Subgroups — C₅×#80656 #14427786

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#916	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5627	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5606	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5171	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5114	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5038	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4813	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4804	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4775	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3050	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×C₅×#237	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₅×#946	C₂²	1	1	yes	characteristic
25	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
26	C₅×#938	C₂²	1	1	yes	characteristic
27	C₅×#937	—	2	1	no	—
28	C₅×D₄×Dic₃	—	2	1	no	—
29	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
30	C₅×#930	C₂²	1	1	yes	characteristic
31	C₅×#924	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₅×#916	—	2	4	no	—
34	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×D₃×C₈	—	2	4	no	—
36	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
40	C₅×#897	C₂²	1	1	yes	characteristic
41	C₅×#895	C₂²	1	1	yes	characteristic
42	C₅×#894	—	2	1	no	—
43	C₅×#893	—	2	1	no	—
44	C₅×#892	C₂²	1	1	yes	characteristic
45	C₅×#892	C₂²	1	1	yes	characteristic
46	C₅×#883	—	2	1	no	—
47	C₅×#882	—	2	1	no	—
48	C₅×#67⋊C₄	—	2	1	no	—
49	C₅×#67⋊C₄	—	2	1	no	—
50	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₅×#835	C₂²	1	1	yes	characteristic, complemented
54	C₅×#832	C₂²	1	1	yes	characteristic, complemented
55	C₅×#821	C₂²	1	1	yes	characteristic, complemented
56	C₅×#817	C₂²	1	1	yes	characteristic, complemented
57	C₅×#816	C₂²	1	1	yes	characteristic, complemented
58	C₅×#810	C₂²	1	1	yes	characteristic, complemented
59	C₅×#809	C₂²	1	1	yes	characteristic, complemented
60	C₅×#807	C₂²	1	1	yes	characteristic, complemented
61	C₅×#807	C₂²	1	1	yes	characteristic, complemented
62	#80656	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#135	—	3	1	no	—
64	C₂³×C₅×C₈	—	3	1	no	—
65	C₅×#525	—	3	1	no	—
66	C₅×#525	—	3	1	no	—
67	C₅×#467	—	3	1	no	—
68	C₅×#467	—	3	1	no	—
69	C₅×#466	—	3	1	no	—
70	C₅×#466	—	3	1	no	—
71	C₅×#465	—	3	1	no	—
72	C₅×#465	—	3	1	no	—
73	C₅×#465	—	3	1	no	—
74	C₅×#465	D₃	1	1	yes	characteristic, complemented
75	C₅×#427	—	3	1	no	—
76	C₅×#416	—	3	1	no	—
77	C₅×#416	—	3	1	no	—
78	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	—	2	1	no	—
84	C₂×C₅×#67	—	2	1	no	—
85	C₂×C₅×#67	—	2	1	no	—
86	C₂²×C₅×Dic₃	—	2	1	no	—
87	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
88	C₅×#239	—	2	2	no	—
89	C₅×#239	—	2	2	no	—
90	C₅×#237	—	2	2	no	—
91	C₅×#237	—	2	2	no	—
92	C₂×C₅×D₁₂	—	2	1	no	—
93	C₂×C₅×D₁₂	—	2	1	no	—
94	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	—	2	2	no	—
96	C₂×C₄×C₅×D₃	—	2	2	no	—
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
99	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
102	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
103	C₃×C₅×SD₁₆	—	2	2	no	—
104	C₂×C₃×C₅×C₈	—	2	2	no	—
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₅×#217	—	2	1	no	—
113	C₅×#217	—	2	1	no	—
114	C₅×#216	—	2	2	no	—
115	C₅×#213	—	2	2	no	—
116	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
117	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
118	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
122	C₅×C₄⋊Dic₃	—	2	1	no	—
123	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
124	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
125	C₅×Dic₃⋊C₄	—	2	1	no	—
126	C₅×Dic₃⋊C₄	—	2	1	no	—
127	C₄×C₅×Dic₃	—	2	1	no	—
128	C₄×C₅×Dic₃	—	2	1	no	—
129	C₂×C₅×C₃⋊C₈	—	2	2	no	—
130	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₅×#204	—	2	2	no	—
133	C₅×D₃×C₈	—	2	2	no	—
134	C₅×D₃×C₈	—	2	2	no	—
135	C₅×D₃×C₈	—	2	2	no	—
136	C₅×D₃×C₈	D₄	1	4	yes	complemented
137	C₂×#916	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
139	#5627	C₂×C₅	1	1	yes	characteristic, complemented
140	#5606	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
142	#5171	C₂×C₅	1	1	yes	characteristic, complemented
143	#5114	C₂×C₅	1	1	yes	characteristic, complemented
144	#5051	C₂×C₅	1	1	yes	characteristic, complemented
145	#5038	C₂×C₅	1	1	yes	characteristic, complemented
146	#4864	C₂×C₅	1	1	yes	characteristic, complemented
147	#4860	C₂×C₅	1	1	yes	characteristic, complemented
148	#4813	C₂×C₅	1	1	yes	characteristic, complemented
149	#4804	C₂×C₅	1	1	yes	characteristic, complemented
150	#4775	C₂×C₅	1	1	yes	characteristic, complemented
151	#4772	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×C₅×#41	—	3	1	no	—
153	C₂×C₅×#41	—	3	1	no	—
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₅×#135	—	6	4	no	—
156	C₂×C₅×Q₁₆	—	3	1	no	—
157	C₂×C₅×SD₁₆	—	3	1	no	—
158	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
159	C₂×C₅×D₈	—	3	1	no	—
160	C₂²×C₅×C₈	—	3	1	no	—
161	C₂²×C₅×C₈	—	3	1	no	—
162	C₂²×C₅×C₈	—	3	1	no	—
163	C₂²×C₅×C₈	—	3	1	no	—
164	C₂²×C₅×C₈	—	3	1	no	—
165	C₂²×C₅×C₈	—	6	4	no	—
166	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
167	C₅×#123	—	6	1	no	—
168	C₅×#123	—	6	1	no	—
169	C₅×C₂²⋊Q₈	—	3	1	no	—
170	C₅×C₂²⋊Q₈	—	3	1	no	—
171	C₅×C₂²⋊Q₈	—	3	1	no	—
172	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
173	C₅×#121	—	3	1	no	—
174	C₅×#121	—	3	1	no	—
175	C₅×#121	—	3	1	no	—
176	C₅×#121	C₂×D₃	1	1	yes	characteristic
177	C₅×#120	—	6	1	no	—
178	C₅×#120	—	6	1	no	—
179	C₄×C₅×D₄	—	6	1	no	—
180	C₄×C₅×D₄	—	6	1	no	—
181	C₄×C₅×D₄	—	6	1	no	—
182	C₄×C₅×D₄	—	6	1	no	—
183	C₅×#117	—	3	1	no	—
184	C₅×#117	—	3	1	no	—
185	C₅×#107	—	3	1	no	—
186	C₅×#107	—	3	1	no	—
187	C₅×#106	—	3	1	no	—
188	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
189	C₅×#103	—	3	1	no	—
190	C₅×#103	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
193	C₅×#102	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
197	#3050	—	3	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₅×D₃	—	2	2	no	—
201	C₂²×C₅×D₃	—	2	2	no	—
202	C₂²×C₅×D₃	—	2	2	no	—
203	C₂²×C₅×D₃	—	2	1	no	—
204	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	4	2	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
218	C₅×#67	—	4	2	no	—
219	C₅×#67	—	4	2	no	—
220	C₅×#67	—	4	2	no	—
221	C₂×C₅×Dic₃	—	2	2	no	—
222	C₂×C₅×Dic₃	—	2	1	no	—
223	C₂×C₅×Dic₃	—	2	1	no	—
224	C₂×C₅×Dic₃	—	2	1	no	—
225	C₂×C₅×Dic₃	—	4	2	no	—
226	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
227	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
228	C₅×D₁₂	—	2	1	no	—
229	C₅×D₁₂	—	2	1	no	—
230	C₅×D₁₂	—	4	2	no	—
231	C₅×D₁₂	—	4	2	no	—
232	C₄×C₅×D₃	—	2	2	no	—
233	C₄×C₅×D₃	—	2	1	no	—
234	C₄×C₅×D₃	—	2	1	no	—
235	C₄×C₅×D₃	—	2	2	no	—
236	C₄×C₅×D₃	—	4	2	no	—
237	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
238	C₄×C₅×D₃	#41	1	2	yes	—
239	C₅×Dic₆	—	2	1	no	—
240	C₅×Dic₆	—	2	1	no	—
241	C₃×C₅×C₈	—	2	1	no	—
242	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
243	C₅×C₃⋊C₈	—	2	1	no	—
244	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
245	C₂×#239	C₂²×C₅	1	1	yes	characteristic
246	C₂×#237	C₂²×C₅	1	1	yes	characteristic
247	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
250	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₃×#121	C₂²×C₅	1	1	yes	characteristic
252	#946	C₂²×C₅	1	1	yes	characteristic
253	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
254	#938	C₂²×C₅	1	1	yes	characteristic
255	#937	—	2	1	no	—
256	D₄×Dic₃	—	2	1	no	—
257	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
258	#930	C₂²×C₅	1	1	yes	characteristic
259	#924	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	#916	—	2	4	no	—
262	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×D₃×C₈	—	2	4	no	—
264	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
268	#897	C₂²×C₅	1	1	yes	characteristic
269	#895	C₂²×C₅	1	1	yes	characteristic
270	#894	—	2	1	no	—
271	#893	—	2	1	no	—
272	#892	C₂²×C₅	1	1	yes	characteristic
273	#892	C₂²×C₅	1	1	yes	characteristic
274	#883	—	2	1	no	—
275	#882	—	2	1	no	—
276	#67⋊C₄	—	2	1	no	—
277	#67⋊C₄	—	2	1	no	—
278	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
281	#835	C₂²×C₅	1	1	yes	characteristic, complemented
282	#832	C₂²×C₅	1	1	yes	characteristic, complemented
283	#821	C₂²×C₅	1	1	yes	characteristic, complemented
284	#817	C₂²×C₅	1	1	yes	characteristic, complemented
285	#816	C₂²×C₅	1	1	yes	characteristic, complemented
286	#810	C₂²×C₅	1	1	yes	characteristic, complemented
287	#809	C₂²×C₅	1	1	yes	characteristic, complemented
288	#807	C₂²×C₅	1	1	yes	characteristic, complemented
289	#807	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₂⁴×C₅	—	3	1	no	—
291	C₅×#41	—	6	2	no	—
292	C₅×#41	—	6	2	no	—
293	C₅×#41	—	6	2	no	—
294	C₅×#41	—	6	2	no	—
295	C₂×C₅×Q₈	—	3	1	no	—
296	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₅×D₄	—	2	1	no	—
298	C₂×C₅×D₄	—	3	1	no	—
299	C₂×C₅×D₄	—	6	1	no	—
300	C₂×C₅×D₄	—	6	1	no	—
301	C₂×C₅×D₄	—	6	1	no	—
302	C₂×C₅×D₄	—	6	1	no	—
303	C₂×C₅×D₄	—	6	1	no	—
304	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	3	1	no	—
310	C₂²×C₄×C₅	—	6	2	no	—
311	C₂²×C₄×C₅	—	6	2	no	—
312	C₂²×C₄×C₅	—	6	1	no	—
313	C₂²×C₄×C₅	—	6	1	no	—
314	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
315	C₅×Q₁₆	—	6	2	no	—
316	C₅×SD₁₆	—	2	2	no	—
317	C₅×SD₁₆	—	6	2	no	—
318	C₅×D₈	—	6	2	no	—
319	C₂×C₅×C₈	—	2	2	no	—
320	C₂×C₅×C₈	—	3	1	no	—
321	C₂×C₅×C₈	—	3	4	no	—
322	C₂×C₅×C₈	—	3	1	no	—
323	C₂×C₅×C₈	—	6	2	no	—
324	C₂×C₅×C₈	—	6	2	no	—
325	C₂×C₅×C₈	—	6	2	no	—
326	C₂×C₅×C₈	—	6	2	no	—
327	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
328	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
329	C₅×C₄⋊C₄	—	2	1	no	—
330	C₅×C₄⋊C₄	—	3	1	no	—
331	C₅×C₄⋊C₄	—	3	1	no	—
332	C₅×C₄⋊C₄	—	6	1	no	—
333	C₅×C₄⋊C₄	—	6	1	no	—
334	C₅×C₄⋊C₄	—	6	1	no	—
335	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
336	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
337	C₅×C₂²⋊C₄	—	2	1	no	—
338	C₅×C₂²⋊C₄	—	2	1	no	—
339	C₅×C₂²⋊C₄	—	6	1	no	—
340	C₅×C₂²⋊C₄	—	6	1	no	—
341	C₅×C₂²⋊C₄	—	6	1	no	—
342	C₅×C₂²⋊C₄	—	6	1	no	—
343	C₅×C₂²⋊C₄	—	6	1	no	—
344	C₅×C₂²⋊C₄	—	6	1	no	—
345	C₅×C₂²⋊C₄	—	6	1	no	—
346	C₅×C₂²⋊C₄	—	6	1	no	—
347	C₄²×C₅	—	6	1	no	—
348	C₄²×C₅	—	6	1	no	—
349	C₂×#135	—	3	1	no	—
350	C₂³×C₈	—	3	1	no	—
351	#525	—	3	1	no	—
352	#525	—	3	1	no	—
353	#467	—	3	1	no	—
354	#467	—	3	1	no	—
355	#466	—	3	1	no	—
356	#466	—	3	1	no	—
357	#465	—	3	1	no	—
358	#465	—	3	1	no	—
359	#465	—	3	1	no	—
360	#465	C₅×D₃	1	1	yes	characteristic, complemented
361	#427	—	3	1	no	—
362	#416	—	3	1	no	—
363	#416	—	3	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	#135	1	2	yes	complemented
370	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₅×D₃	—	2	8	no	—
372	C₂×C₅×D₃	—	2	1	no	—
373	C₂×C₅×D₃	—	2	1	no	—
374	C₂×C₅×D₃	—	2	1	no	—
375	C₂×C₅×D₃	—	2	1	no	—
376	C₂×C₅×D₃	—	4	1	no	—
377	C₂×C₅×D₃	—	4	1	no	—
378	C₂×C₅×D₃	—	4	1	no	—
379	C₂×C₅×D₃	#121	1	2	yes	—
380	C₂×C₅×D₃	#135	1	2	yes	complemented
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	—	4	1	no	—
383	C₃×C₄×C₅	—	4	1	no	—
384	C₃×C₄×C₅	—	4	1	no	—
385	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
387	C₅×Dic₃	—	2	1	no	—
388	C₅×Dic₃	—	4	1	no	—
389	C₅×Dic₃	—	4	1	no	—
390	C₅×Dic₃	—	4	1	no	—
391	C₅×Dic₃	#121	1	2	yes	—
392	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
393	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃×D₄	—	2	1	no	—
395	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
397	C₂×#67	—	2	1	no	—
398	C₂×#67	—	2	1	no	—
399	C₂×#67	—	2	1	no	—
400	C₂²×Dic₃	—	2	1	no	—
401	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
402	#239	—	2	2	no	—
403	#239	—	2	2	no	—
404	#237	—	2	2	no	—
405	#237	—	2	2	no	—
406	C₂×D₁₂	—	2	1	no	—
407	C₂×D₁₂	—	2	1	no	—
408	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₄×D₃	—	2	2	no	—
410	C₂×C₄×D₃	—	2	2	no	—
411	C₂×C₄×D₃	—	2	1	no	—
412	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
413	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
414	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
416	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
417	C₃×SD₁₆	—	2	2	no	—
418	C₂×C₃×C₈	—	2	2	no	—
419	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₃×C₄⋊C₄	—	2	1	no	—
422	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
424	C₃×C₂²⋊C₄	—	2	1	no	—
425	C₃×C₂²⋊C₄	—	2	1	no	—
426	#217	—	2	1	no	—
427	#217	—	2	1	no	—
428	#216	—	2	2	no	—
429	#213	—	2	2	no	—
430	(C₂×D₃)⋊C₄	—	2	1	no	—
431	(C₂×D₃)⋊C₄	—	2	1	no	—
432	(C₂×D₃)⋊C₄	—	2	1	no	—
433	(C₂×D₃)⋊C₄	—	2	1	no	—
434	(C₂×D₃)⋊C₄	—	2	1	no	—
435	(C₂×D₃)⋊C₄	—	2	1	no	—
436	C₄⋊Dic₃	—	2	1	no	—
437	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
438	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
439	Dic₃⋊C₄	—	2	1	no	—
440	Dic₃⋊C₄	—	2	1	no	—
441	C₄×Dic₃	—	2	1	no	—
442	C₄×Dic₃	—	2	1	no	—
443	C₂×C₃⋊C₈	—	2	2	no	—
444	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
446	#204	—	2	2	no	—
447	D₃×C₈	—	2	2	no	—
448	D₃×C₈	—	2	2	no	—
449	D₃×C₈	—	2	2	no	—
450	D₃×C₈	C₅×D₄	1	4	yes	complemented
451	C₂³×C₅	—	2	1	no	—
452	C₂³×C₅	—	3	1	no	—
453	C₂³×C₅	—	3	1	no	—
454	C₂³×C₅	—	6	2	no	—
455	C₂³×C₅	—	6	2	no	—
456	C₂³×C₅	—	6	2	no	—
457	C₂³×C₅	—	6	1	no	—
458	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
459	C₅×Q₈	—	2	1	no	—
460	C₅×Q₈	—	2	1	no	—
461	C₅×Q₈	—	6	1	no	—
462	C₅×Q₈	—	6	1	no	—
463	C₅×D₄	—	2	1	no	—
464	C₅×D₄	—	2	1	no	—
465	C₅×D₄	—	4	2	no	—
466	C₅×D₄	—	6	1	no	—
467	C₅×D₄	—	6	1	no	—
468	C₅×D₄	—	12	2	no	—
469	C₅×D₄	—	12	2	no	—
470	C₅×D₄	—	12	2	no	—
471	C₅×D₄	—	12	2	no	—
472	C₅×D₄	—	12	2	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	3	1	no	—
479	C₂×C₄×C₅	—	3	2	no	—
480	C₂×C₄×C₅	—	3	2	no	—
481	C₂×C₄×C₅	—	3	1	no	—
482	C₂×C₄×C₅	—	6	2	no	—
483	C₂×C₄×C₅	—	6	2	no	—
484	C₂×C₄×C₅	—	6	2	no	—
485	C₂×C₄×C₅	—	6	1	no	—
486	C₂×C₄×C₅	—	6	1	no	—
487	C₂×C₄×C₅	—	6	1	no	—
488	C₂×C₄×C₅	—	6	1	no	—
489	C₂×C₄×C₅	—	6	1	no	—
490	C₂×C₄×C₅	—	12	2	no	—
491	C₂×C₄×C₅	—	12	2	no	—
492	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
494	C₅×C₈	—	2	1	no	—
495	C₅×C₈	—	3	2	no	—
496	C₅×C₈	—	6	1	no	—
497	C₅×C₈	D₃×D₄	1	2	yes	—
498	C₂×#41	—	3	1	no	—
499	C₂×#41	—	3	1	no	—
500	C₂³×C₄	—	3	1	no	—
501	#135	—	6	4	no	—
502	C₂×Q₁₆	—	3	1	no	—
503	C₂×SD₁₆	—	3	1	no	—
504	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	C₂×D₈	—	3	1	no	—
506	C₂²×C₈	—	3	1	no	—
507	C₂²×C₈	—	3	1	no	—
508	C₂²×C₈	—	3	1	no	—
509	C₂²×C₈	—	3	1	no	—
510	C₂²×C₈	—	3	1	no	—
511	C₂²×C₈	—	6	4	no	—
512	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
513	#123	—	6	1	no	—
514	#123	—	6	1	no	—
515	C₂²⋊Q₈	—	3	1	no	—
516	C₂²⋊Q₈	—	3	1	no	—
517	C₂²⋊Q₈	—	3	1	no	—
518	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
519	#121	—	3	1	no	—
520	#121	—	3	1	no	—
521	#121	—	3	1	no	—
522	#121	C₂×C₅×D₃	1	1	yes	characteristic
523	#120	—	6	1	no	—
524	#120	—	6	1	no	—
525	C₄×D₄	—	6	1	no	—
526	C₄×D₄	—	6	1	no	—
527	C₄×D₄	—	6	1	no	—
528	C₄×D₄	—	6	1	no	—
529	#117	—	3	1	no	—
530	#117	—	3	1	no	—
531	#107	—	3	1	no	—
532	#107	—	3	1	no	—
533	#106	—	3	1	no	—
534	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
535	#103	—	3	1	no	—
536	#103	—	3	1	no	—
537	#103	—	3	1	no	—
538	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
539	#102	—	3	1	no	—
540	#102	—	3	1	no	—
541	#102	—	3	1	no	—
542	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
543	C₂×C₃×C₅	—	2	2	no	—
544	C₂×C₃×C₅	—	8	1	no	—
545	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
546	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
547	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
548	C₅×D₃	—	2	2	no	—
549	C₅×D₃	—	2	2	no	—
550	C₅×D₃	—	8	1	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
553	C₂²×D₃	—	2	2	no	—
554	C₂²×D₃	—	2	2	no	—
555	C₂²×D₃	—	2	2	no	—
556	C₂²×D₃	—	2	1	no	—
557	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
558	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	2	1	no	—
561	C₃×D₄	—	2	1	no	—
562	C₃×D₄	—	2	1	no	—
563	C₃×D₄	—	4	2	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
570	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
571	#67	—	4	2	no	—
572	#67	—	4	2	no	—
573	#67	—	4	2	no	—
574	C₂×Dic₃	—	2	2	no	—
575	C₂×Dic₃	—	2	1	no	—
576	C₂×Dic₃	—	2	1	no	—
577	C₂×Dic₃	—	2	1	no	—
578	C₂×Dic₃	—	4	2	no	—
579	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
580	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
581	D₁₂	—	2	1	no	—
582	D₁₂	—	2	1	no	—
583	D₁₂	—	4	2	no	—
584	D₁₂	—	4	2	no	—
585	C₄×D₃	—	2	2	no	—
586	C₄×D₃	—	2	1	no	—
587	C₄×D₃	—	2	1	no	—
588	C₄×D₃	—	2	2	no	—
589	C₄×D₃	—	4	2	no	—
590	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
591	C₄×D₃	C₅×#41	1	2	yes	—
592	Dic₆	—	2	1	no	—
593	Dic₆	—	2	1	no	—
594	C₃×C₈	—	2	1	no	—
595	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
596	C₃⋊C₈	—	2	1	no	—
597	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	3	2	no	—
601	C₂²×C₅	—	3	2	no	—
602	C₂²×C₅	—	4	1	no	—
603	C₂²×C₅	—	4	1	no	—
604	C₂²×C₅	—	4	1	no	—
605	C₂²×C₅	—	6	8	no	—
606	C₂²×C₅	—	6	1	no	—
607	C₂²×C₅	—	6	1	no	—
608	C₂²×C₅	—	6	1	no	—
609	C₂²×C₅	—	6	1	no	—
610	C₂²×C₅	—	12	1	no	—
611	C₂²×C₅	—	12	1	no	—
612	C₂²×C₅	—	12	1	no	—
613	C₂²×C₅	#916	1	2	yes	complemented
614	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	3	2	no	—
617	C₄×C₅	—	4	1	no	—
618	C₄×C₅	—	4	1	no	—
619	C₄×C₅	—	4	1	no	—
620	C₄×C₅	—	6	1	no	—
621	C₄×C₅	—	12	1	no	—
622	C₄×C₅	—	12	1	no	—
623	C₄×C₅	—	12	1	no	—
624	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
625	C₄×C₅	D₃×#41	1	1	yes	characteristic
626	C₂⁴	—	3	1	no	—
627	#41	—	6	2	no	—
628	#41	—	6	2	no	—
629	#41	—	6	2	no	—
630	#41	—	6	2	no	—
631	C₂×Q₈	—	3	1	no	—
632	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	3	1	no	—
635	C₂×D₄	—	6	1	no	—
636	C₂×D₄	—	6	1	no	—
637	C₂×D₄	—	6	1	no	—
638	C₂×D₄	—	6	1	no	—
639	C₂×D₄	—	6	1	no	—
640	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	3	1	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	6	2	no	—
647	C₂²×C₄	—	6	2	no	—
648	C₂²×C₄	—	6	1	no	—
649	C₂²×C₄	—	6	1	no	—
650	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
651	Q₁₆	—	6	2	no	—
652	SD₁₆	—	2	2	no	—
653	SD₁₆	—	6	2	no	—
654	D₈	—	6	2	no	—
655	C₂×C₈	—	2	2	no	—
656	C₂×C₈	—	3	1	no	—
657	C₂×C₈	—	3	4	no	—
658	C₂×C₈	—	3	1	no	—
659	C₂×C₈	—	6	2	no	—
660	C₂×C₈	—	6	2	no	—
661	C₂×C₈	—	6	2	no	—
662	C₂×C₈	—	6	2	no	—
663	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
664	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	3	1	no	—
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	6	1	no	—
669	C₄⋊C₄	—	6	1	no	—
670	C₄⋊C₄	—	6	1	no	—
671	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
672	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	6	1	no	—
676	C₂²⋊C₄	—	6	1	no	—
677	C₂²⋊C₄	—	6	1	no	—
678	C₂²⋊C₄	—	6	1	no	—
679	C₂²⋊C₄	—	6	1	no	—
680	C₂²⋊C₄	—	6	1	no	—
681	C₂²⋊C₄	—	6	1	no	—
682	C₂²⋊C₄	—	6	1	no	—
683	C₄²	—	6	1	no	—
684	C₄²	—	6	1	no	—
685	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	4	1	no	—
689	C₂²×C₃	—	4	1	no	—
690	C₂²×C₃	—	4	1	no	—
691	C₂²×C₃	C₅×#135	1	2	yes	complemented
692	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
693	C₂×D₃	—	2	8	no	—
694	C₂×D₃	—	2	1	no	—
695	C₂×D₃	—	2	1	no	—
696	C₂×D₃	—	2	1	no	—
697	C₂×D₃	—	2	1	no	—
698	C₂×D₃	—	4	1	no	—
699	C₂×D₃	—	4	1	no	—
700	C₂×D₃	—	4	1	no	—
701	C₂×D₃	C₅×#121	1	2	yes	—
702	C₂×D₃	C₅×#135	1	2	yes	complemented
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	4	1	no	—
706	C₃×C₄	—	4	1	no	—
707	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
708	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
709	Dic₃	—	2	1	no	—
710	Dic₃	—	4	1	no	—
711	Dic₃	—	4	1	no	—
712	Dic₃	—	4	1	no	—
713	Dic₃	C₅×#121	1	2	yes	—
714	C₂×C₅	—	2	2	no	—
715	C₂×C₅	—	6	2	no	—
716	C₂×C₅	—	6	2	no	—
717	C₂×C₅	—	8	1	no	—
718	C₂×C₅	—	24	1	no	—
719	C₂×C₅	D₃×#121	1	1	yes	characteristic
720	C₂×C₅	C₂×#916	1	1	yes	characteristic
721	C₂×C₅	D₃×#135	1	1	yes	characteristic
722	C₂³	—	2	1	no	—
723	C₂³	—	3	1	no	—
724	C₂³	—	3	1	no	—
725	C₂³	—	6	2	no	—
726	C₂³	—	6	2	no	—
727	C₂³	—	6	2	no	—
728	C₂³	—	6	1	no	—
729	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	6	1	no	—
733	Q₈	—	6	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	2	no	—
737	D₄	—	6	1	no	—
738	D₄	—	6	1	no	—
739	D₄	—	12	2	no	—
740	D₄	—	12	2	no	—
741	D₄	—	12	2	no	—
742	D₄	—	12	2	no	—
743	D₄	—	12	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	3	1	no	—
750	C₂×C₄	—	3	2	no	—
751	C₂×C₄	—	3	2	no	—
752	C₂×C₄	—	3	1	no	—
753	C₂×C₄	—	6	2	no	—
754	C₂×C₄	—	6	2	no	—
755	C₂×C₄	—	6	2	no	—
756	C₂×C₄	—	6	1	no	—
757	C₂×C₄	—	6	1	no	—
758	C₂×C₄	—	6	1	no	—
759	C₂×C₄	—	6	1	no	—
760	C₂×C₄	—	6	1	no	—
761	C₂×C₄	—	12	2	no	—
762	C₂×C₄	—	12	2	no	—
763	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
764	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
765	C₈	—	2	1	no	—
766	C₈	—	3	2	no	—
767	C₈	—	6	1	no	—
768	C₈	C₅×D₃×D₄	1	2	yes	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	8	1	no	—
771	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
772	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
773	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
774	D₃	—	2	2	no	—
775	D₃	—	2	2	no	—
776	D₃	—	8	1	no	—
777	C₅	#80656	1	1	yes	characteristic, direct product factor, Sylow
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	3	2	no	—
781	C₂²	—	3	2	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	6	8	no	—
786	C₂²	—	6	1	no	—
787	C₂²	—	6	1	no	—
788	C₂²	—	6	1	no	—
789	C₂²	—	6	1	no	—
790	C₂²	—	12	1	no	—
791	C₂²	—	12	1	no	—
792	C₂²	—	12	1	no	—
793	C₂²	C₅×#916	1	2	yes	complemented
794	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	3	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	6	1	no	—
801	C₄	—	12	1	no	—
802	C₄	—	12	1	no	—
803	C₄	—	12	1	no	—
804	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
805	C₄	C₅×D₃×#41	1	1	yes	characteristic
806	C₃	C₅×#3050	1	1	yes	characteristic, complemented, Sylow
807	C₂	—	2	2	no	—
808	C₂	—	6	2	no	—
809	C₂	—	6	2	no	—
810	C₂	—	8	1	no	—
811	C₂	—	24	1	no	—
812	C₂	C₅×D₃×#121	1	1	yes	characteristic
813	C₂	C₂×C₅×#916	1	1	yes	characteristic
814	C₂	C₅×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#465	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#465	D₃
hypocenter	C₃	C₅×#3050
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#465

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#916	C₂	semidirect
2. C₂²×C₅×D₃×C₈	C₂	semidirect
3. C₅×#5627	C₂	semidirect
4. C₅×#5606	C₂	semidirect
5. C₃×C₅×#465	C₂	semidirect
6. C₅×#5171	C₂	semidirect
7. C₅×#5114	C₂	semidirect
8. C₅×#5051	C₂	semidirect
9. C₅×#5038	C₂	semidirect
10. C₅×#4864	C₂	semidirect
11. C₅×#4860	C₂	semidirect
12. C₅×#4813	C₂	semidirect
13. C₅×#4804	C₂	semidirect
14. C₅×#4775	C₂	semidirect
15. C₅×#4772	C₂	semidirect
20. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
25. C₂×C₅×#216	C₂²	semidirect
29. C₂×C₅×#213	C₂²	semidirect
34. C₂×C₅×#204	C₂²	semidirect
50. C₃×C₅×#106	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₅×#835	C₂²	semidirect
54. C₅×#832	C₂²	semidirect
55. C₅×#821	C₂²	semidirect
56. C₅×#817	C₂²	semidirect
57. C₅×#816	C₂²	semidirect
58. C₅×#810	C₂²	semidirect
59. C₅×#809	C₂²	semidirect
60. C₅×#807	C₂²	semidirect
61. C₅×#807	C₂²	semidirect
62. #80656	C₅	direct (N × H)
74. C₅×#465	D₃	semidirect
136. C₅×D₃×C₈	D₄	semidirect
137. C₂×#916	C₂×C₅	semidirect
138. C₂²×D₃×C₈	C₂×C₅	semidirect
139. #5627	C₂×C₅	semidirect
140. #5606	C₂×C₅	semidirect
141. C₃×#465	C₂×C₅	semidirect
142. #5171	C₂×C₅	semidirect
143. #5114	C₂×C₅	semidirect
144. #5051	C₂×C₅	semidirect
145. #5038	C₂×C₅	semidirect
146. #4864	C₂×C₅	semidirect
147. #4860	C₂×C₅	semidirect
148. #4813	C₂×C₅	semidirect
149. #4804	C₂×C₅	semidirect
150. #4775	C₂×C₅	semidirect
151. #4772	C₂×C₅	semidirect
158. C₂×C₅×SD₁₆	C₂×D₃	semidirect
188. C₅×#106	C₂×D₃	semidirect
192. C₅×#103	C₂×D₃	semidirect
196. C₅×#102	C₂×D₃	semidirect
248. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
253. C₂×#216	C₂²×C₅	semidirect
257. C₂×#213	C₂²×C₅	semidirect
262. C₂×#204	C₂²×C₅	semidirect
278. C₃×#106	C₂²×C₅	semidirect
279. C₃×#103	C₂²×C₅	semidirect
280. C₃×#102	C₂²×C₅	semidirect
281. #835	C₂²×C₅	semidirect
282. #832	C₂²×C₅	semidirect
283. #821	C₂²×C₅	semidirect
284. #817	C₂²×C₅	semidirect
285. #816	C₂²×C₅	semidirect
286. #810	C₂²×C₅	semidirect
287. #809	C₂²×C₅	semidirect
288. #807	C₂²×C₅	semidirect
289. #807	C₂²×C₅	semidirect
360. #465	C₅×D₃	semidirect
369. C₂²×C₃×C₅	#135	semidirect
380. C₂×C₅×D₃	#135	semidirect
450. D₃×C₈	C₅×D₄	semidirect
504. C₂×SD₁₆	C₂×C₅×D₃	semidirect
534. #106	C₂×C₅×D₃	semidirect
538. #103	C₂×C₅×D₃	semidirect
542. #102	C₂×C₅×D₃	semidirect
613. C₂²×C₅	#916	semidirect
685. C₃×C₅	#3050	semidirect
691. C₂²×C₃	C₅×#135	semidirect
702. C₂×D₃	C₅×#135	semidirect
777. C₅	#80656	direct (N × H)
793. C₂²	C₅×#916	semidirect
806. C₃	C₅×#3050	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#916	2
C₂²×C₅×D₃×C₈	2
C₅×#5627	2
C₅×#5606	2
C₃×C₅×#465	2
C₅×#5171	2
C₅×#5114	2
C₅×#5051	2
C₅×#5038	2
C₅×#4864	2
C₅×#4860	2
C₅×#4813	2
C₅×#4804	2
C₅×#4775	2
C₅×#4772	2
C₅×#3050	3
#80656	5

Subgroups — C5×#80656 #14427786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80656 #14427786