Subgroups — C₅×#86363 #14480635

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5833	C₂	1	2	yes	maximal, complemented
4	C₅×#5628	C₂	1	4	yes	maximal, complemented
5	C₅×#5627	C₂	1	4	yes	maximal, complemented
6	C₅×#5607	C₂	1	4	yes	maximal, complemented
7	C₅×#5606	C₂	1	4	yes	maximal, complemented
8	C₅×#5605	C₂	1	4	yes	maximal, complemented
9	C₅×#5596	C₂	1	4	yes	maximal, complemented
10	C₅×#5510	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3449	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
14	C₅×D₃×#41	—	2	16	no	—
15	C₂×C₅×#239	C₂²	1	2	yes	—
16	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	complemented
17	C₂×C₅×#237	C₂²	1	2	yes	—
18	C₂×C₅×#237	C₂²	1	4	yes	complemented
19	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
20	C₂×C₅×D₃×D₄	C₂²	1	2	yes	complemented
21	C₂×C₅×#235	C₂²	1	4	yes	—
22	C₂×C₅×#235	C₂²	1	2	yes	complemented
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	complemented
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
26	C₃×C₅×#121	C₂²	1	4	yes	complemented
27	C₃×C₅×#121	C₂²	1	4	yes	complemented
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₅×#946	C₂²	1	4	yes	complemented
30	C₅×#940	C₂²	1	4	yes	complemented
31	C₅×#939	C₂²	1	8	yes	complemented
32	C₅×#938	C₂²	1	4	yes	complemented
33	C₅×#937	C₂²	1	8	yes	complemented
34	C₅×D₄×Dic₃	C₂²	1	4	yes	complemented
35	C₅×#930	C₂²	1	4	yes	complemented
36	C₅×#930	C₂²	1	4	yes	complemented
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₅×#924	C₂²	1	4	yes	complemented
40	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
41	C₅×#897	C₂²	1	4	yes	complemented
42	C₅×#895	C₂²	1	4	yes	complemented
43	C₅×#894	C₂²	1	8	yes	complemented
44	C₅×#893	C₂²	1	4	yes	complemented
45	C₅×#892	C₂²	1	4	yes	complemented
46	C₅×#892	C₂²	1	4	yes	complemented
47	C₅×#888	C₂²	1	4	yes	complemented
48	C₅×#885	C₂²	1	8	yes	complemented
49	C₅×#883	C₂²	1	8	yes	complemented
50	C₅×#882	C₂²	1	8	yes	complemented
51	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
52	#86363	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₂²×C₅×#41	—	3	2	no	—
54	C₅×#537	—	3	2	no	—
55	C₅×#537	—	3	1	no	—
56	C₅×#537	D₃	1	1	yes	characteristic, complemented
57	C₅×#536	—	3	4	no	—
58	C₅×#535	—	3	4	no	—
59	C₅×#534	—	3	4	no	—
60	C₅×#532	—	3	4	no	—
61	C₅×#525	—	3	4	no	—
62	C₅×#525	—	3	4	no	—
63	C₂×C₅×#117	—	3	1	no	—
64	C₂³×C₅×D₃	C₂³	1	4	yes	—
65	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₃×C₅×#41	—	2	8	no	—
67	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
69	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
70	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₅×#67	C₂³	1	4	yes	—
75	C₂×C₅×#67	C₂³	1	4	yes	—
76	C₂×C₅×#67	C₂³	1	4	yes	—
77	C₂×C₅×#67	C₂³	1	8	yes	—
78	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
79	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₅×#239	—	2	8	no	—
82	C₅×D₃×Q₈	—	2	8	no	—
83	C₅×#237	—	2	16	no	—
84	C₅×#237	—	2	8	no	—
85	C₅×D₃×D₄	—	2	16	no	—
86	C₅×D₃×D₄	—	2	8	no	—
87	C₅×#235	—	2	8	no	—
88	C₅×#235	—	2	16	no	—
89	C₂×C₅×D₁₂	C₂³	1	4	yes	—
90	C₂×C₅×D₁₂	C₂³	1	2	yes	—
91	C₂×C₅×D₁₂	C₂³	1	4	yes	—
92	C₂×C₄×C₅×D₃	—	2	16	no	—
93	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
94	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
95	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
96	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
97	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
98	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
99	C₂×C₅×Dic₆	C₂³	1	4	yes	—
100	C₂×C₅×Dic₆	C₂³	1	2	yes	—
101	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
103	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₅×#217	C₂³	1	8	yes	—
105	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
106	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
107	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
108	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
109	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
110	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
111	C₄×C₅×Dic₃	C₂³	1	4	yes	—
112	C₄×C₅×Dic₃	C₂³	1	4	yes	—
113	C₂×D₃×#41	C₂×C₅	1	2	yes	complemented
114	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
115	#5833	C₂×C₅	1	2	yes	complemented
116	#5628	C₂×C₅	1	4	yes	complemented
117	#5627	C₂×C₅	1	4	yes	complemented
118	#5607	C₂×C₅	1	4	yes	complemented
119	#5606	C₂×C₅	1	4	yes	complemented
120	#5605	C₂×C₅	1	4	yes	complemented
121	#5596	C₂×C₅	1	4	yes	complemented
122	#5510	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×C₅×#41	—	3	2	no	—
125	C₂×C₅×#41	—	3	2	no	—
126	C₂×C₅×#41	—	3	4	no	—
127	C₂×C₅×#41	—	3	4	no	—
128	C₂×C₅×#41	—	3	2	no	—
129	C₂×C₅×#41	—	6	16	no	—
130	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
131	C₂²×C₅×Q₈	—	3	2	no	—
132	C₂²×C₅×D₄	—	3	4	no	—
133	C₂²×C₅×D₄	—	3	2	no	—
134	C₂³×C₄×C₅	—	3	1	no	—
135	C₂³×C₄×C₅	—	3	4	no	—
136	C₅×C₄⋊Q₈	—	3	4	no	—
137	C₅×#127	—	3	4	no	—
138	C₅×#124	—	3	8	no	—
139	C₅×#123	—	3	8	no	—
140	C₅×#123	—	3	8	no	—
141	C₅×C₂²⋊Q₈	—	3	4	no	—
142	C₅×C₂²⋊Q₈	—	3	4	no	—
143	C₅×C₂²⋊Q₈	—	3	4	no	—
144	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
145	C₅×#121	—	3	4	no	—
146	C₅×#121	—	3	8	no	—
147	C₅×#121	—	3	4	no	—
148	C₅×#121	—	3	4	no	—
149	C₅×#121	—	3	4	no	—
150	C₅×#121	C₂×D₃	1	4	yes	complemented
151	C₅×#121	C₂×D₃	1	4	yes	complemented
152	C₅×#120	—	3	8	no	—
153	C₅×#120	—	3	8	no	—
154	C₄×C₅×D₄	—	3	4	no	—
155	C₄×C₅×D₄	—	3	4	no	—
156	C₄×C₅×D₄	—	3	8	no	—
157	C₅×#117	—	3	4	no	—
158	C₅×#117	—	3	4	no	—
159	C₂×C₅×C₄⋊C₄	—	3	1	no	—
160	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
161	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
162	C₂×C₄²×C₅	—	3	2	no	—
163	#3449	—	3	1	no	Sylow
164	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
165	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
166	C₂²×C₅×D₃	—	2	8	no	—
167	C₂²×C₅×D₃	—	4	1	no	—
168	C₂²×C₅×D₃	—	4	1	no	—
169	C₂²×C₅×D₃	—	4	4	no	—
170	C₂²×C₅×D₃	—	4	4	no	—
171	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
172	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
173	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
174	C₃×C₅×Q₈	—	2	4	no	—
175	C₃×C₅×D₄	—	2	8	no	—
176	C₃×C₅×D₄	—	2	4	no	—
177	C₃×C₅×D₄	—	4	4	no	—
178	C₂×C₃×C₄×C₅	—	2	8	no	—
179	C₂×C₃×C₄×C₅	—	4	2	no	—
180	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
181	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
182	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
183	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
184	C₅×#67	—	2	8	no	—
185	C₅×#67	—	2	8	no	—
186	C₅×#67	—	2	8	no	—
187	C₅×#67	—	4	8	no	—
188	C₂×C₅×Dic₃	—	2	8	no	—
189	C₂×C₅×Dic₃	—	4	2	no	—
190	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
191	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
192	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
193	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
195	C₅×D₁₂	—	2	8	no	—
196	C₅×D₁₂	—	2	4	no	—
197	C₅×D₁₂	—	4	4	no	—
198	C₄×C₅×D₃	—	2	8	no	—
199	C₄×C₅×D₃	—	2	8	no	—
200	C₄×C₅×D₃	—	2	8	no	—
201	C₄×C₅×D₃	C₂×D₄	1	8	yes	—
202	C₄×C₅×D₃	C₂×D₄	1	8	yes	—
203	C₅×Dic₆	—	2	4	no	—
204	C₅×Dic₆	—	2	8	no	—
205	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
206	D₃×#41	—	2	16	no	—
207	C₂×#239	C₂²×C₅	1	2	yes	—
208	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	complemented
209	C₂×#237	C₂²×C₅	1	2	yes	—
210	C₂×#237	C₂²×C₅	1	4	yes	complemented
211	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
212	C₂×D₃×D₄	C₂²×C₅	1	2	yes	complemented
213	C₂×#235	C₂²×C₅	1	4	yes	—
214	C₂×#235	C₂²×C₅	1	2	yes	complemented
215	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
216	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	complemented
217	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
218	C₃×#121	C₂²×C₅	1	4	yes	complemented
219	C₃×#121	C₂²×C₅	1	4	yes	complemented
220	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
221	#946	C₂²×C₅	1	4	yes	complemented
222	#940	C₂²×C₅	1	4	yes	complemented
223	#939	C₂²×C₅	1	8	yes	complemented
224	#938	C₂²×C₅	1	4	yes	complemented
225	#937	C₂²×C₅	1	8	yes	complemented
226	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
227	#930	C₂²×C₅	1	4	yes	complemented
228	#930	C₂²×C₅	1	4	yes	complemented
229	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
230	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
231	#924	C₂²×C₅	1	4	yes	complemented
232	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
233	#897	C₂²×C₅	1	4	yes	complemented
234	#895	C₂²×C₅	1	4	yes	complemented
235	#894	C₂²×C₅	1	8	yes	complemented
236	#893	C₂²×C₅	1	4	yes	complemented
237	#892	C₂²×C₅	1	4	yes	complemented
238	#892	C₂²×C₅	1	4	yes	complemented
239	#888	C₂²×C₅	1	4	yes	complemented
240	#885	C₂²×C₅	1	8	yes	complemented
241	#883	C₂²×C₅	1	8	yes	complemented
242	#882	C₂²×C₅	1	8	yes	complemented
243	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
244	C₂⁴×C₅	—	3	1	no	—
245	C₂⁴×C₅	—	3	4	no	—
246	C₅×#41	—	2	8	no	—
247	C₅×#41	—	6	16	no	—
248	C₅×#41	—	6	16	no	—
249	C₅×#41	—	6	8	no	—
250	C₅×#41	—	6	8	no	—
251	C₅×#41	—	6	8	no	—
252	C₂×C₅×Q₈	—	3	2	no	—
253	C₂×C₅×Q₈	—	3	4	no	—
254	C₂×C₅×Q₈	—	6	8	no	—
255	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
256	C₂×C₅×D₄	—	3	4	no	—
257	C₂×C₅×D₄	—	3	4	no	—
258	C₂×C₅×D₄	—	3	4	no	—
259	C₂×C₅×D₄	—	3	8	no	—
260	C₂×C₅×D₄	—	3	4	no	—
261	C₂×C₅×D₄	—	3	2	no	—
262	C₂×C₅×D₄	—	3	4	no	—
263	C₂×C₅×D₄	—	6	8	no	—
264	C₂×C₅×D₄	—	6	16	no	—
265	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
266	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
267	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
268	C₂²×C₄×C₅	—	3	1	no	—
269	C₂²×C₄×C₅	—	3	8	no	—
270	C₂²×C₄×C₅	—	3	2	no	—
271	C₂²×C₄×C₅	—	3	2	no	—
272	C₂²×C₄×C₅	—	3	4	no	—
273	C₂²×C₄×C₅	—	3	2	no	—
274	C₂²×C₄×C₅	—	3	4	no	—
275	C₂²×C₄×C₅	—	3	4	no	—
276	C₂²×C₄×C₅	—	3	4	no	—
277	C₂²×C₄×C₅	—	6	16	no	—
278	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
279	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
280	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
281	C₅×C₄⋊C₄	—	3	4	no	—
282	C₅×C₄⋊C₄	—	3	8	no	—
283	C₅×C₄⋊C₄	—	3	4	no	—
284	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
285	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
286	C₅×C₂²⋊C₄	—	3	8	no	—
287	C₅×C₂²⋊C₄	—	3	8	no	—
288	C₅×C₂²⋊C₄	—	3	8	no	—
289	C₅×C₂²⋊C₄	—	3	8	no	—
290	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
291	C₄²×C₅	—	3	4	no	—
292	C₄²×C₅	—	3	4	no	—
293	C₂²×#41	—	3	2	no	—
294	#537	—	3	2	no	—
295	#537	—	3	1	no	—
296	#537	C₅×D₃	1	1	yes	characteristic, complemented
297	#536	—	3	4	no	—
298	#535	—	3	4	no	—
299	#534	—	3	4	no	—
300	#532	—	3	4	no	—
301	#525	—	3	4	no	—
302	#525	—	3	4	no	—
303	C₂×#117	—	3	1	no	—
304	C₂²×C₃×C₅	—	2	1	no	—
305	C₂²×C₃×C₅	—	2	1	no	—
306	C₂²×C₃×C₅	—	2	4	no	—
307	C₂²×C₃×C₅	—	2	4	no	—
308	C₂²×C₃×C₅	—	2	4	no	—
309	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
310	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
311	C₂×C₅×D₃	—	2	2	no	—
312	C₂×C₅×D₃	—	2	2	no	—
313	C₂×C₅×D₃	—	2	4	no	—
314	C₂×C₅×D₃	—	2	4	no	—
315	C₂×C₅×D₃	—	2	4	no	—
316	C₂×C₅×D₃	—	4	4	no	—
317	C₂×C₅×D₃	—	4	16	no	—
318	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
319	C₃×C₄×C₅	—	2	4	no	—
320	C₃×C₄×C₅	—	2	4	no	—
321	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
322	C₅×Dic₃	—	2	4	no	—
323	C₅×Dic₃	—	2	4	no	—
324	C₅×Dic₃	C₂²×D₄	1	2	yes	—
325	C₅×Dic₃	C₂²×D₄	1	2	yes	—
326	C₂³×D₃	C₂³×C₅	1	4	yes	—
327	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
328	C₃×#41	—	2	8	no	—
329	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
330	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
331	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
332	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
333	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
334	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂×#67	C₂³×C₅	1	4	yes	—
337	C₂×#67	C₂³×C₅	1	4	yes	—
338	C₂×#67	C₂³×C₅	1	4	yes	—
339	C₂×#67	C₂³×C₅	1	8	yes	—
340	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
341	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
342	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
343	#239	—	2	8	no	—
344	D₃×Q₈	—	2	8	no	—
345	#237	—	2	16	no	—
346	#237	—	2	8	no	—
347	D₃×D₄	—	2	16	no	—
348	D₃×D₄	—	2	8	no	—
349	#235	—	2	8	no	—
350	#235	—	2	16	no	—
351	C₂×D₁₂	C₂³×C₅	1	4	yes	—
352	C₂×D₁₂	C₂³×C₅	1	2	yes	—
353	C₂×D₁₂	C₂³×C₅	1	4	yes	—
354	C₂×C₄×D₃	—	2	16	no	—
355	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
356	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
357	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
358	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
359	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
360	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
361	C₂×Dic₆	C₂³×C₅	1	4	yes	—
362	C₂×Dic₆	C₂³×C₅	1	2	yes	—
363	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
364	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
365	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
366	#217	C₂³×C₅	1	8	yes	—
367	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
368	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
369	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
370	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
371	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
372	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
373	C₄×Dic₃	C₂³×C₅	1	4	yes	—
374	C₄×Dic₃	C₂³×C₅	1	4	yes	—
375	C₂³×C₅	—	3	2	no	—
376	C₂³×C₅	—	3	4	no	—
377	C₂³×C₅	—	3	4	no	—
378	C₂³×C₅	—	6	8	no	—
379	C₂³×C₅	—	12	1	no	—
380	C₂³×C₅	—	12	1	no	—
381	C₂³×C₅	—	12	4	no	—
382	C₂³×C₅	—	12	4	no	—
383	C₂³×C₅	C₂³×D₃	1	4	yes	—
384	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
385	C₅×Q₈	—	2	4	no	—
386	C₅×Q₈	—	6	8	no	—
387	C₅×Q₈	—	6	4	no	—
388	C₅×D₄	—	2	8	no	—
389	C₅×D₄	—	2	4	no	—
390	C₅×D₄	—	4	4	no	—
391	C₅×D₄	—	6	8	no	—
392	C₅×D₄	—	6	8	no	—
393	C₅×D₄	—	6	8	no	—
394	C₅×D₄	—	6	8	no	—
395	C₅×D₄	—	6	4	no	—
396	C₅×D₄	—	12	4	no	—
397	C₅×D₄	—	12	8	no	—
398	C₂×C₄×C₅	—	2	8	no	—
399	C₂×C₄×C₅	—	3	4	no	—
400	C₂×C₄×C₅	—	3	1	no	—
401	C₂×C₄×C₅	—	3	1	no	—
402	C₂×C₄×C₅	—	3	8	no	—
403	C₂×C₄×C₅	—	3	8	no	—
404	C₂×C₄×C₅	—	3	4	no	—
405	C₂×C₄×C₅	—	3	4	no	—
406	C₂×C₄×C₅	—	4	2	no	—
407	C₂×C₄×C₅	—	6	8	no	—
408	C₂×C₄×C₅	—	6	8	no	—
409	C₂×C₄×C₅	—	6	8	no	—
410	C₂×C₄×C₅	—	6	8	no	—
411	C₂×C₄×C₅	—	12	2	no	—
412	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
413	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
414	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
415	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
416	C₂×#41	—	3	2	no	—
417	C₂×#41	—	3	2	no	—
418	C₂×#41	—	3	4	no	—
419	C₂×#41	—	3	4	no	—
420	C₂×#41	—	3	2	no	—
421	C₂×#41	—	6	16	no	—
422	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
423	C₂²×Q₈	—	3	2	no	—
424	C₂²×D₄	—	3	4	no	—
425	C₂²×D₄	—	3	2	no	—
426	C₂³×C₄	—	3	1	no	—
427	C₂³×C₄	—	3	4	no	—
428	C₄⋊Q₈	—	3	4	no	—
429	#127	—	3	4	no	—
430	#124	—	3	8	no	—
431	#123	—	3	8	no	—
432	#123	—	3	8	no	—
433	C₂²⋊Q₈	—	3	4	no	—
434	C₂²⋊Q₈	—	3	4	no	—
435	C₂²⋊Q₈	—	3	4	no	—
436	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
437	#121	—	3	4	no	—
438	#121	—	3	8	no	—
439	#121	—	3	4	no	—
440	#121	—	3	4	no	—
441	#121	—	3	4	no	—
442	#121	C₂×C₅×D₃	1	4	yes	complemented
443	#121	C₂×C₅×D₃	1	4	yes	complemented
444	#120	—	3	8	no	—
445	#120	—	3	8	no	—
446	C₄×D₄	—	3	4	no	—
447	C₄×D₄	—	3	4	no	—
448	C₄×D₄	—	3	8	no	—
449	#117	—	3	4	no	—
450	#117	—	3	4	no	—
451	C₂×C₄⋊C₄	—	3	1	no	—
452	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
453	C₂×C₂²⋊C₄	—	3	2	no	—
454	C₂×C₄²	—	3	2	no	—
455	C₂×C₃×C₅	—	2	2	no	—
456	C₂×C₃×C₅	—	4	4	no	—
457	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
458	C₂×C₃×C₅	#585	1	1	yes	characteristic
459	C₂×C₃×C₅	#585	1	1	yes	characteristic
460	C₅×D₃	—	2	4	no	—
461	C₅×D₃	—	4	4	no	—
462	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
463	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
464	C₂²×D₃	—	2	8	no	—
465	C₂²×D₃	—	4	1	no	—
466	C₂²×D₃	—	4	1	no	—
467	C₂²×D₃	—	4	4	no	—
468	C₂²×D₃	—	4	4	no	—
469	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
470	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
471	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
472	C₃×Q₈	—	2	4	no	—
473	C₃×D₄	—	2	8	no	—
474	C₃×D₄	—	2	4	no	—
475	C₃×D₄	—	4	4	no	—
476	C₂×C₃×C₄	—	2	8	no	—
477	C₂×C₃×C₄	—	4	2	no	—
478	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
479	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
480	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
481	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
482	#67	—	2	8	no	—
483	#67	—	2	8	no	—
484	#67	—	2	8	no	—
485	#67	—	4	8	no	—
486	C₂×Dic₃	—	2	8	no	—
487	C₂×Dic₃	—	4	2	no	—
488	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
489	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
490	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
491	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
492	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
493	D₁₂	—	2	8	no	—
494	D₁₂	—	2	4	no	—
495	D₁₂	—	4	4	no	—
496	C₄×D₃	—	2	8	no	—
497	C₄×D₃	—	2	8	no	—
498	C₄×D₃	—	2	8	no	—
499	C₄×D₃	C₂×C₅×D₄	1	8	yes	—
500	C₄×D₃	C₂×C₅×D₄	1	8	yes	—
501	Dic₆	—	2	4	no	—
502	Dic₆	—	2	8	no	—
503	C₂²×C₅	—	2	1	no	—
504	C₂²×C₅	—	2	1	no	—
505	C₂²×C₅	—	2	4	no	—
506	C₂²×C₅	—	2	4	no	—
507	C₂²×C₅	—	2	4	no	—
508	C₂²×C₅	—	3	4	no	—
509	C₂²×C₅	—	6	2	no	—
510	C₂²×C₅	—	6	2	no	—
511	C₂²×C₅	—	6	4	no	—
512	C₂²×C₅	—	6	4	no	—
513	C₂²×C₅	—	6	4	no	—
514	C₂²×C₅	—	12	4	no	—
515	C₂²×C₅	—	12	16	no	—
516	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
517	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
518	C₄×C₅	—	2	4	no	—
519	C₄×C₅	—	2	4	no	—
520	C₄×C₅	—	3	2	no	—
521	C₄×C₅	—	3	2	no	—
522	C₄×C₅	—	6	4	no	—
523	C₄×C₅	—	6	4	no	—
524	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
525	C₂⁴	—	3	1	no	—
526	C₂⁴	—	3	4	no	—
527	#41	—	2	8	no	—
528	#41	—	6	16	no	—
529	#41	—	6	16	no	—
530	#41	—	6	8	no	—
531	#41	—	6	8	no	—
532	#41	—	6	8	no	—
533	C₂×Q₈	—	3	2	no	—
534	C₂×Q₈	—	3	4	no	—
535	C₂×Q₈	—	6	8	no	—
536	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
537	C₂×D₄	—	3	4	no	—
538	C₂×D₄	—	3	4	no	—
539	C₂×D₄	—	3	4	no	—
540	C₂×D₄	—	3	8	no	—
541	C₂×D₄	—	3	4	no	—
542	C₂×D₄	—	3	2	no	—
543	C₂×D₄	—	3	4	no	—
544	C₂×D₄	—	6	8	no	—
545	C₂×D₄	—	6	16	no	—
546	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
547	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
548	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
549	C₂²×C₄	—	3	1	no	—
550	C₂²×C₄	—	3	8	no	—
551	C₂²×C₄	—	3	2	no	—
552	C₂²×C₄	—	3	2	no	—
553	C₂²×C₄	—	3	4	no	—
554	C₂²×C₄	—	3	2	no	—
555	C₂²×C₄	—	3	4	no	—
556	C₂²×C₄	—	3	4	no	—
557	C₂²×C₄	—	3	4	no	—
558	C₂²×C₄	—	6	16	no	—
559	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
560	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
561	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
562	C₄⋊C₄	—	3	4	no	—
563	C₄⋊C₄	—	3	8	no	—
564	C₄⋊C₄	—	3	4	no	—
565	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
566	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
567	C₂²⋊C₄	—	3	8	no	—
568	C₂²⋊C₄	—	3	8	no	—
569	C₂²⋊C₄	—	3	8	no	—
570	C₂²⋊C₄	—	3	8	no	—
571	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
572	C₄²	—	3	4	no	—
573	C₄²	—	3	4	no	—
574	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
575	C₂²×C₃	—	2	1	no	—
576	C₂²×C₃	—	2	1	no	—
577	C₂²×C₃	—	2	4	no	—
578	C₂²×C₃	—	2	4	no	—
579	C₂²×C₃	—	2	4	no	—
580	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
581	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
582	C₂×D₃	—	2	2	no	—
583	C₂×D₃	—	2	2	no	—
584	C₂×D₃	—	2	4	no	—
585	C₂×D₃	—	2	4	no	—
586	C₂×D₃	—	2	4	no	—
587	C₂×D₃	—	4	4	no	—
588	C₂×D₃	—	4	16	no	—
589	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
590	C₃×C₄	—	2	4	no	—
591	C₃×C₄	—	2	4	no	—
592	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
593	Dic₃	—	2	4	no	—
594	Dic₃	—	2	4	no	—
595	Dic₃	C₂²×C₅×D₄	1	2	yes	—
596	Dic₃	C₂²×C₅×D₄	1	2	yes	—
597	C₂×C₅	—	2	2	no	—
598	C₂×C₅	—	4	4	no	—
599	C₂×C₅	—	6	4	no	—
600	C₂×C₅	—	12	4	no	—
601	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
602	C₂×C₅	#5966	1	1	yes	characteristic
603	C₂×C₅	#5968	1	1	yes	characteristic
604	C₂³	—	3	2	no	—
605	C₂³	—	3	4	no	—
606	C₂³	—	3	4	no	—
607	C₂³	—	6	8	no	—
608	C₂³	—	12	1	no	—
609	C₂³	—	12	1	no	—
610	C₂³	—	12	4	no	—
611	C₂³	—	12	4	no	—
612	C₂³	C₂³×C₅×D₃	1	4	yes	—
613	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
614	Q₈	—	2	4	no	—
615	Q₈	—	6	8	no	—
616	Q₈	—	6	4	no	—
617	D₄	—	2	8	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	4	no	—
620	D₄	—	6	8	no	—
621	D₄	—	6	8	no	—
622	D₄	—	6	8	no	—
623	D₄	—	6	8	no	—
624	D₄	—	6	4	no	—
625	D₄	—	12	4	no	—
626	D₄	—	12	8	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	3	4	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	8	no	—
632	C₂×C₄	—	3	8	no	—
633	C₂×C₄	—	3	4	no	—
634	C₂×C₄	—	3	4	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	6	8	no	—
637	C₂×C₄	—	6	8	no	—
638	C₂×C₄	—	6	8	no	—
639	C₂×C₄	—	6	8	no	—
640	C₂×C₄	—	12	2	no	—
641	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
642	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
643	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
644	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
645	C₂×C₃	—	2	2	no	—
646	C₂×C₃	—	4	4	no	—
647	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
648	C₂×C₃	C₅×#585	1	1	yes	characteristic
649	C₂×C₃	C₅×#585	1	1	yes	characteristic
650	D₃	—	2	4	no	—
651	D₃	—	4	4	no	—
652	C₅	#86363	1	1	yes	characteristic, direct product factor, Sylow
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	3	4	no	—
659	C₂²	—	6	2	no	—
660	C₂²	—	6	2	no	—
661	C₂²	—	6	4	no	—
662	C₂²	—	6	4	no	—
663	C₂²	—	6	4	no	—
664	C₂²	—	12	4	no	—
665	C₂²	—	12	16	no	—
666	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
667	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
668	C₄	—	2	4	no	—
669	C₄	—	2	4	no	—
670	C₄	—	3	2	no	—
671	C₄	—	3	2	no	—
672	C₄	—	6	4	no	—
673	C₄	—	6	4	no	—
674	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
675	C₃	C₅×#3449	1	1	yes	characteristic, complemented, Sylow
676	C₂	—	2	2	no	—
677	C₂	—	4	4	no	—
678	C₂	—	6	4	no	—
679	C₂	—	12	4	no	—
680	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
681	C₂	C₅×#5966	1	1	yes	characteristic
682	C₂	C₅×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#537	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#537	D₃
hypocenter	C₃	C₅×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#537

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×#41	C₂	semidirect
2. C₃×C₅×#537	C₂	semidirect
3. C₅×#5833	C₂	semidirect
4. C₅×#5628	C₂	semidirect
5. C₅×#5627	C₂	semidirect
6. C₅×#5607	C₂	semidirect
7. C₅×#5606	C₂	semidirect
8. C₅×#5605	C₂	semidirect
9. C₅×#5596	C₂	semidirect
10. C₅×#5510	C₂	semidirect
11. C₂×C₅×#892	C₂	semidirect
13. C₂×C₃×C₅×#41	C₂²	semidirect
16. C₂×C₅×D₃×Q₈	C₂²	semidirect
18. C₂×C₅×#237	C₂²	semidirect
20. C₂×C₅×D₃×D₄	C₂²	semidirect
22. C₂×C₅×#235	C₂²	semidirect
24. C₂²×C₄×C₅×D₃	C₂²	semidirect
25. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
27. C₃×C₅×#121	C₂²	semidirect
28. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
29. C₅×#946	C₂²	semidirect
30. C₅×#940	C₂²	semidirect
31. C₅×#939	C₂²	semidirect
32. C₅×#938	C₂²	semidirect
33. C₅×#937	C₂²	semidirect
34. C₅×D₄×Dic₃	C₂²	semidirect
35. C₅×#930	C₂²	semidirect
36. C₅×#930	C₂²	semidirect
38. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
39. C₅×#924	C₂²	semidirect
40. C₂×C₄×C₅×Dic₃	C₂²	semidirect
41. C₅×#897	C₂²	semidirect
42. C₅×#895	C₂²	semidirect
43. C₅×#894	C₂²	semidirect
44. C₅×#893	C₂²	semidirect
45. C₅×#892	C₂²	semidirect
46. C₅×#892	C₂²	semidirect
47. C₅×#888	C₂²	semidirect
48. C₅×#885	C₂²	semidirect
49. C₅×#883	C₂²	semidirect
50. C₅×#882	C₂²	semidirect
51. C₅×#67⋊C₄	C₂²	semidirect
52. #86363	C₅	direct (N × H)
56. C₅×#537	D₃	semidirect
93. C₂×C₄×C₅×D₃	D₄	semidirect
113. C₂×D₃×#41	C₂×C₅	semidirect
114. C₃×#537	C₂×C₅	semidirect
115. #5833	C₂×C₅	semidirect
116. #5628	C₂×C₅	semidirect
117. #5627	C₂×C₅	semidirect
118. #5607	C₂×C₅	semidirect
119. #5606	C₂×C₅	semidirect
120. #5605	C₂×C₅	semidirect
121. #5596	C₂×C₅	semidirect
122. #5510	C₂×C₅	semidirect
123. C₂×#892	C₂×C₅	semidirect
130. C₂×C₅×#41	C₂×D₃	semidirect
144. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
150. C₅×#121	C₂×D₃	semidirect
151. C₅×#121	C₂×D₃	semidirect
160. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
205. C₂×C₃×#41	C₂²×C₅	semidirect
208. C₂×D₃×Q₈	C₂²×C₅	semidirect
210. C₂×#237	C₂²×C₅	semidirect
212. C₂×D₃×D₄	C₂²×C₅	semidirect
214. C₂×#235	C₂²×C₅	semidirect
216. C₂²×C₄×D₃	C₂²×C₅	semidirect
217. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
218. C₃×#121	C₂²×C₅	semidirect
219. C₃×#121	C₂²×C₅	semidirect
220. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
221. #946	C₂²×C₅	semidirect
222. #940	C₂²×C₅	semidirect
223. #939	C₂²×C₅	semidirect
224. #938	C₂²×C₅	semidirect
225. #937	C₂²×C₅	semidirect
226. D₄×Dic₃	C₂²×C₅	semidirect
227. #930	C₂²×C₅	semidirect
228. #930	C₂²×C₅	semidirect
230. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
231. #924	C₂²×C₅	semidirect
232. C₂×C₄×Dic₃	C₂²×C₅	semidirect
233. #897	C₂²×C₅	semidirect
234. #895	C₂²×C₅	semidirect
235. #894	C₂²×C₅	semidirect
236. #893	C₂²×C₅	semidirect
237. #892	C₂²×C₅	semidirect
238. #892	C₂²×C₅	semidirect
239. #888	C₂²×C₅	semidirect
240. #885	C₂²×C₅	semidirect
241. #883	C₂²×C₅	semidirect
242. #882	C₂²×C₅	semidirect
243. #67⋊C₄	C₂²×C₅	semidirect
296. #537	C₅×D₃	semidirect
355. C₂×C₄×D₃	C₅×D₄	semidirect
422. C₂×#41	C₂×C₅×D₃	semidirect
436. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
442. #121	C₂×C₅×D₃	semidirect
443. #121	C₂×C₅×D₃	semidirect
452. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
574. C₃×C₅	#3449	semidirect
652. C₅	#86363	direct (N × H)
675. C₃	C₅×#3449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₃×C₅×#537	2
C₅×#5833	2
C₅×#5628	2
C₅×#5627	2
C₅×#5607	2
C₅×#5606	2
C₅×#5605	2
C₅×#5596	2
C₅×#5510	2
C₂×C₅×#892	2
C₅×#3449	3
#86363	5

Subgroups — C5×#86363 #14480635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86363 #14480635