Subgroups — C₅×#68276 #14282746

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5600	C₂	1	1	yes	maximal, characteristic
2	C₅×#4718	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4648	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#327	C₂	1	1	yes	maximal, characteristic
5	C₅×#4537	C₂	1	1	yes	maximal, characteristic
6	C₅×#4467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1500	—	3	1	no	maximal, Hall
9	C₃×C₅×#121	C₂²	1	1	yes	characteristic
10	C₅×#936	C₄	1	1	yes	characteristic, complemented
11	C₅×#935	—	2	1	no	—
12	C₅×D₄×Dic₃	—	2	1	no	—
13	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic, complemented
14	C₅×#924	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	—	2	1	no	—
16	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₅×#890	C₄	1	1	yes	characteristic, complemented
18	C₅×#887	C₄	1	1	yes	characteristic, complemented
19	C₅×#879	—	2	1	no	—
20	C₅×#877	—	2	1	no	—
21	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#95	C₂²	1	1	yes	characteristic
23	C₅×C₃⋊#95	—	2	1	no	—
24	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
25	C₅×#830	C₂²	1	1	yes	characteristic
26	C₅×Dic₃⋊C₈	—	2	1	no	—
27	C₅×C₈×Dic₃	—	2	1	no	—
28	#68276	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#529	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₅×#376	—	3	1	no	—
32	C₅×#328	—	3	1	no	—
33	C₅×#328	—	3	1	no	—
34	C₅×#327	—	3	1	no	—
35	C₅×#327	D₃	1	1	yes	characteristic
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	1	no	—
41	C₂²×C₅×Dic₃	—	2	1	no	—
42	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
44	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₅×#217	—	2	1	no	—
49	C₅×#217	—	2	1	no	—
50	C₅×#217	—	2	1	no	—
51	C₅×#217	—	2	1	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	4	no	—
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	#5600	C₂×C₅	1	1	yes	characteristic
65	#4718	C₂×C₅	1	1	yes	characteristic, complemented
66	#4648	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×#327	C₂×C₅	1	1	yes	characteristic
68	#4537	C₂×C₅	1	1	yes	characteristic
69	#4467	C₂×C₅	1	1	yes	characteristic, complemented
70	#4452	C₂×C₅	1	1	yes	characteristic, complemented
71	C₅×#126	—	6	1	no	—
72	C₅×#125	—	3	1	no	—
73	C₅×#124	—	3	1	no	—
74	C₅×#123	—	6	1	no	—
75	C₅×C₂²⋊Q₈	—	3	1	no	—
76	C₅×#121	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×Q₈	—	3	1	no	—
78	C₄×C₅×D₄	—	3	1	no	—
79	C₄×C₅×D₄	—	6	1	no	—
80	C₅×#117	—	6	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×C₄²×C₅	—	6	1	no	—
83	C₅×C₄⋊C₈	—	6	1	no	—
84	C₅×C₂²⋊C₈	—	3	1	no	—
85	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
86	C₄×C₅×C₈	—	6	1	no	—
87	C₅×#95	—	3	1	no	—
88	C₅×#95	—	6	1	no	—
89	C₅×#95	C₂×D₃	1	1	yes	characteristic
90	#1500	—	3	1	no	Sylow
91	C₂³×C₃×C₅	—	2	1	no	—
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₃×C₅×D₄	—	4	1	no	—
94	C₃×C₅×D₄	—	4	1	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₂×C₅×Dic₃	—	2	1	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	1	no	—
108	C₂×C₅×Dic₃	—	2	1	no	—
109	C₂×C₅×Dic₃	—	4	1	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	—	4	2	no	—
112	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₅×Dic₆	—	4	1	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₃×#121	C₂²×C₅	1	1	yes	characteristic
120	#936	C₄×C₅	1	1	yes	characteristic, complemented
121	#935	—	2	1	no	—
122	D₄×Dic₃	—	2	1	no	—
123	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic, complemented
124	#924	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₄×Dic₃	—	2	1	no	—
126	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
127	#890	C₄×C₅	1	1	yes	characteristic, complemented
128	#887	C₄×C₅	1	1	yes	characteristic, complemented
129	#879	—	2	1	no	—
130	#877	—	2	1	no	—
131	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×#95	C₂²×C₅	1	1	yes	characteristic
133	C₃⋊#95	—	2	1	no	—
134	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
135	#830	C₂²×C₅	1	1	yes	characteristic
136	Dic₃⋊C₈	—	2	1	no	—
137	C₈×Dic₃	—	2	1	no	—
138	C₂×C₅×Q₈	—	3	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₅×C₄⋊C₄	—	3	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	C₅×C₄⋊C₄	—	6	1	no	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	6	1	no	—
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₅×C₂²⋊C₄	—	6	1	no	—
159	C₅×C₂²⋊C₄	—	6	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	3	1	no	—
164	C₄²×C₅	—	6	1	no	—
165	C₄²×C₅	—	6	4	no	—
166	#529	—	3	1	no	—
167	#431	—	3	1	no	—
168	#376	—	3	1	no	—
169	#328	—	3	1	no	—
170	#328	—	3	1	no	—
171	#327	—	3	1	no	—
172	#327	C₅×D₃	1	1	yes	characteristic
173	C₂²×C₃×C₅	—	2	1	no	—
174	C₂²×C₃×C₅	—	2	1	no	—
175	C₂²×C₃×C₅	—	4	1	no	—
176	C₂²×C₃×C₅	—	4	1	no	—
177	C₂²×C₃×C₅	—	4	1	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	#135	1	1	yes	characteristic
180	C₂²×C₃×C₅	#135	1	1	yes	characteristic
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	—	4	1	no	—
185	C₅×Dic₃	—	2	1	no	—
186	C₅×Dic₃	—	2	1	no	—
187	C₅×Dic₃	—	2	1	no	—
188	C₅×Dic₃	—	4	2	no	—
189	C₅×Dic₃	—	4	1	no	—
190	C₅×Dic₃	—	4	1	no	—
191	C₅×Dic₃	#104	1	2	yes	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂²×Dic₃	—	2	1	no	—
197	C₂²×Dic₃	—	2	1	no	—
198	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
199	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
200	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂×C₃×C₈	—	2	1	no	—
202	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	2	1	no	—
204	#217	—	2	1	no	—
205	#217	—	2	1	no	—
206	#217	—	2	1	no	—
207	#217	—	2	1	no	—
208	C₄⋊Dic₃	—	2	1	no	—
209	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
210	Dic₃⋊C₄	—	2	1	no	—
211	Dic₃⋊C₄	—	2	1	no	—
212	Dic₃⋊C₄	—	2	1	no	—
213	C₄×Dic₃	—	2	4	no	—
214	C₄×Dic₃	—	2	1	no	—
215	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
216	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
217	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
218	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
222	C₅×Q₈	—	12	1	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	3	1	no	—
229	C₂×C₄×C₅	—	3	1	no	—
230	C₂×C₄×C₅	—	3	1	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	2	no	—
239	C₂×C₄×C₅	—	6	1	no	—
240	C₂×C₄×C₅	—	6	1	no	—
241	C₂×C₄×C₅	—	12	2	no	—
242	C₂×C₄×C₅	—	12	1	no	—
243	C₂×C₄×C₅	—	12	1	no	—
244	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₅×C₈	—	4	1	no	—
247	C₅×C₈	—	12	1	no	—
248	#126	—	6	1	no	—
249	#125	—	3	1	no	—
250	#124	—	3	1	no	—
251	#123	—	6	1	no	—
252	C₂²⋊Q₈	—	3	1	no	—
253	#121	C₂×C₅×D₃	1	1	yes	characteristic
254	C₄×Q₈	—	3	1	no	—
255	C₄×D₄	—	3	1	no	—
256	C₄×D₄	—	6	1	no	—
257	#117	—	6	1	no	—
258	C₂×C₄²	—	3	1	no	—
259	C₂×C₄²	—	6	1	no	—
260	C₄⋊C₈	—	6	1	no	—
261	C₂²⋊C₈	—	3	1	no	—
262	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
263	C₄×C₈	—	6	1	no	—
264	#95	—	3	1	no	—
265	#95	—	6	1	no	—
266	#95	C₂×C₅×D₃	1	1	yes	characteristic
267	C₂×C₃×C₅	—	2	1	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	8	1	no	—
270	C₂×C₃×C₅	#410	1	1	yes	characteristic
271	C₂×C₃×C₅	#416	1	1	yes	characteristic
272	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
275	C₃×D₄	—	4	1	no	—
276	C₃×D₄	—	4	1	no	—
277	C₃×D₄	—	4	1	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂×Dic₃	—	2	1	no	—
286	C₂×Dic₃	—	2	1	no	—
287	C₂×Dic₃	—	2	2	no	—
288	C₂×Dic₃	—	2	2	no	—
289	C₂×Dic₃	—	2	1	no	—
290	C₂×Dic₃	—	2	1	no	—
291	C₂×Dic₃	—	4	1	no	—
292	C₂×Dic₃	—	4	1	no	—
293	C₂×Dic₃	—	4	2	no	—
294	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
298	Dic₆	—	4	1	no	—
299	C₃×C₈	—	4	1	no	—
300	C₃⋊C₈	—	4	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	—	4	1	no	—
306	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×C₅	#912	1	1	yes	characteristic
308	C₂²×C₅	#916	1	1	yes	characteristic
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	3	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	6	1	no	—
315	C₄×C₅	—	6	1	no	—
316	C₄×C₅	—	6	1	no	—
317	C₄×C₅	—	12	2	no	—
318	C₄×C₅	—	12	1	no	—
319	C₄×C₅	—	12	1	no	—
320	C₂×Q₈	—	3	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	3	1	no	—
325	C₂²×C₄	—	3	1	no	—
326	C₂²×C₄	—	6	1	no	—
327	C₂²×C₄	—	6	1	no	—
328	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	6	1	no	—
331	C₄⋊C₄	—	3	1	no	—
332	C₄⋊C₄	—	6	1	no	—
333	C₄⋊C₄	—	6	1	no	—
334	C₄⋊C₄	—	6	1	no	—
335	C₄⋊C₄	—	6	1	no	—
336	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	6	1	no	—
339	C₂²⋊C₄	—	6	1	no	—
340	C₂²⋊C₄	—	6	1	no	—
341	C₂²⋊C₄	—	6	1	no	—
342	C₄²	—	3	1	no	—
343	C₄²	—	3	1	no	—
344	C₄²	—	3	1	no	—
345	C₄²	—	3	1	no	—
346	C₄²	—	6	1	no	—
347	C₄²	—	6	4	no	—
348	C₃×C₅	#1500	1	1	yes	characteristic, complemented, Hall
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	—	4	1	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂²×C₃	C₅×#135	1	1	yes	characteristic
356	C₂²×C₃	C₅×#135	1	1	yes	characteristic
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	1	no	—
361	Dic₃	—	2	1	no	—
362	Dic₃	—	2	1	no	—
363	Dic₃	—	2	1	no	—
364	Dic₃	—	4	2	no	—
365	Dic₃	—	4	1	no	—
366	Dic₃	—	4	1	no	—
367	Dic₃	C₅×#104	1	2	yes	—
368	C₂×C₅	—	2	1	no	—
369	C₂×C₅	—	2	1	no	—
370	C₂×C₅	—	8	1	no	—
371	C₂×C₅	#4740	1	1	yes	characteristic
372	C₂×C₅	#4772	1	1	yes	characteristic
373	C₂×C₅	D₃×#104	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
376	Q₈	—	12	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	3	1	no	—
384	C₂×C₄	—	3	1	no	—
385	C₂×C₄	—	3	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	—	6	1	no	—
391	C₂×C₄	—	6	1	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	1	no	—
394	C₂×C₄	—	6	1	no	—
395	C₂×C₄	—	12	2	no	—
396	C₂×C₄	—	12	1	no	—
397	C₂×C₄	—	12	1	no	—
398	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
399	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
400	C₈	—	4	1	no	—
401	C₈	—	12	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	8	1	no	—
405	C₂×C₃	C₅×#410	1	1	yes	characteristic
406	C₂×C₃	C₅×#416	1	1	yes	characteristic
407	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
408	C₅	#68276	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²	C₅×#912	1	1	yes	characteristic
416	C₂²	C₅×#916	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	3	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	6	1	no	—
423	C₄	—	6	1	no	—
424	C₄	—	6	1	no	—
425	C₄	—	12	2	no	—
426	C₄	—	12	1	no	—
427	C₄	—	12	1	no	—
428	C₃	C₅×#1500	1	1	yes	characteristic, complemented, Sylow
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	8	1	no	—
432	C₂	C₅×#4740	1	1	yes	characteristic
433	C₂	C₅×#4772	1	1	yes	characteristic
434	C₂	C₅×D₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#327	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#327	D₃
hypocenter	C₃	C₅×#1500
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#327

Complements

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

N	H ≅ G/N	type
2. C₅×#4718	C₂	semidirect
3. C₅×#4648	C₂	semidirect
6. C₅×#4467	C₂	semidirect
7. C₅×#4452	C₂	semidirect
10. C₅×#936	C₄	semidirect
13. C₅×D₄×Dic₃	C₄	semidirect
17. C₅×#890	C₄	semidirect
18. C₅×#887	C₄	semidirect
28. #68276	C₅	direct (N × H)
65. #4718	C₂×C₅	semidirect
66. #4648	C₂×C₅	semidirect
69. #4467	C₂×C₅	semidirect
70. #4452	C₂×C₅	semidirect
120. #936	C₄×C₅	semidirect
123. D₄×Dic₃	C₄×C₅	semidirect
127. #890	C₄×C₅	semidirect
128. #887	C₄×C₅	semidirect
348. C₃×C₅	#1500	semidirect
408. C₅	#68276	direct (N × H)
428. C₃	C₅×#1500	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5600	2
C₅×#4718	2
C₅×#4648	2
C₃×C₅×#327	2
C₅×#4537	2
C₅×#4467	2
C₅×#4452	2
C₅×#1500	3
#68276	5

Subgroups — C5×#68276 #14282746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68276 #14282746