Subgroups — C₅×#79648 #14417153

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic
2	C₅×#5572	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5546	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5030	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5018	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4861	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4790	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4772	C₂	1	1	yes	maximal, characteristic
13	C₅×#4758	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2947	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#237	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×#216	C₂²	1	1	yes	characteristic
24	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×#214	C₂²	1	1	yes	characteristic
26	C₄×C₅×#67	—	2	1	no	—
27	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
28	C₅×#915	C₄	1	8	yes	complemented
29	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
30	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₅×#892	—	2	1	no	—
33	C₅×#892	C₂²	1	1	yes	characteristic
34	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₅×#887	—	2	1	no	—
36	C₅×#887	C₂²	1	1	yes	characteristic
37	C₅×#887	C₂²	1	1	yes	characteristic
38	C₅×#67⋊C₄	—	2	1	no	—
39	C₅×#877	—	2	1	no	—
40	C₅×#872	—	2	1	no	—
41	C₅×#872	C₂²	1	1	yes	characteristic
42	C₄×C₅×Dic₆	—	2	1	no	—
43	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
44	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic
46	C₃×C₅×#103	C₂²	1	1	yes	characteristic
47	C₃×C₅×#102	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
49	C₅×#835	C₂²	1	1	yes	characteristic
50	C₅×#832	C₂²	1	1	yes	characteristic
51	C₅×#818	C₂²	1	1	yes	characteristic
52	C₅×#816	C₂²	1	1	yes	characteristic
53	C₅×#816	C₂²	1	1	yes	characteristic
54	C₅×#815	C₂²	1	1	yes	characteristic
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
56	C₅×#810	C₂²	1	1	yes	characteristic
57	C₅×#810	C₂²	1	1	yes	characteristic
58	C₅×#808	C₂²	1	1	yes	characteristic
59	C₅×#807	C₂²	1	1	yes	characteristic
60	C₅×#803	C₂²	1	1	yes	characteristic
61	#79648	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
62	C₂×C₅×#137	—	3	1	no	—
63	C₅×#520	—	3	1	no	—
64	C₅×#519	—	3	1	no	—
65	C₅×#441	—	3	1	no	—
66	C₅×#441	—	3	1	no	—
67	C₅×#440	—	3	1	no	—
68	C₅×#440	—	3	1	no	—
69	C₄×C₅×Q₁₆	—	3	1	no	—
70	C₄×C₅×Q₁₆	—	3	1	no	—
71	C₄×C₅×SD₁₆	—	3	1	no	—
72	C₄×C₅×SD₁₆	D₃	1	1	yes	characteristic, complemented
73	C₅×#428	—	3	1	no	—
74	C₅×#416	—	3	1	no	—
75	C₂×C₅×#103	—	3	1	no	—
76	C₅×#405	—	3	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₅×#67	—	2	1	no	—
81	C₂²×C₅×Dic₃	—	2	1	no	—
82	C₂²×C₅×Dic₃	—	2	1	no	—
83	C₅×D₃×Q₈	—	2	2	no	—
84	C₅×D₃×Q₈	C₂×C₄	1	4	yes	complemented
85	C₅×#237	—	2	2	no	—
86	C₅×#237	C₂×C₄	1	4	yes	—
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	—	2	1	no	—
89	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
90	C₂×C₅×Dic₆	—	2	1	no	—
91	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
92	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
93	C₃×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	—	2	1	no	—
97	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₃×C₄²×C₅	—	2	1	no	—
101	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₅×#217	—	2	1	no	—
103	C₅×#216	C₂×C₄	1	4	yes	complemented
104	C₅×#214	C₂×C₄	1	4	yes	complemented
105	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
106	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
107	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
108	C₅×C₄⋊Dic₃	—	2	1	no	—
109	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₅×Dic₃⋊C₄	—	2	1	no	—
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
117	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
118	C₄×C₅×Dic₃	—	2	1	no	—
119	C₄×C₅×Dic₃	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	—	2	1	no	—
123	C₄×C₅×Dic₃	—	2	1	no	—
124	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
128	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
129	C₅×D₃×C₈	—	2	2	no	—
130	C₂×#915	C₂×C₅	1	1	yes	characteristic
131	#5572	C₂×C₅	1	1	yes	characteristic, complemented
132	#5546	C₂×C₅	1	1	yes	characteristic
133	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
134	#5164	C₂×C₅	1	1	yes	characteristic, complemented
135	#5030	C₂×C₅	1	1	yes	characteristic, complemented
136	#5018	C₂×C₅	1	1	yes	characteristic, complemented
137	#4861	C₂×C₅	1	1	yes	characteristic, complemented
138	#4853	C₂×C₅	1	1	yes	characteristic, complemented
139	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
140	#4790	C₂×C₅	1	1	yes	characteristic, complemented
141	#4772	C₂×C₅	1	1	yes	characteristic
142	#4758	C₂×C₅	1	1	yes	characteristic, complemented
143	C₄×Dic₁₂	C₂×C₅	1	1	yes	characteristic, complemented
144	#4689	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×C₅×#41	—	3	1	no	—
146	C₂²×C₅×Q₈	—	3	1	no	—
147	C₅×#137	—	3	8	no	—
148	C₂×C₅×Q₁₆	—	3	1	no	—
149	C₂×C₅×Q₁₆	—	3	1	no	—
150	C₂×C₅×SD₁₆	—	3	1	no	—
151	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
152	C₂×C₅×M₁₆	—	3	1	no	—
153	C₂²×C₅×C₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	3	1	no	—
156	C₄×C₅×Q₈	—	3	1	no	—
157	C₄×C₅×Q₈	—	3	1	no	—
158	C₄×C₅×Q₈	—	3	1	no	—
159	C₄×C₅×Q₈	—	6	1	no	—
160	C₄×C₅×Q₈	—	6	1	no	—
161	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
162	C₄×C₅×D₄	—	3	1	no	—
163	C₄×C₅×D₄	—	6	1	no	—
164	C₄×C₅×D₄	—	6	1	no	—
165	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
166	C₅×#117	—	3	1	no	—
167	C₅×#117	—	3	1	no	—
168	C₅×#117	—	6	1	no	—
169	C₅×#117	—	6	1	no	—
170	C₅×#117	—	6	1	no	—
171	C₂×C₅×C₄⋊C₄	—	3	1	no	—
172	C₂×C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×#107	—	3	1	no	—
174	C₅×#107	—	3	1	no	—
175	C₅×#106	—	3	1	no	—
176	C₅×#106	C₂×D₃	1	1	yes	characteristic
177	C₅×#103	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#103	—	3	1	no	—
180	C₅×#103	—	3	1	no	—
181	C₅×#103	—	3	1	no	—
182	C₅×#103	C₂×D₃	1	1	yes	characteristic
183	C₅×#102	—	3	1	no	—
184	C₅×#102	C₂×D₃	1	1	yes	characteristic
185	C₅×#97	—	3	1	no	—
186	C₅×#97	—	3	1	no	—
187	C₄×C₅×C₈	—	3	1	no	—
188	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
189	#2947	—	3	1	no	Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
194	C₃×C₅×D₄	—	2	1	no	—
195	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	8	1	no	—
200	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₅×#67	—	2	4	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	4	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	—	2	1	no	—
209	C₂×C₅×Dic₃	—	8	1	no	—
210	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
213	C₄×C₅×D₃	—	2	4	no	—
214	C₄×C₅×D₃	—	8	1	no	—
215	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
216	C₄×C₅×D₃	#41	1	2	yes	—
217	C₅×Dic₆	—	2	1	no	—
218	C₅×Dic₆	—	2	1	no	—
219	C₅×Dic₆	—	2	4	no	—
220	C₅×Dic₆	C₂²×C₄	1	2	yes	—
221	C₅×Dic₆	C₂²×C₄	1	2	yes	—
222	C₃×C₅×C₈	—	2	1	no	—
223	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
224	C₅×C₃⋊C₈	—	2	1	no	—
225	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
226	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×#237	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
229	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
230	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
231	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
232	C₂×#216	C₂²×C₅	1	1	yes	characteristic
233	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
234	C₂×#214	C₂²×C₅	1	1	yes	characteristic
235	C₄×#67	—	2	1	no	—
236	C₂×Dic₃⋊C₄	—	2	1	no	—
237	#915	C₄×C₅	1	8	yes	complemented
238	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
239	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
240	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
241	#892	—	2	1	no	—
242	#892	C₂²×C₅	1	1	yes	characteristic
243	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	#887	—	2	1	no	—
245	#887	C₂²×C₅	1	1	yes	characteristic
246	#887	C₂²×C₅	1	1	yes	characteristic
247	#67⋊C₄	—	2	1	no	—
248	#877	—	2	1	no	—
249	#872	—	2	1	no	—
250	#872	C₂²×C₅	1	1	yes	characteristic
251	C₄×Dic₆	—	2	1	no	—
252	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
253	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
254	C₃×#106	C₂²×C₅	1	1	yes	characteristic
255	C₃×#103	C₂²×C₅	1	1	yes	characteristic
256	C₃×#102	C₂²×C₅	1	1	yes	characteristic
257	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
258	#835	C₂²×C₅	1	1	yes	characteristic
259	#832	C₂²×C₅	1	1	yes	characteristic
260	#818	C₂²×C₅	1	1	yes	characteristic
261	#816	C₂²×C₅	1	1	yes	characteristic
262	#816	C₂²×C₅	1	1	yes	characteristic
263	#815	C₂²×C₅	1	1	yes	characteristic
264	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
265	#810	C₂²×C₅	1	1	yes	characteristic
266	#810	C₂²×C₅	1	1	yes	characteristic
267	#808	C₂²×C₅	1	1	yes	characteristic
268	#807	C₂²×C₅	1	1	yes	characteristic
269	#803	C₂²×C₅	1	1	yes	characteristic
270	C₅×#41	—	3	4	no	—
271	C₅×#41	—	6	2	no	—
272	C₂×C₅×Q₈	—	3	4	no	—
273	C₂×C₅×Q₈	—	3	1	no	—
274	C₂×C₅×Q₈	—	3	1	no	—
275	C₂×C₅×Q₈	—	6	1	no	—
276	C₂×C₅×Q₈	—	6	2	no	—
277	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
278	C₂×C₅×D₄	—	6	1	no	—
279	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	3	1	no	—
282	C₂²×C₄×C₅	—	6	1	no	—
283	C₂²×C₄×C₅	—	6	1	no	—
284	C₂²×C₄×C₅	—	6	1	no	—
285	C₂²×C₄×C₅	—	6	1	no	—
286	C₅×Q₁₆	—	3	4	no	—
287	C₅×Q₁₆	—	3	4	no	—
288	C₅×SD₁₆	—	3	4	no	—
289	C₅×SD₁₆	C₄×D₃	1	4	yes	complemented
290	C₅×M₁₆	—	3	4	no	—
291	C₂×C₅×C₈	—	3	1	no	—
292	C₂×C₅×C₈	—	3	1	no	—
293	C₂×C₅×C₈	—	6	2	no	—
294	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
295	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
296	C₅×C₄⋊C₄	—	2	1	no	—
297	C₅×C₄⋊C₄	—	3	1	no	—
298	C₅×C₄⋊C₄	—	3	1	no	—
299	C₅×C₄⋊C₄	—	3	1	no	—
300	C₅×C₄⋊C₄	—	3	1	no	—
301	C₅×C₄⋊C₄	—	6	1	no	—
302	C₅×C₄⋊C₄	—	6	1	no	—
303	C₅×C₄⋊C₄	—	6	1	no	—
304	C₅×C₄⋊C₄	—	6	1	no	—
305	C₅×C₄⋊C₄	—	6	1	no	—
306	C₅×C₄⋊C₄	—	6	1	no	—
307	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
308	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	—	3	1	no	—
311	C₅×C₂²⋊C₄	—	3	1	no	—
312	C₅×C₂²⋊C₄	—	6	1	no	—
313	C₅×C₂²⋊C₄	—	6	1	no	—
314	C₄²×C₅	—	2	1	no	—
315	C₄²×C₅	—	3	1	no	—
316	C₄²×C₅	—	6	1	no	—
317	C₄²×C₅	—	6	1	no	—
318	C₄²×C₅	—	6	1	no	—
319	C₄²×C₅	—	6	1	no	—
320	C₄²×C₅	—	6	1	no	—
321	C₄²×C₅	—	6	1	no	—
322	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
323	C₂×#137	—	3	1	no	—
324	#520	—	3	1	no	—
325	#519	—	3	1	no	—
326	#441	—	3	1	no	—
327	#441	—	3	1	no	—
328	#440	—	3	1	no	—
329	#440	—	3	1	no	—
330	C₄×Q₁₆	—	3	1	no	—
331	C₄×Q₁₆	—	3	1	no	—
332	C₄×SD₁₆	—	3	1	no	—
333	C₄×SD₁₆	C₅×D₃	1	1	yes	characteristic, complemented
334	#428	—	3	1	no	—
335	#416	—	3	1	no	—
336	C₂×#103	—	3	1	no	—
337	#405	—	3	1	no	—
338	C₂²×C₃×C₅	—	2	2	no	—
339	C₂²×C₃×C₅	—	4	1	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₅×D₃	—	2	1	no	—
343	C₂×C₅×D₃	—	2	1	no	—
344	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
345	C₃×C₄×C₅	—	2	2	no	—
346	C₃×C₄×C₅	—	2	1	no	—
347	C₃×C₄×C₅	—	2	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₃×C₄×C₅	—	4	1	no	—
350	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
351	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
352	C₅×Dic₃	—	2	2	no	—
353	C₅×Dic₃	—	2	2	no	—
354	C₅×Dic₃	—	2	1	no	—
355	C₅×Dic₃	—	2	1	no	—
356	C₅×Dic₃	—	4	1	no	—
357	C₅×Dic₃	—	4	1	no	—
358	C₅×Dic₃	C₄×D₄	1	2	yes	—
359	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
361	C₂²×C₃×C₄	—	2	1	no	—
362	C₂×#67	—	2	1	no	—
363	C₂²×Dic₃	—	2	1	no	—
364	C₂²×Dic₃	—	2	1	no	—
365	D₃×Q₈	—	2	2	no	—
366	D₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
367	#237	—	2	2	no	—
368	#237	C₂×C₄×C₅	1	4	yes	—
369	C₂×C₄×D₃	—	2	1	no	—
370	C₂×C₄×D₃	—	2	1	no	—
371	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
372	C₂×Dic₆	—	2	1	no	—
373	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
374	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
375	C₃×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
376	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₄⋊C₄	—	2	1	no	—
379	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
380	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
381	C₃×C₂²⋊C₄	—	2	1	no	—
382	C₃×C₄²	—	2	1	no	—
383	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
384	#217	—	2	1	no	—
385	#216	C₂×C₄×C₅	1	4	yes	complemented
386	#214	C₂×C₄×C₅	1	4	yes	complemented
387	(C₂×D₃)⋊C₄	—	2	1	no	—
388	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
389	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
390	C₄⋊Dic₃	—	2	1	no	—
391	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
392	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
393	Dic₃⋊C₄	—	2	1	no	—
394	Dic₃⋊C₄	—	2	1	no	—
395	Dic₃⋊C₄	—	2	1	no	—
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	—	2	1	no	—
398	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
399	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
400	C₄×Dic₃	—	2	1	no	—
401	C₄×Dic₃	—	2	1	no	—
402	C₄×Dic₃	—	2	1	no	—
403	C₄×Dic₃	—	2	1	no	—
404	C₄×Dic₃	—	2	1	no	—
405	C₄×Dic₃	—	2	1	no	—
406	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
409	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
410	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	4	yes	complemented
411	D₃×C₈	—	2	2	no	—
412	C₂³×C₅	—	2	1	no	—
413	C₂³×C₅	—	3	1	no	—
414	C₅×Q₈	—	2	1	no	—
415	C₅×Q₈	—	3	2	no	—
416	C₅×Q₈	—	3	2	no	—
417	C₅×Q₈	—	6	4	no	—
418	C₅×Q₈	—	6	1	no	—
419	C₅×Q₈	—	6	1	no	—
420	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
421	C₅×D₄	—	2	1	no	—
422	C₅×D₄	—	6	4	no	—
423	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	3	1	no	—
428	C₂×C₄×C₅	—	3	2	no	—
429	C₂×C₄×C₅	—	3	2	no	—
430	C₂×C₄×C₅	—	3	1	no	—
431	C₂×C₄×C₅	—	3	1	no	—
432	C₂×C₄×C₅	—	6	4	no	—
433	C₂×C₄×C₅	—	6	4	no	—
434	C₂×C₄×C₅	—	6	1	no	—
435	C₂×C₄×C₅	—	6	1	no	—
436	C₂×C₄×C₅	—	6	1	no	—
437	C₂×C₄×C₅	—	6	1	no	—
438	C₂×C₄×C₅	—	8	1	no	—
439	C₂×C₄×C₅	—	24	1	no	—
440	C₂×C₄×C₅	—	24	1	no	—
441	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
442	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
444	C₅×C₈	—	2	1	no	—
445	C₅×C₈	—	3	2	no	—
446	C₅×C₈	—	6	1	no	—
447	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
448	C₂×#41	—	3	1	no	—
449	C₂²×Q₈	—	3	1	no	—
450	#137	—	3	8	no	—
451	C₂×Q₁₆	—	3	1	no	—
452	C₂×Q₁₆	—	3	1	no	—
453	C₂×SD₁₆	—	3	1	no	—
454	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
455	C₂×M₁₆	—	3	1	no	—
456	C₂²×C₈	—	3	1	no	—
457	C₄×Q₈	—	3	1	no	—
458	C₄×Q₈	—	3	1	no	—
459	C₄×Q₈	—	3	1	no	—
460	C₄×Q₈	—	3	1	no	—
461	C₄×Q₈	—	3	1	no	—
462	C₄×Q₈	—	6	1	no	—
463	C₄×Q₈	—	6	1	no	—
464	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
465	C₄×D₄	—	3	1	no	—
466	C₄×D₄	—	6	1	no	—
467	C₄×D₄	—	6	1	no	—
468	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
469	#117	—	3	1	no	—
470	#117	—	3	1	no	—
471	#117	—	6	1	no	—
472	#117	—	6	1	no	—
473	#117	—	6	1	no	—
474	C₂×C₄⋊C₄	—	3	1	no	—
475	C₂×C₄⋊C₄	—	6	1	no	—
476	#107	—	3	1	no	—
477	#107	—	3	1	no	—
478	#106	—	3	1	no	—
479	#106	C₂×C₅×D₃	1	1	yes	characteristic
480	#103	—	3	1	no	—
481	#103	—	3	1	no	—
482	#103	—	3	1	no	—
483	#103	—	3	1	no	—
484	#103	—	3	1	no	—
485	#103	C₂×C₅×D₃	1	1	yes	characteristic
486	#102	—	3	1	no	—
487	#102	C₂×C₅×D₃	1	1	yes	characteristic
488	#97	—	3	1	no	—
489	#97	—	3	1	no	—
490	C₄×C₈	—	3	1	no	—
491	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
492	C₂×C₃×C₅	—	4	2	no	—
493	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
494	C₂×C₃×C₅	#577	1	1	yes	characteristic
495	C₂×C₃×C₅	#578	1	1	yes	characteristic
496	C₅×D₃	—	2	2	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
499	C₃×Q₈	—	2	1	no	—
500	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
501	C₃×D₄	—	2	1	no	—
502	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	8	1	no	—
507	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
509	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
510	#67	—	2	4	no	—
511	C₂×Dic₃	—	2	1	no	—
512	C₂×Dic₃	—	2	1	no	—
513	C₂×Dic₃	—	2	4	no	—
514	C₂×Dic₃	—	2	1	no	—
515	C₂×Dic₃	—	2	1	no	—
516	C₂×Dic₃	—	8	1	no	—
517	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
520	C₄×D₃	—	2	4	no	—
521	C₄×D₃	—	8	1	no	—
522	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
523	C₄×D₃	C₅×#41	1	2	yes	—
524	Dic₆	—	2	1	no	—
525	Dic₆	—	2	1	no	—
526	Dic₆	—	2	4	no	—
527	Dic₆	C₂²×C₄×C₅	1	2	yes	—
528	Dic₆	C₂²×C₄×C₅	1	2	yes	—
529	C₃×C₈	—	2	1	no	—
530	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
531	C₃⋊C₈	—	2	1	no	—
532	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
533	C₂²×C₅	—	2	2	no	—
534	C₂²×C₅	—	3	2	no	—
535	C₂²×C₅	—	4	1	no	—
536	C₂²×C₅	—	4	1	no	—
537	C₂²×C₅	—	6	1	no	—
538	C₂²×C₅	—	6	1	no	—
539	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
540	C₄×C₅	—	2	1	no	—
541	C₄×C₅	—	2	1	no	—
542	C₄×C₅	—	2	2	no	—
543	C₄×C₅	—	3	2	no	—
544	C₄×C₅	—	4	1	no	—
545	C₄×C₅	—	4	1	no	—
546	C₄×C₅	—	6	1	no	—
547	C₄×C₅	—	6	1	no	—
548	C₄×C₅	—	6	2	no	—
549	C₄×C₅	—	6	2	no	—
550	C₄×C₅	—	12	1	no	—
551	C₄×C₅	—	12	1	no	—
552	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
553	C₄×C₅	D₃×#41	1	1	yes	characteristic
554	#41	—	3	4	no	—
555	#41	—	6	2	no	—
556	C₂×Q₈	—	3	4	no	—
557	C₂×Q₈	—	3	1	no	—
558	C₂×Q₈	—	3	1	no	—
559	C₂×Q₈	—	6	1	no	—
560	C₂×Q₈	—	6	2	no	—
561	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
562	C₂×D₄	—	6	1	no	—
563	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	3	1	no	—
566	C₂²×C₄	—	6	1	no	—
567	C₂²×C₄	—	6	1	no	—
568	C₂²×C₄	—	6	1	no	—
569	C₂²×C₄	—	6	1	no	—
570	Q₁₆	—	3	4	no	—
571	Q₁₆	—	3	4	no	—
572	SD₁₆	—	3	4	no	—
573	SD₁₆	C₄×C₅×D₃	1	4	yes	complemented
574	M₁₆	—	3	4	no	—
575	C₂×C₈	—	3	1	no	—
576	C₂×C₈	—	3	1	no	—
577	C₂×C₈	—	6	2	no	—
578	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
579	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	3	1	no	—
582	C₄⋊C₄	—	3	1	no	—
583	C₄⋊C₄	—	3	1	no	—
584	C₄⋊C₄	—	3	1	no	—
585	C₄⋊C₄	—	6	1	no	—
586	C₄⋊C₄	—	6	1	no	—
587	C₄⋊C₄	—	6	1	no	—
588	C₄⋊C₄	—	6	1	no	—
589	C₄⋊C₄	—	6	1	no	—
590	C₄⋊C₄	—	6	1	no	—
591	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
592	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
593	C₂²⋊C₄	—	2	1	no	—
594	C₂²⋊C₄	—	3	1	no	—
595	C₂²⋊C₄	—	3	1	no	—
596	C₂²⋊C₄	—	6	1	no	—
597	C₂²⋊C₄	—	6	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	3	1	no	—
600	C₄²	—	6	1	no	—
601	C₄²	—	6	1	no	—
602	C₄²	—	6	1	no	—
603	C₄²	—	6	1	no	—
604	C₄²	—	6	1	no	—
605	C₄²	—	6	1	no	—
606	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
607	C₃×C₅	#2947	1	1	yes	characteristic, complemented, Hall
608	C₂²×C₃	—	2	2	no	—
609	C₂²×C₃	—	4	1	no	—
610	C₂²×C₃	—	4	1	no	—
611	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
612	C₂×D₃	—	2	1	no	—
613	C₂×D₃	—	2	1	no	—
614	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
615	C₃×C₄	—	2	2	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	4	1	no	—
619	C₃×C₄	—	4	1	no	—
620	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
621	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
622	Dic₃	—	2	2	no	—
623	Dic₃	—	2	2	no	—
624	Dic₃	—	2	1	no	—
625	Dic₃	—	2	1	no	—
626	Dic₃	—	4	1	no	—
627	Dic₃	—	4	1	no	—
628	Dic₃	C₄×C₅×D₄	1	2	yes	—
629	C₂×C₅	—	4	2	no	—
630	C₂×C₅	—	6	2	no	—
631	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
632	C₂×C₅	#5762	1	1	yes	characteristic
633	C₂×C₅	#5771	1	1	yes	characteristic
634	C₂³	—	2	1	no	—
635	C₂³	—	3	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	3	2	no	—
638	Q₈	—	3	2	no	—
639	Q₈	—	6	4	no	—
640	Q₈	—	6	1	no	—
641	Q₈	—	6	1	no	—
642	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
643	D₄	—	2	1	no	—
644	D₄	—	6	4	no	—
645	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	3	1	no	—
650	C₂×C₄	—	3	2	no	—
651	C₂×C₄	—	3	2	no	—
652	C₂×C₄	—	3	1	no	—
653	C₂×C₄	—	3	1	no	—
654	C₂×C₄	—	6	4	no	—
655	C₂×C₄	—	6	4	no	—
656	C₂×C₄	—	6	1	no	—
657	C₂×C₄	—	6	1	no	—
658	C₂×C₄	—	6	1	no	—
659	C₂×C₄	—	6	1	no	—
660	C₂×C₄	—	8	1	no	—
661	C₂×C₄	—	24	1	no	—
662	C₂×C₄	—	24	1	no	—
663	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
664	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
666	C₈	—	2	1	no	—
667	C₈	—	3	2	no	—
668	C₈	—	6	1	no	—
669	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
670	C₂×C₃	—	4	2	no	—
671	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
672	C₂×C₃	C₅×#577	1	1	yes	characteristic
673	C₂×C₃	C₅×#578	1	1	yes	characteristic
674	D₃	—	2	2	no	—
675	C₅	#79648	1	1	yes	characteristic, direct product factor, Sylow
676	C₂²	—	2	2	no	—
677	C₂²	—	3	2	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	6	1	no	—
681	C₂²	—	6	1	no	—
682	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	3	2	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	6	1	no	—
690	C₄	—	6	1	no	—
691	C₄	—	6	2	no	—
692	C₄	—	6	2	no	—
693	C₄	—	12	1	no	—
694	C₄	—	12	1	no	—
695	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
696	C₄	C₅×D₃×#41	1	1	yes	characteristic
697	C₃	C₅×#2947	1	1	yes	characteristic, complemented, Sylow
698	C₂	—	4	2	no	—
699	C₂	—	6	2	no	—
700	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
701	C₂	C₅×#5762	1	1	yes	characteristic
702	C₂	C₅×#5771	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×SD₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#237	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×SD₁₆	D₃
hypocenter	C₃	C₅×#2947
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#5572	C₂	semidirect
4. C₃×C₄×C₅×SD₁₆	C₂	semidirect
5. C₅×#5164	C₂	semidirect
6. C₅×#5030	C₂	semidirect
7. C₅×#5018	C₂	semidirect
8. C₅×#4861	C₂	semidirect
9. C₅×#4853	C₂	semidirect
10. C₅×D₃×#103	C₂	semidirect
11. C₅×#4790	C₂	semidirect
13. C₅×#4758	C₂	semidirect
14. C₄×C₅×Dic₁₂	C₂	semidirect
15. C₅×#4689	C₂	semidirect
28. C₅×#915	C₄	semidirect
61. #79648	C₅	direct (N × H)
72. C₄×C₅×SD₁₆	D₃	semidirect
84. C₅×D₃×Q₈	C₂×C₄	semidirect
93. C₃×C₅×SD₁₆	C₂×C₄	semidirect
103. C₅×#216	C₂×C₄	semidirect
104. C₅×#214	C₂×C₄	semidirect
127. C₅×Dic₁₂	C₂×C₄	semidirect
128. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
131. #5572	C₂×C₅	semidirect
133. C₃×C₄×SD₁₆	C₂×C₅	semidirect
134. #5164	C₂×C₅	semidirect
135. #5030	C₂×C₅	semidirect
136. #5018	C₂×C₅	semidirect
137. #4861	C₂×C₅	semidirect
138. #4853	C₂×C₅	semidirect
139. D₃×#103	C₂×C₅	semidirect
140. #4790	C₂×C₅	semidirect
142. #4758	C₂×C₅	semidirect
143. C₄×Dic₁₂	C₂×C₅	semidirect
144. #4689	C₂×C₅	semidirect
237. #915	C₄×C₅	semidirect
289. C₅×SD₁₆	C₄×D₃	semidirect
333. C₄×SD₁₆	C₅×D₃	semidirect
366. D₃×Q₈	C₂×C₄×C₅	semidirect
375. C₃×SD₁₆	C₂×C₄×C₅	semidirect
385. #216	C₂×C₄×C₅	semidirect
386. #214	C₂×C₄×C₅	semidirect
409. Dic₁₂	C₂×C₄×C₅	semidirect
410. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
573. SD₁₆	C₄×C₅×D₃	semidirect
607. C₃×C₅	#2947	semidirect
675. C₅	#79648	direct (N × H)
697. C₃	C₅×#2947	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#915	2
C₅×#5572	2
C₅×#5546	2
C₃×C₄×C₅×SD₁₆	2
C₅×#5164	2
C₅×#5030	2
C₅×#5018	2
C₅×#4861	2
C₅×#4853	2
C₅×D₃×#103	2
C₅×#4790	2
C₅×#4772	2
C₅×#4758	2
C₄×C₅×Dic₁₂	2
C₅×#4689	2
C₅×#2947	3
#79648	5

Subgroups — C5×#79648 #14417153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79648 #14417153