Subgroups — C₅×#81873 #14439642

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#918	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#916	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5724	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5675	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5190	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5183	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5168	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5092	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4715	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3156	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#237	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₅×#947	C₂²	1	1	yes	characteristic
28	C₅×#944	C₂²	1	1	yes	characteristic
29	C₅×#944	C₂²	1	1	yes	characteristic
30	C₂×C₅×#216	C₂²	1	1	yes	characteristic
31	C₂×C₅×#216	C₂²	1	1	yes	characteristic
32	C₂×C₅×#216	C₂²	1	1	yes	characteristic
33	C₂×C₅×#216	C₂²	1	1	yes	characteristic
34	C₂×C₅×#216	C₂²	1	1	yes	characteristic
35	C₂×C₅×#215	C₂²	1	1	yes	characteristic
36	C₅×#936	C₂²	1	1	yes	characteristic
37	C₂×C₅×#214	C₂²	1	1	yes	characteristic
38	C₂×C₅×#213	C₂²	1	1	yes	characteristic
39	C₅×#918	—	2	4	no	—
40	C₅×D₃×Q₁₆	—	2	4	no	—
41	C₅×#916	—	2	4	no	—
42	C₅×#915	—	2	4	no	—
43	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
44	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
45	C₂×C₅×#204	C₂²	1	1	yes	characteristic
46	C₂×C₅×#204	C₂²	1	1	yes	characteristic
47	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
48	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
49	C₅×#896	—	2	2	no	—
50	C₅×#894	—	2	2	no	—
51	C₅×#883	—	2	2	no	—
52	C₅×#878	—	2	2	no	—
53	C₅×#875	C₂²	1	1	yes	characteristic
54	C₅×#872	C₂²	1	1	yes	characteristic
55	C₅×#869	C₂²	1	1	yes	characteristic
56	C₃×C₅×#97	C₂²	1	1	yes	characteristic
57	C₅×#815	C₂²	1	1	yes	characteristic
58	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
59	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#81873	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₂×C₅×#137	—	3	1	no	—
62	C₂×C₅×#137	—	3	1	no	—
63	C₂×C₅×#135	—	3	1	no	—
64	C₂²×C₅×Q₁₆	—	3	1	no	—
65	C₅×#536	—	3	1	no	—
66	C₅×#536	—	3	1	no	—
67	C₅×#497	—	3	1	no	—
68	C₅×#497	—	3	1	no	—
69	C₅×#497	—	3	1	no	—
70	C₅×#497	D₃	1	1	yes	characteristic, complemented
71	C₅×#495	—	3	1	no	—
72	C₅×#495	—	3	1	no	—
73	C₅×#494	—	3	1	no	—
74	C₅×#494	—	3	1	no	—
75	C₅×#405	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂×C₅×#67	—	2	1	no	—
81	C₂²×C₅×Dic₃	—	2	1	no	—
82	C₅×#239	—	2	2	no	—
83	C₅×#239	—	2	2	no	—
84	C₅×D₃×Q₈	—	2	2	no	—
85	C₅×D₃×Q₈	—	2	2	no	—
86	C₅×D₃×Q₈	—	2	2	no	—
87	C₅×D₃×Q₈	—	2	2	no	—
88	C₅×#237	—	2	2	no	—
89	C₅×#237	—	2	2	no	—
90	C₂×C₅×D₁₂	—	2	1	no	—
91	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₄×C₅×D₃	—	2	1	no	—
94	C₂×C₄×C₅×D₃	—	2	1	no	—
95	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
96	C₂×C₅×Dic₆	—	2	1	no	—
97	C₂×C₅×Dic₆	—	2	1	no	—
98	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
99	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
100	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
101	C₃×C₅×Q₁₆	—	2	2	no	—
102	C₃×C₅×Q₁₆	—	2	2	no	—
103	C₃×C₅×SD₁₆	—	2	2	no	—
104	C₃×C₅×SD₁₆	—	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	2	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₅×#217	—	2	2	no	—
111	C₅×#216	—	2	2	no	—
112	C₅×#216	—	2	2	no	—
113	C₅×#216	—	2	2	no	—
114	C₅×#216	—	2	2	no	—
115	C₅×#216	—	2	2	no	—
116	C₅×#215	—	2	2	no	—
117	C₅×#214	—	2	2	no	—
118	C₅×#213	—	2	2	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
121	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
122	C₅×C₄⋊Dic₃	—	2	2	no	—
123	C₅×Dic₃⋊C₄	—	2	2	no	—
124	C₅×Dic₃⋊C₄	—	2	2	no	—
125	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
126	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
129	C₅×Dic₁₂	—	2	2	no	—
130	C₅×Dic₁₂	—	2	2	no	—
131	C₅×#204	—	2	2	no	—
132	C₅×#204	—	2	2	no	—
133	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	—
134	C₅×D₃×C₈	D₄	1	4	yes	—
135	C₂×#918	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×#916	C₂×C₅	1	1	yes	characteristic
138	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
139	#5724	C₂×C₅	1	1	yes	characteristic, complemented
140	#5675	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
142	#5190	C₂×C₅	1	1	yes	characteristic, complemented
143	#5183	C₂×C₅	1	1	yes	characteristic, complemented
144	#5168	C₂×C₅	1	1	yes	characteristic, complemented
145	#5167	C₂×C₅	1	1	yes	characteristic, complemented
146	#5092	C₂×C₅	1	1	yes	characteristic, complemented
147	#5059	C₂×C₅	1	1	yes	characteristic, complemented
148	#4715	C₂×C₅	1	1	yes	characteristic, complemented
149	#4708	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×C₅×#41	—	3	1	no	—
151	C₂×C₅×#41	—	3	1	no	—
152	C₂²×C₅×Q₈	—	3	1	no	—
153	C₂²×C₅×Q₈	—	3	1	no	—
154	C₅×#137	—	6	4	no	—
155	C₅×#137	—	6	4	no	—
156	C₅×#135	—	6	4	no	—
157	C₂×C₅×Q₁₆	—	3	1	no	—
158	C₂×C₅×Q₁₆	—	3	1	no	—
159	C₂×C₅×Q₁₆	—	3	1	no	—
160	C₂×C₅×Q₁₆	—	3	1	no	—
161	C₂×C₅×Q₁₆	—	3	1	no	—
162	C₂×C₅×Q₁₆	—	3	1	no	—
163	C₂×C₅×Q₁₆	—	3	1	no	—
164	C₂×C₅×Q₁₆	—	6	4	no	—
165	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
166	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
167	C₂×C₅×SD₁₆	—	3	1	no	—
168	C₂×C₅×SD₁₆	—	3	1	no	—
169	C₂×C₅×SD₁₆	—	3	1	no	—
170	C₂×C₅×SD₁₆	—	3	1	no	—
171	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
172	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
173	C₂×C₅×D₈	—	3	1	no	—
174	C₂×C₅×M₁₆	—	3	1	no	—
175	C₂²×C₅×C₈	—	3	1	no	—
176	C₅×C₄⋊Q₈	—	3	1	no	—
177	C₅×C₄⋊Q₈	—	3	1	no	—
178	C₅×C₄⋊Q₈	—	3	1	no	—
179	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
180	C₅×#124	—	3	1	no	—
181	C₅×#124	—	3	1	no	—
182	C₅×#124	—	3	1	no	—
183	C₅×#124	C₂×D₃	1	1	yes	characteristic
184	C₅×#123	—	6	2	no	—
185	C₅×#123	—	6	2	no	—
186	C₅×C₂²⋊Q₈	—	6	2	no	—
187	C₅×C₂²⋊Q₈	—	6	2	no	—
188	C₅×#117	—	3	1	no	—
189	C₅×#97	—	3	1	no	—
190	C₅×#97	C₂×D₃	1	1	yes	characteristic
191	C₄×C₅×C₈	—	3	1	no	—
192	C₄×C₅×C₈	—	3	1	no	—
193	#3156	—	3	1	no	Sylow
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂²×C₅×D₃	—	2	1	no	—
196	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	—	2	1	no	—
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×Q₈	—	2	1	no	—
202	C₃×C₅×Q₈	—	2	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
209	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	C₅×#67	—	4	2	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	2	1	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	4	2	no	—
215	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
216	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
217	C₅×D₁₂	—	2	1	no	—
218	C₅×D₁₂	—	2	1	no	—
219	C₅×D₁₂	—	4	2	no	—
220	C₄×C₅×D₃	—	4	2	no	—
221	C₄×C₅×D₃	—	4	2	no	—
222	C₄×C₅×D₃	—	4	2	no	—
223	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
224	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
225	C₅×Dic₆	—	2	1	no	—
226	C₅×Dic₆	—	2	1	no	—
227	C₅×Dic₆	—	2	1	no	—
228	C₅×Dic₆	—	2	1	no	—
229	C₅×Dic₆	—	2	1	no	—
230	C₅×Dic₆	—	2	1	no	—
231	C₅×Dic₆	—	4	2	no	—
232	C₅×Dic₆	—	4	2	no	—
233	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
234	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
235	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
236	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
237	C₂×#239	C₂²×C₅	1	1	yes	characteristic
238	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×#237	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
246	C₃×#124	C₂²×C₅	1	1	yes	characteristic
247	#947	C₂²×C₅	1	1	yes	characteristic
248	#944	C₂²×C₅	1	1	yes	characteristic
249	#944	C₂²×C₅	1	1	yes	characteristic
250	C₂×#216	C₂²×C₅	1	1	yes	characteristic
251	C₂×#216	C₂²×C₅	1	1	yes	characteristic
252	C₂×#216	C₂²×C₅	1	1	yes	characteristic
253	C₂×#216	C₂²×C₅	1	1	yes	characteristic
254	C₂×#216	C₂²×C₅	1	1	yes	characteristic
255	C₂×#215	C₂²×C₅	1	1	yes	characteristic
256	#936	C₂²×C₅	1	1	yes	characteristic
257	C₂×#214	C₂²×C₅	1	1	yes	characteristic
258	C₂×#213	C₂²×C₅	1	1	yes	characteristic
259	#918	—	2	4	no	—
260	D₃×Q₁₆	—	2	4	no	—
261	#916	—	2	4	no	—
262	#915	—	2	4	no	—
263	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
264	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
265	C₂×#204	C₂²×C₅	1	1	yes	characteristic
266	C₂×#204	C₂²×C₅	1	1	yes	characteristic
267	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
268	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
269	#896	—	2	2	no	—
270	#894	—	2	2	no	—
271	#883	—	2	2	no	—
272	#878	—	2	2	no	—
273	#875	C₂²×C₅	1	1	yes	characteristic
274	#872	C₂²×C₅	1	1	yes	characteristic
275	#869	C₂²×C₅	1	1	yes	characteristic
276	C₃×#97	C₂²×C₅	1	1	yes	characteristic
277	#815	C₂²×C₅	1	1	yes	characteristic
278	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
279	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	C₅×#41	—	6	2	no	—
281	C₅×#41	—	6	2	no	—
282	C₅×#41	—	6	2	no	—
283	C₅×#41	—	6	2	no	—
284	C₂×C₅×Q₈	—	3	1	no	—
285	C₂×C₅×Q₈	—	3	1	no	—
286	C₂×C₅×Q₈	—	3	1	no	—
287	C₂×C₅×Q₈	—	6	1	no	—
288	C₂×C₅×Q₈	—	6	1	no	—
289	C₂×C₅×Q₈	—	6	2	no	—
290	C₂×C₅×Q₈	—	6	2	no	—
291	C₂×C₅×Q₈	—	6	2	no	—
292	C₂×C₅×Q₈	—	6	2	no	—
293	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
295	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
296	C₂×C₅×D₄	—	3	1	no	—
297	C₂×C₅×D₄	—	6	1	no	—
298	C₂×C₅×D₄	—	6	1	no	—
299	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	—	3	1	no	—
301	C₂²×C₄×C₅	—	6	1	no	—
302	C₂²×C₄×C₅	—	6	1	no	—
303	C₂²×C₄×C₅	—	6	1	no	—
304	C₂²×C₄×C₅	—	6	1	no	—
305	C₅×Q₁₆	—	2	2	no	—
306	C₅×Q₁₆	—	2	2	no	—
307	C₅×Q₁₆	—	6	2	no	—
308	C₅×Q₁₆	—	6	2	no	—
309	C₅×Q₁₆	—	6	2	no	—
310	C₅×Q₁₆	—	6	2	no	—
311	C₅×Q₁₆	—	6	2	no	—
312	C₅×Q₁₆	—	6	2	no	—
313	C₅×Q₁₆	—	6	2	no	—
314	C₅×SD₁₆	—	2	2	no	—
315	C₅×SD₁₆	—	2	2	no	—
316	C₅×SD₁₆	—	6	2	no	—
317	C₅×SD₁₆	—	6	2	no	—
318	C₅×SD₁₆	—	6	2	no	—
319	C₅×SD₁₆	—	6	2	no	—
320	C₅×D₈	—	6	2	no	—
321	C₅×M₁₆	—	3	4	no	—
322	C₂×C₅×C₈	—	3	1	no	—
323	C₂×C₅×C₈	—	3	1	no	—
324	C₂×C₅×C₈	—	3	4	no	—
325	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
326	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	3	2	no	—
329	C₅×C₄⋊C₄	—	6	2	no	—
330	C₅×C₄⋊C₄	—	6	2	no	—
331	C₅×C₄⋊C₄	—	6	2	no	—
332	C₅×C₂²⋊C₄	—	2	2	no	—
333	C₅×C₂²⋊C₄	—	3	2	no	—
334	C₅×C₂²⋊C₄	—	6	2	no	—
335	C₅×C₂²⋊C₄	—	6	2	no	—
336	C₅×C₂²⋊C₄	—	6	2	no	—
337	C₄²×C₅	—	3	1	no	—
338	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
339	C₂×#137	—	3	1	no	—
340	C₂×#137	—	3	1	no	—
341	C₂×#135	—	3	1	no	—
342	C₂²×Q₁₆	—	3	1	no	—
343	#536	—	3	1	no	—
344	#536	—	3	1	no	—
345	#497	—	3	1	no	—
346	#497	—	3	1	no	—
347	#497	—	3	1	no	—
348	#497	C₅×D₃	1	1	yes	characteristic, complemented
349	#495	—	3	1	no	—
350	#495	—	3	1	no	—
351	#494	—	3	1	no	—
352	#494	—	3	1	no	—
353	#405	—	3	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	2	no	—
356	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₅×D₃	—	2	2	no	—
358	C₂×C₅×D₃	—	4	1	no	—
359	C₂×C₅×D₃	—	4	2	no	—
360	C₂×C₅×D₃	#127	1	2	yes	—
361	C₃×C₄×C₅	—	2	2	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
366	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
367	C₅×Dic₃	—	2	2	no	—
368	C₅×Dic₃	—	4	1	no	—
369	C₅×Dic₃	—	4	1	no	—
370	C₅×Dic₃	—	4	1	no	—
371	C₅×Dic₃	#127	1	2	yes	—
372	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×#67	—	2	1	no	—
377	C₂²×Dic₃	—	2	1	no	—
378	#239	—	2	2	no	—
379	#239	—	2	2	no	—
380	D₃×Q₈	—	2	2	no	—
381	D₃×Q₈	—	2	2	no	—
382	D₃×Q₈	—	2	2	no	—
383	D₃×Q₈	—	2	2	no	—
384	#237	—	2	2	no	—
385	#237	—	2	2	no	—
386	C₂×D₁₂	—	2	1	no	—
387	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄×D₃	—	2	1	no	—
389	C₂×C₄×D₃	—	2	1	no	—
390	C₂×C₄×D₃	—	2	1	no	—
391	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
392	C₂×Dic₆	—	2	1	no	—
393	C₂×Dic₆	—	2	1	no	—
394	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
395	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
396	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
397	C₃×Q₁₆	—	2	2	no	—
398	C₃×Q₁₆	—	2	2	no	—
399	C₃×SD₁₆	—	2	2	no	—
400	C₃×SD₁₆	—	2	2	no	—
401	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₂²⋊C₄	—	2	2	no	—
405	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
406	#217	—	2	2	no	—
407	#216	—	2	2	no	—
408	#216	—	2	2	no	—
409	#216	—	2	2	no	—
410	#216	—	2	2	no	—
411	#216	—	2	2	no	—
412	#215	—	2	2	no	—
413	#214	—	2	2	no	—
414	#213	—	2	2	no	—
415	(C₂×D₃)⋊C₄	—	2	2	no	—
416	(C₂×D₃)⋊C₄	—	2	2	no	—
417	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
418	C₄⋊Dic₃	—	2	2	no	—
419	Dic₃⋊C₄	—	2	2	no	—
420	Dic₃⋊C₄	—	2	2	no	—
421	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
422	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
425	Dic₁₂	—	2	2	no	—
426	Dic₁₂	—	2	2	no	—
427	#204	—	2	2	no	—
428	#204	—	2	2	no	—
429	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	—
430	D₃×C₈	C₅×D₄	1	4	yes	—
431	C₂³×C₅	—	2	1	no	—
432	C₂³×C₅	—	3	1	no	—
433	C₂³×C₅	—	6	1	no	—
434	C₅×Q₈	—	2	1	no	—
435	C₅×Q₈	—	2	1	no	—
436	C₅×Q₈	—	2	1	no	—
437	C₅×Q₈	—	2	1	no	—
438	C₅×Q₈	—	2	1	no	—
439	C₅×Q₈	—	2	1	no	—
440	C₅×Q₈	—	6	1	no	—
441	C₅×Q₈	—	6	1	no	—
442	C₅×Q₈	—	6	1	no	—
443	C₅×Q₈	—	6	1	no	—
444	C₅×Q₈	—	6	1	no	—
445	C₅×Q₈	—	6	1	no	—
446	C₅×Q₈	—	12	2	no	—
447	C₅×Q₈	—	12	2	no	—
448	C₅×D₄	—	2	1	no	—
449	C₅×D₄	—	2	1	no	—
450	C₅×D₄	—	6	1	no	—
451	C₅×D₄	—	6	1	no	—
452	C₅×D₄	—	12	2	no	—
453	C₅×D₄	—	12	2	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	3	1	no	—
458	C₂×C₄×C₅	—	3	2	no	—
459	C₂×C₄×C₅	—	3	2	no	—
460	C₂×C₄×C₅	—	3	2	no	—
461	C₂×C₄×C₅	—	6	1	no	—
462	C₂×C₄×C₅	—	6	1	no	—
463	C₂×C₄×C₅	—	6	1	no	—
464	C₂×C₄×C₅	—	12	2	no	—
465	C₂×C₄×C₅	—	12	2	no	—
466	C₂×C₄×C₅	—	12	2	no	—
467	C₂×C₄×C₅	—	12	2	no	—
468	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
469	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
470	C₅×C₈	—	3	2	no	—
471	C₅×C₈	—	3	2	no	—
472	C₅×C₈	D₃×D₄	1	2	yes	—
473	C₅×C₈	D₃×D₄	1	2	yes	—
474	C₂×#41	—	3	1	no	—
475	C₂×#41	—	3	1	no	—
476	C₂²×Q₈	—	3	1	no	—
477	C₂²×Q₈	—	3	1	no	—
478	#137	—	6	4	no	—
479	#137	—	6	4	no	—
480	#135	—	6	4	no	—
481	C₂×Q₁₆	—	3	1	no	—
482	C₂×Q₁₆	—	3	1	no	—
483	C₂×Q₁₆	—	3	1	no	—
484	C₂×Q₁₆	—	3	1	no	—
485	C₂×Q₁₆	—	3	1	no	—
486	C₂×Q₁₆	—	3	1	no	—
487	C₂×Q₁₆	—	3	1	no	—
488	C₂×Q₁₆	—	6	4	no	—
489	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
490	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
491	C₂×SD₁₆	—	3	1	no	—
492	C₂×SD₁₆	—	3	1	no	—
493	C₂×SD₁₆	—	3	1	no	—
494	C₂×SD₁₆	—	3	1	no	—
495	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
496	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
497	C₂×D₈	—	3	1	no	—
498	C₂×M₁₆	—	3	1	no	—
499	C₂²×C₈	—	3	1	no	—
500	C₄⋊Q₈	—	3	1	no	—
501	C₄⋊Q₈	—	3	1	no	—
502	C₄⋊Q₈	—	3	1	no	—
503	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
504	#124	—	3	1	no	—
505	#124	—	3	1	no	—
506	#124	—	3	1	no	—
507	#124	C₂×C₅×D₃	1	1	yes	characteristic
508	#123	—	6	2	no	—
509	#123	—	6	2	no	—
510	C₂²⋊Q₈	—	6	2	no	—
511	C₂²⋊Q₈	—	6	2	no	—
512	#117	—	3	1	no	—
513	#97	—	3	1	no	—
514	#97	C₂×C₅×D₃	1	1	yes	characteristic
515	C₄×C₈	—	3	1	no	—
516	C₄×C₈	—	3	1	no	—
517	C₂×C₃×C₅	—	8	1	no	—
518	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
519	C₂×C₃×C₅	#578	1	2	yes	—
520	C₅×D₃	—	2	2	no	—
521	C₅×D₃	—	8	1	no	—
522	C₂³×C₃	—	2	1	no	—
523	C₂²×D₃	—	2	1	no	—
524	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
525	C₃×Q₈	—	2	1	no	—
526	C₃×Q₈	—	2	1	no	—
527	C₃×Q₈	—	2	1	no	—
528	C₃×Q₈	—	2	1	no	—
529	C₃×Q₈	—	2	1	no	—
530	C₃×Q₈	—	2	1	no	—
531	C₃×D₄	—	2	1	no	—
532	C₃×D₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
537	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
538	#67	—	4	2	no	—
539	C₂×Dic₃	—	2	1	no	—
540	C₂×Dic₃	—	2	1	no	—
541	C₂×Dic₃	—	2	1	no	—
542	C₂×Dic₃	—	4	2	no	—
543	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
544	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
545	D₁₂	—	2	1	no	—
546	D₁₂	—	2	1	no	—
547	D₁₂	—	4	2	no	—
548	C₄×D₃	—	4	2	no	—
549	C₄×D₃	—	4	2	no	—
550	C₄×D₃	—	4	2	no	—
551	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
552	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
553	Dic₆	—	2	1	no	—
554	Dic₆	—	2	1	no	—
555	Dic₆	—	2	1	no	—
556	Dic₆	—	2	1	no	—
557	Dic₆	—	2	1	no	—
558	Dic₆	—	2	1	no	—
559	Dic₆	—	4	2	no	—
560	Dic₆	—	4	2	no	—
561	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
562	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
563	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
564	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
565	C₂²×C₅	—	3	2	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	—	4	2	no	—
568	C₂²×C₅	—	6	2	no	—
569	C₂²×C₅	—	12	1	no	—
570	C₂²×C₅	—	12	2	no	—
571	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
572	C₄×C₅	—	2	2	no	—
573	C₄×C₅	—	3	2	no	—
574	C₄×C₅	—	4	1	no	—
575	C₄×C₅	—	4	1	no	—
576	C₄×C₅	—	4	1	no	—
577	C₄×C₅	—	6	2	no	—
578	C₄×C₅	—	12	1	no	—
579	C₄×C₅	—	12	1	no	—
580	C₄×C₅	—	12	1	no	—
581	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
582	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
583	#41	—	6	2	no	—
584	#41	—	6	2	no	—
585	#41	—	6	2	no	—
586	#41	—	6	2	no	—
587	C₂×Q₈	—	3	1	no	—
588	C₂×Q₈	—	3	1	no	—
589	C₂×Q₈	—	3	1	no	—
590	C₂×Q₈	—	6	1	no	—
591	C₂×Q₈	—	6	1	no	—
592	C₂×Q₈	—	6	2	no	—
593	C₂×Q₈	—	6	2	no	—
594	C₂×Q₈	—	6	2	no	—
595	C₂×Q₈	—	6	2	no	—
596	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
597	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
598	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
599	C₂×D₄	—	3	1	no	—
600	C₂×D₄	—	6	1	no	—
601	C₂×D₄	—	6	1	no	—
602	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
603	C₂²×C₄	—	3	1	no	—
604	C₂²×C₄	—	6	1	no	—
605	C₂²×C₄	—	6	1	no	—
606	C₂²×C₄	—	6	1	no	—
607	C₂²×C₄	—	6	1	no	—
608	Q₁₆	—	2	2	no	—
609	Q₁₆	—	2	2	no	—
610	Q₁₆	—	6	2	no	—
611	Q₁₆	—	6	2	no	—
612	Q₁₆	—	6	2	no	—
613	Q₁₆	—	6	2	no	—
614	Q₁₆	—	6	2	no	—
615	Q₁₆	—	6	2	no	—
616	Q₁₆	—	6	2	no	—
617	SD₁₆	—	2	2	no	—
618	SD₁₆	—	2	2	no	—
619	SD₁₆	—	6	2	no	—
620	SD₁₆	—	6	2	no	—
621	SD₁₆	—	6	2	no	—
622	SD₁₆	—	6	2	no	—
623	D₈	—	6	2	no	—
624	M₁₆	—	3	4	no	—
625	C₂×C₈	—	3	1	no	—
626	C₂×C₈	—	3	1	no	—
627	C₂×C₈	—	3	4	no	—
628	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
629	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	3	2	no	—
632	C₄⋊C₄	—	6	2	no	—
633	C₄⋊C₄	—	6	2	no	—
634	C₄⋊C₄	—	6	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	3	2	no	—
637	C₂²⋊C₄	—	6	2	no	—
638	C₂²⋊C₄	—	6	2	no	—
639	C₂²⋊C₄	—	6	2	no	—
640	C₄²	—	3	1	no	—
641	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
642	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
643	C₂²×C₃	—	4	1	no	—
644	C₂²×C₃	—	4	2	no	—
645	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
646	C₂×D₃	—	2	2	no	—
647	C₂×D₃	—	4	1	no	—
648	C₂×D₃	—	4	2	no	—
649	C₂×D₃	C₅×#127	1	2	yes	—
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	1	no	—
653	C₃×C₄	—	4	1	no	—
654	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
655	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
656	Dic₃	—	2	2	no	—
657	Dic₃	—	4	1	no	—
658	Dic₃	—	4	1	no	—
659	Dic₃	—	4	1	no	—
660	Dic₃	C₅×#127	1	2	yes	—
661	C₂×C₅	—	6	2	no	—
662	C₂×C₅	—	8	1	no	—
663	C₂×C₅	—	24	1	no	—
664	C₂×C₅	D₃×#127	1	1	yes	characteristic
665	C₂×C₅	#5779	1	2	yes	—
666	C₂³	—	2	1	no	—
667	C₂³	—	3	1	no	—
668	C₂³	—	6	1	no	—
669	Q₈	—	2	1	no	—
670	Q₈	—	2	1	no	—
671	Q₈	—	2	1	no	—
672	Q₈	—	2	1	no	—
673	Q₈	—	2	1	no	—
674	Q₈	—	2	1	no	—
675	Q₈	—	6	1	no	—
676	Q₈	—	6	1	no	—
677	Q₈	—	6	1	no	—
678	Q₈	—	6	1	no	—
679	Q₈	—	6	1	no	—
680	Q₈	—	6	1	no	—
681	Q₈	—	12	2	no	—
682	Q₈	—	12	2	no	—
683	D₄	—	2	1	no	—
684	D₄	—	2	1	no	—
685	D₄	—	6	1	no	—
686	D₄	—	6	1	no	—
687	D₄	—	12	2	no	—
688	D₄	—	12	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	3	1	no	—
693	C₂×C₄	—	3	2	no	—
694	C₂×C₄	—	3	2	no	—
695	C₂×C₄	—	3	2	no	—
696	C₂×C₄	—	6	1	no	—
697	C₂×C₄	—	6	1	no	—
698	C₂×C₄	—	6	1	no	—
699	C₂×C₄	—	12	2	no	—
700	C₂×C₄	—	12	2	no	—
701	C₂×C₄	—	12	2	no	—
702	C₂×C₄	—	12	2	no	—
703	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
704	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
705	C₈	—	3	2	no	—
706	C₈	—	3	2	no	—
707	C₈	C₅×D₃×D₄	1	2	yes	—
708	C₈	C₅×D₃×D₄	1	2	yes	—
709	C₂×C₃	—	8	1	no	—
710	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
711	C₂×C₃	C₅×#578	1	2	yes	—
712	D₃	—	2	2	no	—
713	D₃	—	8	1	no	—
714	C₅	#81873	1	1	yes	characteristic, direct product factor, Sylow
715	C₂²	—	3	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	6	2	no	—
719	C₂²	—	12	1	no	—
720	C₂²	—	12	2	no	—
721	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	3	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	6	2	no	—
728	C₄	—	12	1	no	—
729	C₄	—	12	1	no	—
730	C₄	—	12	1	no	—
731	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
732	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
733	C₃	C₅×#3156	1	1	yes	characteristic, complemented, Sylow
734	C₂	—	6	2	no	—
735	C₂	—	8	1	no	—
736	C₂	—	24	1	no	—
737	C₂	C₅×D₃×#127	1	1	yes	characteristic
738	C₂	C₅×#5779	1	2	yes	—

	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×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#916	C₂
hypercenter	C₅×#497	D₃
hypocenter	C₃	C₅×#3156
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#918	C₂	semidirect
2. C₂×C₅×D₃×Q₁₆	C₂	semidirect
4. C₂×C₅×#915	C₂	semidirect
5. C₅×#5724	C₂	semidirect
6. C₅×#5675	C₂	semidirect
7. C₃×C₅×#497	C₂	semidirect
8. C₅×#5190	C₂	semidirect
9. C₅×#5183	C₂	semidirect
10. C₅×#5168	C₂	semidirect
11. C₅×#5167	C₂	semidirect
12. C₅×#5092	C₂	semidirect
13. C₅×#5059	C₂	semidirect
14. C₅×#4715	C₂	semidirect
15. C₅×#4708	C₂	semidirect
60. #81873	C₅	direct (N × H)
70. C₅×#497	D₃	semidirect
135. C₂×#918	C₂×C₅	semidirect
136. C₂×D₃×Q₁₆	C₂×C₅	semidirect
138. C₂×#915	C₂×C₅	semidirect
139. #5724	C₂×C₅	semidirect
140. #5675	C₂×C₅	semidirect
141. C₃×#497	C₂×C₅	semidirect
142. #5190	C₂×C₅	semidirect
143. #5183	C₂×C₅	semidirect
144. #5168	C₂×C₅	semidirect
145. #5167	C₂×C₅	semidirect
146. #5092	C₂×C₅	semidirect
147. #5059	C₂×C₅	semidirect
148. #4715	C₂×C₅	semidirect
149. #4708	C₂×C₅	semidirect
348. #497	C₅×D₃	semidirect
642. C₃×C₅	#3156	semidirect
714. C₅	#81873	direct (N × H)
733. C₃	C₅×#3156	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#918	2
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×#916	2
C₂×C₅×#915	2
C₅×#5724	2
C₅×#5675	2
C₃×C₅×#497	2
C₅×#5190	2
C₅×#5183	2
C₅×#5168	2
C₅×#5167	2
C₅×#5092	2
C₅×#5059	2
C₅×#4715	2
C₅×#4708	2
C₅×#3156	3
#81873	5

Subgroups — C5×#81873 #14439642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81873 #14439642