Subgroups — C₅×#80414 #14471503

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5721	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic
4	C₅×#5162	C₂	1	2	yes	maximal
5	C₅×Dic₃×SD₁₆	C₂	1	2	yes	maximal
6	C₅×#5079	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#214	C₂	1	1	yes	maximal, characteristic
8	C₅×#4851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4830	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4792	C₂	1	2	yes	maximal, complemented
11	C₅×#4791	C₂	1	2	yes	maximal, complemented
12	C₅×#3359	—	3	1	no	maximal, Hall
13	C₂²×C₅×Dic₆	—	2	1	no	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
18	C₅×#944	C₂²	1	2	yes	—
19	C₅×D₄×Dic₃	C₂²	1	2	yes	—
20	C₂×C₅×#214	C₂²	1	1	yes	characteristic
21	C₅×#924	—	2	1	no	—
22	C₅×#890	—	2	1	no	—
23	C₅×#889	—	2	2	no	—
24	C₅×#888	C₂²	1	2	yes	—
25	C₅×#887	—	2	1	no	—
26	C₅×#878	—	2	2	no	—
27	C₅×#869	C₂²	1	1	yes	characteristic
28	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₅×#835	C₂²	1	2	yes	—
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#832	C₂²	1	1	yes	characteristic
35	C₅×#817	C₂²	1	2	yes	—
36	C₅×#816	C₂²	1	2	yes	—
37	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×#810	C₂²	1	1	yes	characteristic
40	C₅×#808	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#80414	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#557	—	3	1	no	—
44	C₅×D₄×Q₈	—	3	1	no	—
45	C₅×#487	—	3	2	no	—
46	C₅×#487	—	3	1	no	—
47	C₅×#475	—	3	1	no	—
48	C₅×#475	—	3	2	no	—
49	C₅×#461	—	3	2	no	—
50	C₅×#461	D₃	1	1	yes	characteristic
51	C₅×C₈×Q₈	—	3	1	no	—
52	C₄×C₅×SD₁₆	—	3	2	no	—
53	C₄×C₅×SD₁₆	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₂×C₅×Dic₆	—	2	1	no	—
59	C₂×C₅×Dic₆	—	2	2	no	—
60	C₂×C₅×Dic₆	—	4	4	no	—
61	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
62	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#217	—	2	2	no	—
71	C₅×#214	—	2	2	no	—
72	C₅×C₄⋊Dic₃	—	2	1	no	—
73	C₅×C₄⋊Dic₃	—	2	2	no	—
74	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
75	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
76	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
77	C₅×Dic₃⋊C₄	—	2	1	no	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₅×Dic₃⋊C₄	—	2	2	no	—
80	C₅×Dic₃⋊C₄	—	2	2	no	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	—	2	1	no	—
83	C₄×C₅×Dic₃	—	2	2	no	—
84	C₄×C₅×Dic₃	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	#5721	C₂×C₅	1	1	yes	characteristic, complemented
88	D₄×Dic₆	C₂×C₅	1	1	yes	characteristic
89	C₃×#461	C₂×C₅	1	1	yes	characteristic
90	#5162	C₂×C₅	1	2	yes	—
91	Dic₃×SD₁₆	C₂×C₅	1	2	yes	—
92	#5079	C₂×C₅	1	1	yes	characteristic, complemented
93	C₄×#214	C₂×C₅	1	1	yes	characteristic
94	#4851	C₂×C₅	1	1	yes	characteristic, complemented
95	#4830	C₂×C₅	1	1	yes	characteristic, complemented
96	#4792	C₂×C₅	1	2	yes	complemented
97	#4791	C₂×C₅	1	2	yes	complemented
98	C₂²×C₅×Q₈	—	6	1	no	—
99	C₂×C₅×SD₁₆	—	3	1	no	—
100	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
101	C₅×C₄⋊Q₈	—	3	2	no	—
102	C₅×C₄⋊Q₈	—	3	2	no	—
103	C₅×C₄⋊Q₈	—	3	1	no	—
104	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
105	C₅×#125	—	6	2	no	—
106	C₅×#125	—	6	1	no	—
107	C₅×C₂²⋊Q₈	—	6	2	no	—
108	C₅×C₂²⋊Q₈	—	6	1	no	—
109	C₄×C₅×Q₈	—	3	1	no	—
110	C₄×C₅×Q₈	—	3	2	no	—
111	C₄×C₅×Q₈	—	3	1	no	—
112	C₄×C₅×Q₈	—	6	1	no	—
113	C₄×C₅×D₄	—	3	2	no	—
114	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
115	C₅×#106	—	3	2	no	—
116	C₅×#106	—	3	1	no	—
117	C₅×C₄⋊C₈	—	3	2	no	—
118	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
119	C₅×#103	—	3	2	no	—
120	C₅×#103	—	3	2	no	—
121	C₅×#103	—	3	2	no	—
122	C₅×#103	—	3	1	no	—
123	C₅×#103	C₂×D₃	1	2	yes	—
124	C₅×#102	—	3	1	no	—
125	C₄×C₅×C₈	—	3	2	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	#3359	—	3	1	no	Sylow
128	C₂³×C₃×C₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	#41	1	2	yes	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂×C₅×Dic₃	—	2	1	no	—
140	C₂×C₅×Dic₃	—	2	1	no	—
141	C₂×C₅×Dic₃	—	2	2	no	—
142	C₂×C₅×Dic₃	—	4	4	no	—
143	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
144	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
145	C₅×Dic₆	—	2	1	no	—
146	C₅×Dic₆	—	2	1	no	—
147	C₅×Dic₆	—	4	2	no	—
148	C₅×Dic₆	—	4	4	no	—
149	C₅×Dic₆	SD₁₆	1	4	yes	complemented
150	C₃×C₅×C₈	—	2	2	no	—
151	C₅×C₃⋊C₈	—	2	1	no	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₂²×Dic₆	—	2	1	no	—
154	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
155	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
157	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
158	#944	C₂²×C₅	1	2	yes	—
159	D₄×Dic₃	C₂²×C₅	1	2	yes	—
160	C₂×#214	C₂²×C₅	1	1	yes	characteristic
161	#924	—	2	1	no	—
162	#890	—	2	1	no	—
163	#889	—	2	2	no	—
164	#888	C₂²×C₅	1	2	yes	—
165	#887	—	2	1	no	—
166	#878	—	2	2	no	—
167	#869	C₂²×C₅	1	1	yes	characteristic
168	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
169	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×#103	C₂²×C₅	1	2	yes	—
172	#835	C₂²×C₅	1	2	yes	—
173	#835	C₂²×C₅	1	2	yes	—
174	#832	C₂²×C₅	1	1	yes	characteristic
175	#817	C₂²×C₅	1	2	yes	—
176	#816	C₂²×C₅	1	2	yes	—
177	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
178	C₈×Dic₃	C₂²×C₅	1	2	yes	—
179	#810	C₂²×C₅	1	1	yes	characteristic
180	#808	C₂²×C₅	1	1	yes	characteristic
181	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₅×Q₈	—	3	1	no	—
183	C₂×C₅×Q₈	—	3	1	no	—
184	C₂×C₅×Q₈	—	6	2	no	—
185	C₂×C₅×Q₈	—	6	1	no	—
186	C₂×C₅×Q₈	—	12	4	no	—
187	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
188	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	6	2	no	—
191	C₅×SD₁₆	—	2	4	no	—
192	C₅×SD₁₆	—	6	2	no	—
193	C₂×C₅×C₈	—	3	1	no	—
194	C₂×C₅×C₈	—	3	1	no	—
195	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	3	2	no	—
199	C₅×C₄⋊C₄	—	3	1	no	—
200	C₅×C₄⋊C₄	—	3	2	no	—
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	—	6	2	no	—
203	C₅×C₄⋊C₄	—	6	2	no	—
204	C₅×C₄⋊C₄	—	6	2	no	—
205	C₅×C₄⋊C₄	—	6	2	no	—
206	C₅×C₄⋊C₄	—	6	1	no	—
207	C₅×C₄⋊C₄	—	6	1	no	—
208	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	6	2	no	—
211	C₄²×C₅	—	3	2	no	—
212	C₄²×C₅	—	6	2	no	—
213	C₄²×C₅	—	6	1	no	—
214	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
215	#557	—	3	1	no	—
216	D₄×Q₈	—	3	1	no	—
217	#487	—	3	1	no	—
218	#487	—	3	2	no	—
219	#475	—	3	1	no	—
220	#475	—	3	2	no	—
221	#461	—	3	2	no	—
222	#461	C₅×D₃	1	1	yes	characteristic
223	C₈×Q₈	—	3	1	no	—
224	C₄×SD₁₆	—	3	2	no	—
225	C₄×SD₁₆	—	3	1	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	4	1	no	—
228	C₂²×C₃×C₅	—	4	1	no	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
234	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
236	C₅×Dic₃	—	2	2	no	—
237	C₅×Dic₃	—	4	1	no	—
238	C₅×Dic₃	—	4	2	no	—
239	C₅×Dic₃	—	4	1	no	—
240	C₅×Dic₃	C₂×SD₁₆	1	4	yes	—
241	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
242	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×Dic₃	—	2	2	no	—
245	C₂×Dic₆	—	2	1	no	—
246	C₂×Dic₆	—	2	2	no	—
247	C₂×Dic₆	—	4	4	no	—
248	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
249	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
250	C₃×SD₁₆	—	2	4	no	—
251	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
252	C₃×C₄⋊C₄	—	2	1	no	—
253	C₃×C₄⋊C₄	—	2	1	no	—
254	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
255	C₃×C₂²⋊C₄	—	2	1	no	—
256	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#217	—	2	2	no	—
258	#214	—	2	2	no	—
259	C₄⋊Dic₃	—	2	1	no	—
260	C₄⋊Dic₃	—	2	2	no	—
261	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
262	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
263	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
264	Dic₃⋊C₄	—	2	1	no	—
265	Dic₃⋊C₄	—	2	2	no	—
266	Dic₃⋊C₄	—	2	2	no	—
267	Dic₃⋊C₄	—	2	2	no	—
268	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
269	C₄×Dic₃	—	2	1	no	—
270	C₄×Dic₃	—	2	2	no	—
271	C₄×Dic₃	C₂³×C₅	1	2	yes	—
272	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂³×C₅	—	2	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	3	4	no	—
278	C₅×Q₈	—	6	1	no	—
279	C₅×Q₈	—	6	1	no	—
280	C₅×Q₈	—	12	4	no	—
281	C₅×Q₈	—	12	2	no	—
282	C₅×D₄	—	2	1	no	—
283	C₅×D₄	#237	1	2	yes	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	4	2	no	—
289	C₂×C₄×C₅	—	6	1	no	—
290	C₂×C₄×C₅	—	6	1	no	—
291	C₂×C₄×C₅	—	6	2	no	—
292	C₂×C₄×C₅	—	12	4	no	—
293	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
296	C₅×C₈	—	2	2	no	—
297	C₅×C₈	—	6	1	no	—
298	C₅×C₈	—	6	1	no	—
299	C₂²×Q₈	—	6	1	no	—
300	C₂×SD₁₆	—	3	1	no	—
301	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
302	C₄⋊Q₈	—	3	2	no	—
303	C₄⋊Q₈	—	3	2	no	—
304	C₄⋊Q₈	—	3	1	no	—
305	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
306	#125	—	6	2	no	—
307	#125	—	6	1	no	—
308	C₂²⋊Q₈	—	6	2	no	—
309	C₂²⋊Q₈	—	6	1	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	—	3	2	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	6	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
316	#106	—	3	2	no	—
317	#106	—	3	1	no	—
318	C₄⋊C₈	—	3	2	no	—
319	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
320	#103	—	3	2	no	—
321	#103	—	3	2	no	—
322	#103	—	3	2	no	—
323	#103	—	3	1	no	—
324	#103	C₂×C₅×D₃	1	2	yes	—
325	#102	—	3	1	no	—
326	C₄×C₈	—	3	2	no	—
327	C₄×C₈	—	3	1	no	—
328	C₂×C₃×C₅	—	4	2	no	—
329	C₂×C₃×C₅	#548	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
331	C₂×C₃×C₅	#578	1	1	yes	characteristic
332	C₂³×C₃	—	2	1	no	—
333	C₃×Q₈	—	2	2	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×D₄	—	2	1	no	—
336	C₃×D₄	C₅×#41	1	2	yes	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	4	2	no	—
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
343	C₂×Dic₃	—	2	1	no	—
344	C₂×Dic₃	—	2	1	no	—
345	C₂×Dic₃	—	2	2	no	—
346	C₂×Dic₃	—	4	4	no	—
347	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
348	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
349	Dic₆	—	2	1	no	—
350	Dic₆	—	2	1	no	—
351	Dic₆	—	4	2	no	—
352	Dic₆	—	4	4	no	—
353	Dic₆	C₅×SD₁₆	1	4	yes	complemented
354	C₃×C₈	—	2	2	no	—
355	C₃⋊C₈	—	2	1	no	—
356	C₃⋊C₈	—	2	1	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	3	4	no	—
363	C₄×C₅	—	4	1	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	6	2	no	—
366	C₄×C₅	—	12	2	no	—
367	C₄×C₅	—	12	1	no	—
368	C₄×C₅	—	12	1	no	—
369	C₄×C₅	D₃×SD₁₆	1	2	yes	—
370	C₄×C₅	C₂×#237	1	1	yes	characteristic
371	C₄×C₅	#1010	1	1	yes	characteristic
372	C₂×Q₈	—	3	1	no	—
373	C₂×Q₈	—	3	1	no	—
374	C₂×Q₈	—	6	2	no	—
375	C₂×Q₈	—	6	1	no	—
376	C₂×Q₈	—	12	4	no	—
377	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
378	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	6	2	no	—
381	SD₁₆	—	2	4	no	—
382	SD₁₆	—	6	2	no	—
383	C₂×C₈	—	3	1	no	—
384	C₂×C₈	—	3	1	no	—
385	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	3	2	no	—
389	C₄⋊C₄	—	3	1	no	—
390	C₄⋊C₄	—	3	1	no	—
391	C₄⋊C₄	—	3	2	no	—
392	C₄⋊C₄	—	6	2	no	—
393	C₄⋊C₄	—	6	2	no	—
394	C₄⋊C₄	—	6	2	no	—
395	C₄⋊C₄	—	6	2	no	—
396	C₄⋊C₄	—	6	1	no	—
397	C₄⋊C₄	—	6	1	no	—
398	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	6	2	no	—
401	C₄²	—	3	2	no	—
402	C₄²	—	6	2	no	—
403	C₄²	—	6	1	no	—
404	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
405	C₃×C₅	#3359	1	1	yes	characteristic, complemented, Hall
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	4	1	no	—
408	C₂²×C₃	—	4	1	no	—
409	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	4	1	no	—
413	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
414	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
415	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
416	Dic₃	—	2	2	no	—
417	Dic₃	—	4	1	no	—
418	Dic₃	—	4	2	no	—
419	Dic₃	—	4	1	no	—
420	Dic₃	C₂×C₅×SD₁₆	1	4	yes	—
421	C₂×C₅	—	4	2	no	—
422	C₂×C₅	#5598	1	1	yes	characteristic
423	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
424	C₂×C₅	#5779	1	1	yes	characteristic
425	C₂³	—	2	1	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	3	4	no	—
429	Q₈	—	6	1	no	—
430	Q₈	—	6	1	no	—
431	Q₈	—	12	4	no	—
432	Q₈	—	12	2	no	—
433	D₄	—	2	1	no	—
434	D₄	C₅×#237	1	2	yes	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	6	1	no	—
441	C₂×C₄	—	6	1	no	—
442	C₂×C₄	—	6	2	no	—
443	C₂×C₄	—	12	4	no	—
444	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
445	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	6	1	no	—
449	C₈	—	6	1	no	—
450	C₂×C₃	—	4	2	no	—
451	C₂×C₃	C₅×#548	1	1	yes	characteristic
452	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
453	C₂×C₃	C₅×#578	1	1	yes	characteristic
454	C₅	#80414	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	2	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	3	4	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	6	2	no	—
464	C₄	—	12	2	no	—
465	C₄	—	12	1	no	—
466	C₄	—	12	1	no	—
467	C₄	C₅×D₃×SD₁₆	1	2	yes	—
468	C₄	C₂×C₅×#237	1	1	yes	characteristic
469	C₄	C₅×#1010	1	1	yes	characteristic
470	C₃	C₅×#3359	1	1	yes	characteristic, complemented, Sylow
471	C₂	—	4	2	no	—
472	C₂	C₅×#5598	1	1	yes	characteristic
473	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
474	C₂	C₅×#5779	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×#461	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×D₄	C₂³
hypercenter	C₅×#461	D₃
hypocenter	C₃	C₅×#3359
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#461

Complements

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

N	H ≅ G/N	type
1. C₅×#5721	C₂	semidirect
6. C₅×#5079	C₂	semidirect
8. C₅×#4851	C₂	semidirect
9. C₅×#4830	C₂	semidirect
10. C₅×#4792	C₂	semidirect
11. C₅×#4791	C₂	semidirect
42. #80414	C₅	direct (N × H)
87. #5721	C₂×C₅	semidirect
92. #5079	C₂×C₅	semidirect
94. #4851	C₂×C₅	semidirect
95. #4830	C₂×C₅	semidirect
96. #4792	C₂×C₅	semidirect
97. #4791	C₂×C₅	semidirect
149. C₅×Dic₆	SD₁₆	semidirect
353. Dic₆	C₅×SD₁₆	semidirect
405. C₃×C₅	#3359	semidirect
454. C₅	#80414	direct (N × H)
470. C₃	C₅×#3359	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5721	2
C₅×D₄×Dic₆	2
C₃×C₅×#461	2
C₅×#5162	2
C₅×Dic₃×SD₁₆	2
C₅×#5079	2
C₄×C₅×#214	2
C₅×#4851	2
C₅×#4830	2
C₅×#4792	2
C₅×#4791	2
C₅×#3359	3
#80414	5

Subgroups — C5×#80414 #14471503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80414 #14471503