Subgroups — C₅×#81562 #14437773

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5728	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5716	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5070	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4772	C₂	1	4	yes	maximal, complemented
7	C₅×#4768	C₂	1	4	yes	maximal, complemented
8	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3131	—	3	1	no	maximal, Hall
11	C₂×C₅×#237	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₅×#946	—	2	1	no	—
15	C₅×Q₈×Dic₃	—	2	1	no	—
16	C₅×#938	—	2	1	no	—
17	C₅×#938	—	2	1	no	—
18	C₅×#936	C₂²	1	2	yes	—
19	C₅×D₄×Dic₃	—	2	1	no	—
20	C₅×D₄×Dic₃	—	2	1	no	—
21	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
22	C₅×#897	—	2	1	no	—
23	C₅×#892	C₂²	1	2	yes	—
24	C₅×#890	C₂²	1	2	yes	—
25	C₅×#887	—	2	1	no	—
26	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₅×#869	C₂²	1	1	yes	characteristic
28	C₅×#869	C₂²	1	1	yes	characteristic
29	C₃×C₅×#102	C₂²	1	4	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×#832	C₂²	1	4	yes	—
32	C₅×#816	C₂²	1	4	yes	—
33	C₅×C₈×Dic₃	C₂²	1	2	yes	—
34	C₅×#810	C₂²	1	4	yes	—
35	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	#81562	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#533	—	3	1	no	—
38	C₅×#532	—	3	1	no	—
39	C₅×#488	—	3	4	no	—
40	C₅×#487	—	3	1	no	—
41	C₅×#487	—	3	1	no	—
42	C₅×#486	—	3	1	no	—
43	C₅×#486	D₃	1	1	yes	characteristic, complemented
44	C₅×#416	—	3	4	no	—
45	C₂×C₄×C₅×C₈	—	3	1	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	1	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂×C₅×#67	—	2	2	no	—
51	C₂²×C₅×Dic₃	—	2	2	no	—
52	C₅×#237	—	2	8	no	—
53	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
54	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
56	C₂×C₅×Dic₆	—	2	1	no	—
57	C₂×C₅×Dic₆	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₅×#217	—	2	2	no	—
63	C₅×#217	—	2	2	no	—
64	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
65	C₅×C₄⋊Dic₃	—	2	1	no	—
66	C₅×C₄⋊Dic₃	—	2	1	no	—
67	C₅×C₄⋊Dic₃	—	2	1	no	—
68	C₅×C₄⋊Dic₃	—	2	2	no	—
69	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
70	C₅×Dic₃⋊C₄	—	2	2	no	—
71	C₄×C₅×Dic₃	—	2	2	no	—
72	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
73	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
74	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
76	C₅×D₃×C₈	—	2	4	no	—
77	#5728	C₂×C₅	1	1	yes	characteristic, complemented
78	#5716	C₂×C₅	1	1	yes	characteristic
79	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
80	#5093	C₂×C₅	1	1	yes	characteristic, complemented
81	#5070	C₂×C₅	1	1	yes	characteristic, complemented
82	#4772	C₂×C₅	1	4	yes	complemented
83	#4768	C₂×C₅	1	4	yes	complemented
84	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
85	#4681	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×C₅×#41	—	3	2	no	—
87	C₂²×C₅×C₈	—	3	2	no	—
88	C₅×C₄⋊Q₈	—	3	1	no	—
89	C₅×C₄⋊Q₈	—	3	1	no	—
90	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
91	C₅×#127	C₂×D₃	1	1	yes	characteristic
92	C₅×#125	—	3	2	no	—
93	C₅×#124	—	3	2	no	—
94	C₅×C₂²⋊Q₈	—	6	1	no	—
95	C₅×C₂²⋊Q₈	—	6	1	no	—
96	C₅×#121	—	6	1	no	—
97	C₅×#121	—	6	1	no	—
98	C₄×C₅×Q₈	—	6	1	no	—
99	C₄×C₅×Q₈	—	6	1	no	—
100	C₄×C₅×D₄	—	6	1	no	—
101	C₄×C₅×D₄	—	6	1	no	—
102	C₅×#117	—	3	2	no	—
103	C₂×C₄²×C₅	—	3	1	no	—
104	C₅×#103	—	3	4	no	—
105	C₅×#103	—	3	4	no	—
106	C₅×#102	—	3	4	no	—
107	C₅×#102	C₂×D₃	1	4	yes	—
108	C₄×C₅×C₈	—	3	2	no	—
109	C₄×C₅×C₈	—	3	1	no	—
110	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
111	#3131	—	3	1	no	Sylow
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₃×C₅×D₄	—	2	4	no	—
116	C₃×C₅×D₄	—	4	2	no	—
117	C₃×C₅×D₄	—	4	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₅×#67	—	4	4	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	4	4	no	—
126	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
129	C₄×C₅×D₃	—	2	2	no	—
130	C₄×C₅×D₃	—	2	2	no	—
131	C₄×C₅×D₃	#41	1	4	yes	—
132	C₅×Dic₆	—	2	4	no	—
133	C₅×Dic₆	—	4	2	no	—
134	C₃×C₅×C₈	—	2	2	no	—
135	C₅×C₃⋊C₈	—	2	2	no	—
136	C₂×#237	C₂²×C₅	1	2	yes	—
137	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₃×#127	C₂²×C₅	1	1	yes	characteristic
139	#946	—	2	1	no	—
140	Q₈×Dic₃	—	2	1	no	—
141	#938	—	2	1	no	—
142	#938	—	2	1	no	—
143	#936	C₂²×C₅	1	2	yes	—
144	D₄×Dic₃	—	2	1	no	—
145	D₄×Dic₃	—	2	1	no	—
146	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
147	#897	—	2	1	no	—
148	#892	C₂²×C₅	1	2	yes	—
149	#890	C₂²×C₅	1	2	yes	—
150	#887	—	2	1	no	—
151	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
152	#869	C₂²×C₅	1	1	yes	characteristic
153	#869	C₂²×C₅	1	1	yes	characteristic
154	C₃×#102	C₂²×C₅	1	4	yes	—
155	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
156	#832	C₂²×C₅	1	4	yes	—
157	#816	C₂²×C₅	1	4	yes	—
158	C₈×Dic₃	C₂²×C₅	1	2	yes	—
159	#810	C₂²×C₅	1	4	yes	—
160	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
161	C₅×#41	—	6	8	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	6	2	no	—
168	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
169	C₂²×C₄×C₅	—	3	1	no	—
170	C₂²×C₄×C₅	—	3	1	no	—
171	C₂²×C₄×C₅	—	3	1	no	—
172	C₂²×C₄×C₅	—	6	2	no	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	6	4	no	—
175	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	3	2	no	—
178	C₅×C₄⋊C₄	—	6	2	no	—
179	C₅×C₄⋊C₄	—	6	2	no	—
180	C₅×C₄⋊C₄	—	6	1	no	—
181	C₅×C₄⋊C₄	—	6	1	no	—
182	C₅×C₄⋊C₄	—	6	1	no	—
183	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
184	C₅×C₂²⋊C₄	—	6	2	no	—
185	C₅×C₂²⋊C₄	—	6	2	no	—
186	C₅×C₂²⋊C₄	—	6	2	no	—
187	C₄²×C₅	—	3	1	no	—
188	C₄²×C₅	—	3	1	no	—
189	C₄²×C₅	—	3	1	no	—
190	C₄²×C₅	—	6	2	no	—
191	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
192	#533	—	3	1	no	—
193	#532	—	3	1	no	—
194	#488	—	3	4	no	—
195	#487	—	3	1	no	—
196	#487	—	3	1	no	—
197	#486	—	3	1	no	—
198	#486	C₅×D₃	1	1	yes	characteristic, complemented
199	#416	—	3	4	no	—
200	C₂×C₄×C₈	—	3	1	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	4	2	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₅×D₃	—	2	1	no	—
206	C₂×C₅×D₃	—	2	1	no	—
207	C₂×C₅×D₃	#124	1	2	yes	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	#135	1	2	yes	—
210	C₃×C₄×C₅	#135	1	2	yes	—
211	C₃×C₄×C₅	C₂×#41	1	2	yes	—
212	C₅×Dic₃	—	2	1	no	—
213	C₅×Dic₃	—	2	1	no	—
214	C₅×Dic₃	—	4	2	no	—
215	C₅×Dic₃	—	4	2	no	—
216	C₅×Dic₃	#124	1	2	yes	—
217	C₂×C₃×Q₈	—	2	1	no	—
218	C₂×C₃×D₄	—	2	1	no	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
221	C₂×#67	—	2	2	no	—
222	C₂²×Dic₃	—	2	2	no	—
223	#237	—	2	8	no	—
224	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
225	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
226	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
227	C₂×Dic₆	—	2	1	no	—
228	C₂×Dic₆	C₂³×C₅	1	2	yes	—
229	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
230	C₃×C₄⋊C₄	—	2	1	no	—
231	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
232	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
233	#217	—	2	2	no	—
234	#217	—	2	2	no	—
235	(C₂×D₃)⋊C₄	—	2	2	no	—
236	C₄⋊Dic₃	—	2	1	no	—
237	C₄⋊Dic₃	—	2	1	no	—
238	C₄⋊Dic₃	—	2	1	no	—
239	C₄⋊Dic₃	—	2	2	no	—
240	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
241	Dic₃⋊C₄	—	2	2	no	—
242	C₄×Dic₃	—	2	2	no	—
243	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
244	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
245	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
247	D₃×C₈	—	2	4	no	—
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	—	3	1	no	—
250	C₅×Q₈	—	4	2	no	—
251	C₅×Q₈	—	6	4	no	—
252	C₅×Q₈	—	12	2	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	4	2	no	—
255	C₅×D₄	—	4	2	no	—
256	C₅×D₄	—	12	4	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	3	1	no	—
259	C₂×C₄×C₅	—	3	4	no	—
260	C₂×C₄×C₅	—	3	1	no	—
261	C₂×C₄×C₅	—	3	1	no	—
262	C₂×C₄×C₅	—	6	2	no	—
263	C₂×C₄×C₅	—	6	2	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	12	4	no	—
267	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₅×C₈	—	2	2	no	—
271	C₅×C₈	—	6	2	no	—
272	C₂×#41	—	3	2	no	—
273	C₂²×C₈	—	3	2	no	—
274	C₄⋊Q₈	—	3	1	no	—
275	C₄⋊Q₈	—	3	1	no	—
276	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
277	#127	C₂×C₅×D₃	1	1	yes	characteristic
278	#125	—	3	2	no	—
279	#124	—	3	2	no	—
280	C₂²⋊Q₈	—	6	1	no	—
281	C₂²⋊Q₈	—	6	1	no	—
282	#121	—	6	1	no	—
283	#121	—	6	1	no	—
284	C₄×Q₈	—	6	1	no	—
285	C₄×Q₈	—	6	1	no	—
286	C₄×D₄	—	6	1	no	—
287	C₄×D₄	—	6	1	no	—
288	#117	—	3	2	no	—
289	C₂×C₄²	—	3	1	no	—
290	#103	—	3	4	no	—
291	#103	—	3	4	no	—
292	#102	—	3	4	no	—
293	#102	C₂×C₅×D₃	1	4	yes	—
294	C₄×C₈	—	3	2	no	—
295	C₄×C₈	—	3	1	no	—
296	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
297	C₂×C₃×C₅	—	8	2	no	—
298	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
301	C₅×D₃	—	2	2	no	—
302	C₂³×C₃	—	2	2	no	—
303	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
304	C₃×Q₈	—	4	2	no	—
305	C₃×D₄	—	2	4	no	—
306	C₃×D₄	—	4	2	no	—
307	C₃×D₄	—	4	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
312	#67	—	4	4	no	—
313	C₂×Dic₃	—	2	2	no	—
314	C₂×Dic₃	—	2	2	no	—
315	C₂×Dic₃	—	4	4	no	—
316	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
319	C₄×D₃	—	2	2	no	—
320	C₄×D₃	—	2	2	no	—
321	C₄×D₃	C₅×#41	1	4	yes	—
322	Dic₆	—	2	4	no	—
323	Dic₆	—	4	2	no	—
324	C₃×C₈	—	2	2	no	—
325	C₃⋊C₈	—	2	2	no	—
326	C₂²×C₅	—	3	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	6	1	no	—
331	C₂²×C₅	—	6	1	no	—
332	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
333	C₄×C₅	—	3	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	6	1	no	—
336	C₄×C₅	—	6	1	no	—
337	C₄×C₅	—	12	2	no	—
338	C₄×C₅	—	12	2	no	—
339	C₄×C₅	#912	1	2	yes	—
340	C₄×C₅	#916	1	2	yes	—
341	C₄×C₅	D₃×#41	1	2	yes	—
342	#41	—	6	8	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	3	2	no	—
345	C₂×Q₈	—	6	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	6	2	no	—
349	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
350	C₂²×C₄	—	3	1	no	—
351	C₂²×C₄	—	3	1	no	—
352	C₂²×C₄	—	3	1	no	—
353	C₂²×C₄	—	6	2	no	—
354	C₂×C₈	—	3	2	no	—
355	C₂×C₈	—	6	4	no	—
356	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	6	2	no	—
360	C₄⋊C₄	—	6	2	no	—
361	C₄⋊C₄	—	6	1	no	—
362	C₄⋊C₄	—	6	1	no	—
363	C₄⋊C₄	—	6	1	no	—
364	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
365	C₂²⋊C₄	—	6	2	no	—
366	C₂²⋊C₄	—	6	2	no	—
367	C₂²⋊C₄	—	6	2	no	—
368	C₄²	—	3	1	no	—
369	C₄²	—	3	1	no	—
370	C₄²	—	3	1	no	—
371	C₄²	—	6	2	no	—
372	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₃×C₅	#3131	1	1	yes	characteristic, complemented, Hall
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
378	C₂×D₃	—	2	1	no	—
379	C₂×D₃	—	2	1	no	—
380	C₂×D₃	C₅×#124	1	2	yes	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	C₅×#135	1	2	yes	—
383	C₃×C₄	C₅×#135	1	2	yes	—
384	C₃×C₄	C₂×C₅×#41	1	2	yes	—
385	Dic₃	—	2	1	no	—
386	Dic₃	—	2	1	no	—
387	Dic₃	—	4	2	no	—
388	Dic₃	—	4	2	no	—
389	Dic₃	C₅×#124	1	2	yes	—
390	C₂×C₅	—	6	2	no	—
391	C₂×C₅	—	8	2	no	—
392	C₂×C₅	D₃×#124	1	1	yes	characteristic
393	C₂×C₅	C₂×#912	1	1	yes	characteristic
394	C₂×C₅	C₂×#916	1	1	yes	characteristic
395	C₂³	—	2	2	no	—
396	C₂³	—	3	1	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	6	4	no	—
399	Q₈	—	12	2	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	12	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	3	1	no	—
406	C₂×C₄	—	3	4	no	—
407	C₂×C₄	—	3	1	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	6	2	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	6	2	no	—
413	C₂×C₄	—	12	4	no	—
414	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
415	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	6	2	no	—
419	C₂×C₃	—	8	2	no	—
420	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
421	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
422	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
423	D₃	—	2	2	no	—
424	C₅	#81562	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	3	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	6	1	no	—
430	C₂²	—	6	1	no	—
431	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
432	C₄	—	3	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	6	1	no	—
435	C₄	—	6	1	no	—
436	C₄	—	12	2	no	—
437	C₄	—	12	2	no	—
438	C₄	C₅×#912	1	2	yes	—
439	C₄	C₅×#916	1	2	yes	—
440	C₄	C₅×D₃×#41	1	2	yes	—
441	C₃	C₅×#3131	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	6	2	no	—
443	C₂	—	8	2	no	—
444	C₂	C₅×D₃×#124	1	1	yes	characteristic
445	C₂	C₂×C₅×#912	1	1	yes	characteristic
446	C₂	C₂×C₅×#916	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×#486	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5716	C₂
hypercenter	C₅×#486	D₃
hypocenter	C₃	C₅×#3131
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#486

Complements

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

N	H ≅ G/N	type
1. C₅×#5728	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₅×#5093	C₂	semidirect
5. C₅×#5070	C₂	semidirect
6. C₅×#4772	C₂	semidirect
7. C₅×#4768	C₂	semidirect
8. C₄×C₅×D₃×C₈	C₂	semidirect
9. C₅×#4681	C₂	semidirect
36. #81562	C₅	direct (N × H)
43. C₅×#486	D₃	semidirect
77. #5728	C₂×C₅	semidirect
79. C₃×#486	C₂×C₅	semidirect
80. #5093	C₂×C₅	semidirect
81. #5070	C₂×C₅	semidirect
82. #4772	C₂×C₅	semidirect
83. #4768	C₂×C₅	semidirect
84. C₄×D₃×C₈	C₂×C₅	semidirect
85. #4681	C₂×C₅	semidirect
198. #486	C₅×D₃	semidirect
373. C₃×C₅	#3131	semidirect
424. C₅	#81562	direct (N × H)
441. C₃	C₅×#3131	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5728	2
C₅×#5716	2
C₃×C₅×#486	2
C₅×#5093	2
C₅×#5070	2
C₅×#4772	2
C₅×#4768	2
C₄×C₅×D₃×C₈	2
C₅×#4681	2
C₅×#3131	3
#81562	5

Subgroups — C5×#81562 #14437773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81562 #14437773