Subgroups — C₅×D₃×#563 #14495359

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5735	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
4	C₅×#5712	C₂	1	4	yes	maximal, complemented
5	C₅×D₃×#126	C₂	1	4	yes	maximal, complemented
6	C₅×#5699	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#125	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic
9	C₅×#5672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₃×#123	C₂	1	2	yes	maximal
11	C₅×#5651	C₂	1	2	yes	maximal, complemented
12	C₅×#5646	C₂	1	4	yes	maximal, complemented
13	C₅×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
14	C₂×C₅×#563	—	3	1	no	maximal, Hall
15	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
17	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃×C₅×#126	C₂²	1	4	yes	complemented
21	C₃×C₅×#125	C₂²	1	2	yes	complemented
22	C₃×C₅×#124	C₂²	1	1	yes	characteristic
23	C₃×C₅×#123	C₂²	1	2	yes	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
25	C₅×#947	C₂²	1	1	yes	characteristic
26	C₅×#946	C₂²	1	4	yes	complemented
27	C₅×#944	C₂²	1	2	yes	complemented
28	C₅×#944	C₂²	1	2	yes	complemented
29	C₅×#936	C₂²	1	1	yes	characteristic
30	C₅×#935	C₂²	1	2	yes	—
31	C₅×#929	C₂²	1	2	yes	—
32	C₅×#924	C₂²	1	4	yes	complemented
33	C₅×#898	C₂²	1	4	yes	complemented
34	C₅×#898	C₂²	1	4	yes	complemented
35	C₅×#898	C₂²	1	4	yes	complemented
36	C₅×#897	C₂²	1	4	yes	complemented
37	C₅×#896	C₂²	1	4	yes	complemented
38	C₅×#896	C₂²	1	4	yes	complemented
39	C₅×#894	C₂²	1	4	yes	—
40	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
41	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
42	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
43	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
44	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
45	C₅×#890	C₂²	1	2	yes	complemented
46	C₅×#890	C₂²	1	2	yes	complemented
47	C₅×#889	C₂²	1	4	yes	complemented
48	C₅×#889	C₂²	1	4	yes	complemented
49	C₅×#888	C₂²	1	4	yes	complemented
50	C₅×#888	C₂²	1	4	yes	complemented
51	C₅×#886	C₂²	1	2	yes	—
52	C₅×#885	C₂²	1	4	yes	—
53	C₅×#883	C₂²	1	4	yes	—
54	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
57	C₅×#879	C₂²	1	4	yes	complemented
58	C₅×#879	C₂²	1	4	yes	complemented
59	C₅×#879	C₂²	1	4	yes	complemented
60	C₅×#878	C₂²	1	4	yes	complemented
61	C₅×#878	C₂²	1	4	yes	complemented
62	C₅×#876	C₂²	1	4	yes	complemented
63	C₅×#875	C₂²	1	1	yes	characteristic
64	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
65	C₄²×C₅×D₃	C₂²	1	2	yes	—
66	C₅×#870	C₂²	1	2	yes	complemented
67	C₅×#869	C₂²	1	2	yes	complemented
68	D₃×#563	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#563	—	3	2	no	—
70	C₅×#563	—	3	4	no	—
71	C₅×#563	—	3	2	no	—
72	C₅×#563	—	3	1	no	—
73	C₅×#563	—	3	2	no	—
74	C₅×#563	—	3	4	no	—
75	C₅×#563	D₃	1	1	yes	characteristic, direct product factor
76	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
77	C₂×C₅×#126	—	3	4	no	—
78	C₂×C₅×#125	—	3	2	no	—
79	C₂×C₅×#124	—	3	1	no	—
80	C₂×C₅×#123	—	3	2	no	—
81	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
82	C₂³×C₅×D₃	C₂³	1	2	yes	—
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
87	C₂×C₅×#67	C₂³	1	2	yes	—
88	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
89	C₅×D₃×Q₈	—	4	4	no	—
90	C₅×D₃×Q₈	—	4	2	no	—
91	C₅×D₃×D₄	—	4	2	no	—
92	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
93	C₂×C₄×C₅×D₃	—	4	4	no	—
94	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
95	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
96	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
97	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
99	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
100	C₂×C₅×Dic₆	C₂³	1	2	yes	—
101	C₂×C₅×Dic₆	C₂³	1	2	yes	—
102	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
103	C₂×C₅×Dic₆	C₂³	1	4	yes	—
104	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
106	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₃×C₄²×C₅	C₂³	1	2	yes	—
113	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#217	C₂³	1	4	yes	—
115	C₅×#217	C₂³	1	4	yes	—
116	C₅×#217	C₂³	1	2	yes	—
117	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
118	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
119	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
120	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
121	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
122	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
123	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
124	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
125	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
126	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
127	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
128	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
129	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
130	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
131	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
132	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
133	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
134	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
135	C₄×C₅×Dic₃	C₂³	1	4	yes	—
136	C₄×C₅×Dic₃	C₂³	1	2	yes	—
137	C₄×C₅×Dic₃	C₂³	1	2	yes	—
138	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
139	C₃×#563	C₂×C₅	1	1	yes	characteristic, complemented
140	#5735	C₂×C₅	1	2	yes	complemented
141	D₃×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
142	#5712	C₂×C₅	1	4	yes	complemented
143	D₃×#126	C₂×C₅	1	4	yes	complemented
144	#5699	C₂×C₅	1	2	yes	complemented
145	D₃×#125	C₂×C₅	1	2	yes	complemented
146	D₃×#124	C₂×C₅	1	1	yes	characteristic
147	#5672	C₂×C₅	1	1	yes	characteristic, complemented
148	D₃×#123	C₂×C₅	1	2	yes	—
149	#5651	C₂×C₅	1	2	yes	complemented
150	#5646	C₂×C₅	1	4	yes	complemented
151	D₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
152	C₂²×C₅×Q₈	—	3	2	no	—
153	C₂²×C₅×Q₈	—	3	1	no	—
154	C₂²×C₅×D₄	—	3	1	no	—
155	C₂³×C₄×C₅	—	3	2	no	—
156	C₅×C₄⋊Q₈	—	3	2	no	—
157	C₅×C₄⋊Q₈	—	3	2	no	—
158	C₅×C₄⋊Q₈	—	3	4	no	—
159	C₅×C₄⋊Q₈	—	3	4	no	—
160	C₅×C₄⋊Q₈	—	3	2	no	—
161	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
162	C₅×#126	—	3	4	no	—
163	C₅×#126	—	3	4	no	—
164	C₅×#126	—	3	4	no	—
165	C₅×#126	—	3	4	no	—
166	C₅×#126	—	3	4	no	—
167	C₅×#126	—	3	4	no	—
168	C₅×#126	—	3	4	no	—
169	C₅×#126	C₂×D₃	1	4	yes	complemented
170	C₅×#125	—	3	4	no	—
171	C₅×#125	—	3	4	no	—
172	C₅×#125	—	3	2	no	—
173	C₅×#125	—	3	2	no	—
174	C₅×#125	—	3	2	no	—
175	C₅×#125	C₂×D₃	1	2	yes	complemented
176	C₅×#124	—	3	1	no	—
177	C₅×#124	—	3	1	no	—
178	C₅×#124	—	3	4	no	—
179	C₅×#124	—	3	1	no	—
180	C₅×#124	C₂×D₃	1	1	yes	characteristic
181	C₅×#123	—	3	2	no	—
182	C₅×#123	—	3	2	no	—
183	C₅×#123	—	3	4	no	—
184	C₅×#123	—	3	4	no	—
185	C₅×#123	—	3	2	no	—
186	C₅×#123	C₂×D₃	1	2	yes	—
187	C₅×C₂²⋊Q₈	—	3	4	no	—
188	C₅×C₂²⋊Q₈	—	3	4	no	—
189	C₅×C₂²⋊Q₈	—	3	4	no	—
190	C₅×C₂²⋊Q₈	—	3	4	no	—
191	C₅×C₂²⋊Q₈	—	3	4	no	—
192	C₅×C₂²⋊Q₈	—	3	4	no	—
193	C₅×C₂²⋊Q₈	—	3	4	no	—
194	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
195	C₂×C₅×C₄⋊C₄	—	3	2	no	—
196	C₂×C₅×C₄⋊C₄	—	3	4	no	—
197	C₂×C₅×C₄⋊C₄	—	3	4	no	—
198	C₂×C₅×C₄⋊C₄	—	3	4	no	—
199	C₂×C₅×C₄⋊C₄	—	3	2	no	—
200	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
201	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
202	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
203	C₂×C₄²×C₅	—	3	1	no	—
204	C₂×C₄²×C₅	—	3	2	no	—
205	C₂×#563	—	3	1	no	Sylow
206	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
207	C₂²×C₅×D₃	—	2	4	no	—
208	C₂²×C₅×D₃	—	2	8	no	—
209	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
210	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
211	C₃×C₅×Q₈	—	4	1	no	—
212	C₃×C₅×Q₈	—	4	2	no	—
213	C₃×C₅×D₄	—	4	1	no	—
214	C₂×C₃×C₄×C₅	—	4	2	no	—
215	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
217	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
220	C₅×#67	—	4	2	no	—
221	C₂×C₅×Dic₃	—	4	2	no	—
222	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
223	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
224	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
225	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
226	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
227	C₅×D₁₂	—	4	1	no	—
228	C₄×C₅×D₃	—	2	8	no	—
229	C₄×C₅×D₃	—	2	2	no	—
230	C₄×C₅×D₃	—	2	4	no	—
231	C₄×C₅×D₃	—	2	4	no	—
232	C₄×C₅×D₃	—	2	8	no	—
233	C₄×C₅×D₃	—	4	4	no	—
234	C₅×Dic₆	—	4	1	no	—
235	C₅×Dic₆	—	4	4	no	—
236	C₅×Dic₆	—	4	2	no	—
237	C₅×Dic₆	—	4	2	no	—
238	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
240	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
241	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
242	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
243	C₃×#126	C₂²×C₅	1	4	yes	complemented
244	C₃×#125	C₂²×C₅	1	2	yes	complemented
245	C₃×#124	C₂²×C₅	1	1	yes	characteristic
246	C₃×#123	C₂²×C₅	1	2	yes	—
247	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
248	#947	C₂²×C₅	1	1	yes	characteristic
249	#946	C₂²×C₅	1	4	yes	complemented
250	#944	C₂²×C₅	1	2	yes	complemented
251	#944	C₂²×C₅	1	2	yes	complemented
252	#936	C₂²×C₅	1	1	yes	characteristic
253	#935	C₂²×C₅	1	2	yes	—
254	#929	C₂²×C₅	1	2	yes	—
255	#924	C₂²×C₅	1	4	yes	complemented
256	#898	C₂²×C₅	1	4	yes	complemented
257	#898	C₂²×C₅	1	4	yes	complemented
258	#898	C₂²×C₅	1	4	yes	complemented
259	#897	C₂²×C₅	1	4	yes	complemented
260	#896	C₂²×C₅	1	4	yes	complemented
261	#896	C₂²×C₅	1	4	yes	complemented
262	#894	C₂²×C₅	1	4	yes	—
263	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
264	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
265	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
266	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
267	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
268	#890	C₂²×C₅	1	2	yes	complemented
269	#890	C₂²×C₅	1	2	yes	complemented
270	#889	C₂²×C₅	1	4	yes	complemented
271	#889	C₂²×C₅	1	4	yes	complemented
272	#888	C₂²×C₅	1	4	yes	complemented
273	#888	C₂²×C₅	1	4	yes	complemented
274	#886	C₂²×C₅	1	2	yes	—
275	#885	C₂²×C₅	1	4	yes	—
276	#883	C₂²×C₅	1	4	yes	—
277	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
278	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
279	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
280	#879	C₂²×C₅	1	4	yes	complemented
281	#879	C₂²×C₅	1	4	yes	complemented
282	#879	C₂²×C₅	1	4	yes	complemented
283	#878	C₂²×C₅	1	4	yes	complemented
284	#878	C₂²×C₅	1	4	yes	complemented
285	#876	C₂²×C₅	1	4	yes	complemented
286	#875	C₂²×C₅	1	1	yes	characteristic
287	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
288	C₄²×D₃	C₂²×C₅	1	2	yes	—
289	#870	C₂²×C₅	1	2	yes	complemented
290	#869	C₂²×C₅	1	2	yes	complemented
291	C₂⁴×C₅	—	3	2	no	—
292	C₂×C₅×Q₈	—	3	4	no	—
293	C₂×C₅×Q₈	—	3	2	no	—
294	C₂×C₅×Q₈	—	3	1	no	—
295	C₂×C₅×Q₈	—	3	2	no	—
296	C₂×C₅×Q₈	—	12	4	no	—
297	C₂×C₅×Q₈	—	12	2	no	—
298	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
299	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
300	C₂×C₅×D₄	—	3	2	no	—
301	C₂×C₅×D₄	—	3	1	no	—
302	C₂×C₅×D₄	—	12	2	no	—
303	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
304	C₂²×C₄×C₅	—	3	2	no	—
305	C₂²×C₄×C₅	—	3	2	no	—
306	C₂²×C₄×C₅	—	3	4	no	—
307	C₂²×C₄×C₅	—	3	2	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	3	4	no	—
310	C₂²×C₄×C₅	—	3	4	no	—
311	C₂²×C₄×C₅	—	12	4	no	—
312	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
313	C₅×C₄⋊C₄	—	3	4	no	—
314	C₅×C₄⋊C₄	—	3	2	no	—
315	C₅×C₄⋊C₄	—	3	4	no	—
316	C₅×C₄⋊C₄	—	3	4	no	—
317	C₅×C₄⋊C₄	—	3	4	no	—
318	C₅×C₄⋊C₄	—	3	4	no	—
319	C₅×C₄⋊C₄	—	3	4	no	—
320	C₅×C₄⋊C₄	—	3	4	no	—
321	C₅×C₄⋊C₄	—	3	4	no	—
322	C₅×C₄⋊C₄	—	3	4	no	—
323	C₅×C₄⋊C₄	—	3	4	no	—
324	C₅×C₄⋊C₄	—	3	4	no	—
325	C₅×C₄⋊C₄	—	3	2	no	—
326	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
327	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
328	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
329	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
330	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
331	C₅×C₂²⋊C₄	—	3	4	no	—
332	C₅×C₂²⋊C₄	—	3	4	no	—
333	C₅×C₂²⋊C₄	—	3	2	no	—
334	C₅×C₂²⋊C₄	—	3	4	no	—
335	C₅×C₂²⋊C₄	—	3	4	no	—
336	C₅×C₂²⋊C₄	—	3	4	no	—
337	C₅×C₂²⋊C₄	—	3	4	no	—
338	C₅×C₂²⋊C₄	—	3	4	no	—
339	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
340	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
341	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
342	C₄²×C₅	—	3	1	no	—
343	C₄²×C₅	—	3	2	no	—
344	C₄²×C₅	—	3	2	no	—
345	C₄²×C₅	—	3	4	no	—
346	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
347	C₄²×C₅	C₂²×D₃	1	2	yes	—
348	#563	—	3	2	no	—
349	#563	—	3	4	no	—
350	#563	—	3	2	no	—
351	#563	—	3	1	no	—
352	#563	—	3	2	no	—
353	#563	—	3	4	no	—
354	#563	C₅×D₃	1	1	yes	characteristic, direct product factor
355	C₂×C₄⋊Q₈	—	3	2	no	—
356	C₂×#126	—	3	4	no	—
357	C₂×#125	—	3	2	no	—
358	C₂×#124	—	3	1	no	—
359	C₂×#123	—	3	2	no	—
360	C₂×C₂²⋊Q₈	—	3	4	no	—
361	C₂²×C₃×C₅	—	2	2	no	—
362	C₂²×C₃×C₅	—	2	4	no	—
363	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
364	C₂×C₅×D₃	—	2	2	no	—
365	C₂×C₅×D₃	—	2	4	no	—
366	C₂×C₅×D₃	—	4	8	no	—
367	C₂×C₅×D₃	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₅×D₃	2₋¹⁺⁴	1	4	yes	—
369	C₃×C₄×C₅	—	2	2	no	—
370	C₃×C₄×C₅	—	2	4	no	—
371	C₃×C₄×C₅	—	2	1	no	—
372	C₃×C₄×C₅	—	2	4	no	—
373	C₃×C₄×C₅	—	2	2	no	—
374	C₅×Dic₃	—	2	2	no	—
375	C₅×Dic₃	—	2	4	no	—
376	C₅×Dic₃	—	2	1	no	—
377	C₅×Dic₃	—	2	4	no	—
378	C₅×Dic₃	—	2	2	no	—
379	C₂³×D₃	C₂³×C₅	1	2	yes	—
380	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
382	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
384	C₂×#67	C₂³×C₅	1	2	yes	—
385	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
386	D₃×Q₈	—	4	4	no	—
387	D₃×Q₈	—	4	2	no	—
388	D₃×D₄	—	4	2	no	—
389	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄×D₃	—	4	4	no	—
391	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
392	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
393	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
394	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
396	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
397	C₂×Dic₆	C₂³×C₅	1	2	yes	—
398	C₂×Dic₆	C₂³×C₅	1	2	yes	—
399	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
400	C₂×Dic₆	C₂³×C₅	1	4	yes	—
401	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
402	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
403	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
404	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
405	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
406	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
407	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
408	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
409	C₃×C₄²	C₂³×C₅	1	2	yes	—
410	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
411	#217	C₂³×C₅	1	4	yes	—
412	#217	C₂³×C₅	1	4	yes	—
413	#217	C₂³×C₅	1	2	yes	—
414	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
415	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
416	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
417	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
418	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
419	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
420	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
421	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
422	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
423	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
424	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
425	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
426	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
427	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
428	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
429	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
430	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
431	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
432	C₄×Dic₃	C₂³×C₅	1	4	yes	—
433	C₄×Dic₃	C₂³×C₅	1	2	yes	—
434	C₄×Dic₃	C₂³×C₅	1	2	yes	—
435	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
436	C₂³×C₅	—	3	1	no	—
437	C₂³×C₅	—	3	2	no	—
438	C₂³×C₅	—	6	4	no	—
439	C₂³×C₅	—	6	8	no	—
440	C₂³×C₅	C₂³×D₃	1	2	yes	—
441	C₅×Q₈	—	4	2	no	—
442	C₅×Q₈	—	4	1	no	—
443	C₅×Q₈	—	12	4	no	—
444	C₅×Q₈	—	12	1	no	—
445	C₅×Q₈	—	12	2	no	—
446	C₅×Q₈	—	12	2	no	—
447	C₅×D₄	—	4	1	no	—
448	C₅×D₄	—	12	1	no	—
449	C₅×D₄	—	12	2	no	—
450	C₂×C₄×C₅	—	3	2	no	—
451	C₂×C₄×C₅	—	3	4	no	—
452	C₂×C₄×C₅	—	3	2	no	—
453	C₂×C₄×C₅	—	3	1	no	—
454	C₂×C₄×C₅	—	3	4	no	—
455	C₂×C₄×C₅	—	4	2	no	—
456	C₂×C₄×C₅	—	6	4	no	—
457	C₂×C₄×C₅	—	6	8	no	—
458	C₂×C₄×C₅	—	6	8	no	—
459	C₂×C₄×C₅	—	6	2	no	—
460	C₂×C₄×C₅	—	6	4	no	—
461	C₂×C₄×C₅	—	12	4	no	—
462	C₂×C₄×C₅	—	12	2	no	—
463	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
464	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
465	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
466	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
467	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
468	C₂²×Q₈	—	3	2	no	—
469	C₂²×Q₈	—	3	1	no	—
470	C₂²×D₄	—	3	1	no	—
471	C₂³×C₄	—	3	2	no	—
472	C₄⋊Q₈	—	3	2	no	—
473	C₄⋊Q₈	—	3	2	no	—
474	C₄⋊Q₈	—	3	4	no	—
475	C₄⋊Q₈	—	3	4	no	—
476	C₄⋊Q₈	—	3	2	no	—
477	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
478	#126	—	3	4	no	—
479	#126	—	3	4	no	—
480	#126	—	3	4	no	—
481	#126	—	3	4	no	—
482	#126	—	3	4	no	—
483	#126	—	3	4	no	—
484	#126	—	3	4	no	—
485	#126	C₂×C₅×D₃	1	4	yes	complemented
486	#125	—	3	4	no	—
487	#125	—	3	4	no	—
488	#125	—	3	2	no	—
489	#125	—	3	2	no	—
490	#125	—	3	2	no	—
491	#125	C₂×C₅×D₃	1	2	yes	complemented
492	#124	—	3	1	no	—
493	#124	—	3	1	no	—
494	#124	—	3	4	no	—
495	#124	—	3	1	no	—
496	#124	C₂×C₅×D₃	1	1	yes	characteristic
497	#123	—	3	2	no	—
498	#123	—	3	2	no	—
499	#123	—	3	4	no	—
500	#123	—	3	4	no	—
501	#123	—	3	2	no	—
502	#123	C₂×C₅×D₃	1	2	yes	—
503	C₂²⋊Q₈	—	3	4	no	—
504	C₂²⋊Q₈	—	3	4	no	—
505	C₂²⋊Q₈	—	3	4	no	—
506	C₂²⋊Q₈	—	3	4	no	—
507	C₂²⋊Q₈	—	3	4	no	—
508	C₂²⋊Q₈	—	3	4	no	—
509	C₂²⋊Q₈	—	3	4	no	—
510	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
511	C₂×C₄⋊C₄	—	3	2	no	—
512	C₂×C₄⋊C₄	—	3	4	no	—
513	C₂×C₄⋊C₄	—	3	4	no	—
514	C₂×C₄⋊C₄	—	3	4	no	—
515	C₂×C₄⋊C₄	—	3	2	no	—
516	C₂×C₂²⋊C₄	—	3	4	no	—
517	C₂×C₂²⋊C₄	—	3	4	no	—
518	C₂×C₂²⋊C₄	—	3	2	no	—
519	C₂×C₄²	—	3	1	no	—
520	C₂×C₄²	—	3	2	no	—
521	C₂×C₃×C₅	—	4	2	no	—
522	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
524	C₅×D₃	—	4	2	no	—
525	C₅×D₃	#563	1	4	yes	direct product factor
526	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
527	C₂²×D₃	—	2	4	no	—
528	C₂²×D₃	—	2	8	no	—
529	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
530	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
531	C₃×Q₈	—	4	1	no	—
532	C₃×Q₈	—	4	2	no	—
533	C₃×D₄	—	4	1	no	—
534	C₂×C₃×C₄	—	4	2	no	—
535	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
537	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
538	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
539	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
540	#67	—	4	2	no	—
541	C₂×Dic₃	—	4	2	no	—
542	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
543	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
544	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
545	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
546	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
547	D₁₂	—	4	1	no	—
548	C₄×D₃	—	2	8	no	—
549	C₄×D₃	—	2	2	no	—
550	C₄×D₃	—	2	4	no	—
551	C₄×D₃	—	2	4	no	—
552	C₄×D₃	—	2	8	no	—
553	C₄×D₃	—	4	4	no	—
554	Dic₆	—	4	1	no	—
555	Dic₆	—	4	4	no	—
556	Dic₆	—	4	2	no	—
557	Dic₆	—	4	2	no	—
558	C₂²×C₅	—	2	2	no	—
559	C₂²×C₅	—	2	4	no	—
560	C₂²×C₅	—	3	2	no	—
561	C₂²×C₅	—	3	4	no	—
562	C₂²×C₅	—	6	2	no	—
563	C₂²×C₅	—	6	4	no	—
564	C₂²×C₅	—	12	8	no	—
565	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
566	C₄×C₅	—	2	4	no	—
567	C₄×C₅	—	2	1	no	—
568	C₄×C₅	—	2	2	no	—
569	C₄×C₅	—	2	2	no	—
570	C₄×C₅	—	2	4	no	—
571	C₄×C₅	—	6	4	no	—
572	C₄×C₅	—	6	1	no	—
573	C₄×C₅	—	6	2	no	—
574	C₄×C₅	—	6	2	no	—
575	C₄×C₅	—	6	4	no	—
576	C₂⁴	—	3	2	no	—
577	C₂×Q₈	—	3	4	no	—
578	C₂×Q₈	—	3	2	no	—
579	C₂×Q₈	—	3	1	no	—
580	C₂×Q₈	—	3	2	no	—
581	C₂×Q₈	—	12	4	no	—
582	C₂×Q₈	—	12	2	no	—
583	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
584	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
585	C₂×D₄	—	3	2	no	—
586	C₂×D₄	—	3	1	no	—
587	C₂×D₄	—	12	2	no	—
588	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
589	C₂²×C₄	—	3	2	no	—
590	C₂²×C₄	—	3	2	no	—
591	C₂²×C₄	—	3	4	no	—
592	C₂²×C₄	—	3	2	no	—
593	C₂²×C₄	—	3	1	no	—
594	C₂²×C₄	—	3	4	no	—
595	C₂²×C₄	—	3	4	no	—
596	C₂²×C₄	—	12	4	no	—
597	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
598	C₄⋊C₄	—	3	4	no	—
599	C₄⋊C₄	—	3	2	no	—
600	C₄⋊C₄	—	3	4	no	—
601	C₄⋊C₄	—	3	4	no	—
602	C₄⋊C₄	—	3	4	no	—
603	C₄⋊C₄	—	3	4	no	—
604	C₄⋊C₄	—	3	4	no	—
605	C₄⋊C₄	—	3	4	no	—
606	C₄⋊C₄	—	3	4	no	—
607	C₄⋊C₄	—	3	4	no	—
608	C₄⋊C₄	—	3	4	no	—
609	C₄⋊C₄	—	3	4	no	—
610	C₄⋊C₄	—	3	2	no	—
611	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
612	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
613	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
614	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
615	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
616	C₂²⋊C₄	—	3	4	no	—
617	C₂²⋊C₄	—	3	4	no	—
618	C₂²⋊C₄	—	3	2	no	—
619	C₂²⋊C₄	—	3	4	no	—
620	C₂²⋊C₄	—	3	4	no	—
621	C₂²⋊C₄	—	3	4	no	—
622	C₂²⋊C₄	—	3	4	no	—
623	C₂²⋊C₄	—	3	4	no	—
624	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
625	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
626	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
627	C₄²	—	3	1	no	—
628	C₄²	—	3	2	no	—
629	C₄²	—	3	2	no	—
630	C₄²	—	3	4	no	—
631	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
632	C₄²	C₂²×C₅×D₃	1	2	yes	—
633	C₃×C₅	C₂×#563	1	1	yes	characteristic, complemented, Hall
634	C₂²×C₃	—	2	2	no	—
635	C₂²×C₃	—	2	4	no	—
636	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
637	C₂×D₃	—	2	2	no	—
638	C₂×D₃	—	2	4	no	—
639	C₂×D₃	—	4	8	no	—
640	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
641	C₂×D₃	C₅×2₋¹⁺⁴	1	4	yes	—
642	C₃×C₄	—	2	2	no	—
643	C₃×C₄	—	2	4	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	2	4	no	—
646	C₃×C₄	—	2	2	no	—
647	Dic₃	—	2	2	no	—
648	Dic₃	—	2	4	no	—
649	Dic₃	—	2	1	no	—
650	Dic₃	—	2	4	no	—
651	Dic₃	—	2	2	no	—
652	C₂×C₅	—	3	4	no	—
653	C₂×C₅	—	4	2	no	—
654	C₂×C₅	—	12	2	no	—
655	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×C₅	D₃×2₋¹⁺⁴	1	2	yes	—
657	C₂³	—	3	1	no	—
658	C₂³	—	3	2	no	—
659	C₂³	—	6	4	no	—
660	C₂³	—	6	8	no	—
661	C₂³	C₂³×C₅×D₃	1	2	yes	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	12	4	no	—
665	Q₈	—	12	1	no	—
666	Q₈	—	12	2	no	—
667	Q₈	—	12	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	12	1	no	—
670	D₄	—	12	2	no	—
671	C₂×C₄	—	3	2	no	—
672	C₂×C₄	—	3	4	no	—
673	C₂×C₄	—	3	2	no	—
674	C₂×C₄	—	3	1	no	—
675	C₂×C₄	—	3	4	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	6	8	no	—
678	C₂×C₄	—	6	2	no	—
679	C₂×C₄	—	6	4	no	—
680	C₂×C₄	—	6	4	no	—
681	C₂×C₄	—	6	8	no	—
682	C₂×C₄	—	12	4	no	—
683	C₂×C₄	—	12	2	no	—
684	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
685	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
686	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
687	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
688	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
689	C₂×C₃	—	4	2	no	—
690	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
692	D₃	—	4	2	no	—
693	D₃	C₅×#563	1	4	yes	direct product factor
694	C₅	D₃×#563	1	1	yes	characteristic, direct product factor, Sylow
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	3	2	no	—
698	C₂²	—	3	4	no	—
699	C₂²	—	6	2	no	—
700	C₂²	—	6	4	no	—
701	C₂²	—	12	8	no	—
702	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
703	C₄	—	2	4	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	4	no	—
708	C₄	—	6	4	no	—
709	C₄	—	6	1	no	—
710	C₄	—	6	2	no	—
711	C₄	—	6	2	no	—
712	C₄	—	6	4	no	—
713	C₃	C₂×C₅×#563	1	1	yes	characteristic, complemented, Sylow
714	C₂	—	3	4	no	—
715	C₂	—	4	2	no	—
716	C₂	—	12	2	no	—
717	C₂	C₅×D₃×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂	C₅×D₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#563	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#563	D₃
hypocenter	C₃	C₂×C₅×#563
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#563

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#563	C₂	semidirect
2. C₅×#5735	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₅×#5712	C₂	semidirect
5. C₅×D₃×#126	C₂	semidirect
6. C₅×#5699	C₂	semidirect
7. C₅×D₃×#125	C₂	semidirect
9. C₅×#5672	C₂	semidirect
11. C₅×#5651	C₂	semidirect
12. C₅×#5646	C₂	semidirect
13. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×#126	C₂²	semidirect
21. C₃×C₅×#125	C₂²	semidirect
24. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₅×#946	C₂²	semidirect
27. C₅×#944	C₂²	semidirect
28. C₅×#944	C₂²	semidirect
32. C₅×#924	C₂²	semidirect
33. C₅×#898	C₂²	semidirect
34. C₅×#898	C₂²	semidirect
35. C₅×#898	C₂²	semidirect
36. C₅×#897	C₂²	semidirect
37. C₅×#896	C₂²	semidirect
38. C₅×#896	C₂²	semidirect
45. C₅×#890	C₂²	semidirect
46. C₅×#890	C₂²	semidirect
47. C₅×#889	C₂²	semidirect
48. C₅×#889	C₂²	semidirect
49. C₅×#888	C₂²	semidirect
50. C₅×#888	C₂²	semidirect
57. C₅×#879	C₂²	semidirect
58. C₅×#879	C₂²	semidirect
59. C₅×#879	C₂²	semidirect
60. C₅×#878	C₂²	semidirect
61. C₅×#878	C₂²	semidirect
62. C₅×#876	C₂²	semidirect
66. C₅×#870	C₂²	semidirect
67. C₅×#869	C₂²	semidirect
68. D₃×#563	C₅	direct (N × H)
75. C₅×#563	D₃	direct (N × H)
139. C₃×#563	C₂×C₅	semidirect
140. #5735	C₂×C₅	semidirect
141. D₃×C₄⋊Q₈	C₂×C₅	semidirect
142. #5712	C₂×C₅	semidirect
143. D₃×#126	C₂×C₅	semidirect
144. #5699	C₂×C₅	semidirect
145. D₃×#125	C₂×C₅	semidirect
147. #5672	C₂×C₅	semidirect
149. #5651	C₂×C₅	semidirect
150. #5646	C₂×C₅	semidirect
151. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
161. C₅×C₄⋊Q₈	C₂×D₃	semidirect
169. C₅×#126	C₂×D₃	semidirect
175. C₅×#125	C₂×D₃	semidirect
194. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
242. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
243. C₃×#126	C₂²×C₅	semidirect
244. C₃×#125	C₂²×C₅	semidirect
247. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
249. #946	C₂²×C₅	semidirect
250. #944	C₂²×C₅	semidirect
251. #944	C₂²×C₅	semidirect
255. #924	C₂²×C₅	semidirect
256. #898	C₂²×C₅	semidirect
257. #898	C₂²×C₅	semidirect
258. #898	C₂²×C₅	semidirect
259. #897	C₂²×C₅	semidirect
260. #896	C₂²×C₅	semidirect
261. #896	C₂²×C₅	semidirect
268. #890	C₂²×C₅	semidirect
269. #890	C₂²×C₅	semidirect
270. #889	C₂²×C₅	semidirect
271. #889	C₂²×C₅	semidirect
272. #888	C₂²×C₅	semidirect
273. #888	C₂²×C₅	semidirect
280. #879	C₂²×C₅	semidirect
281. #879	C₂²×C₅	semidirect
282. #879	C₂²×C₅	semidirect
283. #878	C₂²×C₅	semidirect
284. #878	C₂²×C₅	semidirect
285. #876	C₂²×C₅	semidirect
289. #870	C₂²×C₅	semidirect
290. #869	C₂²×C₅	semidirect
354. #563	C₅×D₃	direct (N × H)
477. C₄⋊Q₈	C₂×C₅×D₃	semidirect
485. #126	C₂×C₅×D₃	semidirect
491. #125	C₂×C₅×D₃	semidirect
510. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
525. C₅×D₃	#563	direct (N × H)
633. C₃×C₅	C₂×#563	semidirect
693. D₃	C₅×#563	direct (N × H)
694. C₅	D₃×#563	direct (N × H)
713. C₃	C₂×C₅×#563	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#563	2
C₅×#5735	2
C₅×D₃×C₄⋊Q₈	2
C₅×#5712	2
C₅×D₃×#126	2
C₅×#5699	2
C₅×D₃×#125	2
C₅×D₃×#124	2
C₅×#5672	2
C₅×D₃×#123	2
C₅×#5651	2
C₅×#5646	2
C₅×D₃×C₂²⋊Q₈	2
C₂×C₅×#563	3
D₃×#563	5

Subgroups — C5×D3×#563 #14495359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#563 #14495359