×C₅	semidirect
118. #5522	C₂×C₅	semidirect
119. C₃×#421	C₂×C₅	semidirect
120. C₂×#837	C₂×C₅	semidirect
121. C₂×#825	C₂×C₅	semidirect
122. #5005	C₂×C₅	semidirect
123. #4821	C₂×C₅	semidirect
124. D₃×#104	C₂×C₅	semidirect
142. C₂×C₅×M₁₆	C₂×D₃	semidirect
147. C₅×#117	C₂×D₃	semidirect
155. C₅×#104	C₂×D₃	semidirect
211. #1010	C₄×C₅	semidirect
213. #1009	C₄×C₅	semidirect
216. #1007	C₄×C₅	semidirect
218. #1004	C₄×C₅	semidirect
222. C₂×C₃×M₁₆	C₂²×C₅	semidirect
223. C₃×#117	C₂²×C₅	semidirect
224. C₂×C₄×Dic₃	C₂²×C₅	semidirect
225. C₂×#208	C₂²×C₅	semidirect
227. D₃×M₁₆	C₂²×C₅	semidirect
232. #872	C₂²×C₅	semidirect
233. C₄²×D₃	C₂²×C₅	semidirect
234. C₃×#104	C₂²×C₅	semidirect
235. #837	C₂²×C₅	semidirect
236. #837	C₂²×C₅	semidirect
237. #825	C₂²×C₅	semidirect
238. #825	C₂²×C₅	semidirect
239. #805	C₂²×C₅	semidirect
260. C₅×#41	C₄×D₃	semidirect
267. C₂×C₅×Q₈	C₄×D₃	semidirect
279. C₂×C₅×D₄	C₄×D₃	semidirect
309. #421	C₅×D₃	semidirect
336. C₃×#41	C₂×C₄×C₅	semidirect
338. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
340. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
348. #239	C₂×C₄×C₅	semidirect
350. D₃×Q₈	C₂×C₄×C₅	semidirect
354. #237	C₂×C₄×C₅	semidirect
358. D₃×D₄	C₂×C₄×C₅	semidirect
367. #235	C₂×C₄×C₅	semidirect
372. C₂×D₁₂	C₂×C₄×C₅	semidirect
379. C₂×Dic₆	C₂×C₄×C₅	semidirect
467. C₂×M₁₆	C₂×C₅×D₃	semidirect
472. #117	C₂×C₅×D₃	semidirect
480. #104	C₂×C₅×D₃	semidirect
581. #41	C₄×C₅×D₃	semidirect
588. C₂×Q₈	C₄×C₅×D₃	semidirect
600. C₂×D₄	C₄×C₅×D₃	semidirect
625. C₃×C₅	#2901	semidirect
713. C₅	#78992	direct (N × H)
735. C₃	C₅×#2901	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5964	2
C₅×#5745	2
C₅×#5522	2
C₃×C₅×#421	2
C₂×C₅×#837	2
C₂×C₅×#825	2
C₅×#5005	2
C₅×#4821	2
C₅×D₃×#104	2
C₅×#2901	3
#78992	5

Subgroups — C5×#78992 #14412908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78992 #14412908