Subgroups — C₅×#80072 #14435817

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5827	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5619	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4796	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4788	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4785	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4766	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4720	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3119	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#121	C₂²	1	1	yes	characteristic
21	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×#215	C₂²	1	1	yes	characteristic
24	C₅×#940	C₂²	1	1	yes	characteristic
25	C₅×#939	—	2	1	no	—
26	C₅×#938	—	2	1	no	—
27	C₅×D₄×Dic₃	—	2	1	no	—
28	C₅×D₄×Dic₃	—	2	1	no	—
29	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
30	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
31	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×#213	C₂²	1	1	yes	characteristic
33	C₅×#930	C₂²	1	1	yes	characteristic
34	C₅×#926	—	2	1	no	—
35	C₅×#926	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
37	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
38	C₅×#893	C₂²	1	1	yes	characteristic
39	C₅×#890	C₂²	1	1	yes	characteristic
40	C₅×#886	—	2	1	no	—
41	C₅×#883	—	2	1	no	—
42	C₃×C₅×#103	C₂²	1	1	yes	characteristic
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic
46	C₅×#832	C₂²	1	1	yes	characteristic
47	C₅×#832	C₂²	1	1	yes	characteristic
48	C₅×#832	C₂²	1	1	yes	characteristic
49	C₅×#830	C₂²	1	1	yes	characteristic
50	C₅×#821	C₂²	1	1	yes	characteristic
51	C₅×#821	C₂²	1	1	yes	characteristic
52	C₅×#818	C₂²	1	1	yes	characteristic
53	C₅×#818	C₂²	1	1	yes	characteristic
54	C₅×#815	C₂²	1	1	yes	characteristic
55	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
56	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
58	C₅×#808	C₂²	1	1	yes	characteristic
59	C₅×#808	C₂²	1	1	yes	characteristic
60	#80072	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#540	—	3	1	no	—
62	C₅×#520	—	3	1	no	—
63	C₅×#481	—	3	1	no	—
64	C₅×#480	—	3	1	no	—
65	C₅×#479	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#460	—	3	1	no	—
68	C₅×#459	—	3	1	no	—
69	C₅×#449	—	3	1	no	—
70	C₅×#449	D₃	1	1	yes	characteristic, complemented
71	C₅×#442	—	3	1	no	—
72	C₅×#440	—	3	1	no	—
73	C₄×C₅×SD₁₆	—	3	1	no	—
74	C₄×C₅×D₈	—	3	1	no	—
75	C₅×#433	—	3	1	no	—
76	C₃×C₅×#41	—	2	2	no	—
77	C₃×C₅×#41	—	2	2	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	1	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	—	2	1	no	—
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	1	no	—
87	C₂×C₅×#67	—	2	1	no	—
88	C₂²×C₅×Dic₃	—	2	1	no	—
89	C₂²×C₅×Dic₃	—	2	1	no	—
90	C₂²×C₅×Dic₃	—	2	1	no	—
91	C₂²×C₅×Dic₃	—	2	1	no	—
92	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
93	C₂×C₄×C₅×D₃	—	2	1	no	—
94	C₃×C₅×SD₁₆	—	2	2	no	—
95	C₃×C₅×D₈	—	2	2	no	—
96	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₅×#217	—	2	1	no	—
101	C₅×#217	—	2	1	no	—
102	C₅×#217	—	2	1	no	—
103	C₅×#217	D₄	1	1	yes	characteristic
104	C₅×#217	D₄	1	1	yes	characteristic
105	C₅×#215	—	2	2	no	—
106	C₅×#213	—	2	2	no	—
107	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×C₄⋊Dic₃	—	2	1	no	—
110	C₅×C₄⋊Dic₃	—	2	1	no	—
111	C₅×C₄⋊Dic₃	—	2	1	no	—
112	C₅×C₄⋊Dic₃	—	2	1	no	—
113	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
115	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
118	C₅×Dic₃⋊C₄	—	2	1	no	—
119	C₄×C₅×Dic₃	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
122	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	#5827	C₂×C₅	1	1	yes	characteristic, complemented
126	#5619	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
128	#5238	C₂×C₅	1	1	yes	characteristic, complemented
129	#5164	C₂×C₅	1	1	yes	characteristic, complemented
130	#5163	C₂×C₅	1	1	yes	characteristic, complemented
131	#5150	C₂×C₅	1	1	yes	characteristic, complemented
132	Dic₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
133	#5034	C₂×C₅	1	1	yes	characteristic, complemented
134	#4796	C₂×C₅	1	1	yes	characteristic, complemented
135	#4788	C₂×C₅	1	1	yes	characteristic, complemented
136	#4785	C₂×C₅	1	1	yes	characteristic, complemented
137	#4766	C₂×C₅	1	1	yes	characteristic, complemented
138	#4736	C₂×C₅	1	1	yes	characteristic, complemented
139	#4720	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
141	C₂×C₅×SD₁₆	—	3	1	no	—
142	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
143	C₂×C₅×D₈	—	3	1	no	—
144	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
145	C₅×#127	—	3	1	no	—
146	C₅×#125	—	3	1	no	—
147	C₅×#123	—	6	1	no	—
148	C₅×#123	—	6	1	no	—
149	C₅×#121	—	3	1	no	—
150	C₅×#121	—	6	1	no	—
151	C₅×#121	—	6	1	no	—
152	C₅×#121	C₂×D₃	1	1	yes	characteristic
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×D₄	—	3	1	no	—
156	C₄×C₅×D₄	—	3	1	no	—
157	C₄×C₅×D₄	—	3	1	no	—
158	C₄×C₅×D₄	—	3	1	no	—
159	C₄×C₅×D₄	—	6	1	no	—
160	C₄×C₅×D₄	—	6	1	no	—
161	C₅×#117	—	3	1	no	—
162	C₅×#117	—	6	1	no	—
163	C₂×C₅×C₄⋊C₄	—	3	1	no	—
164	C₂×C₅×C₄⋊C₄	—	6	1	no	—
165	C₅×#107	—	3	1	no	—
166	C₅×#107	—	3	1	no	—
167	C₅×#106	—	3	1	no	—
168	C₅×#106	—	3	1	no	—
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×#103	—	3	1	no	—
172	C₅×#103	C₂×D₃	1	1	yes	characteristic
173	C₅×#102	—	3	1	no	—
174	C₅×#102	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₅×#102	—	3	1	no	—
178	C₅×#102	C₂×D₃	1	1	yes	characteristic
179	C₅×C₂²⋊C₈	—	3	1	no	—
180	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
181	C₅×#97	—	3	1	no	—
182	C₄×C₅×C₈	—	3	1	no	—
183	#3119	—	3	1	no	Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₅×D₃	—	2	1	no	—
188	C₃×C₅×Q₈	—	2	1	no	—
189	C₃×C₅×Q₈	#41	1	2	yes	—
190	C₃×C₅×D₄	—	2	4	no	—
191	C₃×C₅×D₄	—	2	1	no	—
192	C₃×C₅×D₄	—	2	1	no	—
193	C₃×C₅×D₄	—	2	1	no	—
194	C₃×C₅×D₄	—	8	1	no	—
195	C₃×C₅×D₄	#41	1	2	yes	—
196	C₂×C₃×C₄×C₅	—	2	4	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₅×#67	—	8	1	no	—
204	C₅×#67	—	8	1	no	—
205	C₅×#67	—	8	1	no	—
206	C₂×C₅×Dic₃	—	2	1	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	—	8	1	no	—
211	C₂×C₅×Dic₃	—	8	1	no	—
212	C₂×C₅×Dic₃	—	8	1	no	—
213	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
214	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
215	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
216	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
217	C₅×D₁₂	—	2	1	no	—
218	C₅×D₁₂	—	2	1	no	—
219	C₄×C₅×D₃	—	8	1	no	—
220	C₃×C₅×C₈	—	2	1	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	—	2	1	no	—
224	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
227	C₃×#121	C₂²×C₅	1	1	yes	characteristic
228	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
229	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
230	C₂×#215	C₂²×C₅	1	1	yes	characteristic
231	#940	C₂²×C₅	1	1	yes	characteristic
232	#939	—	2	1	no	—
233	#938	—	2	1	no	—
234	D₄×Dic₃	—	2	1	no	—
235	D₄×Dic₃	—	2	1	no	—
236	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
237	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
238	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
239	C₂×#213	C₂²×C₅	1	1	yes	characteristic
240	#930	C₂²×C₅	1	1	yes	characteristic
241	#926	—	2	1	no	—
242	#926	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄⋊Dic₃	—	2	1	no	—
244	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
245	#893	C₂²×C₅	1	1	yes	characteristic
246	#890	C₂²×C₅	1	1	yes	characteristic
247	#886	—	2	1	no	—
248	#883	—	2	1	no	—
249	C₃×#103	C₂²×C₅	1	1	yes	characteristic
250	C₃×#102	C₂²×C₅	1	1	yes	characteristic
251	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	#835	C₂²×C₅	1	1	yes	characteristic
253	#832	C₂²×C₅	1	1	yes	characteristic
254	#832	C₂²×C₅	1	1	yes	characteristic
255	#832	C₂²×C₅	1	1	yes	characteristic
256	#830	C₂²×C₅	1	1	yes	characteristic
257	#821	C₂²×C₅	1	1	yes	characteristic
258	#821	C₂²×C₅	1	1	yes	characteristic
259	#818	C₂²×C₅	1	1	yes	characteristic
260	#818	C₂²×C₅	1	1	yes	characteristic
261	#815	C₂²×C₅	1	1	yes	characteristic
262	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
265	#808	C₂²×C₅	1	1	yes	characteristic
266	#808	C₂²×C₅	1	1	yes	characteristic
267	C₅×#41	—	2	2	no	—
268	C₅×#41	—	2	2	no	—
269	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	2	1	no	—
272	C₂×C₅×D₄	—	3	1	no	—
273	C₂×C₅×D₄	—	6	1	no	—
274	C₂×C₅×D₄	—	6	1	no	—
275	C₂×C₅×D₄	—	6	1	no	—
276	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
277	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
278	C₂²×C₄×C₅	—	2	1	no	—
279	C₂²×C₄×C₅	—	6	1	no	—
280	C₂²×C₄×C₅	—	6	1	no	—
281	C₂²×C₄×C₅	—	6	1	no	—
282	C₂²×C₄×C₅	—	6	1	no	—
283	C₂²×C₄×C₅	—	6	1	no	—
284	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
285	C₅×SD₁₆	—	2	2	no	—
286	C₅×SD₁₆	—	6	2	no	—
287	C₅×D₈	—	2	2	no	—
288	C₅×D₈	—	6	2	no	—
289	C₂×C₅×C₈	—	3	1	no	—
290	C₂×C₅×C₈	—	3	1	no	—
291	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
292	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
293	C₅×C₄⋊C₄	—	3	1	no	—
294	C₅×C₄⋊C₄	—	3	1	no	—
295	C₅×C₄⋊C₄	—	3	1	no	—
296	C₅×C₄⋊C₄	—	3	1	no	—
297	C₅×C₄⋊C₄	—	3	1	no	—
298	C₅×C₄⋊C₄	—	6	1	no	—
299	C₅×C₄⋊C₄	—	6	1	no	—
300	C₅×C₄⋊C₄	—	6	1	no	—
301	C₅×C₄⋊C₄	—	6	1	no	—
302	C₅×C₄⋊C₄	—	6	1	no	—
303	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	3	1	no	—
306	C₅×C₂²⋊C₄	—	3	1	no	—
307	C₅×C₂²⋊C₄	—	6	1	no	—
308	C₅×C₂²⋊C₄	—	6	1	no	—
309	C₅×C₂²⋊C₄	—	6	1	no	—
310	C₅×C₂²⋊C₄	—	6	1	no	—
311	C₅×C₂²⋊C₄	—	6	1	no	—
312	C₄²×C₅	—	3	1	no	—
313	C₄²×C₅	—	3	1	no	—
314	C₄²×C₅	—	6	1	no	—
315	C₄²×C₅	—	6	1	no	—
316	#540	—	3	1	no	—
317	#520	—	3	1	no	—
318	#481	—	3	1	no	—
319	#480	—	3	1	no	—
320	#479	—	3	1	no	—
321	#478	—	3	1	no	—
322	#460	—	3	1	no	—
323	#459	—	3	1	no	—
324	#449	—	3	1	no	—
325	#449	C₅×D₃	1	1	yes	characteristic, complemented
326	#442	—	3	1	no	—
327	#440	—	3	1	no	—
328	C₄×SD₁₆	—	3	1	no	—
329	C₄×D₈	—	3	1	no	—
330	#433	—	3	1	no	—
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	2	2	no	—
333	C₂²×C₃×C₅	—	2	1	no	—
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	—	4	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	—	4	1	no	—
338	C₂²×C₃×C₅	—	4	1	no	—
339	C₂²×C₃×C₅	—	4	1	no	—
340	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₅×D₃	—	4	1	no	—
342	C₂×C₅×D₃	—	4	1	no	—
343	C₂×C₅×D₃	—	4	1	no	—
344	C₃×C₄×C₅	—	2	1	no	—
345	C₃×C₄×C₅	—	2	2	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₅×Dic₃	—	2	1	no	—
350	C₅×Dic₃	—	2	1	no	—
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	—	4	1	no	—
354	C₅×Dic₃	—	4	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₃×#41	—	2	2	no	—
357	C₃×#41	—	2	2	no	—
358	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×D₄	—	2	1	no	—
360	C₂×C₃×D₄	—	2	1	no	—
361	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×#67	—	2	1	no	—
366	C₂×#67	—	2	1	no	—
367	C₂×#67	—	2	1	no	—
368	C₂²×Dic₃	—	2	1	no	—
369	C₂²×Dic₃	—	2	1	no	—
370	C₂²×Dic₃	—	2	1	no	—
371	C₂²×Dic₃	—	2	1	no	—
372	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₄×D₃	—	2	1	no	—
374	C₃×SD₁₆	—	2	2	no	—
375	C₃×D₈	—	2	2	no	—
376	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
379	C₃×C₂²⋊C₄	—	2	1	no	—
380	#217	—	2	1	no	—
381	#217	—	2	1	no	—
382	#217	—	2	1	no	—
383	#217	C₅×D₄	1	1	yes	characteristic
384	#217	C₅×D₄	1	1	yes	characteristic
385	#215	—	2	2	no	—
386	#213	—	2	2	no	—
387	(C₂×D₃)⋊C₄	—	2	1	no	—
388	(C₂×D₃)⋊C₄	—	2	1	no	—
389	C₄⋊Dic₃	—	2	1	no	—
390	C₄⋊Dic₃	—	2	1	no	—
391	C₄⋊Dic₃	—	2	1	no	—
392	C₄⋊Dic₃	—	2	1	no	—
393	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
394	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
395	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
396	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
397	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
398	Dic₃⋊C₄	—	2	1	no	—
399	C₄×Dic₃	—	2	1	no	—
400	C₄×Dic₃	—	2	1	no	—
401	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
402	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂³×C₅	—	2	1	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	6	1	no	—
408	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
409	C₅×Q₈	—	2	1	no	—
410	C₅×Q₈	#237	1	2	yes	—
411	C₅×D₄	—	2	4	no	—
412	C₅×D₄	—	2	1	no	—
413	C₅×D₄	—	2	1	no	—
414	C₅×D₄	—	2	1	no	—
415	C₅×D₄	—	6	1	no	—
416	C₅×D₄	—	6	1	no	—
417	C₅×D₄	—	8	1	no	—
418	C₅×D₄	—	24	1	no	—
419	C₅×D₄	—	24	1	no	—
420	C₅×D₄	—	24	1	no	—
421	C₅×D₄	#237	1	2	yes	—
422	C₂×C₄×C₅	—	2	4	no	—
423	C₂×C₄×C₅	—	2	1	no	—
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	1	no	—
429	C₂×C₄×C₅	—	3	1	no	—
430	C₂×C₄×C₅	—	3	1	no	—
431	C₂×C₄×C₅	—	6	1	no	—
432	C₂×C₄×C₅	—	6	1	no	—
433	C₂×C₄×C₅	—	6	1	no	—
434	C₂×C₄×C₅	—	24	1	no	—
435	C₂×C₄×C₅	—	24	1	no	—
436	C₂×C₄×C₅	—	24	1	no	—
437	C₂×C₄×C₅	—	24	1	no	—
438	C₂×C₄×C₅	—	24	1	no	—
439	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
441	C₅×C₈	—	2	1	no	—
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	6	1	no	—
444	C₅×C₈	—	6	1	no	—
445	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
446	C₂×SD₁₆	—	3	1	no	—
447	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
448	C₂×D₈	—	3	1	no	—
449	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
450	#127	—	3	1	no	—
451	#125	—	3	1	no	—
452	#123	—	6	1	no	—
453	#123	—	6	1	no	—
454	#121	—	3	1	no	—
455	#121	—	6	1	no	—
456	#121	—	6	1	no	—
457	#121	C₂×C₅×D₃	1	1	yes	characteristic
458	C₄×Q₈	—	3	1	no	—
459	C₄×Q₈	—	3	1	no	—
460	C₄×D₄	—	3	1	no	—
461	C₄×D₄	—	3	1	no	—
462	C₄×D₄	—	3	1	no	—
463	C₄×D₄	—	3	1	no	—
464	C₄×D₄	—	6	1	no	—
465	C₄×D₄	—	6	1	no	—
466	#117	—	3	1	no	—
467	#117	—	6	1	no	—
468	C₂×C₄⋊C₄	—	3	1	no	—
469	C₂×C₄⋊C₄	—	6	1	no	—
470	#107	—	3	1	no	—
471	#107	—	3	1	no	—
472	#106	—	3	1	no	—
473	#106	—	3	1	no	—
474	C₄⋊C₈	—	3	1	no	—
475	C₄⋊C₈	—	3	1	no	—
476	#103	—	3	1	no	—
477	#103	C₂×C₅×D₃	1	1	yes	characteristic
478	#102	—	3	1	no	—
479	#102	—	3	1	no	—
480	#102	—	3	1	no	—
481	#102	—	3	1	no	—
482	#102	—	3	1	no	—
483	#102	C₂×C₅×D₃	1	1	yes	characteristic
484	C₂²⋊C₈	—	3	1	no	—
485	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
486	#97	—	3	1	no	—
487	C₄×C₈	—	3	1	no	—
488	C₂×C₃×C₅	—	4	1	no	—
489	C₂×C₃×C₅	—	4	2	no	—
490	C₂×C₃×C₅	—	8	1	no	—
491	C₂×C₃×C₅	#525	1	1	yes	characteristic
492	C₂×C₃×C₅	#576	1	1	yes	characteristic
493	C₂×C₃×C₅	#577	1	1	yes	characteristic
494	C₅×D₃	—	8	1	no	—
495	C₂³×C₃	—	2	1	no	—
496	C₂³×C₃	—	2	1	no	—
497	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂²×D₃	—	2	1	no	—
499	C₃×Q₈	—	2	1	no	—
500	C₃×Q₈	C₅×#41	1	2	yes	—
501	C₃×D₄	—	2	4	no	—
502	C₃×D₄	—	2	1	no	—
503	C₃×D₄	—	2	1	no	—
504	C₃×D₄	—	2	1	no	—
505	C₃×D₄	—	8	1	no	—
506	C₃×D₄	C₅×#41	1	2	yes	—
507	C₂×C₃×C₄	—	2	4	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
514	#67	—	8	1	no	—
515	#67	—	8	1	no	—
516	#67	—	8	1	no	—
517	C₂×Dic₃	—	2	1	no	—
518	C₂×Dic₃	—	2	1	no	—
519	C₂×Dic₃	—	2	1	no	—
520	C₂×Dic₃	—	8	1	no	—
521	C₂×Dic₃	—	8	1	no	—
522	C₂×Dic₃	—	8	1	no	—
523	C₂×Dic₃	—	8	1	no	—
524	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
525	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
526	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
527	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
528	D₁₂	—	2	1	no	—
529	D₁₂	—	2	1	no	—
530	C₄×D₃	—	8	1	no	—
531	C₃×C₈	—	2	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃⋊C₈	—	2	1	no	—
534	C₃⋊C₈	—	2	1	no	—
535	C₂²×C₅	—	2	1	no	—
536	C₂²×C₅	—	2	1	no	—
537	C₂²×C₅	—	2	1	no	—
538	C₂²×C₅	—	2	2	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	—	4	1	no	—
544	C₂²×C₅	—	12	1	no	—
545	C₂²×C₅	—	12	1	no	—
546	C₂²×C₅	—	12	1	no	—
547	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
548	C₄×C₅	—	2	1	no	—
549	C₄×C₅	—	2	2	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	6	1	no	—
552	C₄×C₅	—	6	1	no	—
553	C₄×C₅	—	6	1	no	—
554	C₄×C₅	—	6	1	no	—
555	C₄×C₅	—	12	1	no	—
556	C₄×C₅	—	12	1	no	—
557	C₄×C₅	—	12	1	no	—
558	C₄×C₅	C₂×#237	1	1	yes	characteristic
559	C₄×C₅	C₂×#237	1	1	yes	characteristic
560	#41	—	2	2	no	—
561	#41	—	2	2	no	—
562	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	3	1	no	—
566	C₂×D₄	—	6	1	no	—
567	C₂×D₄	—	6	1	no	—
568	C₂×D₄	—	6	1	no	—
569	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
570	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	6	1	no	—
573	C₂²×C₄	—	6	1	no	—
574	C₂²×C₄	—	6	1	no	—
575	C₂²×C₄	—	6	1	no	—
576	C₂²×C₄	—	6	1	no	—
577	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
578	SD₁₆	—	2	2	no	—
579	SD₁₆	—	6	2	no	—
580	D₈	—	2	2	no	—
581	D₈	—	6	2	no	—
582	C₂×C₈	—	3	1	no	—
583	C₂×C₈	—	3	1	no	—
584	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
585	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₄⋊C₄	—	3	1	no	—
587	C₄⋊C₄	—	3	1	no	—
588	C₄⋊C₄	—	3	1	no	—
589	C₄⋊C₄	—	3	1	no	—
590	C₄⋊C₄	—	3	1	no	—
591	C₄⋊C₄	—	6	1	no	—
592	C₄⋊C₄	—	6	1	no	—
593	C₄⋊C₄	—	6	1	no	—
594	C₄⋊C₄	—	6	1	no	—
595	C₄⋊C₄	—	6	1	no	—
596	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	3	1	no	—
599	C₂²⋊C₄	—	3	1	no	—
600	C₂²⋊C₄	—	6	1	no	—
601	C₂²⋊C₄	—	6	1	no	—
602	C₂²⋊C₄	—	6	1	no	—
603	C₂²⋊C₄	—	6	1	no	—
604	C₂²⋊C₄	—	6	1	no	—
605	C₄²	—	3	1	no	—
606	C₄²	—	3	1	no	—
607	C₄²	—	6	1	no	—
608	C₄²	—	6	1	no	—
609	C₃×C₅	#3119	1	1	yes	characteristic, complemented, Hall
610	C₂²×C₃	—	2	1	no	—
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
620	C₂×D₃	—	4	1	no	—
621	C₂×D₃	—	4	1	no	—
622	C₂×D₃	—	4	1	no	—
623	C₃×C₄	—	2	1	no	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	4	1	no	—
626	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
627	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
628	Dic₃	—	2	1	no	—
629	Dic₃	—	2	1	no	—
630	Dic₃	—	2	1	no	—
631	Dic₃	—	2	1	no	—
632	Dic₃	—	4	1	no	—
633	Dic₃	—	4	1	no	—
634	Dic₃	—	4	1	no	—
635	C₂×C₅	—	4	1	no	—
636	C₂×C₅	—	4	2	no	—
637	C₂×C₅	—	8	1	no	—
638	C₂×C₅	—	24	1	no	—
639	C₂×C₅	#5586	1	1	yes	characteristic
640	C₂×C₅	#5769	1	1	yes	characteristic
641	C₂×C₅	#5775	1	1	yes	characteristic
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	6	1	no	—
645	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
646	Q₈	—	2	1	no	—
647	Q₈	C₅×#237	1	2	yes	—
648	D₄	—	2	4	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	1	no	—
652	D₄	—	6	1	no	—
653	D₄	—	6	1	no	—
654	D₄	—	8	1	no	—
655	D₄	—	24	1	no	—
656	D₄	—	24	1	no	—
657	D₄	—	24	1	no	—
658	D₄	C₅×#237	1	2	yes	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	3	1	no	—
665	C₂×C₄	—	3	1	no	—
666	C₂×C₄	—	3	1	no	—
667	C₂×C₄	—	3	1	no	—
668	C₂×C₄	—	6	1	no	—
669	C₂×C₄	—	6	1	no	—
670	C₂×C₄	—	6	1	no	—
671	C₂×C₄	—	24	1	no	—
672	C₂×C₄	—	24	1	no	—
673	C₂×C₄	—	24	1	no	—
674	C₂×C₄	—	24	1	no	—
675	C₂×C₄	—	24	1	no	—
676	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
677	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
678	C₈	—	2	1	no	—
679	C₈	—	2	1	no	—
680	C₈	—	6	1	no	—
681	C₈	—	6	1	no	—
682	C₂×C₃	—	4	1	no	—
683	C₂×C₃	—	4	2	no	—
684	C₂×C₃	—	8	1	no	—
685	C₂×C₃	C₅×#525	1	1	yes	characteristic
686	C₂×C₃	C₅×#576	1	1	yes	characteristic
687	C₂×C₃	C₅×#577	1	1	yes	characteristic
688	D₃	—	8	1	no	—
689	C₅	#80072	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	12	1	no	—
700	C₂²	—	12	1	no	—
701	C₂²	—	12	1	no	—
702	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
703	C₄	—	2	1	no	—
704	C₄	—	2	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	6	1	no	—
707	C₄	—	6	1	no	—
708	C₄	—	6	1	no	—
709	C₄	—	6	1	no	—
710	C₄	—	12	1	no	—
711	C₄	—	12	1	no	—
712	C₄	—	12	1	no	—
713	C₄	C₂×C₅×#237	1	1	yes	characteristic
714	C₄	C₂×C₅×#237	1	1	yes	characteristic
715	C₃	C₅×#3119	1	1	yes	characteristic, complemented, Sylow
716	C₂	—	4	1	no	—
717	C₂	—	4	2	no	—
718	C₂	—	8	1	no	—
719	C₂	—	24	1	no	—
720	C₂	C₅×#5586	1	1	yes	characteristic
721	C₂	C₅×#5769	1	1	yes	characteristic
722	C₂	C₅×#5775	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×#449	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#449	D₃
hypocenter	C₃	C₅×#3119
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#449

Complements

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

N	H ≅ G/N	type
1. C₅×#5827	C₂	semidirect
2. C₅×#5619	C₂	semidirect
3. C₃×C₅×#449	C₂	semidirect
4. C₅×#5238	C₂	semidirect
5. C₅×#5164	C₂	semidirect
6. C₅×#5163	C₂	semidirect
7. C₅×#5150	C₂	semidirect
8. C₅×Dic₃×D₈	C₂	semidirect
9. C₅×#5034	C₂	semidirect
10. C₅×#4796	C₂	semidirect
11. C₅×#4788	C₂	semidirect
12. C₅×#4785	C₂	semidirect
13. C₅×#4766	C₂	semidirect
14. C₅×#4736	C₂	semidirect
15. C₅×#4720	C₂	semidirect
60. #80072	C₅	direct (N × H)
70. C₅×#449	D₃	semidirect
125. #5827	C₂×C₅	semidirect
126. #5619	C₂×C₅	semidirect
127. C₃×#449	C₂×C₅	semidirect
128. #5238	C₂×C₅	semidirect
129. #5164	C₂×C₅	semidirect
130. #5163	C₂×C₅	semidirect
131. #5150	C₂×C₅	semidirect
132. Dic₃×D₈	C₂×C₅	semidirect
133. #5034	C₂×C₅	semidirect
134. #4796	C₂×C₅	semidirect
135. #4788	C₂×C₅	semidirect
136. #4785	C₂×C₅	semidirect
137. #4766	C₂×C₅	semidirect
138. #4736	C₂×C₅	semidirect
139. #4720	C₂×C₅	semidirect
325. #449	C₅×D₃	semidirect
609. C₃×C₅	#3119	semidirect
689. C₅	#80072	direct (N × H)
715. C₃	C₅×#3119	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5827	2
C₅×#5619	2
C₃×C₅×#449	2
C₅×#5238	2
C₅×#5164	2
C₅×#5163	2
C₅×#5150	2
C₅×Dic₃×D₈	2
C₅×#5034	2
C₅×#4796	2
C₅×#4788	2
C₅×#4785	2
C₅×#4766	2
C₅×#4736	2
C₅×#4720	2
C₅×#3119	3
#80072	5

Subgroups — C5×#80072 #14435817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80072 #14435817