Subgroups — C₅×D₃×#537 #14480557

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 712 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×#5629	C₂	1	4	yes	maximal, complemented
5	C₅×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
6	C₅×#5608	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
8	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
9	C₅×#5597	C₂	1	4	yes	maximal, complemented
10	C₅×#5510	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#537	—	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	complemented
16	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
17	C₂×C₅×#237	C₂²	1	4	yes	complemented
18	C₂×C₅×#237	C₂²	1	2	yes	complemented
19	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
20	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
21	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
22	C₂×C₅×#235	C₂²	1	2	yes	complemented
23	C₂×C₅×#235	C₂²	1	4	yes	complemented
24	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
25	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
26	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃×C₅×#121	C₂²	1	4	yes	complemented
29	C₃×C₅×#121	C₂²	1	4	yes	complemented
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₅×#946	C₂²	1	4	yes	complemented
32	C₅×#939	C₂²	1	8	yes	complemented
33	C₅×#939	C₂²	1	8	yes	complemented
34	C₅×#938	C₂²	1	4	yes	complemented
35	C₅×#938	C₂²	1	4	yes	complemented
36	C₅×#930	C₂²	1	4	yes	complemented
37	C₅×#930	C₂²	1	4	yes	complemented
38	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₅×#924	C₂²	1	4	yes	complemented
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
41	C₅×#897	C₂²	1	4	yes	complemented
42	C₅×#896	C₂²	1	8	yes	complemented
43	C₅×#895	C₂²	1	4	yes	complemented
44	C₅×#895	C₂²	1	4	yes	complemented
45	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
46	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
47	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
48	C₅×#884	C₂²	1	8	yes	complemented
49	C₅×#884	C₂²	1	8	yes	complemented
50	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	—
51	C₅×#878	C₂²	1	8	yes	complemented
52	D₃×#537	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	4	no	—
56	C₅×#537	—	3	4	no	—
57	C₅×#537	—	3	4	no	—
58	C₅×#537	—	3	1	no	—
59	C₅×#537	D₃	1	1	yes	characteristic, direct product factor
60	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
61	C₂×C₅×#121	—	3	4	no	—
62	C₂×C₅×#121	—	3	4	no	—
63	C₂²×C₅×C₄⋊C₄	—	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×D₃×D₄	—	4	8	no	—
88	C₅×#235	—	2	8	no	—
89	C₅×#235	—	2	16	no	—
90	C₂×C₅×D₁₂	C₂³	1	4	yes	—
91	C₂×C₅×D₁₂	C₂³	1	2	yes	—
92	C₂×C₅×D₁₂	C₂³	1	4	yes	—
93	C₂×C₄×C₅×D₃	—	2	16	no	—
94	C₂×C₄×C₅×D₃	—	4	4	no	—
95	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
96	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
97	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
98	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
99	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
100	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
101	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
102	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
103	C₂×C₅×Dic₆	C₂³	1	4	yes	—
104	C₂×C₅×Dic₆	C₂³	1	2	yes	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
106	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₅×#217	C₂³	1	8	yes	—
109	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
110	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
111	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
112	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
113	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
114	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
115	C₂×D₃×#41	C₂×C₅	1	2	yes	complemented
116	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
117	#5833	C₂×C₅	1	2	yes	complemented
118	#5629	C₂×C₅	1	4	yes	complemented
119	D₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
120	#5608	C₂×C₅	1	4	yes	complemented
121	D₃×#121	C₂×C₅	1	4	yes	complemented
122	D₃×#121	C₂×C₅	1	4	yes	complemented
123	#5597	C₂×C₅	1	4	yes	complemented
124	#5510	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
126	C₂×C₅×#41	—	3	2	no	—
127	C₂×C₅×#41	—	3	4	no	—
128	C₂×C₅×#41	—	3	2	no	—
129	C₂×C₅×#41	—	3	4	no	—
130	C₂×C₅×#41	—	3	2	no	—
131	C₂×C₅×#41	—	6	16	no	—
132	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
133	C₂²×C₅×Q₈	—	3	2	no	—
134	C₂²×C₅×D₄	—	3	2	no	—
135	C₂²×C₅×D₄	—	3	4	no	—
136	C₂²×C₅×D₄	—	3	4	no	—
137	C₂³×C₄×C₅	—	3	1	no	—
138	C₂³×C₄×C₅	—	3	4	no	—
139	C₂³×C₄×C₅	—	3	2	no	—
140	C₅×C₂²⋊Q₈	—	3	4	no	—
141	C₅×C₂²⋊Q₈	—	3	4	no	—
142	C₅×C₂²⋊Q₈	—	3	8	no	—
143	C₅×C₂²⋊Q₈	—	3	4	no	—
144	C₅×C₂²⋊Q₈	—	3	8	no	—
145	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
146	C₅×#121	—	3	4	no	—
147	C₅×#121	—	3	4	no	—
148	C₅×#121	—	3	8	no	—
149	C₅×#121	—	3	8	no	—
150	C₅×#121	—	3	4	no	—
151	C₅×#121	—	3	4	no	—
152	C₅×#121	—	3	4	no	—
153	C₅×#121	—	3	4	no	—
154	C₅×#121	—	3	8	no	—
155	C₅×#121	—	3	8	no	—
156	C₅×#121	C₂×D₃	1	4	yes	complemented
157	C₅×#121	C₂×D₃	1	4	yes	complemented
158	C₂×C₅×C₄⋊C₄	—	3	2	no	—
159	C₂×C₅×C₄⋊C₄	—	3	1	no	—
160	C₂×C₅×C₄⋊C₄	—	3	4	no	—
161	C₂×C₅×C₄⋊C₄	—	3	4	no	—
162	C₂×C₅×C₄⋊C₄	—	3	4	no	—
163	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
165	C₂×#537	—	3	1	no	Sylow
166	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
167	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
168	C₂²×C₅×D₃	—	2	2	no	—
169	C₂²×C₅×D₃	—	2	2	no	—
170	C₂²×C₅×D₃	—	2	8	no	—
171	C₂²×C₅×D₃	—	2	8	no	—
172	C₂²×C₅×D₃	—	2	8	no	—
173	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
174	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
175	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
176	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
177	C₃×C₅×Q₈	—	2	4	no	—
178	C₃×C₅×D₄	—	2	8	no	—
179	C₃×C₅×D₄	—	2	4	no	—
180	C₃×C₅×D₄	—	4	4	no	—
181	C₂×C₃×C₄×C₅	—	2	8	no	—
182	C₂×C₃×C₄×C₅	—	4	2	no	—
183	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
184	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
185	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
186	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
187	C₅×#67	—	2	8	no	—
188	C₅×#67	—	2	8	no	—
189	C₅×#67	—	2	8	no	—
190	C₅×#67	—	4	8	no	—
191	C₂×C₅×Dic₃	—	2	8	no	—
192	C₂×C₅×Dic₃	—	4	2	no	—
193	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	complemented
194	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
195	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
196	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
197	C₅×D₁₂	—	2	8	no	—
198	C₅×D₁₂	—	2	4	no	—
199	C₅×D₁₂	—	4	4	no	—
200	C₄×C₅×D₃	—	2	8	no	—
201	C₄×C₅×D₃	—	2	8	no	—
202	C₄×C₅×D₃	—	2	8	no	—
203	C₄×C₅×D₃	—	2	8	no	—
204	C₄×C₅×D₃	—	4	4	no	—
205	C₄×C₅×D₃	C₂×D₄	1	8	yes	—
206	C₄×C₅×D₃	C₂×D₄	1	8	yes	complemented
207	C₅×Dic₆	—	2	4	no	—
208	C₅×Dic₆	—	2	8	no	—
209	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
210	D₃×#41	—	2	16	no	—
211	C₂×#239	C₂²×C₅	1	2	yes	complemented
212	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
213	C₂×#237	C₂²×C₅	1	4	yes	complemented
214	C₂×#237	C₂²×C₅	1	2	yes	complemented
215	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
216	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
217	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
218	C₂×#235	C₂²×C₅	1	2	yes	complemented
219	C₂×#235	C₂²×C₅	1	4	yes	complemented
220	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
221	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
222	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
223	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
224	C₃×#121	C₂²×C₅	1	4	yes	complemented
225	C₃×#121	C₂²×C₅	1	4	yes	complemented
226	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
227	#946	C₂²×C₅	1	4	yes	complemented
228	#939	C₂²×C₅	1	8	yes	complemented
229	#939	C₂²×C₅	1	8	yes	complemented
230	#938	C₂²×C₅	1	4	yes	complemented
231	#938	C₂²×C₅	1	4	yes	complemented
232	#930	C₂²×C₅	1	4	yes	complemented
233	#930	C₂²×C₅	1	4	yes	complemented
234	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
235	#924	C₂²×C₅	1	4	yes	complemented
236	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
237	#897	C₂²×C₅	1	4	yes	complemented
238	#896	C₂²×C₅	1	8	yes	complemented
239	#895	C₂²×C₅	1	4	yes	complemented
240	#895	C₂²×C₅	1	4	yes	complemented
241	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
242	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
243	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
244	#884	C₂²×C₅	1	8	yes	complemented
245	#884	C₂²×C₅	1	8	yes	complemented
246	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
247	#878	C₂²×C₅	1	8	yes	complemented
248	C₂⁴×C₅	—	3	1	no	—
249	C₂⁴×C₅	—	3	4	no	—
250	C₅×#41	—	2	8	no	—
251	C₅×#41	—	6	16	no	—
252	C₅×#41	—	6	16	no	—
253	C₅×#41	—	6	8	no	—
254	C₅×#41	—	6	8	no	—
255	C₅×#41	—	6	8	no	—
256	C₂×C₅×Q₈	—	3	4	no	—
257	C₂×C₅×Q₈	—	3	2	no	—
258	C₂×C₅×Q₈	—	6	8	no	—
259	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
260	C₂×C₅×D₄	—	3	4	no	—
261	C₂×C₅×D₄	—	3	4	no	—
262	C₂×C₅×D₄	—	3	4	no	—
263	C₂×C₅×D₄	—	3	8	no	—
264	C₂×C₅×D₄	—	3	4	no	—
265	C₂×C₅×D₄	—	3	2	no	—
266	C₂×C₅×D₄	—	3	4	no	—
267	C₂×C₅×D₄	—	6	8	no	—
268	C₂×C₅×D₄	—	6	16	no	—
269	C₂×C₅×D₄	—	12	8	no	—
270	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
271	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
272	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	3	8	no	—
275	C₂²×C₄×C₅	—	3	2	no	—
276	C₂²×C₄×C₅	—	3	2	no	—
277	C₂²×C₄×C₅	—	3	4	no	—
278	C₂²×C₄×C₅	—	3	2	no	—
279	C₂²×C₄×C₅	—	3	4	no	—
280	C₂²×C₄×C₅	—	3	4	no	—
281	C₂²×C₄×C₅	—	3	4	no	—
282	C₂²×C₄×C₅	—	3	4	no	—
283	C₂²×C₄×C₅	—	3	4	no	—
284	C₂²×C₄×C₅	—	6	16	no	—
285	C₂²×C₄×C₅	—	12	4	no	—
286	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
287	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
288	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
289	C₅×C₄⋊C₄	—	3	8	no	—
290	C₅×C₄⋊C₄	—	3	4	no	—
291	C₅×C₄⋊C₄	—	3	8	no	—
292	C₅×C₄⋊C₄	—	3	4	no	—
293	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
294	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
295	C₅×C₂²⋊C₄	—	3	8	no	—
296	C₅×C₂²⋊C₄	—	3	8	no	—
297	C₅×C₂²⋊C₄	—	3	8	no	—
298	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
299	C₂²×#41	—	3	2	no	—
300	#537	—	3	2	no	—
301	#537	—	3	4	no	—
302	#537	—	3	4	no	—
303	#537	—	3	4	no	—
304	#537	—	3	1	no	—
305	#537	C₅×D₃	1	1	yes	characteristic, direct product factor
306	C₂×C₂²⋊Q₈	—	3	4	no	—
307	C₂×#121	—	3	4	no	—
308	C₂×#121	—	3	4	no	—
309	C₂²×C₄⋊C₄	—	3	1	no	—
310	C₂²×C₃×C₅	—	2	1	no	—
311	C₂²×C₃×C₅	—	2	1	no	—
312	C₂²×C₃×C₅	—	2	4	no	—
313	C₂²×C₃×C₅	—	2	4	no	—
314	C₂²×C₃×C₅	—	2	4	no	—
315	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
316	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
317	C₂×C₅×D₃	—	2	1	no	—
318	C₂×C₅×D₃	—	2	1	no	—
319	C₂×C₅×D₃	—	2	8	no	—
320	C₂×C₅×D₃	—	2	4	no	—
321	C₂×C₅×D₃	—	2	4	no	—
322	C₂×C₅×D₃	—	2	4	no	—
323	C₂×C₅×D₃	—	4	16	no	—
324	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
325	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
326	C₂×C₅×D₃	H(5,𝔽₂)	1	2	yes	—
327	C₂×C₅×D₃	2₋¹⁺⁴	1	2	yes	—
328	C₃×C₄×C₅	—	2	4	no	—
329	C₃×C₄×C₅	—	2	4	no	—
330	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
331	C₅×Dic₃	—	2	4	no	—
332	C₅×Dic₃	—	2	4	no	—
333	C₅×Dic₃	C₂²×D₄	1	4	yes	—
334	C₂³×D₃	C₂³×C₅	1	4	yes	—
335	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
336	C₃×#41	—	2	8	no	—
337	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
338	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
339	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
340	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
341	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
342	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
343	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂×#67	C₂³×C₅	1	4	yes	—
345	C₂×#67	C₂³×C₅	1	4	yes	—
346	C₂×#67	C₂³×C₅	1	4	yes	—
347	C₂×#67	C₂³×C₅	1	8	yes	—
348	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
349	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
350	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
351	#239	—	2	8	no	—
352	D₃×Q₈	—	2	8	no	—
353	#237	—	2	16	no	—
354	#237	—	2	8	no	—
355	D₃×D₄	—	2	16	no	—
356	D₃×D₄	—	2	8	no	—
357	D₃×D₄	—	4	8	no	—
358	#235	—	2	8	no	—
359	#235	—	2	16	no	—
360	C₂×D₁₂	C₂³×C₅	1	4	yes	—
361	C₂×D₁₂	C₂³×C₅	1	2	yes	—
362	C₂×D₁₂	C₂³×C₅	1	4	yes	—
363	C₂×C₄×D₃	—	2	16	no	—
364	C₂×C₄×D₃	—	4	4	no	—
365	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
366	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
367	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
368	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
369	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
370	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
371	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
372	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
373	C₂×Dic₆	C₂³×C₅	1	4	yes	—
374	C₂×Dic₆	C₂³×C₅	1	2	yes	—
375	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
376	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
377	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
378	#217	C₂³×C₅	1	8	yes	—
379	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
380	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
381	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
382	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
383	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
384	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
385	C₂³×C₅	—	3	1	no	—
386	C₂³×C₅	—	3	4	no	—
387	C₂³×C₅	—	3	1	no	—
388	C₂³×C₅	—	3	4	no	—
389	C₂³×C₅	—	6	2	no	—
390	C₂³×C₅	—	6	2	no	—
391	C₂³×C₅	—	6	8	no	—
392	C₂³×C₅	—	6	8	no	—
393	C₂³×C₅	—	6	8	no	—
394	C₂³×C₅	C₂³×D₃	1	4	yes	—
395	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
396	C₅×Q₈	—	2	4	no	—
397	C₅×Q₈	—	6	8	no	—
398	C₅×Q₈	—	6	4	no	—
399	C₅×D₄	—	2	8	no	—
400	C₅×D₄	—	2	4	no	—
401	C₅×D₄	—	4	4	no	—
402	C₅×D₄	—	6	8	no	—
403	C₅×D₄	—	6	8	no	—
404	C₅×D₄	—	6	8	no	—
405	C₅×D₄	—	6	8	no	—
406	C₅×D₄	—	6	4	no	—
407	C₅×D₄	—	12	4	no	—
408	C₅×D₄	—	12	8	no	—
409	C₂×C₄×C₅	—	2	8	no	—
410	C₂×C₄×C₅	—	3	4	no	—
411	C₂×C₄×C₅	—	3	2	no	—
412	C₂×C₄×C₅	—	3	8	no	—
413	C₂×C₄×C₅	—	3	8	no	—
414	C₂×C₄×C₅	—	3	4	no	—
415	C₂×C₄×C₅	—	3	4	no	—
416	C₂×C₄×C₅	—	4	2	no	—
417	C₂×C₄×C₅	—	6	8	no	—
418	C₂×C₄×C₅	—	6	8	no	—
419	C₂×C₄×C₅	—	6	8	no	—
420	C₂×C₄×C₅	—	6	8	no	—
421	C₂×C₄×C₅	—	6	8	no	—
422	C₂×C₄×C₅	—	12	4	no	—
423	C₂×C₄×C₅	—	12	2	no	—
424	C₂×C₄×C₅	D₃×D₄	1	4	yes	complemented
425	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
426	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
427	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
428	C₂×#41	—	3	2	no	—
429	C₂×#41	—	3	4	no	—
430	C₂×#41	—	3	2	no	—
431	C₂×#41	—	3	4	no	—
432	C₂×#41	—	3	2	no	—
433	C₂×#41	—	6	16	no	—
434	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
435	C₂²×Q₈	—	3	2	no	—
436	C₂²×D₄	—	3	2	no	—
437	C₂²×D₄	—	3	4	no	—
438	C₂²×D₄	—	3	4	no	—
439	C₂³×C₄	—	3	1	no	—
440	C₂³×C₄	—	3	4	no	—
441	C₂³×C₄	—	3	2	no	—
442	C₂²⋊Q₈	—	3	4	no	—
443	C₂²⋊Q₈	—	3	4	no	—
444	C₂²⋊Q₈	—	3	8	no	—
445	C₂²⋊Q₈	—	3	4	no	—
446	C₂²⋊Q₈	—	3	8	no	—
447	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
448	#121	—	3	4	no	—
449	#121	—	3	4	no	—
450	#121	—	3	8	no	—
451	#121	—	3	8	no	—
452	#121	—	3	4	no	—
453	#121	—	3	4	no	—
454	#121	—	3	4	no	—
455	#121	—	3	4	no	—
456	#121	—	3	8	no	—
457	#121	—	3	8	no	—
458	#121	C₂×C₅×D₃	1	4	yes	complemented
459	#121	C₂×C₅×D₃	1	4	yes	complemented
460	C₂×C₄⋊C₄	—	3	2	no	—
461	C₂×C₄⋊C₄	—	3	1	no	—
462	C₂×C₄⋊C₄	—	3	4	no	—
463	C₂×C₄⋊C₄	—	3	4	no	—
464	C₂×C₄⋊C₄	—	3	4	no	—
465	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
466	C₂×C₂²⋊C₄	—	3	8	no	—
467	C₂×C₃×C₅	—	2	2	no	—
468	C₂×C₃×C₅	—	4	4	no	—
469	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
470	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₅×D₃	—	2	2	no	—
473	C₅×D₃	—	4	4	no	—
474	C₅×D₃	#537	1	4	yes	direct product factor
475	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
476	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
477	C₂²×D₃	—	2	2	no	—
478	C₂²×D₃	—	2	2	no	—
479	C₂²×D₃	—	2	8	no	—
480	C₂²×D₃	—	2	8	no	—
481	C₂²×D₃	—	2	8	no	—
482	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
483	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
484	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
485	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
486	C₃×Q₈	—	2	4	no	—
487	C₃×D₄	—	2	8	no	—
488	C₃×D₄	—	2	4	no	—
489	C₃×D₄	—	4	4	no	—
490	C₂×C₃×C₄	—	2	8	no	—
491	C₂×C₃×C₄	—	4	2	no	—
492	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
493	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
494	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
495	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
496	#67	—	2	8	no	—
497	#67	—	2	8	no	—
498	#67	—	2	8	no	—
499	#67	—	4	8	no	—
500	C₂×Dic₃	—	2	8	no	—
501	C₂×Dic₃	—	4	2	no	—
502	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	complemented
503	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
504	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
505	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
506	D₁₂	—	2	8	no	—
507	D₁₂	—	2	4	no	—
508	D₁₂	—	4	4	no	—
509	C₄×D₃	—	2	8	no	—
510	C₄×D₃	—	2	8	no	—
511	C₄×D₃	—	2	8	no	—
512	C₄×D₃	—	2	8	no	—
513	C₄×D₃	—	4	4	no	—
514	C₄×D₃	C₂×C₅×D₄	1	8	yes	—
515	C₄×D₃	C₂×C₅×D₄	1	8	yes	complemented
516	Dic₆	—	2	4	no	—
517	Dic₆	—	2	8	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	4	no	—
521	C₂²×C₅	—	2	4	no	—
522	C₂²×C₅	—	2	4	no	—
523	C₂²×C₅	—	3	2	no	—
524	C₂²×C₅	—	3	2	no	—
525	C₂²×C₅	—	3	2	no	—
526	C₂²×C₅	—	3	2	no	—
527	C₂²×C₅	—	6	8	no	—
528	C₂²×C₅	—	6	1	no	—
529	C₂²×C₅	—	6	1	no	—
530	C₂²×C₅	—	6	4	no	—
531	C₂²×C₅	—	6	4	no	—
532	C₂²×C₅	—	6	4	no	—
533	C₂²×C₅	—	12	16	no	—
534	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
535	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
536	C₄×C₅	—	2	4	no	—
537	C₄×C₅	—	2	4	no	—
538	C₄×C₅	—	3	4	no	—
539	C₄×C₅	—	6	4	no	—
540	C₄×C₅	—	6	4	no	—
541	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
542	C₂⁴	—	3	1	no	—
543	C₂⁴	—	3	4	no	—
544	#41	—	2	8	no	—
545	#41	—	6	16	no	—
546	#41	—	6	16	no	—
547	#41	—	6	8	no	—
548	#41	—	6	8	no	—
549	#41	—	6	8	no	—
550	C₂×Q₈	—	3	4	no	—
551	C₂×Q₈	—	3	2	no	—
552	C₂×Q₈	—	6	8	no	—
553	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
554	C₂×D₄	—	3	4	no	—
555	C₂×D₄	—	3	4	no	—
556	C₂×D₄	—	3	4	no	—
557	C₂×D₄	—	3	8	no	—
558	C₂×D₄	—	3	4	no	—
559	C₂×D₄	—	3	2	no	—
560	C₂×D₄	—	3	4	no	—
561	C₂×D₄	—	6	8	no	—
562	C₂×D₄	—	6	16	no	—
563	C₂×D₄	—	12	8	no	—
564	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
565	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
566	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
567	C₂²×C₄	—	3	1	no	—
568	C₂²×C₄	—	3	8	no	—
569	C₂²×C₄	—	3	2	no	—
570	C₂²×C₄	—	3	2	no	—
571	C₂²×C₄	—	3	4	no	—
572	C₂²×C₄	—	3	2	no	—
573	C₂²×C₄	—	3	4	no	—
574	C₂²×C₄	—	3	4	no	—
575	C₂²×C₄	—	3	4	no	—
576	C₂²×C₄	—	3	4	no	—
577	C₂²×C₄	—	3	4	no	—
578	C₂²×C₄	—	6	16	no	—
579	C₂²×C₄	—	12	4	no	—
580	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
581	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
582	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
583	C₄⋊C₄	—	3	8	no	—
584	C₄⋊C₄	—	3	4	no	—
585	C₄⋊C₄	—	3	8	no	—
586	C₄⋊C₄	—	3	4	no	—
587	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
588	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
589	C₂²⋊C₄	—	3	8	no	—
590	C₂²⋊C₄	—	3	8	no	—
591	C₂²⋊C₄	—	3	8	no	—
592	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
593	C₃×C₅	C₂×#537	1	1	yes	characteristic, complemented, Hall
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	1	no	—
596	C₂²×C₃	—	2	4	no	—
597	C₂²×C₃	—	2	4	no	—
598	C₂²×C₃	—	2	4	no	—
599	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
600	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
601	C₂×D₃	—	2	1	no	—
602	C₂×D₃	—	2	1	no	—
603	C₂×D₃	—	2	8	no	—
604	C₂×D₃	—	2	4	no	—
605	C₂×D₃	—	2	4	no	—
606	C₂×D₃	—	2	4	no	—
607	C₂×D₃	—	4	16	no	—
608	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
609	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
610	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
611	C₂×D₃	C₅×2₋¹⁺⁴	1	2	yes	—
612	C₃×C₄	—	2	4	no	—
613	C₃×C₄	—	2	4	no	—
614	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
615	Dic₃	—	2	4	no	—
616	Dic₃	—	2	4	no	—
617	Dic₃	C₂²×C₅×D₄	1	4	yes	—
618	C₂×C₅	—	2	2	no	—
619	C₂×C₅	—	3	4	no	—
620	C₂×C₅	—	4	4	no	—
621	C₂×C₅	—	6	2	no	—
622	C₂×C₅	—	12	4	no	—
623	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
624	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂×C₅	D₃×2₋¹⁺⁴	1	1	yes	characteristic
626	C₂³	—	3	1	no	—
627	C₂³	—	3	4	no	—
628	C₂³	—	3	1	no	—
629	C₂³	—	3	4	no	—
630	C₂³	—	6	2	no	—
631	C₂³	—	6	2	no	—
632	C₂³	—	6	8	no	—
633	C₂³	—	6	8	no	—
634	C₂³	—	6	8	no	—
635	C₂³	C₂³×C₅×D₃	1	4	yes	—
636	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
637	Q₈	—	2	4	no	—
638	Q₈	—	6	8	no	—
639	Q₈	—	6	4	no	—
640	D₄	—	2	8	no	—
641	D₄	—	2	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	6	8	no	—
644	D₄	—	6	8	no	—
645	D₄	—	6	8	no	—
646	D₄	—	6	8	no	—
647	D₄	—	6	4	no	—
648	D₄	—	12	4	no	—
649	D₄	—	12	8	no	—
650	C₂×C₄	—	2	8	no	—
651	C₂×C₄	—	3	4	no	—
652	C₂×C₄	—	3	2	no	—
653	C₂×C₄	—	3	8	no	—
654	C₂×C₄	—	3	8	no	—
655	C₂×C₄	—	3	4	no	—
656	C₂×C₄	—	3	4	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	6	8	no	—
659	C₂×C₄	—	6	8	no	—
660	C₂×C₄	—	6	8	no	—
661	C₂×C₄	—	6	8	no	—
662	C₂×C₄	—	6	8	no	—
663	C₂×C₄	—	12	4	no	—
664	C₂×C₄	—	12	2	no	—
665	C₂×C₄	C₅×D₃×D₄	1	4	yes	complemented
666	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
667	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
668	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
669	C₂×C₃	—	2	2	no	—
670	C₂×C₃	—	4	4	no	—
671	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
672	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
674	D₃	—	2	2	no	—
675	D₃	—	4	4	no	—
676	D₃	C₅×#537	1	4	yes	direct product factor
677	C₅	D₃×#537	1	1	yes	characteristic, direct product factor, Sylow
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	3	2	no	—
684	C₂²	—	3	2	no	—
685	C₂²	—	3	2	no	—
686	C₂²	—	3	2	no	—
687	C₂²	—	6	8	no	—
688	C₂²	—	6	1	no	—
689	C₂²	—	6	1	no	—
690	C₂²	—	6	4	no	—
691	C₂²	—	6	4	no	—
692	C₂²	—	6	4	no	—
693	C₂²	—	12	16	no	—
694	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
695	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
696	C₄	—	2	4	no	—
697	C₄	—	2	4	no	—
698	C₄	—	3	4	no	—
699	C₄	—	6	4	no	—
700	C₄	—	6	4	no	—
701	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
702	C₃	C₂×C₅×#537	1	1	yes	characteristic, complemented, Sylow
703	C₂	—	2	2	no	—
704	C₂	—	3	4	no	—
705	C₂	—	4	4	no	—
706	C₂	—	6	2	no	—
707	C₂	—	12	4	no	—
708	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
709	C₂	C₅×D₃×H(5,𝔽₂)	1	1	yes	characteristic
710	C₂	C₅×D₃×2₋¹⁺⁴	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	C₂×C₅×#537
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×#5629	C₂	semidirect
5. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
6. C₅×#5608	C₂	semidirect
7. C₅×D₃×#121	C₂	semidirect
8. C₅×D₃×#121	C₂	semidirect
9. C₅×#5597	C₂	semidirect
10. C₅×#5510	C₂	semidirect
11. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
13. C₂×C₃×C₅×#41	C₂²	semidirect
15. C₂×C₅×#239	C₂²	semidirect
17. C₂×C₅×#237	C₂²	semidirect
18. C₂×C₅×#237	C₂²	semidirect
22. C₂×C₅×#235	C₂²	semidirect
23. C₂×C₅×#235	C₂²	semidirect
27. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₃×C₅×#121	C₂²	semidirect
29. C₃×C₅×#121	C₂²	semidirect
30. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₅×#946	C₂²	semidirect
32. C₅×#939	C₂²	semidirect
33. C₅×#939	C₂²	semidirect
34. C₅×#938	C₂²	semidirect
35. C₅×#938	C₂²	semidirect
36. C₅×#930	C₂²	semidirect
37. C₅×#930	C₂²	semidirect
38. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
39. C₅×#924	C₂²	semidirect
40. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
41. C₅×#897	C₂²	semidirect
42. C₅×#896	C₂²	semidirect
43. C₅×#895	C₂²	semidirect
44. C₅×#895	C₂²	semidirect
47. C₅×D₃×C₄⋊C₄	C₂²	semidirect
48. C₅×#884	C₂²	semidirect
49. C₅×#884	C₂²	semidirect
51. C₅×#878	C₂²	semidirect
52. D₃×#537	C₅	direct (N × H)
59. C₅×#537	D₃	direct (N × H)
95. C₂×C₄×C₅×D₃	D₄	semidirect
115. C₂×D₃×#41	C₂×C₅	semidirect
116. C₃×#537	C₂×C₅	semidirect
117. #5833	C₂×C₅	semidirect
118. #5629	C₂×C₅	semidirect
119. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
120. #5608	C₂×C₅	semidirect
121. D₃×#121	C₂×C₅	semidirect
122. D₃×#121	C₂×C₅	semidirect
123. #5597	C₂×C₅	semidirect
124. #5510	C₂×C₅	semidirect
125. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
132. C₂×C₅×#41	C₂×D₃	semidirect
145. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
156. C₅×#121	C₂×D₃	semidirect
157. C₅×#121	C₂×D₃	semidirect
163. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
183. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
193. C₂×C₅×Dic₃	C₂×D₄	semidirect
206. C₄×C₅×D₃	C₂×D₄	semidirect
209. C₂×C₃×#41	C₂²×C₅	semidirect
211. C₂×#239	C₂²×C₅	semidirect
213. C₂×#237	C₂²×C₅	semidirect
214. C₂×#237	C₂²×C₅	semidirect
218. C₂×#235	C₂²×C₅	semidirect
219. C₂×#235	C₂²×C₅	semidirect
223. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
224. C₃×#121	C₂²×C₅	semidirect
225. C₃×#121	C₂²×C₅	semidirect
226. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
227. #946	C₂²×C₅	semidirect
228. #939	C₂²×C₅	semidirect
229. #939	C₂²×C₅	semidirect
230. #938	C₂²×C₅	semidirect
231. #938	C₂²×C₅	semidirect
232. #930	C₂²×C₅	semidirect
233. #930	C₂²×C₅	semidirect
234. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
235. #924	C₂²×C₅	semidirect
236. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
237. #897	C₂²×C₅	semidirect
238. #896	C₂²×C₅	semidirect
239. #895	C₂²×C₅	semidirect
240. #895	C₂²×C₅	semidirect
243. D₃×C₄⋊C₄	C₂²×C₅	semidirect
244. #884	C₂²×C₅	semidirect
245. #884	C₂²×C₅	semidirect
247. #878	C₂²×C₅	semidirect
305. #537	C₅×D₃	direct (N × H)
365. C₂×C₄×D₃	C₅×D₄	semidirect
424. C₂×C₄×C₅	D₃×D₄	semidirect
434. C₂×#41	C₂×C₅×D₃	semidirect
447. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
458. #121	C₂×C₅×D₃	semidirect
459. #121	C₂×C₅×D₃	semidirect
465. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
474. C₅×D₃	#537	direct (N × H)
492. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
502. C₂×Dic₃	C₂×C₅×D₄	semidirect
515. C₄×D₃	C₂×C₅×D₄	semidirect
593. C₃×C₅	C₂×#537	semidirect
665. C₂×C₄	C₅×D₃×D₄	semidirect
676. D₃	C₅×#537	direct (N × H)
677. C₅	D₃×#537	direct (N × H)
702. C₃	C₂×C₅×#537	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×#5629	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5608	2
C₅×D₃×#121	2
C₅×#5597	2
C₅×#5510	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#537	3
D₃×#537	5

Subgroups — C5×D3×#537 #14480557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#537 #14480557