Subgroups — C₅×#86467 #14481499

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5719	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5716	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5698	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5688	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5660	C₂	1	4	yes	maximal, complemented
7	C₅×#5649	C₂	1	4	yes	maximal, complemented
8	C₅×#5613	C₂	1	4	yes	maximal, complemented
9	C₅×#5606	C₂	1	2	yes	maximal, complemented
10	C₅×#5603	C₂	1	2	yes	maximal, complemented
11	C₅×#5600	C₂	1	4	yes	maximal, complemented
12	C₅×#5561	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#237	C₂	1	2	yes	maximal, complemented
14	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5518	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3455	—	3	1	no	maximal, Hall
17	C₂×C₅×#237	C₂²	1	2	yes	—
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#123	C₂²	1	4	yes	complemented
22	C₃×C₅×#121	C₂²	1	4	yes	—
23	C₃×C₅×#121	C₂²	1	2	yes	—
24	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₅×#939	C₂²	1	4	yes	—
27	C₅×#938	C₂²	1	4	yes	—
28	C₅×#938	C₂²	1	2	yes	—
29	C₅×#937	C₂²	1	4	yes	—
30	C₅×#936	C₂²	1	4	yes	—
31	C₅×#936	C₂²	1	2	yes	complemented
32	C₅×#935	C₂²	1	4	yes	—
33	C₅×#935	C₂²	1	4	yes	complemented
34	C₅×D₄×Dic₃	C₂²	1	4	yes	—
35	C₅×D₄×Dic₃	C₂²	1	4	yes	complemented
36	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
37	C₅×#929	C₂²	1	4	yes	—
38	C₄×C₅×#67	C₂²	1	4	yes	—
39	C₅×#926	C₂²	1	1	yes	characteristic
40	C₅×#924	C₂²	1	2	yes	—
41	C₅×#924	C₂²	1	4	yes	complemented
42	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
43	C₅×#898	C₂²	1	4	yes	—
44	C₅×#897	C₂²	1	2	yes	—
45	C₅×#896	C₂²	1	4	yes	—
46	C₅×#892	C₂²	1	2	yes	—
47	C₅×#892	C₂²	1	2	yes	—
48	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
49	C₅×#890	C₂²	1	4	yes	complemented
50	C₅×#889	C₂²	1	4	yes	complemented
51	C₅×#888	C₂²	1	2	yes	complemented
52	C₅×#887	C₂²	1	4	yes	complemented
53	C₅×#887	C₂²	1	2	yes	complemented
54	C₅×#885	C₂²	1	4	yes	—
55	C₅×#883	C₂²	1	4	yes	—
56	C₅×#67⋊C₄	C₂²	1	4	yes	—
57	C₅×#67⋊C₄	C₂²	1	4	yes	—
58	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₅×#879	C₂²	1	4	yes	—
60	C₅×#879	C₂²	1	4	yes	complemented
61	C₅×#879	C₂²	1	4	yes	complemented
62	C₅×#878	C₂²	1	4	yes	complemented
63	C₅×#877	C₂²	1	2	yes	—
64	C₅×#877	C₂²	1	4	yes	complemented
65	C₅×#872	C₂²	1	1	yes	characteristic
66	C₅×#872	C₂²	1	1	yes	characteristic
67	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
68	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
69	C₅×#870	C₂²	1	1	yes	characteristic, complemented
70	C₅×#869	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
72	#86467	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
73	C₅×#542	—	3	2	no	—
74	C₅×#542	—	3	2	no	—
75	C₅×#541	—	3	1	no	—
76	C₅×#541	—	3	1	no	—
77	C₅×#540	—	3	1	no	—
78	C₅×#540	D₃	1	1	yes	characteristic, complemented
79	C₅×#539	—	3	4	no	—
80	C₅×#538	—	3	4	no	—
81	C₅×#533	—	3	1	no	—
82	C₅×#532	—	3	1	no	—
83	C₅×#529	—	3	4	no	—
84	C₅×#529	—	3	4	no	—
85	C₅×#525	—	3	2	no	—
86	C₄×C₅×#41	—	3	2	no	—
87	C₂×C₅×#117	—	3	1	no	—
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
90	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
91	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
94	C₂×C₅×#67	C₂³	1	4	yes	—
95	C₂×C₅×#67	C₂³	1	4	yes	—
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
98	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
99	C₅×#237	—	2	8	no	—
100	C₂×C₄×C₅×D₃	—	2	4	no	—
101	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
104	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
105	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
106	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
107	C₂×C₅×Dic₆	C₂³	1	2	yes	—
108	C₂×C₅×Dic₆	C₂³	1	4	yes	—
109	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
111	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₅×#217	C₂³	1	2	yes	—
118	C₅×#217	C₂³	1	4	yes	—
119	C₅×#217	C₂³	1	4	yes	—
120	C₅×#217	C₂³	1	4	yes	—
121	C₅×#217	C₂³	1	4	yes	—
122	C₅×#217	C₂³	1	4	yes	—
123	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
124	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
125	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
126	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
127	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
128	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
129	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
130	C₅×C₄⋊Dic₃	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	2	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	4	yes	—
139	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
140	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
141	C₄×C₅×Dic₃	C₂³	1	2	yes	—
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×#540	C₂×C₅	1	1	yes	characteristic, complemented
146	#5719	C₂×C₅	1	1	yes	characteristic, complemented
147	#5716	C₂×C₅	1	1	yes	characteristic, complemented
148	#5698	C₂×C₅	1	1	yes	characteristic, complemented
149	#5688	C₂×C₅	1	1	yes	characteristic, complemented
150	#5660	C₂×C₅	1	4	yes	complemented
151	#5649	C₂×C₅	1	4	yes	complemented
152	#5613	C₂×C₅	1	4	yes	complemented
153	#5606	C₂×C₅	1	2	yes	complemented
154	#5603	C₂×C₅	1	2	yes	complemented
155	#5600	C₂×C₅	1	4	yes	complemented
156	#5561	C₂×C₅	1	2	yes	complemented
157	C₄×#237	C₂×C₅	1	2	yes	complemented
158	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
159	#5518	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×C₅×#41	—	3	2	no	—
161	C₂³×C₄×C₅	—	3	1	no	—
162	C₅×C₄⋊Q₈	—	3	2	no	—
163	C₅×C₄⋊Q₈	—	3	1	no	—
164	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
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×#125	—	3	4	no	—
170	C₅×#125	—	3	4	no	—
171	C₅×#125	—	3	1	no	—
172	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
173	C₅×#124	—	3	4	no	—
174	C₅×#124	—	3	2	no	—
175	C₅×#124	—	3	4	no	—
176	C₅×#123	—	3	4	no	—
177	C₅×#123	—	3	4	no	—
178	C₅×#123	—	3	4	no	—
179	C₅×#123	—	3	4	no	—
180	C₅×#123	C₂×D₃	1	4	yes	complemented
181	C₅×C₂²⋊Q₈	—	3	2	no	—
182	C₅×C₂²⋊Q₈	—	3	4	no	—
183	C₅×C₂²⋊Q₈	—	3	4	no	—
184	C₅×C₂²⋊Q₈	—	3	2	no	—
185	C₅×C₂²⋊Q₈	—	3	4	no	—
186	C₅×#121	—	3	2	no	—
187	C₅×#121	—	3	4	no	—
188	C₅×#121	—	3	4	no	—
189	C₅×#121	C₂×D₃	1	2	yes	—
190	C₅×#121	C₂×D₃	1	4	yes	—
191	C₅×#120	—	3	4	no	—
192	C₄×C₅×Q₈	—	3	2	no	—
193	C₄×C₅×Q₈	—	3	4	no	—
194	C₄×C₅×Q₈	—	3	2	no	—
195	C₄×C₅×D₄	—	3	4	no	—
196	C₄×C₅×D₄	—	3	2	no	—
197	C₄×C₅×D₄	—	3	4	no	—
198	C₄×C₅×D₄	—	3	4	no	—
199	C₄×C₅×D₄	—	3	4	no	—
200	C₄×C₅×D₄	—	3	4	no	—
201	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
202	C₅×#117	—	3	1	no	—
203	C₅×#117	—	3	2	no	—
204	C₅×#117	—	3	2	no	—
205	C₅×#117	—	3	2	no	—
206	C₅×#117	—	3	4	no	—
207	C₅×#117	—	3	1	no	—
208	C₅×#117	—	3	1	no	—
209	C₅×#117	C₂×D₃	1	1	yes	characteristic
210	C₂×C₅×C₄⋊C₄	—	3	2	no	—
211	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
212	C₂×C₄²×C₅	—	3	4	no	—
213	C₂×C₄²×C₅	—	3	1	no	—
214	C₂×C₄²×C₅	—	3	1	no	—
215	#3455	—	3	1	no	Sylow
216	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
217	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
218	C₂²×C₅×D₃	—	2	2	no	—
219	C₂²×C₅×D₃	—	4	2	no	—
220	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
222	C₃×C₅×D₄	—	2	4	no	—
223	C₃×C₅×D₄	—	4	4	no	—
224	C₃×C₅×D₄	—	4	4	no	—
225	C₂×C₃×C₄×C₅	—	2	2	no	—
226	C₂×C₃×C₄×C₅	—	4	4	no	—
227	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
228	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
229	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
231	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
232	C₅×#67	—	2	8	no	—
233	C₅×#67	—	4	4	no	—
234	C₂×C₅×Dic₃	—	2	2	no	—
235	C₂×C₅×Dic₃	—	2	8	no	—
236	C₂×C₅×Dic₃	—	4	4	no	—
237	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
238	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
239	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
240	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
241	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
243	C₄×C₅×D₃	—	2	2	no	—
244	C₄×C₅×D₃	—	2	2	no	—
245	C₄×C₅×D₃	—	2	2	no	—
246	C₄×C₅×D₃	—	4	2	no	—
247	C₄×C₅×D₃	—	4	2	no	—
248	C₄×C₅×D₃	#41	1	4	yes	—
249	C₅×Dic₆	—	2	4	no	—
250	C₅×Dic₆	—	4	4	no	—
251	C₂×#237	C₂²×C₅	1	2	yes	—
252	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
253	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₃×#123	C₂²×C₅	1	4	yes	complemented
256	C₃×#121	C₂²×C₅	1	4	yes	—
257	C₃×#121	C₂²×C₅	1	2	yes	—
258	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
259	C₃×#117	C₂²×C₅	1	1	yes	characteristic
260	#939	C₂²×C₅	1	4	yes	—
261	#938	C₂²×C₅	1	4	yes	—
262	#938	C₂²×C₅	1	2	yes	—
263	#937	C₂²×C₅	1	4	yes	—
264	#936	C₂²×C₅	1	4	yes	—
265	#936	C₂²×C₅	1	2	yes	complemented
266	#935	C₂²×C₅	1	4	yes	—
267	#935	C₂²×C₅	1	4	yes	complemented
268	D₄×Dic₃	C₂²×C₅	1	4	yes	—
269	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
270	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
271	#929	C₂²×C₅	1	4	yes	—
272	C₄×#67	C₂²×C₅	1	4	yes	—
273	#926	C₂²×C₅	1	1	yes	characteristic
274	#924	C₂²×C₅	1	2	yes	—
275	#924	C₂²×C₅	1	4	yes	complemented
276	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
277	#898	C₂²×C₅	1	4	yes	—
278	#897	C₂²×C₅	1	2	yes	—
279	#896	C₂²×C₅	1	4	yes	—
280	#892	C₂²×C₅	1	2	yes	—
281	#892	C₂²×C₅	1	2	yes	—
282	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
283	#890	C₂²×C₅	1	4	yes	complemented
284	#889	C₂²×C₅	1	4	yes	complemented
285	#888	C₂²×C₅	1	2	yes	complemented
286	#887	C₂²×C₅	1	4	yes	complemented
287	#887	C₂²×C₅	1	2	yes	complemented
288	#885	C₂²×C₅	1	4	yes	—
289	#883	C₂²×C₅	1	4	yes	—
290	#67⋊C₄	C₂²×C₅	1	4	yes	—
291	#67⋊C₄	C₂²×C₅	1	4	yes	—
292	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
293	#879	C₂²×C₅	1	4	yes	—
294	#879	C₂²×C₅	1	4	yes	complemented
295	#879	C₂²×C₅	1	4	yes	complemented
296	#878	C₂²×C₅	1	4	yes	complemented
297	#877	C₂²×C₅	1	2	yes	—
298	#877	C₂²×C₅	1	4	yes	complemented
299	#872	C₂²×C₅	1	1	yes	characteristic
300	#872	C₂²×C₅	1	1	yes	characteristic
301	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
302	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
303	#870	C₂²×C₅	1	1	yes	characteristic, complemented
304	#869	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
306	C₂⁴×C₅	—	3	1	no	—
307	C₅×#41	—	6	8	no	—
308	C₂×C₅×Q₈	—	3	2	no	—
309	C₂×C₅×Q₈	—	3	4	no	—
310	C₂×C₅×D₄	—	3	4	no	—
311	C₂×C₅×D₄	—	3	4	no	—
312	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
313	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
314	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
315	C₂²×C₄×C₅	—	3	1	no	—
316	C₂²×C₄×C₅	—	3	4	no	—
317	C₂²×C₄×C₅	—	3	1	no	—
318	C₂²×C₄×C₅	—	3	4	no	—
319	C₂²×C₄×C₅	—	3	1	no	—
320	C₂²×C₄×C₅	—	3	1	no	—
321	C₂²×C₄×C₅	—	3	1	no	—
322	C₂²×C₄×C₅	—	3	2	no	—
323	C₂²×C₄×C₅	—	3	2	no	—
324	C₂²×C₄×C₅	—	6	4	no	—
325	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
327	C₅×C₄⋊C₄	—	3	2	no	—
328	C₅×C₄⋊C₄	—	3	2	no	—
329	C₅×C₄⋊C₄	—	3	2	no	—
330	C₅×C₄⋊C₄	—	3	2	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	—	3	4	no	—
335	C₅×C₄⋊C₄	—	3	4	no	—
336	C₅×C₄⋊C₄	—	3	4	no	—
337	C₅×C₄⋊C₄	—	3	4	no	—
338	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
339	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
340	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
341	C₅×C₂²⋊C₄	—	3	2	no	—
342	C₅×C₂²⋊C₄	—	3	4	no	—
343	C₅×C₂²⋊C₄	—	3	4	no	—
344	C₅×C₂²⋊C₄	—	3	4	no	—
345	C₅×C₂²⋊C₄	—	3	4	no	—
346	C₅×C₂²⋊C₄	—	3	4	no	—
347	C₅×C₂²⋊C₄	—	3	2	no	—
348	C₅×C₂²⋊C₄	—	3	2	no	—
349	C₅×C₂²⋊C₄	—	3	4	no	—
350	C₅×C₂²⋊C₄	—	3	4	no	—
351	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
352	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
353	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
354	C₄²×C₅	—	3	2	no	—
355	C₄²×C₅	—	3	2	no	—
356	C₄²×C₅	—	3	4	no	—
357	C₄²×C₅	—	3	1	no	—
358	C₄²×C₅	—	3	1	no	—
359	C₄²×C₅	—	3	4	no	—
360	C₄²×C₅	—	3	4	no	—
361	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
362	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
363	#542	—	3	2	no	—
364	#542	—	3	2	no	—
365	#541	—	3	1	no	—
366	#541	—	3	1	no	—
367	#540	—	3	1	no	—
368	#540	C₅×D₃	1	1	yes	characteristic, complemented
369	#539	—	3	4	no	—
370	#538	—	3	4	no	—
371	#533	—	3	1	no	—
372	#532	—	3	1	no	—
373	#529	—	3	4	no	—
374	#529	—	3	4	no	—
375	#525	—	3	2	no	—
376	C₄×#41	—	3	2	no	—
377	C₂×#117	—	3	1	no	—
378	C₂²×C₃×C₅	—	2	4	no	—
379	C₂²×C₃×C₅	—	2	1	no	—
380	C₂²×C₃×C₅	—	2	4	no	—
381	C₂²×C₃×C₅	—	2	4	no	—
382	C₂²×C₃×C₅	—	2	2	no	—
383	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
384	C₂×C₅×D₃	—	2	2	no	—
385	C₂×C₅×D₃	—	2	1	no	—
386	C₂×C₅×D₃	—	2	2	no	—
387	C₂×C₅×D₃	—	4	4	no	—
388	C₂×C₅×D₃	C₂×#41	1	2	yes	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	2	4	no	—
391	C₃×C₄×C₅	—	2	2	no	—
392	C₃×C₄×C₅	—	2	2	no	—
393	C₃×C₄×C₅	C₂×#41	1	2	yes	—
394	C₅×Dic₃	—	2	4	no	—
395	C₅×Dic₃	—	2	1	no	—
396	C₅×Dic₃	—	2	2	no	—
397	C₅×Dic₃	—	2	4	no	—
398	C₅×Dic₃	—	2	2	no	—
399	C₅×Dic₃	C₂×#41	1	2	yes	—
400	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
402	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
403	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
406	C₂×#67	C₂³×C₅	1	4	yes	—
407	C₂×#67	C₂³×C₅	1	4	yes	—
408	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
409	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
410	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
411	#237	—	2	8	no	—
412	C₂×C₄×D₃	—	2	4	no	—
413	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
417	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
418	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
419	C₂×Dic₆	C₂³×C₅	1	2	yes	—
420	C₂×Dic₆	C₂³×C₅	1	4	yes	—
421	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
422	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
423	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
424	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
425	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
426	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
427	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
428	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
429	#217	C₂³×C₅	1	2	yes	—
430	#217	C₂³×C₅	1	4	yes	—
431	#217	C₂³×C₅	1	4	yes	—
432	#217	C₂³×C₅	1	4	yes	—
433	#217	C₂³×C₅	1	4	yes	—
434	#217	C₂³×C₅	1	4	yes	—
435	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
436	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
437	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
438	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
439	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
440	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
441	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
442	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
443	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
444	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
445	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
446	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
447	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
448	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
449	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
450	C₄×Dic₃	C₂³×C₅	1	4	yes	—
451	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
452	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
453	C₄×Dic₃	C₂³×C₅	1	2	yes	—
454	C₄×Dic₃	C₂³×C₅	1	2	yes	—
455	C₄×Dic₃	C₂³×C₅	1	4	yes	—
456	C₄×Dic₃	C₂³×C₅	1	4	yes	—
457	C₂³×C₅	—	3	1	no	—
458	C₂³×C₅	—	3	1	no	—
459	C₂³×C₅	—	6	2	no	—
460	C₂³×C₅	—	12	2	no	—
461	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
462	C₂³×C₅	C₂³×D₃	1	4	yes	—
463	C₅×Q₈	—	6	4	no	—
464	C₅×Q₈	—	12	4	no	—
465	C₅×D₄	—	2	4	no	—
466	C₅×D₄	—	4	4	no	—
467	C₅×D₄	—	4	4	no	—
468	C₅×D₄	—	6	8	no	—
469	C₅×D₄	—	12	4	no	—
470	C₂×C₄×C₅	—	2	2	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	4	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	3	2	no	—
475	C₂×C₄×C₅	—	3	4	no	—
476	C₂×C₄×C₅	—	3	4	no	—
477	C₂×C₄×C₅	—	3	1	no	—
478	C₂×C₄×C₅	—	4	4	no	—
479	C₂×C₄×C₅	—	6	2	no	—
480	C₂×C₄×C₅	—	6	2	no	—
481	C₂×C₄×C₅	—	6	2	no	—
482	C₂×C₄×C₅	—	6	8	no	—
483	C₂×C₄×C₅	—	6	2	no	—
484	C₂×C₄×C₅	—	12	2	no	—
485	C₂×C₄×C₅	—	12	2	no	—
486	C₂×C₄×C₅	—	12	4	no	—
487	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
488	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
489	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
490	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
491	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
492	C₂×#41	—	3	2	no	—
493	C₂³×C₄	—	3	1	no	—
494	C₄⋊Q₈	—	3	2	no	—
495	C₄⋊Q₈	—	3	1	no	—
496	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
497	#126	—	3	4	no	—
498	#126	—	3	4	no	—
499	#126	—	3	4	no	—
500	#126	—	3	4	no	—
501	#125	—	3	4	no	—
502	#125	—	3	4	no	—
503	#125	—	3	1	no	—
504	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	#124	—	3	4	no	—
506	#124	—	3	2	no	—
507	#124	—	3	4	no	—
508	#123	—	3	4	no	—
509	#123	—	3	4	no	—
510	#123	—	3	4	no	—
511	#123	—	3	4	no	—
512	#123	C₂×C₅×D₃	1	4	yes	complemented
513	C₂²⋊Q₈	—	3	2	no	—
514	C₂²⋊Q₈	—	3	4	no	—
515	C₂²⋊Q₈	—	3	2	no	—
516	C₂²⋊Q₈	—	3	4	no	—
517	C₂²⋊Q₈	—	3	4	no	—
518	#121	—	3	2	no	—
519	#121	—	3	4	no	—
520	#121	—	3	4	no	—
521	#121	C₂×C₅×D₃	1	2	yes	—
522	#121	C₂×C₅×D₃	1	4	yes	—
523	#120	—	3	4	no	—
524	C₄×Q₈	—	3	2	no	—
525	C₄×Q₈	—	3	4	no	—
526	C₄×Q₈	—	3	2	no	—
527	C₄×D₄	—	3	2	no	—
528	C₄×D₄	—	3	4	no	—
529	C₄×D₄	—	3	4	no	—
530	C₄×D₄	—	3	4	no	—
531	C₄×D₄	—	3	4	no	—
532	C₄×D₄	—	3	4	no	—
533	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
534	#117	—	3	1	no	—
535	#117	—	3	2	no	—
536	#117	—	3	2	no	—
537	#117	—	3	2	no	—
538	#117	—	3	4	no	—
539	#117	—	3	1	no	—
540	#117	—	3	1	no	—
541	#117	C₂×C₅×D₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	—	3	2	no	—
543	C₂×C₂²⋊C₄	—	3	2	no	—
544	C₂×C₄²	—	3	4	no	—
545	C₂×C₄²	—	3	1	no	—
546	C₂×C₄²	—	3	1	no	—
547	C₂×C₃×C₅	—	4	1	no	—
548	C₂×C₃×C₅	—	4	4	no	—
549	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
550	C₂×C₃×C₅	#585	1	2	yes	—
551	C₅×D₃	—	2	2	no	—
552	C₅×D₃	—	4	1	no	—
553	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
554	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
555	C₂²×D₃	—	2	2	no	—
556	C₂²×D₃	—	4	2	no	—
557	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
558	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
559	C₃×D₄	—	2	4	no	—
560	C₃×D₄	—	4	4	no	—
561	C₃×D₄	—	4	4	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	4	4	no	—
564	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
565	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
566	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
567	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
569	#67	—	2	8	no	—
570	#67	—	4	4	no	—
571	C₂×Dic₃	—	2	2	no	—
572	C₂×Dic₃	—	2	8	no	—
573	C₂×Dic₃	—	4	4	no	—
574	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
575	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
576	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
577	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
578	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
579	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
580	C₄×D₃	—	2	2	no	—
581	C₄×D₃	—	2	2	no	—
582	C₄×D₃	—	2	2	no	—
583	C₄×D₃	—	4	2	no	—
584	C₄×D₃	—	4	2	no	—
585	C₄×D₃	C₅×#41	1	4	yes	—
586	Dic₆	—	2	4	no	—
587	Dic₆	—	4	4	no	—
588	C₂²×C₅	—	2	1	no	—
589	C₂²×C₅	—	2	4	no	—
590	C₂²×C₅	—	2	4	no	—
591	C₂²×C₅	—	2	4	no	—
592	C₂²×C₅	—	2	2	no	—
593	C₂²×C₅	—	3	2	no	—
594	C₂²×C₅	—	6	2	no	—
595	C₂²×C₅	—	6	1	no	—
596	C₂²×C₅	—	6	2	no	—
597	C₂²×C₅	—	12	4	no	—
598	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
599	C₄×C₅	—	2	1	no	—
600	C₄×C₅	—	2	2	no	—
601	C₄×C₅	—	2	4	no	—
602	C₄×C₅	—	2	2	no	—
603	C₄×C₅	—	3	2	no	—
604	C₄×C₅	—	6	1	no	—
605	C₄×C₅	—	6	4	no	—
606	C₄×C₅	—	6	2	no	—
607	C₄×C₅	—	6	4	no	—
608	C₄×C₅	—	6	2	no	—
609	C₄×C₅	D₃×#41	1	2	yes	—
610	C₂⁴	—	3	1	no	—
611	#41	—	6	8	no	—
612	C₂×Q₈	—	3	2	no	—
613	C₂×Q₈	—	3	4	no	—
614	C₂×D₄	—	3	4	no	—
615	C₂×D₄	—	3	4	no	—
616	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
617	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
618	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
619	C₂²×C₄	—	3	1	no	—
620	C₂²×C₄	—	3	4	no	—
621	C₂²×C₄	—	3	1	no	—
622	C₂²×C₄	—	3	4	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	1	no	—
626	C₂²×C₄	—	3	2	no	—
627	C₂²×C₄	—	3	2	no	—
628	C₂²×C₄	—	6	4	no	—
629	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
630	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
631	C₄⋊C₄	—	3	2	no	—
632	C₄⋊C₄	—	3	2	no	—
633	C₄⋊C₄	—	3	2	no	—
634	C₄⋊C₄	—	3	2	no	—
635	C₄⋊C₄	—	3	4	no	—
636	C₄⋊C₄	—	3	4	no	—
637	C₄⋊C₄	—	3	4	no	—
638	C₄⋊C₄	—	3	4	no	—
639	C₄⋊C₄	—	3	4	no	—
640	C₄⋊C₄	—	3	4	no	—
641	C₄⋊C₄	—	3	4	no	—
642	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
643	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
644	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
645	C₂²⋊C₄	—	3	2	no	—
646	C₂²⋊C₄	—	3	4	no	—
647	C₂²⋊C₄	—	3	4	no	—
648	C₂²⋊C₄	—	3	4	no	—
649	C₂²⋊C₄	—	3	4	no	—
650	C₂²⋊C₄	—	3	4	no	—
651	C₂²⋊C₄	—	3	2	no	—
652	C₂²⋊C₄	—	3	2	no	—
653	C₂²⋊C₄	—	3	4	no	—
654	C₂²⋊C₄	—	3	4	no	—
655	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
656	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
657	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
658	C₄²	—	3	2	no	—
659	C₄²	—	3	2	no	—
660	C₄²	—	3	4	no	—
661	C₄²	—	3	1	no	—
662	C₄²	—	3	1	no	—
663	C₄²	—	3	4	no	—
664	C₄²	—	3	4	no	—
665	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
666	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
667	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
668	C₂²×C₃	—	2	4	no	—
669	C₂²×C₃	—	2	1	no	—
670	C₂²×C₃	—	2	4	no	—
671	C₂²×C₃	—	2	4	no	—
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
674	C₂×D₃	—	2	2	no	—
675	C₂×D₃	—	2	1	no	—
676	C₂×D₃	—	2	2	no	—
677	C₂×D₃	—	4	4	no	—
678	C₂×D₃	C₂×C₅×#41	1	2	yes	—
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	4	no	—
681	C₃×C₄	—	2	2	no	—
682	C₃×C₄	—	2	2	no	—
683	C₃×C₄	C₂×C₅×#41	1	2	yes	—
684	Dic₃	—	2	4	no	—
685	Dic₃	—	2	1	no	—
686	Dic₃	—	2	2	no	—
687	Dic₃	—	2	4	no	—
688	Dic₃	—	2	2	no	—
689	Dic₃	C₂×C₅×#41	1	2	yes	—
690	C₂×C₅	—	4	1	no	—
691	C₂×C₅	—	4	4	no	—
692	C₂×C₅	—	6	2	no	—
693	C₂×C₅	—	12	1	no	—
694	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
695	C₂×C₅	#5966	1	2	yes	—
696	C₂³	—	3	1	no	—
697	C₂³	—	3	1	no	—
698	C₂³	—	6	2	no	—
699	C₂³	—	12	2	no	—
700	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
701	C₂³	C₂³×C₅×D₃	1	4	yes	—
702	Q₈	—	6	4	no	—
703	Q₈	—	12	4	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	4	no	—
706	D₄	—	4	4	no	—
707	D₄	—	6	8	no	—
708	D₄	—	12	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	3	1	no	—
711	C₂×C₄	—	3	4	no	—
712	C₂×C₄	—	3	2	no	—
713	C₂×C₄	—	3	2	no	—
714	C₂×C₄	—	3	4	no	—
715	C₂×C₄	—	3	4	no	—
716	C₂×C₄	—	3	1	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	6	2	no	—
719	C₂×C₄	—	6	2	no	—
720	C₂×C₄	—	6	2	no	—
721	C₂×C₄	—	6	8	no	—
722	C₂×C₄	—	6	2	no	—
723	C₂×C₄	—	12	2	no	—
724	C₂×C₄	—	12	2	no	—
725	C₂×C₄	—	12	4	no	—
726	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
727	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
728	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
729	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
730	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
731	C₂×C₃	—	4	1	no	—
732	C₂×C₃	—	4	4	no	—
733	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
734	C₂×C₃	C₅×#585	1	2	yes	—
735	D₃	—	2	2	no	—
736	D₃	—	4	1	no	—
737	C₅	#86467	1	1	yes	characteristic, direct product factor, Sylow
738	C₂²	—	2	1	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	3	2	no	—
744	C₂²	—	6	2	no	—
745	C₂²	—	6	1	no	—
746	C₂²	—	6	2	no	—
747	C₂²	—	12	4	no	—
748	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
749	C₄	—	2	1	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	3	2	no	—
754	C₄	—	6	1	no	—
755	C₄	—	6	4	no	—
756	C₄	—	6	2	no	—
757	C₄	—	6	4	no	—
758	C₄	—	6	2	no	—
759	C₄	C₅×D₃×#41	1	2	yes	—
760	C₃	C₅×#3455	1	1	yes	characteristic, complemented, Sylow
761	C₂	—	4	1	no	—
762	C₂	—	4	4	no	—
763	C₂	—	6	2	no	—
764	C₂	—	12	1	no	—
765	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
766	C₂	C₅×#5966	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×#540	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#540	D₃
hypocenter	C₃	C₅×#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#540

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#540	C₂	semidirect
2. C₅×#5719	C₂	semidirect
3. C₅×#5716	C₂	semidirect
4. C₅×#5698	C₂	semidirect
5. C₅×#5688	C₂	semidirect
6. C₅×#5660	C₂	semidirect
7. C₅×#5649	C₂	semidirect
8. C₅×#5613	C₂	semidirect
9. C₅×#5606	C₂	semidirect
10. C₅×#5603	C₂	semidirect
11. C₅×#5600	C₂	semidirect
12. C₅×#5561	C₂	semidirect
13. C₄×C₅×#237	C₂	semidirect
14. C₅×D₃×#117	C₂	semidirect
15. C₅×#5518	C₂	semidirect
19. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₅×#125	C₂²	semidirect
21. C₃×C₅×#123	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
31. C₅×#936	C₂²	semidirect
33. C₅×#935	C₂²	semidirect
35. C₅×D₄×Dic₃	C₂²	semidirect
36. C₅×D₄×Dic₃	C₂²	semidirect
41. C₅×#924	C₂²	semidirect
42. C₂×C₄×C₅×Dic₃	C₂²	semidirect
49. C₅×#890	C₂²	semidirect
50. C₅×#889	C₂²	semidirect
51. C₅×#888	C₂²	semidirect
52. C₅×#887	C₂²	semidirect
53. C₅×#887	C₂²	semidirect
60. C₅×#879	C₂²	semidirect
61. C₅×#879	C₂²	semidirect
62. C₅×#878	C₂²	semidirect
64. C₅×#877	C₂²	semidirect
69. C₅×#870	C₂²	semidirect
70. C₅×#869	C₂²	semidirect
71. C₄×C₅×Dic₆	C₂²	semidirect
72. #86467	C₅	direct (N × H)
78. C₅×#540	D₃	semidirect
145. C₃×#540	C₂×C₅	semidirect
146. #5719	C₂×C₅	semidirect
147. #5716	C₂×C₅	semidirect
148. #5698	C₂×C₅	semidirect
149. #5688	C₂×C₅	semidirect
150. #5660	C₂×C₅	semidirect
151. #5649	C₂×C₅	semidirect
152. #5613	C₂×C₅	semidirect
153. #5606	C₂×C₅	semidirect
154. #5603	C₂×C₅	semidirect
155. #5600	C₂×C₅	semidirect
156. #5561	C₂×C₅	semidirect
157. C₄×#237	C₂×C₅	semidirect
158. D₃×#117	C₂×C₅	semidirect
159. #5518	C₂×C₅	semidirect
164. C₅×#127	C₂×D₃	semidirect
172. C₅×#125	C₂×D₃	semidirect
180. C₅×#123	C₂×D₃	semidirect
201. C₄×C₅×D₄	C₂×D₃	semidirect
253. C₃×#127	C₂²×C₅	semidirect
254. C₃×#125	C₂²×C₅	semidirect
255. C₃×#123	C₂²×C₅	semidirect
258. C₃×C₄×D₄	C₂²×C₅	semidirect
265. #936	C₂²×C₅	semidirect
267. #935	C₂²×C₅	semidirect
269. D₄×Dic₃	C₂²×C₅	semidirect
270. D₄×Dic₃	C₂²×C₅	semidirect
275. #924	C₂²×C₅	semidirect
276. C₂×C₄×Dic₃	C₂²×C₅	semidirect
283. #890	C₂²×C₅	semidirect
284. #889	C₂²×C₅	semidirect
285. #888	C₂²×C₅	semidirect
286. #887	C₂²×C₅	semidirect
287. #887	C₂²×C₅	semidirect
294. #879	C₂²×C₅	semidirect
295. #879	C₂²×C₅	semidirect
296. #878	C₂²×C₅	semidirect
298. #877	C₂²×C₅	semidirect
303. #870	C₂²×C₅	semidirect
304. #869	C₂²×C₅	semidirect
305. C₄×Dic₆	C₂²×C₅	semidirect
368. #540	C₅×D₃	semidirect
496. #127	C₂×C₅×D₃	semidirect
504. #125	C₂×C₅×D₃	semidirect
512. #123	C₂×C₅×D₃	semidirect
533. C₄×D₄	C₂×C₅×D₃	semidirect
667. C₃×C₅	#3455	semidirect
737. C₅	#86467	direct (N × H)
760. C₃	C₅×#3455	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#540	2
C₅×#5719	2
C₅×#5716	2
C₅×#5698	2
C₅×#5688	2
C₅×#5660	2
C₅×#5649	2
C₅×#5613	2
C₅×#5606	2
C₅×#5603	2
C₅×#5600	2
C₅×#5561	2
C₄×C₅×#237	2
C₅×D₃×#117	2
C₅×#5518	2
C₅×#3455	3
#86467	5

Subgroups — C5×#86467 #14481499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86467 #14481499