Subgroups — C₅×#80136 #14435586

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5798	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5643	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5217	C₂	1	1	yes	maximal, characteristic
5	C₅×#5165	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5165	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5045	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4785	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4761	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4759	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4756	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4737	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4720	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3118	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#217	—	2	1	no	—
22	C₂×C₅×#217	—	2	1	no	—
23	C₅×#947	C₂²	1	1	yes	characteristic, complemented
24	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₅×D₄×Dic₃	—	2	1	no	—
26	C₅×D₄×Dic₃	—	2	1	no	—
27	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
28	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
29	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
30	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×#213	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	C₂²	1	1	yes	characteristic
35	C₅×#926	C₂²	1	1	yes	characteristic
36	C₅×#898	—	2	1	no	—
37	C₅×#897	—	2	1	no	—
38	C₅×#893	C₂²	1	1	yes	characteristic, complemented
39	C₅×#888	C₂²	1	1	yes	characteristic, complemented
40	C₅×#885	—	2	1	no	—
41	C₅×#883	—	2	1	no	—
42	C₃×C₅×#102	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, complemented
46	C₅×#835	C₂²	1	1	yes	characteristic, complemented
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, complemented
51	C₅×#821	C₂²	1	1	yes	characteristic, complemented
52	C₅×#818	C₂²	1	1	yes	characteristic, complemented
53	C₅×#817	C₂²	1	1	yes	characteristic, complemented
54	C₅×#815	C₂²	1	1	yes	characteristic, complemented
55	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₅×#808	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	#80136	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	—	3	1	no	—
62	C₅×#518	—	3	1	no	—
63	C₅×#485	—	3	1	no	—
64	C₅×#482	—	3	1	no	—
65	C₅×#476	—	3	1	no	—
66	C₅×#474	—	3	1	no	—
67	C₅×#463	—	3	1	no	—
68	C₅×#463	—	3	1	no	—
69	C₅×#450	D₃	1	1	yes	characteristic, complemented
70	C₅×#447	—	3	1	no	—
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	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	—	2	2	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	C₂³	1	1	yes	characteristic
84	C₂×C₅×#67	—	2	1	no	—
85	C₂²×C₅×Dic₃	—	2	1	no	—
86	C₂²×C₅×Dic₃	—	2	1	no	—
87	C₂²×C₅×Dic₃	—	2	1	no	—
88	C₂²×C₅×Dic₃	—	2	1	no	—
89	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
90	C₂×C₄×C₅×D₃	—	2	1	no	—
91	C₂×C₅×Dic₆	—	2	1	no	—
92	C₃×C₅×SD₁₆	—	2	2	no	—
93	C₃×C₅×SD₁₆	—	2	2	no	—
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×C₂²⋊C₄	—	2	1	no	—
99	C₅×#217	—	2	1	no	—
100	C₅×#217	—	2	1	no	—
101	C₅×#217	—	2	1	no	—
102	C₅×#217	—	2	1	no	—
103	C₅×#217	—	2	1	no	—
104	C₅×#217	D₄	1	1	yes	characteristic
105	C₅×#217	D₄	1	1	yes	characteristic
106	C₅×#213	—	2	2	no	—
107	C₅×#213	—	2	2	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	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	#5798	C₂×C₅	1	1	yes	characteristic, complemented
126	#5643	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
128	#5217	C₂×C₅	1	1	yes	characteristic
129	#5165	C₂×C₅	1	1	yes	characteristic, complemented
130	#5165	C₂×C₅	1	1	yes	characteristic, complemented
131	#5164	C₂×C₅	1	1	yes	characteristic, complemented
132	Dic₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
133	#5045	C₂×C₅	1	1	yes	characteristic, complemented
134	#4785	C₂×C₅	1	1	yes	characteristic, complemented
135	#4761	C₂×C₅	1	1	yes	characteristic, complemented
136	#4759	C₂×C₅	1	1	yes	characteristic, complemented
137	#4756	C₂×C₅	1	1	yes	characteristic, complemented
138	#4737	C₂×C₅	1	1	yes	characteristic, complemented
139	#4720	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
141	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
142	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
143	C₂×C₅×D₈	—	3	1	no	—
144	C₂×C₅×D₈	—	3	1	no	—
145	C₅×C₄⋊Q₈	—	3	1	no	—
146	C₅×#126	—	6	1	no	—
147	C₅×#124	—	3	1	no	—
148	C₅×#124	—	6	1	no	—
149	C₅×#123	—	6	1	no	—
150	C₅×C₂²⋊Q₈	—	6	1	no	—
151	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
152	C₅×#121	—	3	1	no	—
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×D₄	—	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	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
164	C₂×C₅×C₂²⋊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	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
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	#3118	—	3	1	no	Sylow
184	C₂³×C₃×C₅	—	2	4	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	—	2	1	no	—
187	C₂³×C₃×C₅	—	8	1	no	—
188	C₂³×C₃×C₅	—	8	1	no	—
189	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×D₄	—	2	4	no	—
194	C₃×C₅×D₄	—	2	1	no	—
195	C₃×C₅×D₄	—	2	1	no	—
196	C₃×C₅×D₄	#41	1	2	yes	—
197	C₃×C₅×D₄	#41	1	2	yes	—
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	—	2	1	no	—
202	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
204	C₅×#67	—	8	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	1	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	—	8	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	C₂×D₄	1	1	yes	characteristic
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	C₅×D₁₂	—	2	1	no	—
217	C₅×D₁₂	—	2	1	no	—
218	C₄×C₅×D₃	—	8	1	no	—
219	C₅×Dic₆	—	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	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×#217	—	2	1	no	—
229	C₂×#217	—	2	1	no	—
230	#947	C₂²×C₅	1	1	yes	characteristic, complemented
231	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
232	D₄×Dic₃	—	2	1	no	—
233	D₄×Dic₃	—	2	1	no	—
234	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
235	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
236	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
237	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
238	C₂×#213	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	C₂²×C₅	1	1	yes	characteristic
242	#926	C₂²×C₅	1	1	yes	characteristic
243	#898	—	2	1	no	—
244	#897	—	2	1	no	—
245	#893	C₂²×C₅	1	1	yes	characteristic, complemented
246	#888	C₂²×C₅	1	1	yes	characteristic, complemented
247	#885	—	2	1	no	—
248	#883	—	2	1	no	—
249	C₃×#102	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, complemented
253	#835	C₂²×C₅	1	1	yes	characteristic, complemented
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, complemented
258	#821	C₂²×C₅	1	1	yes	characteristic, complemented
259	#818	C₂²×C₅	1	1	yes	characteristic, complemented
260	#817	C₂²×C₅	1	1	yes	characteristic, complemented
261	#815	C₂²×C₅	1	1	yes	characteristic, complemented
262	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
263	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
265	#808	C₂²×C₅	1	1	yes	characteristic, complemented
266	#807	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	—	2	1	no	—
268	C₂×C₅×Q₈	—	6	1	no	—
269	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₅×D₄	—	2	2	no	—
271	C₂×C₅×D₄	—	2	2	no	—
272	C₂×C₅×D₄	—	2	1	no	—
273	C₂×C₅×D₄	—	3	1	no	—
274	C₂×C₅×D₄	—	6	1	no	—
275	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
277	C₂²×C₄×C₅	—	6	1	no	—
278	C₂²×C₄×C₅	—	6	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	C₂²×D₃	1	1	yes	characteristic
283	C₅×SD₁₆	—	2	2	no	—
284	C₅×SD₁₆	—	2	2	no	—
285	C₅×D₈	—	6	2	no	—
286	C₅×D₈	—	6	2	no	—
287	C₂×C₅×C₈	—	3	1	no	—
288	C₂×C₅×C₈	—	3	1	no	—
289	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	—	3	1	no	—
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	—	6	1	no	—
298	C₅×C₄⋊C₄	—	6	1	no	—
299	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	3	1	no	—
302	C₅×C₂²⋊C₄	—	3	1	no	—
303	C₅×C₂²⋊C₄	—	6	1	no	—
304	C₅×C₂²⋊C₄	—	6	1	no	—
305	C₅×C₂²⋊C₄	—	6	1	no	—
306	C₅×C₂²⋊C₄	—	6	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	#542	—	3	1	no	—
317	#518	—	3	1	no	—
318	#485	—	3	1	no	—
319	#482	—	3	1	no	—
320	#476	—	3	1	no	—
321	#474	—	3	1	no	—
322	#463	—	3	1	no	—
323	#463	—	3	1	no	—
324	#450	C₅×D₃	1	1	yes	characteristic, complemented
325	#447	—	3	1	no	—
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	2	no	—
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	—	2	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	—	8	4	no	—
341	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₅×D₃	—	4	1	no	—
343	C₂×C₅×D₃	—	4	1	no	—
344	C₂×C₅×D₃	—	4	1	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₅×Dic₃	—	2	1	no	—
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	—	2	1	no	—
354	C₅×Dic₃	—	4	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₅×Dic₃	—	4	1	no	—
357	C₂⁴×C₃	—	2	1	no	—
358	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×D₄	—	2	2	no	—
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	—	2	1	no	—
362	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×#67	—	2	1	no	—
366	C₂²×Dic₃	—	2	1	no	—
367	C₂²×Dic₃	—	2	1	no	—
368	C₂²×Dic₃	—	2	1	no	—
369	C₂²×Dic₃	—	2	1	no	—
370	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₄×D₃	—	2	1	no	—
372	C₂×Dic₆	—	2	1	no	—
373	C₃×SD₁₆	—	2	2	no	—
374	C₃×SD₁₆	—	2	2	no	—
375	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₃×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
384	#217	—	2	1	no	—
385	#217	C₅×D₄	1	1	yes	characteristic
386	#217	C₅×D₄	1	1	yes	characteristic
387	#213	—	2	2	no	—
388	#213	—	2	2	no	—
389	(C₂×D₃)⋊C₄	—	2	1	no	—
390	(C₂×D₃)⋊C₄	—	2	1	no	—
391	(C₂×D₃)⋊C₄	—	2	1	no	—
392	(C₂×D₃)⋊C₄	—	2	1	no	—
393	C₄⋊Dic₃	—	2	1	no	—
394	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
395	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
396	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
397	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
398	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
399	Dic₃⋊C₄	—	2	1	no	—
400	C₄×Dic₃	—	2	1	no	—
401	C₄×Dic₃	—	2	1	no	—
402	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
403	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂³×C₅	—	2	4	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	2	1	no	—
409	C₂³×C₅	—	6	1	no	—
410	C₂³×C₅	—	8	1	no	—
411	C₂³×C₅	—	8	1	no	—
412	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
413	C₅×Q₈	—	2	1	no	—
414	C₅×Q₈	—	2	1	no	—
415	C₅×Q₈	—	24	1	no	—
416	C₅×D₄	—	2	4	no	—
417	C₅×D₄	—	2	1	no	—
418	C₅×D₄	—	2	1	no	—
419	C₅×D₄	—	6	1	no	—
420	C₅×D₄	—	6	1	no	—
421	C₅×D₄	—	24	1	no	—
422	C₅×D₄	#237	1	2	yes	—
423	C₅×D₄	#237	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	—	2	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	—	3	1	no	—
432	C₂×C₄×C₅	—	6	1	no	—
433	C₂×C₄×C₅	—	6	1	no	—
434	C₂×C₄×C₅	—	6	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	—	24	1	no	—
440	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	2	1	no	—
444	C₅×C₈	—	6	1	no	—
445	C₅×C₈	—	6	1	no	—
446	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
447	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
448	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
449	C₂×D₈	—	3	1	no	—
450	C₂×D₈	—	3	1	no	—
451	C₄⋊Q₈	—	3	1	no	—
452	#126	—	6	1	no	—
453	#124	—	3	1	no	—
454	#124	—	6	1	no	—
455	#123	—	6	1	no	—
456	C₂²⋊Q₈	—	6	1	no	—
457	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
458	#121	—	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	—	3	1	no	—
465	C₄×D₄	—	6	1	no	—
466	C₄×D₄	—	6	1	no	—
467	#117	—	3	1	no	—
468	#117	—	3	1	no	—
469	C₂×C₂²⋊C₄	—	6	1	no	—
470	C₂×C₂²⋊C₄	—	6	1	no	—
471	#107	—	3	1	no	—
472	#107	—	3	1	no	—
473	#106	—	3	1	no	—
474	#106	—	3	1	no	—
475	C₄⋊C₈	—	3	1	no	—
476	C₄⋊C₈	—	3	1	no	—
477	#103	—	3	1	no	—
478	#103	—	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	#102	C₂×C₅×D₃	1	1	yes	characteristic
485	C₂²⋊C₈	—	3	1	no	—
486	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
487	#97	—	3	1	no	—
488	C₄×C₈	—	3	1	no	—
489	C₂×C₃×C₅	—	4	1	no	—
490	C₂×C₃×C₅	—	4	2	no	—
491	C₂×C₃×C₅	—	4	2	no	—
492	C₂×C₃×C₅	#525	1	1	yes	characteristic
493	C₂×C₃×C₅	#576	1	1	yes	characteristic
494	C₂×C₃×C₅	#577	1	1	yes	characteristic
495	C₅×D₃	—	8	1	no	—
496	C₂³×C₃	—	2	4	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	—	2	1	no	—
499	C₂³×C₃	—	8	1	no	—
500	C₂³×C₃	—	8	1	no	—
501	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
502	C₂²×D₃	—	2	1	no	—
503	C₃×Q₈	—	2	1	no	—
504	C₃×Q₈	—	2	1	no	—
505	C₃×D₄	—	2	4	no	—
506	C₃×D₄	—	2	1	no	—
507	C₃×D₄	—	2	1	no	—
508	C₃×D₄	C₅×#41	1	2	yes	—
509	C₃×D₄	C₅×#41	1	2	yes	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
515	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	Dic₆	—	8	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃×C₈	—	2	1	no	—
534	C₃⋊C₈	—	2	1	no	—
535	C₃⋊C₈	—	2	1	no	—
536	C₂²×C₅	—	2	1	no	—
537	C₂²×C₅	—	2	1	no	—
538	C₂²×C₅	—	2	1	no	—
539	C₂²×C₅	—	2	2	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	—	4	1	no	—
544	C₂²×C₅	—	4	1	no	—
545	C₂²×C₅	—	8	4	no	—
546	C₂²×C₅	—	12	1	no	—
547	C₂²×C₅	—	12	1	no	—
548	C₂²×C₅	—	12	1	no	—
549	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
550	C₄×C₅	—	2	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	6	1	no	—
554	C₄×C₅	—	6	1	no	—
555	C₄×C₅	—	6	1	no	—
556	C₄×C₅	—	6	1	no	—
557	C₄×C₅	—	12	1	no	—
558	C₄×C₅	—	12	1	no	—
559	C₄×C₅	—	12	1	no	—
560	C₄×C₅	C₂×#237	1	1	yes	characteristic
561	C₄×C₅	C₂×#237	1	1	yes	characteristic
562	C₂⁴	—	2	1	no	—
563	C₂×Q₈	—	6	1	no	—
564	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	3	1	no	—
569	C₂×D₄	—	6	1	no	—
570	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
571	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
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	—	2	2	no	—
580	D₈	—	6	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	—	2	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	—	3	1	no	—
592	C₄⋊C₄	—	6	1	no	—
593	C₄⋊C₄	—	6	1	no	—
594	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	3	1	no	—
597	C₂²⋊C₄	—	3	1	no	—
598	C₂²⋊C₄	—	6	1	no	—
599	C₂²⋊C₄	—	6	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	C₂²⋊C₄	—	6	1	no	—
606	C₂²⋊C₄	—	6	1	no	—
607	C₄²	—	3	1	no	—
608	C₄²	—	3	1	no	—
609	C₄²	—	6	1	no	—
610	C₄²	—	6	1	no	—
611	C₃×C₅	#3118	1	1	yes	characteristic, complemented, Hall
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	8	4	no	—
622	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
623	C₂×D₃	—	4	1	no	—
624	C₂×D₃	—	4	1	no	—
625	C₂×D₃	—	4	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	4	1	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
630	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
631	Dic₃	—	2	1	no	—
632	Dic₃	—	2	1	no	—
633	Dic₃	—	2	1	no	—
634	Dic₃	—	2	1	no	—
635	Dic₃	—	4	1	no	—
636	Dic₃	—	4	1	no	—
637	Dic₃	—	4	1	no	—
638	C₂×C₅	—	4	1	no	—
639	C₂×C₅	—	4	2	no	—
640	C₂×C₅	—	4	2	no	—
641	C₂×C₅	—	24	1	no	—
642	C₂×C₅	#5586	1	1	yes	characteristic
643	C₂×C₅	#5762	1	1	yes	characteristic
644	C₂×C₅	#5774	1	1	yes	characteristic
645	C₂³	—	2	4	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	6	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	—	8	1	no	—
651	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
652	Q₈	—	2	1	no	—
653	Q₈	—	2	1	no	—
654	Q₈	—	24	1	no	—
655	D₄	—	2	4	no	—
656	D₄	—	2	1	no	—
657	D₄	—	2	1	no	—
658	D₄	—	6	1	no	—
659	D₄	—	6	1	no	—
660	D₄	—	24	1	no	—
661	D₄	C₅×#237	1	2	yes	—
662	D₄	C₅×#237	1	2	yes	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	3	1	no	—
668	C₂×C₄	—	3	1	no	—
669	C₂×C₄	—	3	1	no	—
670	C₂×C₄	—	3	1	no	—
671	C₂×C₄	—	6	1	no	—
672	C₂×C₄	—	6	1	no	—
673	C₂×C₄	—	6	1	no	—
674	C₂×C₄	—	24	1	no	—
675	C₂×C₄	—	24	1	no	—
676	C₂×C₄	—	24	1	no	—
677	C₂×C₄	—	24	1	no	—
678	C₂×C₄	—	24	1	no	—
679	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	6	1	no	—
684	C₈	—	6	1	no	—
685	C₂×C₃	—	4	1	no	—
686	C₂×C₃	—	4	2	no	—
687	C₂×C₃	—	4	2	no	—
688	C₂×C₃	C₅×#525	1	1	yes	characteristic
689	C₂×C₃	C₅×#576	1	1	yes	characteristic
690	C₂×C₃	C₅×#577	1	1	yes	characteristic
691	D₃	—	8	1	no	—
692	C₅	#80136	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	8	4	no	—
703	C₂²	—	12	1	no	—
704	C₂²	—	12	1	no	—
705	C₂²	—	12	1	no	—
706	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	6	1	no	—
711	C₄	—	6	1	no	—
712	C₄	—	6	1	no	—
713	C₄	—	6	1	no	—
714	C₄	—	12	1	no	—
715	C₄	—	12	1	no	—
716	C₄	—	12	1	no	—
717	C₄	C₂×C₅×#237	1	1	yes	characteristic
718	C₄	C₂×C₅×#237	1	1	yes	characteristic
719	C₃	C₅×#3118	1	1	yes	characteristic, complemented, Sylow
720	C₂	—	4	1	no	—
721	C₂	—	4	2	no	—
722	C₂	—	4	2	no	—
723	C₂	—	24	1	no	—
724	C₂	C₅×#5586	1	1	yes	characteristic
725	C₂	C₅×#5762	1	1	yes	characteristic
726	C₂	C₅×#5774	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×#450	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5217	C₂
hypercenter	C₅×#450	D₃
hypocenter	C₃	C₅×#3118
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#450

Complements

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

N	H ≅ G/N	type
1. C₅×#5798	C₂	semidirect
2. C₅×#5643	C₂	semidirect
3. C₃×C₅×#450	C₂	semidirect
5. C₅×#5165	C₂	semidirect
6. C₅×#5165	C₂	semidirect
7. C₅×#5164	C₂	semidirect
8. C₅×Dic₃×SD₁₆	C₂	semidirect
9. C₅×#5045	C₂	semidirect
10. C₅×#4785	C₂	semidirect
11. C₅×#4761	C₂	semidirect
12. C₅×#4759	C₂	semidirect
13. C₅×#4756	C₂	semidirect
14. C₅×#4737	C₂	semidirect
15. C₅×#4720	C₂	semidirect
23. C₅×#947	C₂²	semidirect
24. C₅×Q₈×Dic₃	C₂²	semidirect
38. C₅×#893	C₂²	semidirect
39. C₅×#888	C₂²	semidirect
45. C₅×#835	C₂²	semidirect
46. C₅×#835	C₂²	semidirect
50. C₅×#821	C₂²	semidirect
51. C₅×#821	C₂²	semidirect
52. C₅×#818	C₂²	semidirect
53. C₅×#817	C₂²	semidirect
54. C₅×#815	C₂²	semidirect
55. C₅×Dic₃⋊C₈	C₂²	semidirect
56. C₅×Dic₃⋊C₈	C₂²	semidirect
57. C₅×C₈×Dic₃	C₂²	semidirect
58. C₅×#808	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. #80136	C₅	direct (N × H)
69. C₅×#450	D₃	semidirect
125. #5798	C₂×C₅	semidirect
126. #5643	C₂×C₅	semidirect
127. C₃×#450	C₂×C₅	semidirect
129. #5165	C₂×C₅	semidirect
130. #5165	C₂×C₅	semidirect
131. #5164	C₂×C₅	semidirect
132. Dic₃×SD₁₆	C₂×C₅	semidirect
133. #5045	C₂×C₅	semidirect
134. #4785	C₂×C₅	semidirect
135. #4761	C₂×C₅	semidirect
136. #4759	C₂×C₅	semidirect
137. #4756	C₂×C₅	semidirect
138. #4737	C₂×C₅	semidirect
139. #4720	C₂×C₅	semidirect
230. #947	C₂²×C₅	semidirect
231. Q₈×Dic₃	C₂²×C₅	semidirect
245. #893	C₂²×C₅	semidirect
246. #888	C₂²×C₅	semidirect
252. #835	C₂²×C₅	semidirect
253. #835	C₂²×C₅	semidirect
257. #821	C₂²×C₅	semidirect
258. #821	C₂²×C₅	semidirect
259. #818	C₂²×C₅	semidirect
260. #817	C₂²×C₅	semidirect
261. #815	C₂²×C₅	semidirect
262. Dic₃⋊C₈	C₂²×C₅	semidirect
263. Dic₃⋊C₈	C₂²×C₅	semidirect
264. C₈×Dic₃	C₂²×C₅	semidirect
265. #808	C₂²×C₅	semidirect
266. #807	C₂²×C₅	semidirect
324. #450	C₅×D₃	semidirect
611. C₃×C₅	#3118	semidirect
692. C₅	#80136	direct (N × H)
719. C₃	C₅×#3118	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5798	2
C₅×#5643	2
C₃×C₅×#450	2
C₅×#5217	2
C₅×#5165	2
C₅×#5164	2
C₅×Dic₃×SD₁₆	2
C₅×#5045	2
C₅×#4785	2
C₅×#4761	2
C₅×#4759	2
C₅×#4756	2
C₅×#4737	2
C₅×#4720	2
C₅×#3118	3
#80136	5

Subgroups — C5×#80136 #14435586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80136 #14435586