Subgroups — C₅×#83676 #14472061

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic
2	C₅×#5567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5056	C₂	1	2	yes	maximal
6	C₅×#5054	C₂	1	2	yes	maximal
7	C₄×C₅×#216	C₂	1	2	yes	maximal, complemented
8	C₅×Q₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5022	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×#214	C₂	1	1	yes	maximal, characteristic
11	C₅×#5007	C₂	1	1	yes	maximal, characteristic
12	C₅×#3364	—	3	1	no	maximal, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#126	—	2	2	no	—
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	—	2	1	no	—
21	C₅×#944	—	2	1	no	—
22	C₂×C₅×#216	C₂²	1	2	yes	—
23	C₂×C₅×#214	C₂²	1	1	yes	characteristic
24	C₅×#889	—	2	2	no	—
25	C₅×#887	—	2	1	no	—
26	C₅×#870	C₂²	1	2	yes	—
27	C₅×#869	C₂²	1	1	yes	characteristic
28	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	2	yes	—
30	C₅×#835	C₂²	1	2	yes	—
31	C₅×#835	C₂²	1	2	yes	—
32	C₅×#835	C₂²	1	2	yes	—
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#832	C₂²	1	1	yes	characteristic
35	C₅×#810	C₂²	1	1	yes	characteristic
36	C₅×#808	C₂²	1	1	yes	characteristic
37	C₅×#807	C₂²	1	2	yes	—
38	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
39	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
42	#83676	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#557	—	3	1	no	—
44	C₅×#556	D₃	1	1	yes	characteristic
45	C₅×#488	—	3	2	no	—
46	C₅×#487	—	3	1	no	—
47	C₅×#479	—	3	2	no	—
48	C₅×#474	—	3	1	no	—
49	C₅×#464	—	3	2	no	—
50	C₅×#462	—	3	1	no	—
51	C₅×C₈×Q₈	—	3	1	no	—
52	C₄×C₅×Q₁₆	—	3	2	no	—
53	C₄×C₅×SD₁₆	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₅×Dic₆	—	2	1	no	—
59	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	2	yes	—
72	C₅×#216	—	2	4	no	—
73	C₅×#214	—	2	2	no	—
74	C₅×C₄⋊Dic₃	—	2	1	no	—
75	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
76	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
77	C₅×Dic₃⋊C₄	—	2	1	no	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₅×Dic₃⋊C₄	—	2	2	no	—
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₄×C₅×Dic₃	—	2	2	no	—
82	C₄×C₅×Dic₃	—	2	1	no	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₃×#556	C₂×C₅	1	1	yes	characteristic
87	#5567	C₂×C₅	1	1	yes	characteristic, complemented
88	#5090	C₂×C₅	1	1	yes	characteristic, complemented
89	#5079	C₂×C₅	1	1	yes	characteristic, complemented
90	#5056	C₂×C₅	1	2	yes	—
91	#5054	C₂×C₅	1	2	yes	—
92	C₄×#216	C₂×C₅	1	2	yes	complemented
93	Q₈×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
94	#5022	C₂×C₅	1	2	yes	complemented
95	C₄×#214	C₂×C₅	1	1	yes	characteristic
96	#5007	C₂×C₅	1	1	yes	characteristic
97	C₂×C₅×Q₁₆	—	3	2	no	—
98	C₂×C₅×SD₁₆	—	3	1	no	—
99	C₅×C₄⋊Q₈	—	3	1	no	—
100	C₅×C₄⋊Q₈	—	6	1	no	—
101	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
102	C₅×#126	—	2	2	no	—
103	C₅×#125	—	3	2	no	—
104	C₅×#125	—	6	2	no	—
105	C₅×#124	C₂×D₃	1	2	yes	—
106	C₅×C₂²⋊Q₈	—	2	1	no	—
107	C₄×C₅×Q₈	—	3	1	no	—
108	C₄×C₅×Q₈	—	3	2	no	—
109	C₄×C₅×Q₈	—	6	1	no	—
110	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
111	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
113	C₅×#117	—	2	1	no	—
114	C₅×#107	—	3	2	no	—
115	C₅×#106	—	3	1	no	—
116	C₅×C₄⋊C₈	—	3	1	no	—
117	C₅×C₄⋊C₈	—	3	2	no	—
118	C₅×#103	—	3	2	no	—
119	C₅×#103	—	3	2	no	—
120	C₅×#103	—	3	2	no	—
121	C₅×#103	—	3	1	no	—
122	C₅×#102	—	3	1	no	—
123	C₅×#102	—	3	2	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	—	3	2	no	—
126	#3364	—	3	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₅×Dic₆	—	2	1	no	—
145	C₅×Dic₆	—	4	2	no	—
146	C₅×Dic₆	#41	1	2	yes	—
147	C₅×C₃⋊C₈	—	2	1	no	—
148	C₅×C₃⋊C₈	—	2	2	no	—
149	C₅×C₃⋊C₈	—	2	1	no	—
150	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
151	C₃×#126	—	2	2	no	—
152	C₃×#124	C₂²×C₅	1	2	yes	—
153	C₃×C₂²⋊Q₈	—	2	1	no	—
154	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
155	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
157	C₃×#117	—	2	1	no	—
158	#944	—	2	1	no	—
159	C₂×#216	C₂²×C₅	1	2	yes	—
160	C₂×#214	C₂²×C₅	1	1	yes	characteristic
161	#889	—	2	2	no	—
162	#887	—	2	1	no	—
163	#870	C₂²×C₅	1	2	yes	—
164	#869	C₂²×C₅	1	1	yes	characteristic
165	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
166	C₄×Dic₆	C₂²×C₅	1	2	yes	—
167	#835	C₂²×C₅	1	2	yes	—
168	#835	C₂²×C₅	1	2	yes	—
169	#835	C₂²×C₅	1	2	yes	—
170	#832	C₂²×C₅	1	2	yes	—
171	#832	C₂²×C₅	1	1	yes	characteristic
172	#810	C₂²×C₅	1	1	yes	characteristic
173	#808	C₂²×C₅	1	1	yes	characteristic
174	#807	C₂²×C₅	1	2	yes	—
175	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
176	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
177	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
178	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
179	C₂×C₅×Q₈	—	3	1	no	—
180	C₂×C₅×Q₈	—	6	1	no	—
181	C₂×C₅×Q₈	#67	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
183	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₅×Q₁₆	—	6	4	no	—
186	C₅×SD₁₆	—	6	2	no	—
187	C₂×C₅×C₈	—	3	1	no	—
188	C₂×C₅×C₈	—	3	2	no	—
189	C₂×C₅×C₈	—	3	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	3	1	no	—
194	C₅×C₄⋊C₄	—	3	2	no	—
195	C₅×C₄⋊C₄	—	6	1	no	—
196	C₅×C₄⋊C₄	—	6	2	no	—
197	C₅×C₄⋊C₄	—	6	2	no	—
198	C₅×C₄⋊C₄	—	6	2	no	—
199	C₅×C₄⋊C₄	—	6	1	no	—
200	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
201	C₅×C₄⋊C₄	#67	1	2	yes	—
202	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₅×C₂²⋊C₄	—	2	1	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	—	6	2	no	—
208	C₄²×C₅	—	6	1	no	—
209	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₄²×C₅	C₂²×D₃	1	2	yes	—
211	#557	—	3	1	no	—
212	#556	C₅×D₃	1	1	yes	characteristic
213	#488	—	3	2	no	—
214	#487	—	3	1	no	—
215	#479	—	3	2	no	—
216	#474	—	3	1	no	—
217	#464	—	3	2	no	—
218	#462	—	3	1	no	—
219	C₈×Q₈	—	3	1	no	—
220	C₄×Q₁₆	—	3	2	no	—
221	C₄×SD₁₆	—	3	1	no	—
222	C₂²×C₃×C₅	—	4	1	no	—
223	C₂²×C₃×C₅	—	4	1	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	4	2	no	—
230	C₃×C₄×C₅	—	4	1	no	—
231	C₃×C₄×C₅	#135	1	2	yes	—
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
234	C₅×Dic₃	—	2	2	no	—
235	C₅×Dic₃	—	4	2	no	—
236	C₅×Dic₃	—	4	1	no	—
237	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
238	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
239	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	—	2	1	no	—
241	C₂×Dic₆	—	2	1	no	—
242	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	—	2	2	no	—
245	C₃×C₄⋊C₄	—	2	1	no	—
246	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
248	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
249	C₃×C₂²⋊C₄	—	2	2	no	—
250	C₃×C₂²⋊C₄	—	2	1	no	—
251	C₃×C₂²⋊C₄	—	2	2	no	—
252	C₃×C₄²	—	2	2	no	—
253	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
254	C₃×C₄²	C₂³×C₅	1	2	yes	—
255	#216	—	2	4	no	—
256	#214	—	2	2	no	—
257	C₄⋊Dic₃	—	2	1	no	—
258	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
259	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
260	Dic₃⋊C₄	—	2	1	no	—
261	Dic₃⋊C₄	—	2	2	no	—
262	Dic₃⋊C₄	—	2	2	no	—
263	Dic₃⋊C₄	—	2	2	no	—
264	C₄×Dic₃	—	2	2	no	—
265	C₄×Dic₃	—	2	1	no	—
266	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
268	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂³×C₅	—	2	1	no	—
270	C₅×Q₈	—	2	2	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	2	2	no	—
273	C₅×Q₈	—	3	2	no	—
274	C₅×Q₈	—	6	1	no	—
275	C₅×Q₈	—	12	2	no	—
276	C₅×D₄	—	2	1	no	—
277	C₅×D₄	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	4	2	no	—
281	C₂×C₄×C₅	—	6	1	no	—
282	C₂×C₄×C₅	—	6	1	no	—
283	C₂×C₄×C₅	—	6	2	no	—
284	C₂×C₄×C₅	C₂×#67	1	2	yes	—
285	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×#67	1	2	yes	—
287	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
289	C₅×C₈	—	6	1	no	—
290	C₅×C₈	—	6	2	no	—
291	C₅×C₈	—	6	1	no	—
292	C₂×Q₁₆	—	3	2	no	—
293	C₂×SD₁₆	—	3	1	no	—
294	C₄⋊Q₈	—	3	1	no	—
295	C₄⋊Q₈	—	6	1	no	—
296	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
297	#126	—	2	2	no	—
298	#125	—	3	2	no	—
299	#125	—	6	2	no	—
300	#124	C₂×C₅×D₃	1	2	yes	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₄×Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	—	6	1	no	—
305	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
306	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
307	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
308	#117	—	2	1	no	—
309	#107	—	3	2	no	—
310	#106	—	3	1	no	—
311	C₄⋊C₈	—	3	1	no	—
312	C₄⋊C₈	—	3	2	no	—
313	#103	—	3	2	no	—
314	#103	—	3	2	no	—
315	#103	—	3	2	no	—
316	#103	—	3	1	no	—
317	#102	—	3	1	no	—
318	#102	—	3	2	no	—
319	C₄×C₈	—	3	1	no	—
320	C₄×C₈	—	3	2	no	—
321	C₂×C₃×C₅	—	8	1	no	—
322	C₂×C₃×C₅	#548	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
324	C₂×C₃×C₅	#578	1	1	yes	characteristic
325	C₂³×C₃	—	2	1	no	—
326	C₃×Q₈	—	2	2	no	—
327	C₃×Q₈	—	2	2	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×D₄	—	2	1	no	—
330	C₃×D₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	4	2	no	—
334	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
335	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
336	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
339	C₂×Dic₃	—	2	1	no	—
340	C₂×Dic₃	—	2	1	no	—
341	C₂×Dic₃	—	2	2	no	—
342	Dic₆	—	2	1	no	—
343	Dic₆	—	4	2	no	—
344	Dic₆	C₅×#41	1	2	yes	—
345	C₃⋊C₈	—	2	1	no	—
346	C₃⋊C₈	—	2	2	no	—
347	C₃⋊C₈	—	2	1	no	—
348	C₂²×C₅	—	4	1	no	—
349	C₂²×C₅	—	4	1	no	—
350	C₂²×C₅	—	4	1	no	—
351	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	4	1	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	—	6	2	no	—
358	C₄×C₅	—	12	2	no	—
359	C₄×C₅	—	12	1	no	—
360	C₄×C₅	#950	1	2	yes	—
361	C₄×C₅	D₃×#41	1	1	yes	characteristic
362	C₄×C₅	#1010	1	1	yes	characteristic
363	C₂×Q₈	—	3	1	no	—
364	C₂×Q₈	—	6	1	no	—
365	C₂×Q₈	C₅×#67	1	1	yes	characteristic
366	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
367	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	Q₁₆	—	6	4	no	—
370	SD₁₆	—	6	2	no	—
371	C₂×C₈	—	3	1	no	—
372	C₂×C₈	—	3	2	no	—
373	C₂×C₈	—	3	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	3	1	no	—
378	C₄⋊C₄	—	3	2	no	—
379	C₄⋊C₄	—	6	1	no	—
380	C₄⋊C₄	—	6	2	no	—
381	C₄⋊C₄	—	6	2	no	—
382	C₄⋊C₄	—	6	2	no	—
383	C₄⋊C₄	—	6	1	no	—
384	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
385	C₄⋊C₄	C₅×#67	1	2	yes	—
386	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	6	2	no	—
392	C₄²	—	6	1	no	—
393	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
394	C₄²	C₂²×C₅×D₃	1	2	yes	—
395	C₃×C₅	#3364	1	1	yes	characteristic, complemented, Hall
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	4	1	no	—
399	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	4	2	no	—
404	C₃×C₄	—	4	1	no	—
405	C₃×C₄	C₅×#135	1	2	yes	—
406	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
407	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
408	Dic₃	—	2	2	no	—
409	Dic₃	—	4	2	no	—
410	Dic₃	—	4	1	no	—
411	C₂×C₅	—	8	1	no	—
412	C₂×C₅	C₂×#950	1	1	yes	characteristic
413	C₂×C₅	#5831	1	1	yes	characteristic
414	C₂×C₅	#5838	1	1	yes	characteristic
415	C₂³	—	2	1	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	3	2	no	—
420	Q₈	—	6	1	no	—
421	Q₈	—	12	2	no	—
422	D₄	—	2	1	no	—
423	D₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	6	1	no	—
428	C₂×C₄	—	6	1	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	C₂×C₅×#67	1	2	yes	—
431	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
432	C₂×C₄	C₂×C₅×#67	1	2	yes	—
433	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
434	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
435	C₈	—	6	1	no	—
436	C₈	—	6	2	no	—
437	C₈	—	6	1	no	—
438	C₂×C₃	—	8	1	no	—
439	C₂×C₃	C₅×#548	1	1	yes	characteristic
440	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
441	C₂×C₃	C₅×#578	1	1	yes	characteristic
442	C₅	#83676	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	6	2	no	—
453	C₄	—	12	2	no	—
454	C₄	—	12	1	no	—
455	C₄	C₅×#950	1	2	yes	—
456	C₄	C₅×D₃×#41	1	1	yes	characteristic
457	C₄	C₅×#1010	1	1	yes	characteristic
458	C₃	C₅×#3364	1	1	yes	characteristic, complemented, Sylow
459	C₂	—	8	1	no	—
460	C₂	C₂×C₅×#950	1	1	yes	characteristic
461	C₂	C₅×#5831	1	1	yes	characteristic
462	C₂	C₅×#5838	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#556	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×D₄	C₂³
hypercenter	C₅×#556	D₃
hypocenter	C₃	C₅×#3364
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×Q₈ ◁ C₅×#556

Complements

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

N	H ≅ G/N	type
2. C₅×#5567	C₂	semidirect
3. C₅×#5090	C₂	semidirect
4. C₅×#5079	C₂	semidirect
7. C₄×C₅×#216	C₂	semidirect
8. C₅×Q₈×C₃⋊C₈	C₂	semidirect
9. C₅×#5022	C₂	semidirect
42. #83676	C₅	direct (N × H)
87. #5567	C₂×C₅	semidirect
88. #5090	C₂×C₅	semidirect
89. #5079	C₂×C₅	semidirect
92. C₄×#216	C₂×C₅	semidirect
93. Q₈×C₃⋊C₈	C₂×C₅	semidirect
94. #5022	C₂×C₅	semidirect
395. C₃×C₅	#3364	semidirect
442. C₅	#83676	direct (N × H)
458. C₃	C₅×#3364	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#556	2
C₅×#5567	2
C₅×#5090	2
C₅×#5079	2
C₅×#5056	2
C₅×#5054	2
C₄×C₅×#216	2
C₅×Q₈×C₃⋊C₈	2
C₅×#5022	2
C₄×C₅×#214	2
C₅×#5007	2
C₅×#3364	3
#83676	5

Subgroups — C5×#83676 #14472061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83676 #14472061