Subgroups — C₅×#75300 #14324441

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4989	C₂	1	1	yes	maximal, characteristic
4	C₅×#4980	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₅×#4928	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4668	C₂	1	1	yes	maximal, characteristic
9	C₅×#4667	C₂	1	1	yes	maximal, characteristic
10	C₅×#4666	C₂	1	1	yes	maximal, characteristic
11	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic
12	C₅×#4654	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4653	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4646	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4646	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2329	—	3	1	no	maximal, Hall
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₅×#897	C₄	1	8	yes	complemented
39	C₃×C₅×#95	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	1	yes	characteristic
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#95	C₂²	1	1	yes	characteristic
43	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
44	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
45	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
46	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
47	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
48	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	#75300	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
55	C₅×#391	—	3	1	no	—
56	C₅×#391	—	3	1	no	—
57	C₅×#389	—	3	1	no	—
58	C₅×#389	—	3	1	no	—
59	C₅×#387	—	3	1	no	—
60	C₅×#387	—	3	1	no	—
61	C₅×#387	—	3	1	no	—
62	C₅×#387	D₃	1	1	yes	characteristic, complemented
63	C₅×#385	—	3	1	no	—
64	C₅×#385	—	3	1	no	—
65	C₅×#380	—	3	1	no	—
66	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
67	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
68	C₂×C₅×#95	—	3	1	no	—
69	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	—	2	2	no	—
85	C₂×C₄×C₅×D₃	—	4	1	no	—
86	C₂×C₄×C₅×D₃	—	4	1	no	—
87	C₂×C₄×C₅×D₃	—	4	1	no	—
88	C₂×C₄×C₅×D₃	—	4	1	no	—
89	C₂×C₄×C₅×D₃	—	4	1	no	—
90	C₂×C₄×C₅×D₃	—	4	1	no	—
91	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
92	C₂×C₄×C₅×D₃	Q₈	1	4	yes	complemented
93	C₂×C₅×Dic₆	—	4	1	no	—
94	C₂×C₅×Dic₆	—	4	1	no	—
95	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
96	C₃×C₅×C₄⋊C₄	—	4	1	no	—
97	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
98	C₃×C₄²×C₅	—	4	1	no	—
99	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
100	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
101	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
102	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
103	C₅×C₄⋊Dic₃	—	4	1	no	—
104	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
105	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
106	C₅×Dic₃⋊C₄	—	4	1	no	—
107	C₅×Dic₃⋊C₄	—	4	1	no	—
108	C₅×Dic₃⋊C₄	—	4	1	no	—
109	C₅×Dic₃⋊C₄	—	4	1	no	—
110	C₄×C₅×Dic₃	—	4	1	no	—
111	C₄×C₅×Dic₃	—	4	1	no	—
112	C₄×C₅×Dic₃	—	4	1	no	—
113	C₂×#897	C₂×C₅	1	1	yes	characteristic
114	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
115	#4989	C₂×C₅	1	1	yes	characteristic
116	#4980	C₂×C₅	1	1	yes	characteristic, complemented
117	#4972	C₂×C₅	1	1	yes	characteristic, complemented
118	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
119	#4928	C₂×C₅	1	1	yes	characteristic, complemented
120	#4668	C₂×C₅	1	1	yes	characteristic
121	#4667	C₂×C₅	1	1	yes	characteristic
122	#4666	C₂×C₅	1	1	yes	characteristic
123	D₃×#95	C₂×C₅	1	1	yes	characteristic
124	#4654	C₂×C₅	1	1	yes	characteristic, complemented
125	#4653	C₂×C₅	1	1	yes	characteristic, complemented
126	#4646	C₂×C₅	1	1	yes	characteristic, complemented
127	#4646	C₂×C₅	1	1	yes	characteristic, complemented
128	C₂²×C₅×Q₈	—	3	1	no	—
129	C₂³×C₄×C₅	—	3	1	no	—
130	C₂³×C₄×C₅	—	3	1	no	—
131	C₂³×C₄×C₅	—	3	1	no	—
132	C₅×C₂²⋊Q₈	—	3	8	no	—
133	C₂×C₅×C₄⋊C₄	—	3	1	no	—
134	C₂×C₅×C₄⋊C₄	—	3	1	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	3	1	no	—
137	C₂×C₅×C₄⋊C₄	—	3	1	no	—
138	C₂×C₅×C₄⋊C₄	—	3	1	no	—
139	C₂×C₅×C₄⋊C₄	—	3	1	no	—
140	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
142	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
143	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
144	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
146	C₂×C₄²×C₅	—	3	1	no	—
147	C₂×C₄²×C₅	—	3	1	no	—
148	C₂×C₄²×C₅	—	3	1	no	—
149	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
150	C₅×#95	—	3	1	no	—
151	C₅×#95	—	3	1	no	—
152	C₅×#95	—	3	1	no	—
153	C₅×#95	—	3	1	no	—
154	C₅×#95	—	3	1	no	—
155	C₅×#95	—	3	1	no	—
156	C₅×#95	—	3	1	no	—
157	C₅×#95	—	3	1	no	—
158	C₅×#95	—	3	1	no	—
159	C₅×#95	—	3	1	no	—
160	C₅×#95	C₂×D₃	1	1	yes	characteristic
161	C₅×#95	C₂×D₃	1	1	yes	characteristic
162	C₅×#95	C₂×D₃	1	1	yes	characteristic
163	C₅×#95	C₂×D₃	1	1	yes	characteristic
164	#2329	—	3	1	no	Sylow
165	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
166	C₂²×C₅×D₃	—	2	1	no	—
167	C₂²×C₅×D₃	—	2	1	no	—
168	C₂²×C₅×D₃	—	2	1	no	—
169	C₂²×C₅×D₃	—	2	1	no	—
170	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
171	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
172	C₂²×C₅×D₃	#41	1	2	yes	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
191	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
193	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
194	C₂×C₅×Dic₃	—	2	1	no	—
195	C₂×C₅×Dic₃	—	2	1	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	—	2	1	no	—
198	C₂×C₅×Dic₃	—	2	1	no	—
199	C₂×C₅×Dic₃	—	2	1	no	—
200	C₂×C₅×Dic₃	—	2	1	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	1	no	—
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	1	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	—	2	1	no	—
209	C₂×C₅×Dic₃	—	2	1	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
212	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
213	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
214	C₂×C₅×Dic₃	C₂×Q₈	1	2	yes	—
215	C₄×C₅×D₃	—	4	4	no	—
216	C₄×C₅×D₃	—	4	4	no	—
217	C₄×C₅×D₃	—	4	4	no	—
218	C₅×Dic₆	—	4	4	no	—
219	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
220	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
221	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
222	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
226	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
233	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
240	#897	C₄×C₅	1	8	yes	complemented
241	C₃×#95	C₂²×C₅	1	1	yes	characteristic
242	C₃×#95	C₂²×C₅	1	1	yes	characteristic
243	C₃×#95	C₂²×C₅	1	1	yes	characteristic
244	C₃×#95	C₂²×C₅	1	1	yes	characteristic
245	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
246	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
247	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
248	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
249	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
250	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
251	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
252	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
253	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
254	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
255	C₂⁴×C₅	—	3	1	no	—
256	C₂×C₅×Q₈	—	3	4	no	—
257	C₂×C₅×Q₈	—	12	1	no	—
258	C₂×C₅×Q₈	—	12	1	no	—
259	C₂²×C₄×C₅	—	3	1	no	—
260	C₂²×C₄×C₅	—	3	1	no	—
261	C₂²×C₄×C₅	—	3	1	no	—
262	C₂²×C₄×C₅	—	3	1	no	—
263	C₂²×C₄×C₅	—	3	4	no	—
264	C₂²×C₄×C₅	—	3	4	no	—
265	C₂²×C₄×C₅	—	3	1	no	—
266	C₂²×C₄×C₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	1	no	—
268	C₂²×C₄×C₅	—	6	2	no	—
269	C₂²×C₄×C₅	—	12	1	no	—
270	C₂²×C₄×C₅	—	12	1	no	—
271	C₂²×C₄×C₅	—	12	1	no	—
272	C₂²×C₄×C₅	—	12	1	no	—
273	C₂²×C₄×C₅	—	12	1	no	—
274	C₂²×C₄×C₅	—	12	1	no	—
275	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
276	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
277	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
278	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
282	C₅×C₄⋊C₄	—	3	4	no	—
283	C₅×C₄⋊C₄	—	3	4	no	—
284	C₅×C₄⋊C₄	—	4	1	no	—
285	C₅×C₄⋊C₄	—	12	1	no	—
286	C₅×C₄⋊C₄	—	12	1	no	—
287	C₅×C₄⋊C₄	—	12	1	no	—
288	C₅×C₄⋊C₄	—	12	1	no	—
289	C₅×C₄⋊C₄	—	12	1	no	—
290	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	complemented
291	C₅×C₂²⋊C₄	—	3	4	no	—
292	C₅×C₂²⋊C₄	—	3	4	no	—
293	C₅×C₂²⋊C₄	—	6	2	no	—
294	C₅×C₂²⋊C₄	—	6	2	no	—
295	C₄²×C₅	—	4	1	no	—
296	C₄²×C₅	—	12	1	no	—
297	C₄²×C₅	—	12	1	no	—
298	C₄²×C₅	—	12	1	no	—
299	C₂×C₂²⋊Q₈	—	3	1	no	—
300	#391	—	3	1	no	—
301	#391	—	3	1	no	—
302	#389	—	3	1	no	—
303	#389	—	3	1	no	—
304	#387	—	3	1	no	—
305	#387	—	3	1	no	—
306	#387	—	3	1	no	—
307	#387	C₅×D₃	1	1	yes	characteristic, complemented
308	#385	—	3	1	no	—
309	#385	—	3	1	no	—
310	#380	—	3	1	no	—
311	C₄×C₂²⋊C₄	—	3	1	no	—
312	C₄×C₂²⋊C₄	—	3	1	no	—
313	C₂×#95	—	3	1	no	—
314	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
315	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
316	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
317	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
321	C₂×C₅×D₃	—	2	2	no	—
322	C₂×C₅×D₃	—	2	2	no	—
323	C₂×C₅×D₃	—	2	2	no	—
324	C₂×C₅×D₃	—	2	2	no	—
325	C₂×C₅×D₃	—	2	2	no	—
326	C₂×C₅×D₃	—	2	2	no	—
327	C₂×C₅×D₃	C₄×Q₈	1	4	yes	—
328	C₃×C₄×C₅	—	2	2	no	—
329	C₃×C₄×C₅	—	2	2	no	—
330	C₃×C₄×C₅	—	2	2	no	—
331	C₃×C₄×C₅	—	2	2	no	—
332	C₃×C₄×C₅	—	4	1	no	—
333	C₃×C₄×C₅	—	4	1	no	—
334	C₃×C₄×C₅	—	4	1	no	—
335	C₅×Dic₃	—	2	2	no	—
336	C₅×Dic₃	—	2	2	no	—
337	C₅×Dic₃	—	2	2	no	—
338	C₅×Dic₃	—	2	2	no	—
339	C₅×Dic₃	—	4	1	no	—
340	C₅×Dic₃	—	4	1	no	—
341	C₅×Dic₃	—	4	1	no	—
342	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
351	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
352	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
353	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
354	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
355	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
356	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
357	C₂×C₄×D₃	—	2	2	no	—
358	C₂×C₄×D₃	—	4	1	no	—
359	C₂×C₄×D₃	—	4	1	no	—
360	C₂×C₄×D₃	—	4	1	no	—
361	C₂×C₄×D₃	—	4	1	no	—
362	C₂×C₄×D₃	—	4	1	no	—
363	C₂×C₄×D₃	—	4	1	no	—
364	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
365	C₂×C₄×D₃	C₅×Q₈	1	4	yes	complemented
366	C₂×Dic₆	—	4	1	no	—
367	C₂×Dic₆	—	4	1	no	—
368	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
369	C₃×C₄⋊C₄	—	4	1	no	—
370	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
371	C₃×C₄²	—	4	1	no	—
372	(C₂×D₃)⋊C₄	—	2	2	no	—
373	(C₂×D₃)⋊C₄	—	2	2	no	—
374	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
375	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
376	C₄⋊Dic₃	—	4	1	no	—
377	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
378	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
379	Dic₃⋊C₄	—	4	1	no	—
380	Dic₃⋊C₄	—	4	1	no	—
381	Dic₃⋊C₄	—	4	1	no	—
382	Dic₃⋊C₄	—	4	1	no	—
383	C₄×Dic₃	—	4	1	no	—
384	C₄×Dic₃	—	4	1	no	—
385	C₄×Dic₃	—	4	1	no	—
386	C₂³×C₅	—	3	2	no	—
387	C₂³×C₅	—	3	2	no	—
388	C₂³×C₅	—	3	2	no	—
389	C₂³×C₅	—	6	1	no	—
390	C₂³×C₅	—	6	1	no	—
391	C₂³×C₅	—	6	1	no	—
392	C₂³×C₅	—	6	1	no	—
393	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
394	C₅×Q₈	—	12	4	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	3	2	no	—
413	C₂×C₄×C₅	—	3	2	no	—
414	C₂×C₄×C₅	—	3	2	no	—
415	C₂×C₄×C₅	—	3	2	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	6	1	no	—
418	C₂×C₄×C₅	—	6	1	no	—
419	C₂×C₄×C₅	—	6	1	no	—
420	C₂×C₄×C₅	—	6	1	no	—
421	C₂×C₄×C₅	—	6	1	no	—
422	C₂×C₄×C₅	—	6	1	no	—
423	C₂×C₄×C₅	—	6	1	no	—
424	C₂×C₄×C₅	—	6	1	no	—
425	C₂×C₄×C₅	—	6	1	no	—
426	C₂×C₄×C₅	—	6	1	no	—
427	C₂×C₄×C₅	—	6	1	no	—
428	C₂×C₄×C₅	—	6	1	no	—
429	C₂×C₄×C₅	—	6	1	no	—
430	C₂×C₄×C₅	—	6	1	no	—
431	C₂×C₄×C₅	—	6	1	no	—
432	C₂×C₄×C₅	—	6	1	no	—
433	C₂×C₄×C₅	—	12	4	no	—
434	C₂×C₄×C₅	—	12	4	no	—
435	C₂×C₄×C₅	—	12	4	no	—
436	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
437	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
438	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
439	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
440	C₂²×Q₈	—	3	1	no	—
441	C₂³×C₄	—	3	1	no	—
442	C₂³×C₄	—	3	1	no	—
443	C₂³×C₄	—	3	1	no	—
444	C₂²⋊Q₈	—	3	8	no	—
445	C₂×C₄⋊C₄	—	3	1	no	—
446	C₂×C₄⋊C₄	—	3	1	no	—
447	C₂×C₄⋊C₄	—	3	1	no	—
448	C₂×C₄⋊C₄	—	3	1	no	—
449	C₂×C₄⋊C₄	—	3	1	no	—
450	C₂×C₄⋊C₄	—	3	1	no	—
451	C₂×C₄⋊C₄	—	3	1	no	—
452	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	—	3	1	no	—
455	C₂×C₂²⋊C₄	—	3	1	no	—
456	C₂×C₂²⋊C₄	—	3	1	no	—
457	C₂×C₂²⋊C₄	—	3	1	no	—
458	C₂×C₄²	—	3	1	no	—
459	C₂×C₄²	—	3	1	no	—
460	C₂×C₄²	—	3	1	no	—
461	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
462	#95	—	3	1	no	—
463	#95	—	3	1	no	—
464	#95	—	3	1	no	—
465	#95	—	3	1	no	—
466	#95	—	3	1	no	—
467	#95	—	3	1	no	—
468	#95	—	3	1	no	—
469	#95	—	3	1	no	—
470	#95	—	3	1	no	—
471	#95	—	3	1	no	—
472	#95	C₂×C₅×D₃	1	1	yes	characteristic
473	#95	C₂×C₅×D₃	1	1	yes	characteristic
474	#95	C₂×C₅×D₃	1	1	yes	characteristic
475	#95	C₂×C₅×D₃	1	1	yes	characteristic
476	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
477	C₂×C₃×C₅	#518	1	1	yes	characteristic
478	C₂×C₃×C₅	#520	1	1	yes	characteristic
479	C₂×C₃×C₅	#538	1	1	yes	characteristic
480	C₂×C₃×C₅	#539	1	1	yes	characteristic
481	C₂×C₃×C₅	#543	1	1	yes	characteristic
482	C₂×C₃×C₅	#544	1	1	yes	characteristic
483	C₅×D₃	—	2	4	no	—
484	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
485	C₂²×D₃	—	2	1	no	—
486	C₂²×D₃	—	2	1	no	—
487	C₂²×D₃	—	2	1	no	—
488	C₂²×D₃	—	2	1	no	—
489	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
490	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
491	C₂²×D₃	C₅×#41	1	2	yes	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
510	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
511	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
512	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
513	C₂×Dic₃	—	2	1	no	—
514	C₂×Dic₃	—	2	1	no	—
515	C₂×Dic₃	—	2	1	no	—
516	C₂×Dic₃	—	2	1	no	—
517	C₂×Dic₃	—	2	1	no	—
518	C₂×Dic₃	—	2	1	no	—
519	C₂×Dic₃	—	2	1	no	—
520	C₂×Dic₃	—	2	1	no	—
521	C₂×Dic₃	—	2	1	no	—
522	C₂×Dic₃	—	2	1	no	—
523	C₂×Dic₃	—	2	1	no	—
524	C₂×Dic₃	—	2	1	no	—
525	C₂×Dic₃	—	2	1	no	—
526	C₂×Dic₃	—	2	1	no	—
527	C₂×Dic₃	—	2	1	no	—
528	C₂×Dic₃	—	2	1	no	—
529	C₂×Dic₃	—	2	1	no	—
530	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
531	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
532	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
533	C₂×Dic₃	C₂×C₅×Q₈	1	2	yes	—
534	C₄×D₃	—	4	4	no	—
535	C₄×D₃	—	4	4	no	—
536	C₄×D₃	—	4	4	no	—
537	Dic₆	—	4	4	no	—
538	C₂²×C₅	—	3	4	no	—
539	C₂²×C₅	—	6	2	no	—
540	C₂²×C₅	—	6	2	no	—
541	C₂²×C₅	—	6	2	no	—
542	C₂²×C₅	—	6	2	no	—
543	C₂²×C₅	—	6	2	no	—
544	C₂²×C₅	—	6	2	no	—
545	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
546	C₂²×C₅	#1004	1	1	yes	characteristic
547	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
548	C₂²×C₅	D₃×#41	1	1	yes	characteristic
549	C₂²×C₅	#1009	1	1	yes	characteristic
550	C₂²×C₅	#1009	1	1	yes	characteristic
551	C₂²×C₅	#1010	1	1	yes	characteristic
552	C₄×C₅	—	2	2	no	—
553	C₄×C₅	—	2	2	no	—
554	C₄×C₅	—	2	2	no	—
555	C₄×C₅	—	2	2	no	—
556	C₄×C₅	—	4	1	no	—
557	C₄×C₅	—	4	1	no	—
558	C₄×C₅	—	4	1	no	—
559	C₄×C₅	—	6	2	no	—
560	C₄×C₅	—	6	2	no	—
561	C₄×C₅	—	6	2	no	—
562	C₄×C₅	—	6	2	no	—
563	C₄×C₅	—	12	1	no	—
564	C₄×C₅	—	12	1	no	—
565	C₄×C₅	—	12	1	no	—
566	C₂⁴	—	3	1	no	—
567	C₂×Q₈	—	3	4	no	—
568	C₂×Q₈	—	12	1	no	—
569	C₂×Q₈	—	12	1	no	—
570	C₂²×C₄	—	3	1	no	—
571	C₂²×C₄	—	3	1	no	—
572	C₂²×C₄	—	3	1	no	—
573	C₂²×C₄	—	3	1	no	—
574	C₂²×C₄	—	3	4	no	—
575	C₂²×C₄	—	3	4	no	—
576	C₂²×C₄	—	3	1	no	—
577	C₂²×C₄	—	3	1	no	—
578	C₂²×C₄	—	3	1	no	—
579	C₂²×C₄	—	6	2	no	—
580	C₂²×C₄	—	12	1	no	—
581	C₂²×C₄	—	12	1	no	—
582	C₂²×C₄	—	12	1	no	—
583	C₂²×C₄	—	12	1	no	—
584	C₂²×C₄	—	12	1	no	—
585	C₂²×C₄	—	12	1	no	—
586	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
588	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
589	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
590	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
592	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
593	C₄⋊C₄	—	3	4	no	—
594	C₄⋊C₄	—	3	4	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	—	12	1	no	—
597	C₄⋊C₄	—	12	1	no	—
598	C₄⋊C₄	—	12	1	no	—
599	C₄⋊C₄	—	12	1	no	—
600	C₄⋊C₄	—	12	1	no	—
601	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
602	C₂²⋊C₄	—	3	4	no	—
603	C₂²⋊C₄	—	3	4	no	—
604	C₂²⋊C₄	—	6	2	no	—
605	C₂²⋊C₄	—	6	2	no	—
606	C₄²	—	4	1	no	—
607	C₄²	—	12	1	no	—
608	C₄²	—	12	1	no	—
609	C₄²	—	12	1	no	—
610	C₃×C₅	#2329	1	1	yes	characteristic, complemented, Hall
611	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
612	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
613	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
614	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
618	C₂×D₃	—	2	2	no	—
619	C₂×D₃	—	2	2	no	—
620	C₂×D₃	—	2	2	no	—
621	C₂×D₃	—	2	2	no	—
622	C₂×D₃	—	2	2	no	—
623	C₂×D₃	—	2	2	no	—
624	C₂×D₃	C₄×C₅×Q₈	1	4	yes	—
625	C₃×C₄	—	2	2	no	—
626	C₃×C₄	—	2	2	no	—
627	C₃×C₄	—	2	2	no	—
628	C₃×C₄	—	2	2	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	—	4	1	no	—
631	C₃×C₄	—	4	1	no	—
632	Dic₃	—	2	2	no	—
633	Dic₃	—	2	2	no	—
634	Dic₃	—	2	2	no	—
635	Dic₃	—	2	2	no	—
636	Dic₃	—	4	1	no	—
637	Dic₃	—	4	1	no	—
638	Dic₃	—	4	1	no	—
639	C₂×C₅	—	6	4	no	—
640	C₂×C₅	#5521	1	1	yes	characteristic
641	C₂×C₅	#5546	1	1	yes	characteristic
642	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
643	C₂×C₅	#5634	1	1	yes	characteristic
644	C₂×C₅	#5657	1	1	yes	characteristic
645	C₂×C₅	#5689	1	1	yes	characteristic
646	C₂×C₅	#5707	1	1	yes	characteristic
647	C₂³	—	3	2	no	—
648	C₂³	—	3	2	no	—
649	C₂³	—	3	2	no	—
650	C₂³	—	6	1	no	—
651	C₂³	—	6	1	no	—
652	C₂³	—	6	1	no	—
653	C₂³	—	6	1	no	—
654	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
655	Q₈	—	12	4	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	3	2	no	—
674	C₂×C₄	—	3	2	no	—
675	C₂×C₄	—	3	2	no	—
676	C₂×C₄	—	3	2	no	—
677	C₂×C₄	—	6	1	no	—
678	C₂×C₄	—	6	1	no	—
679	C₂×C₄	—	6	1	no	—
680	C₂×C₄	—	6	1	no	—
681	C₂×C₄	—	6	1	no	—
682	C₂×C₄	—	6	1	no	—
683	C₂×C₄	—	6	1	no	—
684	C₂×C₄	—	6	1	no	—
685	C₂×C₄	—	6	1	no	—
686	C₂×C₄	—	6	1	no	—
687	C₂×C₄	—	6	1	no	—
688	C₂×C₄	—	6	1	no	—
689	C₂×C₄	—	6	1	no	—
690	C₂×C₄	—	6	1	no	—
691	C₂×C₄	—	6	1	no	—
692	C₂×C₄	—	6	1	no	—
693	C₂×C₄	—	6	1	no	—
694	C₂×C₄	—	12	4	no	—
695	C₂×C₄	—	12	4	no	—
696	C₂×C₄	—	12	4	no	—
697	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
698	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
699	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
700	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
701	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
702	C₂×C₃	C₅×#518	1	1	yes	characteristic
703	C₂×C₃	C₅×#520	1	1	yes	characteristic
704	C₂×C₃	C₅×#538	1	1	yes	characteristic
705	C₂×C₃	C₅×#539	1	1	yes	characteristic
706	C₂×C₃	C₅×#543	1	1	yes	characteristic
707	C₂×C₃	C₅×#544	1	1	yes	characteristic
708	D₃	—	2	4	no	—
709	C₅	#75300	1	1	yes	characteristic, direct product factor, Sylow
710	C₂²	—	3	4	no	—
711	C₂²	—	6	2	no	—
712	C₂²	—	6	2	no	—
713	C₂²	—	6	2	no	—
714	C₂²	—	6	2	no	—
715	C₂²	—	6	2	no	—
716	C₂²	—	6	2	no	—
717	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
718	C₂²	C₅×#1004	1	1	yes	characteristic
719	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
720	C₂²	C₅×D₃×#41	1	1	yes	characteristic
721	C₂²	C₅×#1009	1	1	yes	characteristic
722	C₂²	C₅×#1009	1	1	yes	characteristic
723	C₂²	C₅×#1010	1	1	yes	characteristic
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	6	2	no	—
732	C₄	—	6	2	no	—
733	C₄	—	6	2	no	—
734	C₄	—	6	2	no	—
735	C₄	—	12	1	no	—
736	C₄	—	12	1	no	—
737	C₄	—	12	1	no	—
738	C₃	C₅×#2329	1	1	yes	characteristic, complemented, Sylow
739	C₂	—	6	4	no	—
740	C₂	C₅×#5521	1	1	yes	characteristic
741	C₂	C₅×#5546	1	1	yes	characteristic
742	C₂	C₄×C₅×D₃×Q₈	1	1	yes	characteristic
743	C₂	C₅×#5634	1	1	yes	characteristic
744	C₂	C₅×#5657	1	1	yes	characteristic
745	C₂	C₅×#5689	1	1	yes	characteristic
746	C₂	C₅×#5707	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#387	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#387	D₃
hypocenter	C₃	C₅×#2329
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#387

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#387	C₂	semidirect
4. C₅×#4980	C₂	semidirect
5. C₅×#4972	C₂	semidirect
7. C₅×#4928	C₂	semidirect
12. C₅×#4654	C₂	semidirect
13. C₅×#4653	C₂	semidirect
14. C₅×#4646	C₂	semidirect
15. C₅×#4646	C₂	semidirect
38. C₅×#897	C₄	semidirect
53. #75300	C₅	direct (N × H)
62. C₅×#387	D₃	semidirect
92. C₂×C₄×C₅×D₃	Q₈	semidirect
95. C₂×C₅×Dic₆	C₂×C₄	semidirect
97. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
104. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
105. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
114. C₃×#387	C₂×C₅	semidirect
116. #4980	C₂×C₅	semidirect
117. #4972	C₂×C₅	semidirect
119. #4928	C₂×C₅	semidirect
124. #4654	C₂×C₅	semidirect
125. #4653	C₂×C₅	semidirect
126. #4646	C₂×C₅	semidirect
127. #4646	C₂×C₅	semidirect
240. #897	C₄×C₅	semidirect
290. C₅×C₄⋊C₄	C₄×D₃	semidirect
307. #387	C₅×D₃	semidirect
365. C₂×C₄×D₃	C₅×Q₈	semidirect
368. C₂×Dic₆	C₂×C₄×C₅	semidirect
370. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
377. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
378. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
601. C₄⋊C₄	C₄×C₅×D₃	semidirect
610. C₃×C₅	#2329	semidirect
709. C₅	#75300	direct (N × H)
738. C₃	C₅×#2329	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#897	2
C₃×C₅×#387	2
C₅×#4989	2
C₅×#4980	2
C₅×#4972	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4928	2
C₅×#4668	2
C₅×#4667	2
C₅×#4666	2
C₅×D₃×#95	2
C₅×#4654	2
C₅×#4653	2
C₅×#4646	2
C₅×#2329	3
#75300	5

Subgroups — C5×#75300 #14324441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75300 #14324441