Subgroups — C₅×#79090 #14430783

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5521	C₂	1	1	yes	maximal, characteristic
2	C₅×#5519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5131	C₂	1	1	yes	maximal, characteristic
5	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
7	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4847	C₂	1	2	yes	maximal, complemented
9	C₅×#4847	C₂	1	2	yes	maximal, complemented
10	C₅×#4846	C₂	1	2	yes	maximal, complemented
11	C₅×#4842	C₂	1	2	yes	maximal, complemented
12	C₅×#3081	—	3	1	no	maximal, Hall
13	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₅×#926	C₂²	1	1	yes	characteristic
18	C₅×#926	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#893	—	2	1	no	—
21	C₅×#893	—	2	1	no	—
22	C₅×#890	—	2	1	no	—
23	C₅×#888	—	2	1	no	—
24	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
25	C₅×#878	—	2	2	no	—
26	C₄×C₅×D₁₂	C₂²	1	2	yes	—
27	C₄×C₅×D₁₂	C₂²	1	2	yes	—
28	C₅×#870	C₂²	1	2	yes	complemented
29	C₅×#869	C₂²	1	2	yes	complemented
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
32	C₅×#821	C₂²	1	2	yes	—
33	C₅×#821	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	2	yes	—
35	C₅×#821	C₂²	1	2	yes	—
36	C₅×#818	C₂²	1	1	yes	characteristic, complemented
37	C₅×#818	C₂²	1	2	yes	complemented
38	C₅×#818	C₂²	1	1	yes	characteristic, complemented
39	C₅×#817	C₂²	1	1	yes	characteristic, complemented
40	C₅×#817	C₂²	1	2	yes	complemented
41	C₅×#817	C₂²	1	1	yes	characteristic, complemented
42	#79090	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#544	—	3	1	no	—
44	C₅×#518	—	3	1	no	—
45	C₅×#478	—	3	2	no	—
46	C₅×#478	—	3	2	no	—
47	C₅×#476	—	3	2	no	—
48	C₅×#474	—	3	2	no	—
49	C₅×#428	—	3	1	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#424	D₃	1	1	yes	characteristic, complemented
52	C₅×#418	—	3	1	no	—
53	C₂×C₅×#102	—	3	1	no	—
54	C₂³×C₅×D₃	—	2	1	no	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	—	2	1	no	—
57	C₂×C₅×D₁₂	—	2	1	no	—
58	C₂×C₅×D₁₂	—	2	2	no	—
59	C₂×C₅×D₁₂	Q₈	1	4	yes	complemented
60	C₂×C₅×D₁₂	C₂³	1	2	yes	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₅×Dic₆	—	2	2	no	—
64	C₃×C₅×M₁₆	—	2	2	no	—
65	C₂×C₃×C₅×C₈	—	2	2	no	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	—
73	C₅×#217	—	2	1	no	—
74	C₅×#217	—	2	1	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
76	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
77	C₅×C₄⋊Dic₃	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	2	1	no	—
79	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
81	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₄×C₅×Dic₃	—	2	1	no	—
87	C₄×C₅×Dic₃	—	2	1	no	—
88	#5521	C₂×C₅	1	1	yes	characteristic
89	#5519	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
91	#5131	C₂×C₅	1	1	yes	characteristic
92	#5121	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×#821	C₂×C₅	1	1	yes	characteristic
94	#5106	C₂×C₅	1	1	yes	characteristic, complemented
95	#4847	C₂×C₅	1	2	yes	complemented
96	#4847	C₂×C₅	1	2	yes	complemented
97	#4846	C₂×C₅	1	2	yes	complemented
98	#4842	C₂×C₅	1	2	yes	complemented
99	C₂²×C₅×D₄	—	3	1	no	—
100	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	3	2	no	—
103	C₅×C₄⋊Q₈	—	6	1	no	—
104	C₅×#125	—	3	2	no	—
105	C₅×#125	—	6	1	no	—
106	C₅×C₂²⋊Q₈	—	6	2	no	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	6	1	no	—
110	C₄×C₅×D₄	—	6	1	no	—
111	C₅×#117	—	3	1	no	—
112	C₅×#117	—	3	1	no	—
113	C₅×#117	C₂×D₃	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	—	3	1	no	—
115	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
116	C₅×#107	—	3	1	no	—
117	C₅×#107	—	3	1	no	—
118	C₅×#107	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×#106	—	3	1	no	—
121	C₅×#106	—	3	2	no	—
122	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
123	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×#102	—	3	2	no	—
128	#3081	—	3	1	no	Sylow
129	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₅×D₃	—	2	2	no	—
131	C₂²×C₅×D₃	—	2	4	no	—
132	C₂²×C₅×D₃	—	8	1	no	—
133	C₂²×C₅×D₃	—	8	1	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
138	C₂×C₃×C₄×C₅	#41	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×C₅×Dic₃	—	2	1	no	—
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	1	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	—	8	1	no	—
146	C₅×D₁₂	—	2	4	no	—
147	C₅×D₁₂	—	2	2	no	—
148	C₅×D₁₂	C₂×Q₈	1	4	yes	—
149	C₄×C₅×D₃	—	8	2	no	—
150	C₄×C₅×D₃	—	8	2	no	—
151	C₅×Dic₆	—	8	2	no	—
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	—	2	1	no	—
154	C₃×C₅×C₈	—	2	2	no	—
155	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
158	C₃×#117	C₂²×C₅	1	1	yes	characteristic
159	#926	C₂²×C₅	1	1	yes	characteristic
160	#926	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
162	#893	—	2	1	no	—
163	#893	—	2	1	no	—
164	#890	—	2	1	no	—
165	#888	—	2	1	no	—
166	D₃×C₂²⋊C₄	—	2	2	no	—
167	#878	—	2	2	no	—
168	C₄×D₁₂	C₂²×C₅	1	2	yes	—
169	C₄×D₁₂	C₂²×C₅	1	2	yes	—
170	#870	C₂²×C₅	1	2	yes	complemented
171	#869	C₂²×C₅	1	2	yes	complemented
172	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
173	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
174	#821	C₂²×C₅	1	2	yes	—
175	#821	C₂²×C₅	1	2	yes	—
176	#821	C₂²×C₅	1	2	yes	—
177	#821	C₂²×C₅	1	2	yes	—
178	#818	C₂²×C₅	1	2	yes	complemented
179	#818	C₂²×C₅	1	1	yes	characteristic, complemented
180	#818	C₂²×C₅	1	1	yes	characteristic, complemented
181	#817	C₂²×C₅	1	2	yes	complemented
182	#817	C₂²×C₅	1	1	yes	characteristic, complemented
183	#817	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₂⁴×C₅	—	6	1	no	—
185	C₂×C₅×Q₈	—	6	2	no	—
186	C₂×C₅×D₄	—	3	4	no	—
187	C₂×C₅×D₄	—	3	2	no	—
188	C₂×C₅×D₄	—	6	1	no	—
189	C₂×C₅×D₄	—	6	2	no	—
190	C₂²×C₄×C₅	—	6	1	no	—
191	C₂²×C₄×C₅	—	6	2	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₅×M₁₆	—	2	2	no	—
195	C₂×C₅×C₈	—	2	2	no	—
196	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
199	C₅×C₄⋊C₄	—	3	2	no	—
200	C₅×C₄⋊C₄	—	3	1	no	—
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×C₄⋊C₄	—	3	1	no	—
204	C₅×C₄⋊C₄	—	6	1	no	—
205	C₅×C₄⋊C₄	—	6	2	no	—
206	C₅×C₄⋊C₄	—	6	2	no	—
207	C₅×C₄⋊C₄	—	6	2	no	—
208	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
209	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
210	C₅×C₂²⋊C₄	—	6	1	no	—
211	C₅×C₂²⋊C₄	—	6	1	no	—
212	C₅×C₂²⋊C₄	—	6	2	no	—
213	C₅×C₂²⋊C₄	—	6	2	no	—
214	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
215	C₄²×C₅	—	6	1	no	—
216	C₄²×C₅	—	6	1	no	—
217	C₄²×C₅	C₂²×D₃	1	2	yes	—
218	#544	—	3	1	no	—
219	#518	—	3	1	no	—
220	#478	—	3	2	no	—
221	#478	—	3	2	no	—
222	#476	—	3	2	no	—
223	#474	—	3	2	no	—
224	#428	—	3	1	no	—
225	#427	—	3	1	no	—
226	#424	C₅×D₃	1	1	yes	characteristic, complemented
227	#418	—	3	1	no	—
228	C₂×#102	—	3	1	no	—
229	C₂²×C₃×C₅	—	2	1	no	—
230	C₂²×C₃×C₅	—	2	1	no	—
231	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₅×D₃	—	2	4	no	—
234	C₂×C₅×D₃	—	4	2	no	—
235	C₂×C₅×D₃	—	4	2	no	—
236	C₂×C₅×D₃	—	8	4	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
240	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₅×Dic₃	—	4	1	no	—
243	C₅×Dic₃	—	4	2	no	—
244	C₅×Dic₃	—	4	1	no	—
245	C₅×Dic₃	—	4	1	no	—
246	C₅×Dic₃	—	4	1	no	—
247	C₂³×D₃	—	2	1	no	—
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×Dic₃	—	2	1	no	—
250	C₂×D₁₂	—	2	1	no	—
251	C₂×D₁₂	—	2	2	no	—
252	C₂×D₁₂	C₅×Q₈	1	4	yes	complemented
253	C₂×D₁₂	C₂³×C₅	1	2	yes	—
254	C₂×C₄×D₃	—	2	2	no	—
255	C₂×C₄×D₃	—	2	2	no	—
256	C₂×Dic₆	—	2	2	no	—
257	C₃×M₁₆	—	2	2	no	—
258	C₂×C₃×C₈	—	2	2	no	—
259	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
261	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
264	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
265	C₃×C₄²	C₂³×C₅	1	2	yes	—
266	#217	—	2	1	no	—
267	#217	—	2	1	no	—
268	(C₂×D₃)⋊C₄	—	2	2	no	—
269	(C₂×D₃)⋊C₄	—	2	2	no	—
270	C₄⋊Dic₃	—	2	2	no	—
271	C₄⋊Dic₃	—	2	1	no	—
272	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
273	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
275	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
276	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
277	Dic₃⋊C₄	—	2	2	no	—
278	Dic₃⋊C₄	—	2	2	no	—
279	C₄×Dic₃	—	2	1	no	—
280	C₄×Dic₃	—	2	1	no	—
281	C₂³×C₅	—	6	2	no	—
282	C₂³×C₅	—	6	4	no	—
283	C₂³×C₅	—	24	1	no	—
284	C₂³×C₅	—	24	1	no	—
285	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
286	C₅×Q₈	—	24	2	no	—
287	C₅×D₄	—	3	4	no	—
288	C₅×D₄	—	6	4	no	—
289	C₅×D₄	—	6	2	no	—
290	C₂×C₄×C₅	—	6	1	no	—
291	C₂×C₄×C₅	—	6	1	no	—
292	C₂×C₄×C₅	—	6	1	no	—
293	C₂×C₄×C₅	—	6	1	no	—
294	C₂×C₄×C₅	—	6	2	no	—
295	C₂×C₄×C₅	—	24	2	no	—
296	C₂×C₄×C₅	—	24	2	no	—
297	C₂×C₄×C₅	—	24	1	no	—
298	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
299	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
300	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
301	C₂×C₄×C₅	#237	1	2	yes	—
302	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	1	no	—
306	C₅×C₈	—	2	2	no	—
307	C₂²×D₄	—	3	1	no	—
308	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
309	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
310	C₄⋊Q₈	—	3	2	no	—
311	C₄⋊Q₈	—	6	1	no	—
312	#125	—	3	2	no	—
313	#125	—	6	1	no	—
314	C₂²⋊Q₈	—	6	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	6	1	no	—
318	C₄×D₄	—	6	1	no	—
319	#117	—	3	1	no	—
320	#117	—	3	1	no	—
321	#117	C₂×C₅×D₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	—	3	1	no	—
323	C₂×C₂²⋊C₄	—	6	2	no	—
324	#107	—	3	1	no	—
325	#107	—	3	1	no	—
326	#107	—	3	2	no	—
327	#106	—	3	1	no	—
328	#106	—	3	1	no	—
329	#106	—	3	2	no	—
330	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
331	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
332	#102	—	3	2	no	—
333	#102	—	3	2	no	—
334	#102	—	3	2	no	—
335	#102	—	3	2	no	—
336	C₂×C₃×C₅	—	2	2	no	—
337	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₃×C₅	#576	1	1	yes	characteristic
339	C₂×C₃×C₅	#577	1	1	yes	characteristic
340	C₅×D₃	—	4	4	no	—
341	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×D₃	—	2	2	no	—
343	C₂²×D₃	—	2	4	no	—
344	C₂²×D₃	—	8	1	no	—
345	C₂²×D₃	—	8	1	no	—
346	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
347	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
348	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
350	C₂×C₃×C₄	C₅×#41	1	2	yes	—
351	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
352	C₂×Dic₃	—	2	1	no	—
353	C₂×Dic₃	—	2	1	no	—
354	C₂×Dic₃	—	2	1	no	—
355	C₂×Dic₃	—	2	1	no	—
356	C₂×Dic₃	—	2	2	no	—
357	C₂×Dic₃	—	8	1	no	—
358	D₁₂	—	2	4	no	—
359	D₁₂	—	2	2	no	—
360	D₁₂	C₂×C₅×Q₈	1	4	yes	—
361	C₄×D₃	—	8	2	no	—
362	C₄×D₃	—	8	2	no	—
363	Dic₆	—	8	2	no	—
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	—	2	1	no	—
366	C₃×C₈	—	2	2	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	6	4	no	—
370	C₂²×C₅	—	12	2	no	—
371	C₂²×C₅	—	12	2	no	—
372	C₂²×C₅	—	24	4	no	—
373	C₂²×C₅	#897	1	2	yes	—
374	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	12	1	no	—
378	C₄×C₅	—	12	1	no	—
379	C₄×C₅	—	12	1	no	—
380	C₄×C₅	—	12	2	no	—
381	C₄×C₅	—	12	1	no	—
382	C₄×C₅	#897	1	2	yes	—
383	C₄×C₅	C₂×#237	1	1	yes	characteristic
384	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
385	C₂⁴	—	6	1	no	—
386	C₂×Q₈	—	6	2	no	—
387	C₂×D₄	—	3	4	no	—
388	C₂×D₄	—	3	2	no	—
389	C₂×D₄	—	6	1	no	—
390	C₂×D₄	—	6	2	no	—
391	C₂²×C₄	—	6	1	no	—
392	C₂²×C₄	—	6	2	no	—
393	C₂²×C₄	—	6	2	no	—
394	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
395	M₁₆	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
398	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
399	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₄⋊C₄	—	3	2	no	—
401	C₄⋊C₄	—	3	1	no	—
402	C₄⋊C₄	—	3	1	no	—
403	C₄⋊C₄	—	3	1	no	—
404	C₄⋊C₄	—	3	1	no	—
405	C₄⋊C₄	—	6	1	no	—
406	C₄⋊C₄	—	6	2	no	—
407	C₄⋊C₄	—	6	2	no	—
408	C₄⋊C₄	—	6	2	no	—
409	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
410	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
411	C₂²⋊C₄	—	6	1	no	—
412	C₂²⋊C₄	—	6	1	no	—
413	C₂²⋊C₄	—	6	2	no	—
414	C₂²⋊C₄	—	6	2	no	—
415	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
416	C₄²	—	6	1	no	—
417	C₄²	—	6	1	no	—
418	C₄²	C₂²×C₅×D₃	1	2	yes	—
419	C₃×C₅	#3081	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
423	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
424	C₂×D₃	—	2	4	no	—
425	C₂×D₃	—	4	2	no	—
426	C₂×D₃	—	4	2	no	—
427	C₂×D₃	—	8	4	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
431	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
432	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
433	Dic₃	—	4	1	no	—
434	Dic₃	—	4	2	no	—
435	Dic₃	—	4	1	no	—
436	Dic₃	—	4	1	no	—
437	Dic₃	—	4	1	no	—
438	C₂×C₅	—	2	2	no	—
439	C₂×C₅	—	12	4	no	—
440	C₂×C₅	C₂×#897	1	1	yes	characteristic
441	C₂×C₅	#5751	1	1	yes	characteristic
442	C₂×C₅	#5752	1	1	yes	characteristic
443	C₂³	—	6	2	no	—
444	C₂³	—	6	4	no	—
445	C₂³	—	24	1	no	—
446	C₂³	—	24	1	no	—
447	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
448	Q₈	—	24	2	no	—
449	D₄	—	3	4	no	—
450	D₄	—	6	4	no	—
451	D₄	—	6	2	no	—
452	C₂×C₄	—	6	1	no	—
453	C₂×C₄	—	6	1	no	—
454	C₂×C₄	—	6	1	no	—
455	C₂×C₄	—	6	1	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	24	2	no	—
458	C₂×C₄	—	24	2	no	—
459	C₂×C₄	—	24	1	no	—
460	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
461	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
462	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
463	C₂×C₄	C₅×#237	1	2	yes	—
464	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
465	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	2	1	no	—
468	C₈	—	2	2	no	—
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
471	C₂×C₃	C₅×#576	1	1	yes	characteristic
472	C₂×C₃	C₅×#577	1	1	yes	characteristic
473	D₃	—	4	4	no	—
474	C₅	#79090	1	1	yes	characteristic, direct product factor, Sylow
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	6	4	no	—
478	C₂²	—	12	2	no	—
479	C₂²	—	12	2	no	—
480	C₂²	—	24	4	no	—
481	C₂²	C₅×#897	1	2	yes	—
482	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	12	1	no	—
486	C₄	—	12	1	no	—
487	C₄	—	12	1	no	—
488	C₄	—	12	2	no	—
489	C₄	—	12	1	no	—
490	C₄	C₅×#897	1	2	yes	—
491	C₄	C₂×C₅×#237	1	1	yes	characteristic
492	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
493	C₃	C₅×#3081	1	1	yes	characteristic, complemented, Sylow
494	C₂	—	2	2	no	—
495	C₂	—	12	4	no	—
496	C₂	C₂×C₅×#897	1	1	yes	characteristic
497	C₂	C₅×#5751	1	1	yes	characteristic
498	C₂	C₅×#5752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₅×#424	D₃
hypocenter	C₃	C₅×#3081
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#424

Complements

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

N	H ≅ G/N	type
2. C₅×#5519	C₂	semidirect
3. C₃×C₅×#424	C₂	semidirect
5. C₅×#5121	C₂	semidirect
7. C₅×#5106	C₂	semidirect
8. C₅×#4847	C₂	semidirect
9. C₅×#4847	C₂	semidirect
10. C₅×#4846	C₂	semidirect
11. C₅×#4842	C₂	semidirect
28. C₅×#870	C₂²	semidirect
29. C₅×#869	C₂²	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×C₄⋊C₈	C₂²	semidirect
36. C₅×#818	C₂²	semidirect
37. C₅×#818	C₂²	semidirect
38. C₅×#818	C₂²	semidirect
39. C₅×#817	C₂²	semidirect
40. C₅×#817	C₂²	semidirect
41. C₅×#817	C₂²	semidirect
42. #79090	C₅	direct (N × H)
51. C₅×#424	D₃	semidirect
59. C₂×C₅×D₁₂	Q₈	semidirect
89. #5519	C₂×C₅	semidirect
90. C₃×#424	C₂×C₅	semidirect
92. #5121	C₂×C₅	semidirect
94. #5106	C₂×C₅	semidirect
95. #4847	C₂×C₅	semidirect
96. #4847	C₂×C₅	semidirect
97. #4846	C₂×C₅	semidirect
98. #4842	C₂×C₅	semidirect
122. C₅×C₄⋊C₈	C₂×D₃	semidirect
123. C₅×C₄⋊C₈	C₂×D₃	semidirect
170. #870	C₂²×C₅	semidirect
171. #869	C₂²×C₅	semidirect
172. C₃×C₄⋊C₈	C₂²×C₅	semidirect
173. C₃×C₄⋊C₈	C₂²×C₅	semidirect
178. #818	C₂²×C₅	semidirect
179. #818	C₂²×C₅	semidirect
180. #818	C₂²×C₅	semidirect
181. #817	C₂²×C₅	semidirect
182. #817	C₂²×C₅	semidirect
183. #817	C₂²×C₅	semidirect
226. #424	C₅×D₃	semidirect
252. C₂×D₁₂	C₅×Q₈	semidirect
330. C₄⋊C₈	C₂×C₅×D₃	semidirect
331. C₄⋊C₈	C₂×C₅×D₃	semidirect
419. C₃×C₅	#3081	semidirect
474. C₅	#79090	direct (N × H)
493. C₃	C₅×#3081	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5521	2
C₅×#5519	2
C₃×C₅×#424	2
C₅×#5131	2
C₅×#5121	2
C₂×C₅×#821	2
C₅×#5106	2
C₅×#4847	2
C₅×#4846	2
C₅×#4842	2
C₅×#3081	3
#79090	5

Subgroups — C5×#79090 #14430783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79090 #14430783