Subgroups — C₅×D₃×#541 #14481187

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5731	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#126	C₂	1	4	yes	maximal
5	C₅×#5701	C₂	1	4	yes	maximal, complemented
6	C₅×#5698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5696	C₂	1	4	yes	maximal, complemented
8	C₅×D₃×#125	C₂	1	4	yes	maximal, complemented
9	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
11	C₅×#5625	C₂	1	2	yes	maximal, complemented
12	C₅×#5583	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×D₃×Q₈	C₂	1	2	yes	maximal, complemented
14	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
15	C₅×#5518	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#541	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#126	C₂²	1	4	yes	—
21	C₃×C₅×#125	C₂²	1	4	yes	complemented
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₅×#946	C₂²	1	2	yes	—
27	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
28	C₅×#944	C₂²	1	2	yes	complemented
29	C₅×#926	C₂²	1	1	yes	characteristic
30	C₅×#924	C₂²	1	2	yes	—
31	C₅×#898	C₂²	1	4	yes	—
32	C₅×#898	C₂²	1	4	yes	—
33	C₅×#898	C₂²	1	4	yes	—
34	C₅×#897	C₂²	1	2	yes	—
35	C₅×#896	C₂²	1	4	yes	—
36	C₅×#892	C₂²	1	2	yes	—
37	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
38	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
40	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
41	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
42	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
43	C₅×#890	C₂²	1	4	yes	complemented
44	C₅×#890	C₂²	1	4	yes	complemented
45	C₅×#890	C₂²	1	2	yes	complemented
46	C₅×#889	C₂²	1	4	yes	complemented
47	C₅×#889	C₂²	1	4	yes	complemented
48	C₅×#889	C₂²	1	4	yes	complemented
49	C₅×#889	C₂²	1	4	yes	complemented
50	C₅×#889	C₂²	1	4	yes	complemented
51	C₅×#888	C₂²	1	4	yes	complemented
52	C₅×#887	C₂²	1	4	yes	complemented
53	C₅×#887	C₂²	1	2	yes	complemented
54	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₅×#879	C₂²	1	4	yes	—
57	C₅×#879	C₂²	1	4	yes	—
58	C₅×#879	C₂²	1	4	yes	—
59	C₅×#878	C₂²	1	4	yes	—
60	C₅×#877	C₂²	1	2	yes	—
61	C₅×#876	C₂²	1	4	yes	—
62	C₅×#872	C₂²	1	1	yes	characteristic
63	C₅×#872	C₂²	1	1	yes	characteristic
64	C₄²×C₅×D₃	C₂²	1	4	yes	—
65	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
66	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
67	C₅×#870	C₂²	1	4	yes	complemented
68	C₅×#870	C₂²	1	1	yes	characteristic, complemented
69	C₅×#869	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
71	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
72	D₃×#541	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
73	C₅×#541	—	3	1	no	—
74	C₅×#541	—	3	4	no	—
75	C₅×#541	—	3	4	no	—
76	C₅×#541	—	3	1	no	—
77	C₅×#541	—	3	2	no	—
78	C₅×#541	—	3	2	no	—
79	C₅×#541	—	3	1	no	—
80	C₅×#541	D₃	1	1	yes	characteristic, direct product factor
81	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
82	C₂×C₅×#126	—	3	4	no	—
83	C₂×C₅×#125	—	3	1	no	—
84	C₂×C₅×#125	—	3	4	no	—
85	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
86	C₂×C₄×C₅×Q₈	—	3	2	no	—
87	C₂×C₅×#117	—	3	1	no	—
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₅×D₃×Q₈	—	2	8	no	—
93	C₂×C₄×C₅×D₃	—	2	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	4	yes	—
98	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
102	C₂×C₅×Dic₆	C₂³	1	2	yes	—
103	C₂×C₅×Dic₆	C₂³	1	4	yes	—
104	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	2	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	4	yes	—
109	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
110	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₃×C₄²×C₅	C₂³	1	4	yes	—
114	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₅×#217	C₂³	1	2	yes	—
116	C₅×#217	C₂³	1	4	yes	—
117	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
118	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
119	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
120	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
121	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
122	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
123	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
124	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
125	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
126	C₅×C₄⋊Dic₃	C₂³	1	2	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	2	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	2	yes	—
135	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
136	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
137	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
138	C₄×C₅×Dic₃	C₂³	1	2	yes	—
139	C₄×C₅×Dic₃	C₂³	1	4	yes	—
140	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
141	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
142	C₄×C₅×Dic₃	C₂³	1	2	yes	—
143	C₄×C₅×Dic₃	C₂³	1	4	yes	—
144	C₄×C₅×Dic₃	C₂³	1	4	yes	—
145	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
146	#5731	C₂×C₅	1	1	yes	characteristic, complemented
147	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
148	D₃×#126	C₂×C₅	1	4	yes	—
149	#5701	C₂×C₅	1	4	yes	complemented
150	#5698	C₂×C₅	1	1	yes	characteristic, complemented
151	#5696	C₂×C₅	1	4	yes	complemented
152	D₃×#125	C₂×C₅	1	4	yes	complemented
153	D₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
154	D₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
155	#5625	C₂×C₅	1	2	yes	complemented
156	#5583	C₂×C₅	1	2	yes	complemented
157	C₄×D₃×Q₈	C₂×C₅	1	2	yes	complemented
158	D₃×#117	C₂×C₅	1	1	yes	characteristic
159	#5518	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂²×C₅×Q₈	—	3	2	no	—
161	C₂³×C₄×C₅	—	3	1	no	—
162	C₅×C₄⋊Q₈	—	3	2	no	—
163	C₅×C₄⋊Q₈	—	3	4	no	—
164	C₅×C₄⋊Q₈	—	3	1	no	—
165	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
166	C₅×#126	—	3	4	no	—
167	C₅×#126	—	3	4	no	—
168	C₅×#126	—	3	4	no	—
169	C₅×#126	—	3	4	no	—
170	C₅×#126	—	3	4	no	—
171	C₅×#126	—	3	4	no	—
172	C₅×#126	—	3	4	no	—
173	C₅×#126	C₂×D₃	1	4	yes	—
174	C₅×#125	—	3	4	no	—
175	C₅×#125	—	3	4	no	—
176	C₅×#125	—	3	4	no	—
177	C₅×#125	—	3	4	no	—
178	C₅×#125	—	3	4	no	—
179	C₅×#125	—	3	2	no	—
180	C₅×#125	—	3	4	no	—
181	C₅×#125	—	3	4	no	—
182	C₅×#125	—	3	1	no	—
183	C₅×#125	—	3	4	no	—
184	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
185	C₅×#125	C₂×D₃	1	4	yes	complemented
186	C₅×C₂²⋊Q₈	—	3	2	no	—
187	C₅×C₂²⋊Q₈	—	3	2	no	—
188	C₅×C₂²⋊Q₈	—	3	4	no	—
189	C₅×C₂²⋊Q₈	—	3	2	no	—
190	C₅×C₂²⋊Q₈	—	3	4	no	—
191	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
192	C₄×C₅×Q₈	—	3	2	no	—
193	C₄×C₅×Q₈	—	3	4	no	—
194	C₄×C₅×Q₈	—	3	2	no	—
195	C₄×C₅×Q₈	—	3	4	no	—
196	C₄×C₅×Q₈	—	3	2	no	—
197	C₄×C₅×Q₈	C₂×D₃	1	2	yes	complemented
198	C₅×#117	—	3	1	no	—
199	C₅×#117	—	3	2	no	—
200	C₅×#117	—	3	2	no	—
201	C₅×#117	—	3	1	no	—
202	C₅×#117	—	3	1	no	—
203	C₅×#117	C₂×D₃	1	1	yes	characteristic
204	C₂×C₅×C₄⋊C₄	—	3	2	no	—
205	C₂×C₅×C₄⋊C₄	—	3	2	no	—
206	C₂×C₅×C₄⋊C₄	—	3	4	no	—
207	C₂×C₅×C₄⋊C₄	—	3	4	no	—
208	C₂×C₅×C₄⋊C₄	—	3	4	no	—
209	C₂×C₅×C₄⋊C₄	—	3	4	no	—
210	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
211	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
212	C₂×C₄²×C₅	—	3	1	no	—
213	C₂×C₄²×C₅	—	3	1	no	—
214	C₂×C₄²×C₅	—	3	4	no	—
215	C₂×#541	—	3	1	no	Sylow
216	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
217	C₂²×C₅×D₃	—	2	2	no	—
218	C₂²×C₅×D₃	—	2	4	no	—
219	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
221	C₃×C₅×Q₈	—	2	4	no	—
222	C₂×C₃×C₄×C₅	—	2	2	no	—
223	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
224	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
226	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
227	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₂×C₅×Dic₃	—	2	2	no	—
230	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
231	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
232	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
233	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
234	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
236	C₄×C₅×D₃	—	2	2	no	—
237	C₄×C₅×D₃	—	2	8	no	—
238	C₄×C₅×D₃	—	2	4	no	—
239	C₄×C₅×D₃	—	2	8	no	—
240	C₄×C₅×D₃	—	2	4	no	—
241	C₄×C₅×D₃	—	2	2	no	—
242	C₄×C₅×D₃	—	2	2	no	—
243	C₄×C₅×D₃	#41	1	4	yes	—
244	C₅×Dic₆	—	2	4	no	—
245	C₅×Dic₆	—	2	8	no	—
246	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
247	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
248	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₃×#126	C₂²×C₅	1	4	yes	—
250	C₃×#125	C₂²×C₅	1	4	yes	complemented
251	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
253	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
254	C₃×#117	C₂²×C₅	1	1	yes	characteristic
255	#946	C₂²×C₅	1	2	yes	—
256	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
257	#944	C₂²×C₅	1	2	yes	complemented
258	#926	C₂²×C₅	1	1	yes	characteristic
259	#924	C₂²×C₅	1	2	yes	—
260	#898	C₂²×C₅	1	4	yes	—
261	#898	C₂²×C₅	1	4	yes	—
262	#898	C₂²×C₅	1	4	yes	—
263	#897	C₂²×C₅	1	2	yes	—
264	#896	C₂²×C₅	1	4	yes	—
265	#892	C₂²×C₅	1	2	yes	—
266	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
267	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
268	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
269	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
270	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
271	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
272	#890	C₂²×C₅	1	4	yes	complemented
273	#890	C₂²×C₅	1	4	yes	complemented
274	#890	C₂²×C₅	1	2	yes	complemented
275	#889	C₂²×C₅	1	4	yes	complemented
276	#889	C₂²×C₅	1	4	yes	complemented
277	#889	C₂²×C₅	1	4	yes	complemented
278	#889	C₂²×C₅	1	4	yes	complemented
279	#889	C₂²×C₅	1	4	yes	complemented
280	#888	C₂²×C₅	1	4	yes	complemented
281	#887	C₂²×C₅	1	4	yes	complemented
282	#887	C₂²×C₅	1	2	yes	complemented
283	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
284	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
285	#879	C₂²×C₅	1	4	yes	—
286	#879	C₂²×C₅	1	4	yes	—
287	#879	C₂²×C₅	1	4	yes	—
288	#878	C₂²×C₅	1	4	yes	—
289	#877	C₂²×C₅	1	2	yes	—
290	#876	C₂²×C₅	1	4	yes	—
291	#872	C₂²×C₅	1	1	yes	characteristic
292	#872	C₂²×C₅	1	1	yes	characteristic
293	C₄²×D₃	C₂²×C₅	1	4	yes	—
294	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
295	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
296	#870	C₂²×C₅	1	4	yes	complemented
297	#870	C₂²×C₅	1	1	yes	characteristic, complemented
298	#869	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
300	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
301	C₂⁴×C₅	—	3	1	no	—
302	C₂×C₅×Q₈	—	3	4	no	—
303	C₂×C₅×Q₈	—	3	2	no	—
304	C₂×C₅×Q₈	—	6	8	no	—
305	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	2	no	—
309	C₂²×C₄×C₅	—	3	2	no	—
310	C₂²×C₄×C₅	—	3	4	no	—
311	C₂²×C₄×C₅	—	3	4	no	—
312	C₂²×C₄×C₅	—	3	1	no	—
313	C₂²×C₄×C₅	—	3	1	no	—
314	C₂²×C₄×C₅	—	3	1	no	—
315	C₂²×C₄×C₅	—	6	4	no	—
316	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
317	C₅×C₄⋊C₄	—	3	2	no	—
318	C₅×C₄⋊C₄	—	3	2	no	—
319	C₅×C₄⋊C₄	—	3	2	no	—
320	C₅×C₄⋊C₄	—	3	4	no	—
321	C₅×C₄⋊C₄	—	3	2	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	4	no	—
326	C₅×C₄⋊C₄	—	3	4	no	—
327	C₅×C₄⋊C₄	—	3	4	no	—
328	C₅×C₄⋊C₄	—	3	4	no	—
329	C₅×C₄⋊C₄	—	3	4	no	—
330	C₅×C₄⋊C₄	—	3	4	no	—
331	C₅×C₄⋊C₄	—	3	4	no	—
332	C₅×C₄⋊C₄	—	3	4	no	—
333	C₅×C₄⋊C₄	—	3	4	no	—
334	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
335	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
336	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
337	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
338	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
339	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
340	C₅×C₂²⋊C₄	—	3	2	no	—
341	C₅×C₂²⋊C₄	—	3	4	no	—
342	C₅×C₂²⋊C₄	—	3	2	no	—
343	C₅×C₂²⋊C₄	—	3	2	no	—
344	C₅×C₂²⋊C₄	—	3	4	no	—
345	C₅×C₂²⋊C₄	—	3	4	no	—
346	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
347	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
348	C₄²×C₅	—	3	2	no	—
349	C₄²×C₅	—	3	1	no	—
350	C₄²×C₅	—	3	2	no	—
351	C₄²×C₅	—	3	1	no	—
352	C₄²×C₅	—	3	4	no	—
353	C₄²×C₅	—	3	4	no	—
354	C₄²×C₅	—	3	4	no	—
355	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
356	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
357	C₄²×C₅	C₂²×D₃	1	4	yes	—
358	#541	—	3	1	no	—
359	#541	—	3	4	no	—
360	#541	—	3	4	no	—
361	#541	—	3	1	no	—
362	#541	—	3	2	no	—
363	#541	—	3	2	no	—
364	#541	—	3	1	no	—
365	#541	C₅×D₃	1	1	yes	characteristic, direct product factor
366	C₂×C₄⋊Q₈	—	3	1	no	—
367	C₂×#126	—	3	4	no	—
368	C₂×#125	—	3	1	no	—
369	C₂×#125	—	3	4	no	—
370	C₂×C₂²⋊Q₈	—	3	2	no	—
371	C₂×C₄×Q₈	—	3	2	no	—
372	C₂×#117	—	3	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	2	no	—
375	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
376	C₂×C₅×D₃	—	2	1	no	—
377	C₂×C₅×D₃	—	2	2	no	—
378	C₂×C₅×D₃	—	4	4	no	—
379	C₂×C₅×D₃	C₂×#41	1	2	yes	—
380	C₂×C₅×D₃	2₋¹⁺⁴	1	4	yes	—
381	C₃×C₄×C₅	—	2	4	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	2	no	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	2	4	no	—
386	C₃×C₄×C₅	C₂×#41	1	2	yes	—
387	C₅×Dic₃	—	2	4	no	—
388	C₅×Dic₃	—	2	1	no	—
389	C₅×Dic₃	—	2	2	no	—
390	C₅×Dic₃	—	2	4	no	—
391	C₅×Dic₃	—	2	2	no	—
392	C₅×Dic₃	C₂×#41	1	2	yes	—
393	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
397	D₃×Q₈	—	2	8	no	—
398	C₂×C₄×D₃	—	2	4	no	—
399	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
400	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
401	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
402	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
403	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
407	C₂×Dic₆	C₂³×C₅	1	2	yes	—
408	C₂×Dic₆	C₂³×C₅	1	4	yes	—
409	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
410	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
411	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
412	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
413	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
414	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
415	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
416	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
417	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
418	C₃×C₄²	C₂³×C₅	1	4	yes	—
419	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
420	#217	C₂³×C₅	1	2	yes	—
421	#217	C₂³×C₅	1	4	yes	—
422	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
423	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
424	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
425	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
426	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
427	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
428	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
429	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
430	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
431	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
432	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
433	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
434	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
435	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
436	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
437	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
438	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
439	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
440	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
441	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
442	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
443	C₄×Dic₃	C₂³×C₅	1	2	yes	—
444	C₄×Dic₃	C₂³×C₅	1	4	yes	—
445	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
446	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
447	C₄×Dic₃	C₂³×C₅	1	2	yes	—
448	C₄×Dic₃	C₂³×C₅	1	4	yes	—
449	C₄×Dic₃	C₂³×C₅	1	4	yes	—
450	C₂³×C₅	—	3	1	no	—
451	C₂³×C₅	—	3	1	no	—
452	C₂³×C₅	—	6	2	no	—
453	C₂³×C₅	—	6	4	no	—
454	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
455	C₅×Q₈	—	2	4	no	—
456	C₅×Q₈	—	6	8	no	—
457	C₅×Q₈	—	6	4	no	—
458	C₂×C₄×C₅	—	2	2	no	—
459	C₂×C₄×C₅	—	3	1	no	—
460	C₂×C₄×C₅	—	3	4	no	—
461	C₂×C₄×C₅	—	3	2	no	—
462	C₂×C₄×C₅	—	3	2	no	—
463	C₂×C₄×C₅	—	3	4	no	—
464	C₂×C₄×C₅	—	3	4	no	—
465	C₂×C₄×C₅	—	3	1	no	—
466	C₂×C₄×C₅	—	6	2	no	—
467	C₂×C₄×C₅	—	6	4	no	—
468	C₂×C₄×C₅	—	6	4	no	—
469	C₂×C₄×C₅	—	6	8	no	—
470	C₂×C₄×C₅	—	6	2	no	—
471	C₂×C₄×C₅	—	6	8	no	—
472	C₂×C₄×C₅	—	6	2	no	—
473	C₂×C₄×C₅	—	6	2	no	—
474	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
475	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
476	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
477	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
478	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
480	C₂²×Q₈	—	3	2	no	—
481	C₂³×C₄	—	3	1	no	—
482	C₄⋊Q₈	—	3	2	no	—
483	C₄⋊Q₈	—	3	4	no	—
484	C₄⋊Q₈	—	3	1	no	—
485	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
486	#126	—	3	4	no	—
487	#126	—	3	4	no	—
488	#126	—	3	4	no	—
489	#126	—	3	4	no	—
490	#126	—	3	4	no	—
491	#126	—	3	4	no	—
492	#126	—	3	4	no	—
493	#126	C₂×C₅×D₃	1	4	yes	—
494	#125	—	3	4	no	—
495	#125	—	3	4	no	—
496	#125	—	3	4	no	—
497	#125	—	3	4	no	—
498	#125	—	3	4	no	—
499	#125	—	3	2	no	—
500	#125	—	3	4	no	—
501	#125	—	3	4	no	—
502	#125	—	3	1	no	—
503	#125	—	3	4	no	—
504	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	#125	C₂×C₅×D₃	1	4	yes	complemented
506	C₂²⋊Q₈	—	3	2	no	—
507	C₂²⋊Q₈	—	3	2	no	—
508	C₂²⋊Q₈	—	3	4	no	—
509	C₂²⋊Q₈	—	3	2	no	—
510	C₂²⋊Q₈	—	3	4	no	—
511	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	—
512	C₄×Q₈	—	3	2	no	—
513	C₄×Q₈	—	3	4	no	—
514	C₄×Q₈	—	3	2	no	—
515	C₄×Q₈	—	3	4	no	—
516	C₄×Q₈	—	3	2	no	—
517	C₄×Q₈	C₂×C₅×D₃	1	2	yes	complemented
518	#117	—	3	1	no	—
519	#117	—	3	2	no	—
520	#117	—	3	2	no	—
521	#117	—	3	1	no	—
522	#117	—	3	1	no	—
523	#117	C₂×C₅×D₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	—	3	2	no	—
525	C₂×C₄⋊C₄	—	3	2	no	—
526	C₂×C₄⋊C₄	—	3	4	no	—
527	C₂×C₄⋊C₄	—	3	4	no	—
528	C₂×C₄⋊C₄	—	3	4	no	—
529	C₂×C₄⋊C₄	—	3	4	no	—
530	C₂×C₂²⋊C₄	—	3	2	no	—
531	C₂×C₂²⋊C₄	—	3	4	no	—
532	C₂×C₄²	—	3	1	no	—
533	C₂×C₄²	—	3	1	no	—
534	C₂×C₄²	—	3	4	no	—
535	C₂×C₃×C₅	—	4	1	no	—
536	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
537	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
538	C₅×D₃	—	4	1	no	—
539	C₅×D₃	#541	1	4	yes	direct product factor
540	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
541	C₂²×D₃	—	2	2	no	—
542	C₂²×D₃	—	2	4	no	—
543	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
544	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
545	C₃×Q₈	—	2	4	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
548	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
549	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
550	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
551	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
553	C₂×Dic₃	—	2	2	no	—
554	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
555	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
556	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
557	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
558	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
559	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
560	C₄×D₃	—	2	2	no	—
561	C₄×D₃	—	2	8	no	—
562	C₄×D₃	—	2	4	no	—
563	C₄×D₃	—	2	8	no	—
564	C₄×D₃	—	2	4	no	—
565	C₄×D₃	—	2	2	no	—
566	C₄×D₃	—	2	2	no	—
567	C₄×D₃	C₅×#41	1	4	yes	—
568	Dic₆	—	2	4	no	—
569	Dic₆	—	2	8	no	—
570	C₂²×C₅	—	2	1	no	—
571	C₂²×C₅	—	2	2	no	—
572	C₂²×C₅	—	3	2	no	—
573	C₂²×C₅	—	3	4	no	—
574	C₂²×C₅	—	6	1	no	—
575	C₂²×C₅	—	6	2	no	—
576	C₂²×C₅	—	12	4	no	—
577	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
578	C₄×C₅	—	2	1	no	—
579	C₄×C₅	—	2	4	no	—
580	C₄×C₅	—	2	2	no	—
581	C₄×C₅	—	2	2	no	—
582	C₄×C₅	—	2	4	no	—
583	C₄×C₅	—	3	2	no	—
584	C₄×C₅	—	6	1	no	—
585	C₄×C₅	—	6	4	no	—
586	C₄×C₅	—	6	2	no	—
587	C₄×C₅	—	6	2	no	—
588	C₄×C₅	—	6	4	no	—
589	C₄×C₅	D₃×#41	1	2	yes	—
590	C₂⁴	—	3	1	no	—
591	C₂×Q₈	—	3	4	no	—
592	C₂×Q₈	—	3	2	no	—
593	C₂×Q₈	—	6	8	no	—
594	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
595	C₂²×C₄	—	3	1	no	—
596	C₂²×C₄	—	3	1	no	—
597	C₂²×C₄	—	3	2	no	—
598	C₂²×C₄	—	3	2	no	—
599	C₂²×C₄	—	3	4	no	—
600	C₂²×C₄	—	3	4	no	—
601	C₂²×C₄	—	3	1	no	—
602	C₂²×C₄	—	3	1	no	—
603	C₂²×C₄	—	3	1	no	—
604	C₂²×C₄	—	6	4	no	—
605	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
606	C₄⋊C₄	—	3	2	no	—
607	C₄⋊C₄	—	3	2	no	—
608	C₄⋊C₄	—	3	2	no	—
609	C₄⋊C₄	—	3	4	no	—
610	C₄⋊C₄	—	3	2	no	—
611	C₄⋊C₄	—	3	4	no	—
612	C₄⋊C₄	—	3	4	no	—
613	C₄⋊C₄	—	3	4	no	—
614	C₄⋊C₄	—	3	4	no	—
615	C₄⋊C₄	—	3	4	no	—
616	C₄⋊C₄	—	3	4	no	—
617	C₄⋊C₄	—	3	4	no	—
618	C₄⋊C₄	—	3	4	no	—
619	C₄⋊C₄	—	3	4	no	—
620	C₄⋊C₄	—	3	4	no	—
621	C₄⋊C₄	—	3	4	no	—
622	C₄⋊C₄	—	3	4	no	—
623	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
624	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
625	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
626	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
627	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
628	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
629	C₂²⋊C₄	—	3	2	no	—
630	C₂²⋊C₄	—	3	4	no	—
631	C₂²⋊C₄	—	3	2	no	—
632	C₂²⋊C₄	—	3	2	no	—
633	C₂²⋊C₄	—	3	4	no	—
634	C₂²⋊C₄	—	3	4	no	—
635	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
636	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
637	C₄²	—	3	2	no	—
638	C₄²	—	3	1	no	—
639	C₄²	—	3	2	no	—
640	C₄²	—	3	1	no	—
641	C₄²	—	3	4	no	—
642	C₄²	—	3	4	no	—
643	C₄²	—	3	4	no	—
644	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
645	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
646	C₄²	C₂²×C₅×D₃	1	4	yes	—
647	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
648	C₂²×C₃	—	2	1	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
651	C₂×D₃	—	2	1	no	—
652	C₂×D₃	—	2	2	no	—
653	C₂×D₃	—	4	4	no	—
654	C₂×D₃	C₂×C₅×#41	1	2	yes	—
655	C₂×D₃	C₅×2₋¹⁺⁴	1	4	yes	—
656	C₃×C₄	—	2	4	no	—
657	C₃×C₄	—	2	1	no	—
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	2	no	—
660	C₃×C₄	—	2	4	no	—
661	C₃×C₄	C₂×C₅×#41	1	2	yes	—
662	Dic₃	—	2	4	no	—
663	Dic₃	—	2	1	no	—
664	Dic₃	—	2	2	no	—
665	Dic₃	—	2	4	no	—
666	Dic₃	—	2	2	no	—
667	Dic₃	C₂×C₅×#41	1	2	yes	—
668	C₂×C₅	—	3	4	no	—
669	C₂×C₅	—	4	1	no	—
670	C₂×C₅	—	12	1	no	—
671	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
672	C₂×C₅	D₃×2₋¹⁺⁴	1	2	yes	—
673	C₂³	—	3	1	no	—
674	C₂³	—	3	1	no	—
675	C₂³	—	6	2	no	—
676	C₂³	—	6	4	no	—
677	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
678	Q₈	—	2	4	no	—
679	Q₈	—	6	8	no	—
680	Q₈	—	6	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	3	1	no	—
683	C₂×C₄	—	3	4	no	—
684	C₂×C₄	—	3	2	no	—
685	C₂×C₄	—	3	2	no	—
686	C₂×C₄	—	3	4	no	—
687	C₂×C₄	—	3	4	no	—
688	C₂×C₄	—	3	1	no	—
689	C₂×C₄	—	6	2	no	—
690	C₂×C₄	—	6	2	no	—
691	C₂×C₄	—	6	8	no	—
692	C₂×C₄	—	6	4	no	—
693	C₂×C₄	—	6	4	no	—
694	C₂×C₄	—	6	8	no	—
695	C₂×C₄	—	6	2	no	—
696	C₂×C₄	—	6	2	no	—
697	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
698	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
699	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
700	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
701	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
702	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
703	C₂×C₃	—	4	1	no	—
704	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
705	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
706	D₃	—	4	1	no	—
707	D₃	C₅×#541	1	4	yes	direct product factor
708	C₅	D₃×#541	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	3	2	no	—
712	C₂²	—	3	4	no	—
713	C₂²	—	6	1	no	—
714	C₂²	—	6	2	no	—
715	C₂²	—	12	4	no	—
716	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	4	no	—
722	C₄	—	3	2	no	—
723	C₄	—	6	1	no	—
724	C₄	—	6	4	no	—
725	C₄	—	6	2	no	—
726	C₄	—	6	2	no	—
727	C₄	—	6	4	no	—
728	C₄	C₅×D₃×#41	1	2	yes	—
729	C₃	C₂×C₅×#541	1	1	yes	characteristic, complemented, Sylow
730	C₂	—	3	4	no	—
731	C₂	—	4	1	no	—
732	C₂	—	12	1	no	—
733	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
734	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×#541	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂³×C₅×D₃	C₂³
hypercenter	C₅×#541	D₃
hypocenter	C₃	C₂×C₅×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#541

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#541	C₂	semidirect
2. C₅×#5731	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
5. C₅×#5701	C₂	semidirect
6. C₅×#5698	C₂	semidirect
7. C₅×#5696	C₂	semidirect
8. C₅×D₃×#125	C₂	semidirect
9. C₅×D₃×#125	C₂	semidirect
11. C₅×#5625	C₂	semidirect
12. C₅×#5583	C₂	semidirect
13. C₄×C₅×D₃×Q₈	C₂	semidirect
15. C₅×#5518	C₂	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₅×#125	C₂²	semidirect
22. C₃×C₅×#125	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
27. C₅×Q₈×Dic₃	C₂²	semidirect
28. C₅×#944	C₂²	semidirect
43. C₅×#890	C₂²	semidirect
44. C₅×#890	C₂²	semidirect
45. C₅×#890	C₂²	semidirect
46. C₅×#889	C₂²	semidirect
47. C₅×#889	C₂²	semidirect
48. C₅×#889	C₂²	semidirect
49. C₅×#889	C₂²	semidirect
50. C₅×#889	C₂²	semidirect
51. C₅×#888	C₂²	semidirect
52. C₅×#887	C₂²	semidirect
53. C₅×#887	C₂²	semidirect
67. C₅×#870	C₂²	semidirect
68. C₅×#870	C₂²	semidirect
69. C₅×#869	C₂²	semidirect
70. C₄×C₅×Dic₆	C₂²	semidirect
71. C₄×C₅×Dic₆	C₂²	semidirect
72. D₃×#541	C₅	direct (N × H)
80. C₅×#541	D₃	direct (N × H)
145. C₃×#541	C₂×C₅	semidirect
146. #5731	C₂×C₅	semidirect
147. D₃×C₄⋊Q₈	C₂×C₅	semidirect
149. #5701	C₂×C₅	semidirect
150. #5698	C₂×C₅	semidirect
151. #5696	C₂×C₅	semidirect
152. D₃×#125	C₂×C₅	semidirect
153. D₃×#125	C₂×C₅	semidirect
155. #5625	C₂×C₅	semidirect
156. #5583	C₂×C₅	semidirect
157. C₄×D₃×Q₈	C₂×C₅	semidirect
159. #5518	C₂×C₅	semidirect
165. C₅×C₄⋊Q₈	C₂×D₃	semidirect
184. C₅×#125	C₂×D₃	semidirect
185. C₅×#125	C₂×D₃	semidirect
197. C₄×C₅×Q₈	C₂×D₃	semidirect
248. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
250. C₃×#125	C₂²×C₅	semidirect
251. C₃×#125	C₂²×C₅	semidirect
253. C₃×C₄×Q₈	C₂²×C₅	semidirect
256. Q₈×Dic₃	C₂²×C₅	semidirect
257. #944	C₂²×C₅	semidirect
272. #890	C₂²×C₅	semidirect
273. #890	C₂²×C₅	semidirect
274. #890	C₂²×C₅	semidirect
275. #889	C₂²×C₅	semidirect
276. #889	C₂²×C₅	semidirect
277. #889	C₂²×C₅	semidirect
278. #889	C₂²×C₅	semidirect
279. #889	C₂²×C₅	semidirect
280. #888	C₂²×C₅	semidirect
281. #887	C₂²×C₅	semidirect
282. #887	C₂²×C₅	semidirect
296. #870	C₂²×C₅	semidirect
297. #870	C₂²×C₅	semidirect
298. #869	C₂²×C₅	semidirect
299. C₄×Dic₆	C₂²×C₅	semidirect
300. C₄×Dic₆	C₂²×C₅	semidirect
365. #541	C₅×D₃	direct (N × H)
485. C₄⋊Q₈	C₂×C₅×D₃	semidirect
504. #125	C₂×C₅×D₃	semidirect
505. #125	C₂×C₅×D₃	semidirect
517. C₄×Q₈	C₂×C₅×D₃	semidirect
539. C₅×D₃	#541	direct (N × H)
647. C₃×C₅	C₂×#541	semidirect
707. D₃	C₅×#541	direct (N × H)
708. C₅	D₃×#541	direct (N × H)
729. C₃	C₂×C₅×#541	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#541	2
C₅×#5731	2
C₅×D₃×C₄⋊Q₈	2
C₅×D₃×#126	2
C₅×#5701	2
C₅×#5698	2
C₅×#5696	2
C₅×D₃×#125	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5625	2
C₅×#5583	2
C₄×C₅×D₃×Q₈	2
C₅×D₃×#117	2
C₅×#5518	2
C₂×C₅×#541	3
D₃×#541	5

Subgroups — C5×D3×#541 #14481187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#541 #14481187