Subgroups — C₅×#80158 #14458431

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×#67	C₂	1	1	yes	maximal, characteristic
2	C₅×#5635	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5171	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5169	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5163	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5048	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4777	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4761	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4760	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4735	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3295	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	—	2	1	no	—
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₅×#953	—	2	1	no	—
24	C₅×#946	C₂²	1	1	yes	characteristic, complemented
25	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
27	C₅×#940	C₂²	1	1	yes	characteristic
28	C₅×#939	—	2	1	no	—
29	C₅×#938	C₂²	1	1	yes	characteristic
30	C₅×#937	—	2	1	no	—
31	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#930	C₂²	1	1	yes	characteristic
33	C₄×C₅×#67	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₅×#897	—	2	1	no	—
38	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₅×#889	—	2	1	no	—
40	C₅×#888	C₂²	1	1	yes	characteristic, complemented
41	C₅×#67⋊C₄	—	2	1	no	—
42	C₅×#878	—	2	1	no	—
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×#835	C₂²	1	1	yes	characteristic, complemented
47	C₅×#832	C₂²	1	1	yes	characteristic
48	C₅×#832	C₂²	1	1	yes	characteristic
49	C₅×#832	C₂²	1	1	yes	characteristic, complemented
50	C₅×#832	C₂²	1	1	yes	characteristic, complemented
51	C₅×#821	C₂²	1	1	yes	characteristic, complemented
52	C₅×#821	C₂²	1	1	yes	characteristic, complemented
53	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×#817	C₂²	1	1	yes	characteristic, complemented
55	C₅×#817	C₂²	1	1	yes	characteristic, complemented
56	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₅×#809	C₂²	1	1	yes	characteristic, complemented
59	C₅×#808	C₂²	1	1	yes	characteristic, complemented
60	#80158	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#554	—	3	1	no	—
62	C₅×D₄²	—	3	1	no	—
63	C₅×#486	—	3	1	no	—
64	C₅×#481	—	3	1	no	—
65	C₅×#481	—	3	1	no	—
66	C₅×#476	—	3	1	no	—
67	C₅×#465	—	3	1	no	—
68	C₅×#465	—	3	1	no	—
69	C₅×#460	—	3	1	no	—
70	C₅×#450	—	3	1	no	—
71	C₅×#450	D₃	1	1	yes	characteristic, complemented
72	C₄×C₅×SD₁₆	—	3	1	no	—
73	C₅×C₈×D₄	—	3	1	no	—
74	C₂×C₅×#102	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₂³×C₅×D₃	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	—	4	1	no	—
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	1	no	—
87	C₂×C₅×#67	—	2	1	no	—
88	C₂×C₅×#67	—	2	1	no	—
89	C₂×C₅×#67	—	2	1	no	—
90	C₂×C₅×#67	—	4	4	no	—
91	C₂×C₅×#67	D₄	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	—	2	1	no	—
93	C₂²×C₅×Dic₃	—	2	1	no	—
94	C₅×D₃×D₄	—	2	2	no	—
95	C₅×D₃×D₄	—	4	1	no	—
96	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₅×Dic₆	—	2	1	no	—
100	C₃×C₅×SD₁₆	—	2	2	no	—
101	C₃×C₅×SD₁₆	—	4	1	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₅×#217	—	2	1	no	—
108	C₅×#217	—	2	1	no	—
109	C₅×#217	D₄	1	1	yes	characteristic
110	C₅×#215	—	4	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
112	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
113	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	—	2	1	no	—
115	C₅×C₄⋊Dic₃	—	2	1	no	—
116	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
118	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
119	C₅×Dic₃⋊C₄	—	2	1	no	—
120	C₅×Dic₃⋊C₄	—	2	1	no	—
121	C₅×Dic₃⋊C₄	—	2	1	no	—
122	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
123	C₄×C₅×Dic₃	—	2	1	no	—
124	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	—	4	1	no	—
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₅×D₃×C₈	—	4	1	no	—
129	D₄×#67	C₂×C₅	1	1	yes	characteristic
130	#5635	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
132	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
133	#5171	C₂×C₅	1	1	yes	characteristic, complemented
134	#5169	C₂×C₅	1	1	yes	characteristic, complemented
135	#5163	C₂×C₅	1	1	yes	characteristic, complemented
136	Dic₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
137	#5048	C₂×C₅	1	1	yes	characteristic, complemented
138	#4777	C₂×C₅	1	1	yes	characteristic, complemented
139	D₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
140	#4761	C₂×C₅	1	1	yes	characteristic, complemented
141	#4760	C₂×C₅	1	1	yes	characteristic, complemented
142	#4735	C₂×C₅	1	1	yes	characteristic, complemented
143	#67⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₅×D₄	—	3	1	no	—
145	C₂²×C₅×D₄	—	6	1	no	—
146	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	—	3	1	no	—
148	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
149	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
150	C₂²×C₅×C₈	—	3	1	no	—
151	C₂²×C₅×C₈	—	3	1	no	—
152	C₅×C₄⋊Q₈	—	3	1	no	—
153	C₅×#127	—	3	1	no	—
154	C₅×#125	—	6	1	no	—
155	C₅×C₂²⋊Q₈	—	3	1	no	—
156	C₅×C₂²⋊Q₈	—	6	1	no	—
157	C₅×C₂²⋊Q₈	—	6	1	no	—
158	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
159	C₅×#121	—	3	1	no	—
160	C₅×#121	—	3	1	no	—
161	C₅×#121	—	6	1	no	—
162	C₅×#120	—	6	1	no	—
163	C₅×#120	—	6	1	no	—
164	C₄×C₅×Q₈	—	3	1	no	—
165	C₄×C₅×D₄	—	3	1	no	—
166	C₄×C₅×D₄	—	3	1	no	—
167	C₄×C₅×D₄	—	6	1	no	—
168	C₂×C₅×C₄⋊C₄	—	3	1	no	—
169	C₂×C₅×C₄⋊C₄	—	3	1	no	—
170	C₅×#106	—	3	1	no	—
171	C₅×#106	—	3	1	no	—
172	C₅×#106	—	3	1	no	—
173	C₅×C₄⋊C₈	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₅×#102	—	3	1	no	—
178	C₅×#102	—	3	1	no	—
179	C₅×#102	—	3	1	no	—
180	C₅×#102	—	3	1	no	—
181	C₅×#102	—	3	1	no	—
182	C₅×#102	C₂×D₃	1	1	yes	characteristic
183	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
186	C₄×C₅×C₈	—	3	1	no	—
187	#3295	—	3	1	no	Sylow
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	4	2	no	—
191	C₂³×C₃×C₅	—	4	2	no	—
192	C₂³×C₃×C₅	—	8	1	no	—
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₅×D₃	—	2	1	no	—
195	C₂²×C₅×D₃	—	4	2	no	—
196	C₂²×C₅×D₃	—	4	2	no	—
197	C₂²×C₅×D₃	—	8	1	no	—
198	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×D₄	—	2	1	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	4	2	no	—
205	C₃×C₅×D₄	#41	1	2	yes	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₅×#67	—	4	2	no	—
213	C₅×#67	—	4	2	no	—
214	C₅×#67	—	4	2	no	—
215	C₅×#67	—	4	2	no	—
216	C₅×#67	—	8	1	no	—
217	C₅×#67	SD₁₆	1	4	yes	complemented
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	2	1	no	—
220	C₂×C₅×Dic₃	—	2	1	no	—
221	C₂×C₅×Dic₃	—	4	2	no	—
222	C₂×C₅×Dic₃	—	8	1	no	—
223	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
224	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
225	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
226	C₅×D₁₂	—	2	1	no	—
227	C₅×D₁₂	—	2	1	no	—
228	C₄×C₅×D₃	—	2	1	no	—
229	C₄×C₅×D₃	—	2	1	no	—
230	C₄×C₅×D₃	—	8	1	no	—
231	C₅×Dic₆	—	8	1	no	—
232	C₃×C₅×C₈	—	2	1	no	—
233	C₃×C₅×C₈	—	2	1	no	—
234	C₅×C₃⋊C₈	—	2	1	no	—
235	C₅×C₃⋊C₈	—	2	1	no	—
236	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
237	C₂²×#67	—	2	1	no	—
238	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
242	#953	—	2	1	no	—
243	#946	C₂²×C₅	1	1	yes	characteristic, complemented
244	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
246	#940	C₂²×C₅	1	1	yes	characteristic
247	#939	—	2	1	no	—
248	#938	C₂²×C₅	1	1	yes	characteristic
249	#937	—	2	1	no	—
250	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
251	#930	C₂²×C₅	1	1	yes	characteristic
252	C₄×#67	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
256	#897	—	2	1	no	—
257	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
258	#889	—	2	1	no	—
259	#888	C₂²×C₅	1	1	yes	characteristic, complemented
260	#67⋊C₄	—	2	1	no	—
261	#878	—	2	1	no	—
262	C₃×#102	C₂²×C₅	1	1	yes	characteristic
263	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
265	#835	C₂²×C₅	1	1	yes	characteristic, complemented
266	#832	C₂²×C₅	1	1	yes	characteristic
267	#832	C₂²×C₅	1	1	yes	characteristic
268	#832	C₂²×C₅	1	1	yes	characteristic, complemented
269	#832	C₂²×C₅	1	1	yes	characteristic, complemented
270	#821	C₂²×C₅	1	1	yes	characteristic, complemented
271	#821	C₂²×C₅	1	1	yes	characteristic, complemented
272	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
273	#817	C₂²×C₅	1	1	yes	characteristic, complemented
274	#817	C₂²×C₅	1	1	yes	characteristic, complemented
275	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
277	#809	C₂²×C₅	1	1	yes	characteristic, complemented
278	#808	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	—	2	1	no	—
280	C₂⁴×C₅	—	6	1	no	—
281	C₂×C₅×Q₈	—	6	1	no	—
282	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₅×D₄	—	2	2	no	—
284	C₂×C₅×D₄	—	2	1	no	—
285	C₂×C₅×D₄	—	3	1	no	—
286	C₂×C₅×D₄	—	3	1	no	—
287	C₂×C₅×D₄	—	4	1	no	—
288	C₂×C₅×D₄	—	6	1	no	—
289	C₂×C₅×D₄	—	6	1	no	—
290	C₂×C₅×D₄	—	6	1	no	—
291	C₂×C₅×D₄	—	6	2	no	—
292	C₂×C₅×D₄	—	6	1	no	—
293	C₂×C₅×D₄	—	6	1	no	—
294	C₂×C₅×D₄	—	12	1	no	—
295	C₂×C₅×D₄	—	12	4	no	—
296	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	6	1	no	—
300	C₂²×C₄×C₅	—	6	1	no	—
301	C₂²×C₄×C₅	—	6	1	no	—
302	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
303	C₅×SD₁₆	—	2	2	no	—
304	C₅×SD₁₆	—	4	1	no	—
305	C₅×SD₁₆	—	12	1	no	—
306	C₂×C₅×C₈	—	3	1	no	—
307	C₂×C₅×C₈	—	3	1	no	—
308	C₂×C₅×C₈	—	12	1	no	—
309	C₂×C₅×C₈	—	12	1	no	—
310	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
311	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
312	C₅×C₄⋊C₄	—	2	1	no	—
313	C₅×C₄⋊C₄	—	3	1	no	—
314	C₅×C₄⋊C₄	—	3	1	no	—
315	C₅×C₄⋊C₄	—	3	1	no	—
316	C₅×C₄⋊C₄	—	3	1	no	—
317	C₅×C₄⋊C₄	—	6	1	no	—
318	C₅×C₄⋊C₄	—	6	1	no	—
319	C₅×C₄⋊C₄	—	6	1	no	—
320	C₅×C₄⋊C₄	—	6	1	no	—
321	C₅×C₄⋊C₄	—	6	1	no	—
322	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	—	2	1	no	—
324	C₅×C₂²⋊C₄	—	3	1	no	—
325	C₅×C₂²⋊C₄	—	3	1	no	—
326	C₅×C₂²⋊C₄	—	6	1	no	—
327	C₅×C₂²⋊C₄	—	6	1	no	—
328	C₅×C₂²⋊C₄	—	6	1	no	—
329	C₅×C₂²⋊C₄	—	6	1	no	—
330	C₄²×C₅	—	3	1	no	—
331	C₄²×C₅	—	6	1	no	—
332	#554	—	3	1	no	—
333	D₄²	—	3	1	no	—
334	#486	—	3	1	no	—
335	#481	—	3	1	no	—
336	#481	—	3	1	no	—
337	#476	—	3	1	no	—
338	#465	—	3	1	no	—
339	#465	—	3	1	no	—
340	#460	—	3	1	no	—
341	#450	—	3	1	no	—
342	#450	C₅×D₃	1	1	yes	characteristic, complemented
343	C₄×SD₁₆	—	3	1	no	—
344	C₈×D₄	—	3	1	no	—
345	C₂×#102	—	3	1	no	—
346	C₂×#102	—	3	1	no	—
347	C₂²×C₃×C₅	—	2	1	no	—
348	C₂²×C₃×C₅	—	2	1	no	—
349	C₂²×C₃×C₅	—	2	2	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	8	4	no	—
356	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
357	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₅×D₃	—	2	1	no	—
359	C₂×C₅×D₃	—	2	1	no	—
360	C₂×C₅×D₃	—	4	1	no	—
361	C₂×C₅×D₃	—	4	1	no	—
362	C₂×C₅×D₃	—	4	1	no	—
363	C₂×C₅×D₃	—	8	4	no	—
364	C₂×C₅×D₃	C₂×SD₁₆	1	2	yes	—
365	C₃×C₄×C₅	—	2	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₃×C₄×C₅	—	4	1	no	—
368	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
369	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
370	C₅×Dic₃	—	2	1	no	—
371	C₅×Dic₃	—	2	1	no	—
372	C₅×Dic₃	—	4	1	no	—
373	C₅×Dic₃	—	4	1	no	—
374	C₅×Dic₃	—	4	1	no	—
375	C₅×Dic₃	C₂×SD₁₆	1	2	yes	—
376	C₂⁴×C₃	—	2	1	no	—
377	C₂³×D₃	—	2	1	no	—
378	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×D₄	—	2	2	no	—
380	C₂×C₃×D₄	—	2	1	no	—
381	C₂×C₃×D₄	—	4	1	no	—
382	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×#67	—	2	1	no	—
386	C₂×#67	—	2	1	no	—
387	C₂×#67	—	2	1	no	—
388	C₂×#67	—	2	1	no	—
389	C₂×#67	—	2	1	no	—
390	C₂×#67	—	4	4	no	—
391	C₂×#67	C₅×D₄	1	1	yes	characteristic
392	C₂²×Dic₃	—	2	1	no	—
393	C₂²×Dic₃	—	2	1	no	—
394	D₃×D₄	—	2	2	no	—
395	D₃×D₄	—	4	1	no	—
396	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₄×D₃	—	2	1	no	—
398	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
399	C₂×Dic₆	—	2	1	no	—
400	C₃×SD₁₆	—	2	2	no	—
401	C₃×SD₁₆	—	4	1	no	—
402	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₃×C₄⋊C₄	—	2	1	no	—
405	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₂²⋊C₄	—	2	1	no	—
407	#217	—	2	1	no	—
408	#217	—	2	1	no	—
409	#217	C₅×D₄	1	1	yes	characteristic
410	#215	—	4	1	no	—
411	(C₂×D₃)⋊C₄	—	2	1	no	—
412	(C₂×D₃)⋊C₄	—	2	1	no	—
413	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
414	C₄⋊Dic₃	—	2	1	no	—
415	C₄⋊Dic₃	—	2	1	no	—
416	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
417	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
418	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
419	Dic₃⋊C₄	—	2	1	no	—
420	Dic₃⋊C₄	—	2	1	no	—
421	Dic₃⋊C₄	—	2	1	no	—
422	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
423	C₄×Dic₃	—	2	1	no	—
424	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₃⋊C₈	—	4	1	no	—
426	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
428	D₃×C₈	—	4	1	no	—
429	C₂³×C₅	—	2	1	no	—
430	C₂³×C₅	—	2	1	no	—
431	C₂³×C₅	—	3	1	no	—
432	C₂³×C₅	—	4	2	no	—
433	C₂³×C₅	—	4	2	no	—
434	C₂³×C₅	—	6	1	no	—
435	C₂³×C₅	—	8	1	no	—
436	C₂³×C₅	—	12	2	no	—
437	C₂³×C₅	—	12	2	no	—
438	C₂³×C₅	—	24	1	no	—
439	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
440	C₅×Q₈	—	2	1	no	—
441	C₅×Q₈	—	2	1	no	—
442	C₅×Q₈	—	24	1	no	—
443	C₅×D₄	—	2	1	no	—
444	C₅×D₄	—	2	1	no	—
445	C₅×D₄	—	2	1	no	—
446	C₅×D₄	—	3	4	no	—
447	C₅×D₄	—	4	2	no	—
448	C₅×D₄	—	6	1	no	—
449	C₅×D₄	—	6	1	no	—
450	C₅×D₄	—	12	2	no	—
451	C₅×D₄	—	12	2	no	—
452	C₅×D₄	—	12	2	no	—
453	C₅×D₄	—	12	2	no	—
454	C₅×D₄	—	24	1	no	—
455	C₅×D₄	#237	1	2	yes	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	3	1	no	—
461	C₂×C₄×C₅	—	3	1	no	—
462	C₂×C₄×C₅	—	3	1	no	—
463	C₂×C₄×C₅	—	6	1	no	—
464	C₂×C₄×C₅	—	6	1	no	—
465	C₂×C₄×C₅	—	6	1	no	—
466	C₂×C₄×C₅	—	6	1	no	—
467	C₂×C₄×C₅	—	6	1	no	—
468	C₂×C₄×C₅	—	12	2	no	—
469	C₂×C₄×C₅	—	24	1	no	—
470	C₂×C₄×C₅	—	24	1	no	—
471	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
472	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
473	C₅×C₈	—	2	1	no	—
474	C₅×C₈	—	2	1	no	—
475	C₅×C₈	—	6	1	no	—
476	C₅×C₈	—	6	1	no	—
477	C₂²×D₄	—	3	1	no	—
478	C₂²×D₄	—	6	1	no	—
479	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
480	C₂×SD₁₆	—	3	1	no	—
481	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
482	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
483	C₂²×C₈	—	3	1	no	—
484	C₂²×C₈	—	3	1	no	—
485	C₄⋊Q₈	—	3	1	no	—
486	#127	—	3	1	no	—
487	#125	—	6	1	no	—
488	C₂²⋊Q₈	—	3	1	no	—
489	C₂²⋊Q₈	—	6	1	no	—
490	C₂²⋊Q₈	—	6	1	no	—
491	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
492	#121	—	3	1	no	—
493	#121	—	3	1	no	—
494	#121	—	6	1	no	—
495	#120	—	6	1	no	—
496	#120	—	6	1	no	—
497	C₄×Q₈	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	6	1	no	—
501	C₂×C₄⋊C₄	—	3	1	no	—
502	C₂×C₄⋊C₄	—	3	1	no	—
503	#106	—	3	1	no	—
504	#106	—	3	1	no	—
505	#106	—	3	1	no	—
506	C₄⋊C₈	—	3	1	no	—
507	#103	—	3	1	no	—
508	#102	—	3	1	no	—
509	#102	—	3	1	no	—
510	#102	—	3	1	no	—
511	#102	—	3	1	no	—
512	#102	—	3	1	no	—
513	#102	—	3	1	no	—
514	#102	—	3	1	no	—
515	#102	C₂×C₅×D₃	1	1	yes	characteristic
516	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
517	C₂²⋊C₈	—	3	1	no	—
518	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
519	C₄×C₈	—	3	1	no	—
520	C₂×C₃×C₅	—	2	2	no	—
521	C₂×C₃×C₅	—	4	2	no	—
522	C₂×C₃×C₅	—	8	1	no	—
523	C₂×C₃×C₅	#546	1	1	yes	characteristic
524	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
525	C₂×C₃×C₅	#576	1	1	yes	characteristic
526	C₅×D₃	—	2	2	no	—
527	C₅×D₃	—	8	1	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	—	2	1	no	—
530	C₂³×C₃	—	4	2	no	—
531	C₂³×C₃	—	4	2	no	—
532	C₂³×C₃	—	8	1	no	—
533	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
534	C₂²×D₃	—	2	1	no	—
535	C₂²×D₃	—	4	2	no	—
536	C₂²×D₃	—	4	2	no	—
537	C₂²×D₃	—	8	1	no	—
538	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
539	C₃×Q₈	—	2	1	no	—
540	C₃×Q₈	—	2	1	no	—
541	C₃×D₄	—	2	1	no	—
542	C₃×D₄	—	2	1	no	—
543	C₃×D₄	—	2	1	no	—
544	C₃×D₄	—	4	2	no	—
545	C₃×D₄	C₅×#41	1	2	yes	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	#67	—	4	2	no	—
553	#67	—	4	2	no	—
554	#67	—	4	2	no	—
555	#67	—	4	2	no	—
556	#67	—	8	1	no	—
557	#67	C₅×SD₁₆	1	4	yes	complemented
558	C₂×Dic₃	—	2	1	no	—
559	C₂×Dic₃	—	2	1	no	—
560	C₂×Dic₃	—	2	1	no	—
561	C₂×Dic₃	—	4	2	no	—
562	C₂×Dic₃	—	8	1	no	—
563	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
564	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
566	D₁₂	—	2	1	no	—
567	D₁₂	—	2	1	no	—
568	C₄×D₃	—	2	1	no	—
569	C₄×D₃	—	2	1	no	—
570	C₄×D₃	—	8	1	no	—
571	Dic₆	—	8	1	no	—
572	C₃×C₈	—	2	1	no	—
573	C₃×C₈	—	2	1	no	—
574	C₃⋊C₈	—	2	1	no	—
575	C₃⋊C₈	—	2	1	no	—
576	C₂²×C₅	—	2	1	no	—
577	C₂²×C₅	—	2	1	no	—
578	C₂²×C₅	—	2	2	no	—
579	C₂²×C₅	—	3	2	no	—
580	C₂²×C₅	—	4	1	no	—
581	C₂²×C₅	—	4	1	no	—
582	C₂²×C₅	—	4	1	no	—
583	C₂²×C₅	—	4	1	no	—
584	C₂²×C₅	—	4	1	no	—
585	C₂²×C₅	—	6	1	no	—
586	C₂²×C₅	—	6	1	no	—
587	C₂²×C₅	—	8	4	no	—
588	C₂²×C₅	—	12	1	no	—
589	C₂²×C₅	—	12	1	no	—
590	C₂²×C₅	—	12	1	no	—
591	C₂²×C₅	—	24	4	no	—
592	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
593	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
594	C₄×C₅	—	2	1	no	—
595	C₄×C₅	—	3	2	no	—
596	C₄×C₅	—	4	1	no	—
597	C₄×C₅	—	4	1	no	—
598	C₄×C₅	—	6	1	no	—
599	C₄×C₅	—	6	1	no	—
600	C₄×C₅	—	12	1	no	—
601	C₄×C₅	—	12	1	no	—
602	C₄×C₅	—	12	1	no	—
603	C₄×C₅	C₂×#237	1	1	yes	characteristic
604	C₄×C₅	#1004	1	1	yes	characteristic
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	6	1	no	—
607	C₂×Q₈	—	6	1	no	—
608	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	3	1	no	—
612	C₂×D₄	—	3	1	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	—	6	1	no	—
615	C₂×D₄	—	6	1	no	—
616	C₂×D₄	—	6	1	no	—
617	C₂×D₄	—	6	2	no	—
618	C₂×D₄	—	6	1	no	—
619	C₂×D₄	—	6	1	no	—
620	C₂×D₄	—	12	1	no	—
621	C₂×D₄	—	12	4	no	—
622	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
623	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	6	1	no	—
626	C₂²×C₄	—	6	1	no	—
627	C₂²×C₄	—	6	1	no	—
628	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
629	SD₁₆	—	2	2	no	—
630	SD₁₆	—	4	1	no	—
631	SD₁₆	—	12	1	no	—
632	C₂×C₈	—	3	1	no	—
633	C₂×C₈	—	3	1	no	—
634	C₂×C₈	—	12	1	no	—
635	C₂×C₈	—	12	1	no	—
636	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	3	1	no	—
640	C₄⋊C₄	—	3	1	no	—
641	C₄⋊C₄	—	3	1	no	—
642	C₄⋊C₄	—	3	1	no	—
643	C₄⋊C₄	—	6	1	no	—
644	C₄⋊C₄	—	6	1	no	—
645	C₄⋊C₄	—	6	1	no	—
646	C₄⋊C₄	—	6	1	no	—
647	C₄⋊C₄	—	6	1	no	—
648	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	3	1	no	—
651	C₂²⋊C₄	—	3	1	no	—
652	C₂²⋊C₄	—	6	1	no	—
653	C₂²⋊C₄	—	6	1	no	—
654	C₂²⋊C₄	—	6	1	no	—
655	C₂²⋊C₄	—	6	1	no	—
656	C₄²	—	3	1	no	—
657	C₄²	—	6	1	no	—
658	C₃×C₅	#3295	1	1	yes	characteristic, complemented, Hall
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	1	no	—
661	C₂²×C₃	—	2	2	no	—
662	C₂²×C₃	—	4	1	no	—
663	C₂²×C₃	—	4	1	no	—
664	C₂²×C₃	—	4	1	no	—
665	C₂²×C₃	—	4	1	no	—
666	C₂²×C₃	—	4	1	no	—
667	C₂²×C₃	—	8	4	no	—
668	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
669	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
670	C₂×D₃	—	2	1	no	—
671	C₂×D₃	—	2	1	no	—
672	C₂×D₃	—	4	1	no	—
673	C₂×D₃	—	4	1	no	—
674	C₂×D₃	—	4	1	no	—
675	C₂×D₃	—	8	4	no	—
676	C₂×D₃	C₂×C₅×SD₁₆	1	2	yes	—
677	C₃×C₄	—	2	1	no	—
678	C₃×C₄	—	4	1	no	—
679	C₃×C₄	—	4	1	no	—
680	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
681	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
682	Dic₃	—	2	1	no	—
683	Dic₃	—	2	1	no	—
684	Dic₃	—	4	1	no	—
685	Dic₃	—	4	1	no	—
686	Dic₃	—	4	1	no	—
687	Dic₃	C₂×C₅×SD₁₆	1	2	yes	—
688	C₂×C₅	—	2	2	no	—
689	C₂×C₅	—	4	2	no	—
690	C₂×C₅	—	6	2	no	—
691	C₂×C₅	—	8	1	no	—
692	C₂×C₅	—	24	1	no	—
693	C₂×C₅	#5591	1	1	yes	characteristic
694	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
695	C₂×C₅	#5774	1	1	yes	characteristic
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	3	1	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	—	6	1	no	—
702	C₂³	—	8	1	no	—
703	C₂³	—	12	2	no	—
704	C₂³	—	12	2	no	—
705	C₂³	—	24	1	no	—
706	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
707	Q₈	—	2	1	no	—
708	Q₈	—	2	1	no	—
709	Q₈	—	24	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	2	1	no	—
713	D₄	—	3	4	no	—
714	D₄	—	4	2	no	—
715	D₄	—	6	1	no	—
716	D₄	—	6	1	no	—
717	D₄	—	12	2	no	—
718	D₄	—	12	2	no	—
719	D₄	—	12	2	no	—
720	D₄	—	12	2	no	—
721	D₄	—	24	1	no	—
722	D₄	C₅×#237	1	2	yes	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	3	1	no	—
728	C₂×C₄	—	3	1	no	—
729	C₂×C₄	—	3	1	no	—
730	C₂×C₄	—	6	1	no	—
731	C₂×C₄	—	6	1	no	—
732	C₂×C₄	—	6	1	no	—
733	C₂×C₄	—	6	1	no	—
734	C₂×C₄	—	6	1	no	—
735	C₂×C₄	—	12	2	no	—
736	C₂×C₄	—	24	1	no	—
737	C₂×C₄	—	24	1	no	—
738	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
740	C₈	—	2	1	no	—
741	C₈	—	2	1	no	—
742	C₈	—	6	1	no	—
743	C₈	—	6	1	no	—
744	C₂×C₃	—	2	2	no	—
745	C₂×C₃	—	4	2	no	—
746	C₂×C₃	—	8	1	no	—
747	C₂×C₃	C₅×#546	1	1	yes	characteristic
748	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
749	C₂×C₃	C₅×#576	1	1	yes	characteristic
750	D₃	—	2	2	no	—
751	D₃	—	8	1	no	—
752	C₅	#80158	1	1	yes	characteristic, direct product factor, Sylow
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	3	2	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	6	1	no	—
763	C₂²	—	6	1	no	—
764	C₂²	—	8	4	no	—
765	C₂²	—	12	1	no	—
766	C₂²	—	12	1	no	—
767	C₂²	—	12	1	no	—
768	C₂²	—	24	4	no	—
769	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
770	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	3	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	6	1	no	—
776	C₄	—	6	1	no	—
777	C₄	—	12	1	no	—
778	C₄	—	12	1	no	—
779	C₄	—	12	1	no	—
780	C₄	C₂×C₅×#237	1	1	yes	characteristic
781	C₄	C₅×#1004	1	1	yes	characteristic
782	C₃	C₅×#3295	1	1	yes	characteristic, complemented, Sylow
783	C₂	—	2	2	no	—
784	C₂	—	4	2	no	—
785	C₂	—	6	2	no	—
786	C₂	—	8	1	no	—
787	C₂	—	24	1	no	—
788	C₂	C₅×#5591	1	1	yes	characteristic
789	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
790	C₂	C₅×#5774	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#450	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×D₄×#67	C₂
hypercenter	C₅×#450	D₃
hypocenter	C₃	C₅×#3295
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#450

Complements

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

N	H ≅ G/N	type
2. C₅×#5635	C₂	semidirect
3. C₃×C₅×#450	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5171	C₂	semidirect
6. C₅×#5169	C₂	semidirect
7. C₅×#5163	C₂	semidirect
8. C₅×Dic₃×SD₁₆	C₂	semidirect
9. C₅×#5048	C₂	semidirect
10. C₅×#4777	C₂	semidirect
11. C₅×D₃×#102	C₂	semidirect
12. C₅×#4761	C₂	semidirect
13. C₅×#4760	C₂	semidirect
14. C₅×#4735	C₂	semidirect
15. C₅×#67⋊C₈	C₂	semidirect
21. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
22. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
24. C₅×#946	C₂²	semidirect
25. C₅×Q₈×Dic₃	C₂²	semidirect
26. C₂×C₅×#215	C₂²	semidirect
34. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
35. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
36. C₂×C₅×D₃×C₈	C₂²	semidirect
38. C₅×D₃×C₄⋊C₄	C₂²	semidirect
40. C₅×#888	C₂²	semidirect
44. C₃×C₅×#102	C₂²	semidirect
45. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
46. C₅×#835	C₂²	semidirect
49. C₅×#832	C₂²	semidirect
50. C₅×#832	C₂²	semidirect
51. C₅×#821	C₂²	semidirect
52. C₅×#821	C₂²	semidirect
53. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
54. C₅×#817	C₂²	semidirect
55. C₅×#817	C₂²	semidirect
56. C₅×Dic₃⋊C₈	C₂²	semidirect
57. C₅×C₈×Dic₃	C₂²	semidirect
58. C₅×#809	C₂²	semidirect
59. C₅×#808	C₂²	semidirect
60. #80158	C₅	direct (N × H)
71. C₅×#450	D₃	semidirect
130. #5635	C₂×C₅	semidirect
131. C₃×#450	C₂×C₅	semidirect
132. C₂×#832	C₂×C₅	semidirect
133. #5171	C₂×C₅	semidirect
134. #5169	C₂×C₅	semidirect
135. #5163	C₂×C₅	semidirect
136. Dic₃×SD₁₆	C₂×C₅	semidirect
137. #5048	C₂×C₅	semidirect
138. #4777	C₂×C₅	semidirect
139. D₃×#102	C₂×C₅	semidirect
140. #4761	C₂×C₅	semidirect
141. #4760	C₂×C₅	semidirect
142. #4735	C₂×C₅	semidirect
143. #67⋊C₈	C₂×C₅	semidirect
149. C₂×C₅×SD₁₆	C₂×D₃	semidirect
158. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
183. C₅×#102	C₂×D₃	semidirect
185. C₅×C₂²⋊C₈	C₂×D₃	semidirect
217. C₅×#67	SD₁₆	semidirect
240. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
241. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
243. #946	C₂²×C₅	semidirect
244. Q₈×Dic₃	C₂²×C₅	semidirect
245. C₂×#215	C₂²×C₅	semidirect
253. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
254. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
255. C₂×D₃×C₈	C₂²×C₅	semidirect
257. D₃×C₄⋊C₄	C₂²×C₅	semidirect
259. #888	C₂²×C₅	semidirect
263. C₃×#102	C₂²×C₅	semidirect
264. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
265. #835	C₂²×C₅	semidirect
268. #832	C₂²×C₅	semidirect
269. #832	C₂²×C₅	semidirect
270. #821	C₂²×C₅	semidirect
271. #821	C₂²×C₅	semidirect
272. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
273. #817	C₂²×C₅	semidirect
274. #817	C₂²×C₅	semidirect
275. Dic₃⋊C₈	C₂²×C₅	semidirect
276. C₈×Dic₃	C₂²×C₅	semidirect
277. #809	C₂²×C₅	semidirect
278. #808	C₂²×C₅	semidirect
342. #450	C₅×D₃	semidirect
482. C₂×SD₁₆	C₂×C₅×D₃	semidirect
491. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
516. #102	C₂×C₅×D₃	semidirect
518. C₂²⋊C₈	C₂×C₅×D₃	semidirect
557. #67	C₅×SD₁₆	semidirect
658. C₃×C₅	#3295	semidirect
752. C₅	#80158	direct (N × H)
782. C₃	C₅×#3295	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×#67	2
C₅×#5635	2
C₃×C₅×#450	2
C₂×C₅×#832	2
C₅×#5171	2
C₅×#5169	2
C₅×#5163	2
C₅×Dic₃×SD₁₆	2
C₅×#5048	2
C₅×#4777	2
C₅×D₃×#102	2
C₅×#4761	2
C₅×#4760	2
C₅×#4735	2
C₅×#67⋊C₈	2
C₅×#3295	3
#80158	5

Subgroups — C5×#80158 #14458431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80158 #14458431