Subgroups — C₅×#69898 #14295505

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5132	C₂	1	1	yes	maximal, characteristic
4	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5006	C₂	1	1	yes	maximal, characteristic
6	C₅×#4559	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1757	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₅×#926	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#901	—	2	1	no	—
17	C₅×#901	—	2	1	no	—
18	C₅×#901	—	2	1	no	—
19	C₅×#901	—	2	1	no	—
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	2	yes	complemented
21	C₂×C₅×D₃×C₈	C₄	1	2	yes	complemented
22	C₃×C₅×#97	—	2	1	no	—
23	C₃×C₄×C₅×C₈	—	2	1	no	—
24	C₅×#824	C₄	1	2	yes	complemented
25	C₅×#823	C₄	1	2	yes	complemented
26	C₅×#815	—	2	1	no	—
27	C₅×C₈×Dic₃	—	2	1	no	—
28	C₅×#806	C₄	1	4	yes	—
29	#69898	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×#131	—	3	1	no	—
31	C₅×#413	—	3	1	no	—
32	C₅×#410	—	3	1	no	—
33	C₅×#405	—	3	1	no	—
34	C₅×#405	D₃	1	1	yes	characteristic, complemented
35	C₅×#344	—	3	1	no	—
36	C₅×#344	—	3	1	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₅×#67	C₂×C₄	1	2	yes	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	—	2	1	no	—
41	C₅×#235	—	2	1	no	—
42	C₅×#235	—	2	1	no	—
43	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
46	C₃×C₅×M₁₆	—	2	1	no	—
47	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₅×#217	C₂×C₄	1	2	yes	—
59	C₅×C₄⋊Dic₃	—	2	1	no	—
60	C₄×C₅×Dic₃	—	2	1	no	—
61	C₅×#208	—	2	1	no	—
62	C₅×#208	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	C₂×C₄	1	2	yes	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
67	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
68	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
69	C₅×D₃×C₈	—	2	2	no	—
70	C₅×D₃×C₈	—	2	2	no	—
71	C₂×#901	C₂×C₅	1	1	yes	characteristic
72	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
73	#5132	C₂×C₅	1	1	yes	characteristic
74	#5101	C₂×C₅	1	1	yes	characteristic, complemented
75	#5006	C₂×C₅	1	1	yes	characteristic
76	#4559	C₂×C₅	1	1	yes	characteristic, complemented
77	#4533	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×C₅×#41	—	3	1	no	—
79	C₅×#131	—	6	1	no	—
80	C₅×#131	—	6	1	no	—
81	C₅×#131	—	6	1	no	—
82	C₅×#131	—	6	1	no	—
83	C₂×C₅×M₁₆	—	3	1	no	—
84	C₂×C₅×M₁₆	—	3	2	no	—
85	C₂×C₅×M₁₆	—	3	1	no	—
86	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₅×C₈	—	3	2	no	—
88	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	C₅×#117	—	3	1	no	—
90	C₅×#117	C₂×D₃	1	1	yes	characteristic
91	C₅×#101	—	3	2	no	—
92	C₅×#100	—	3	2	no	—
93	C₅×#99	—	3	4	no	—
94	C₅×#97	—	2	1	no	—
95	C₅×#97	—	6	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	6	1	no	—
98	#1757	—	3	1	no	Sylow
99	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₅×D₃	C₄²	1	2	yes	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₅×#67	—	2	2	no	—
109	C₅×#67	—	2	2	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	C₄²	1	2	yes	—
112	C₅×D₁₂	—	2	1	no	—
113	C₅×D₁₂	—	2	1	no	—
114	C₄×C₅×D₃	—	2	2	no	—
115	C₄×C₅×D₃	—	2	2	no	—
116	C₅×Dic₆	—	2	1	no	—
117	C₅×Dic₆	—	2	1	no	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
121	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
122	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₅×C₃⋊C₈	—	2	2	no	—
125	C₂×#235	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
127	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
128	C₃×#117	C₂²×C₅	1	1	yes	characteristic
129	#926	C₂²×C₅	1	1	yes	characteristic
130	C₂×#208	C₂²×C₅	1	1	yes	characteristic
131	C₂×#208	C₂²×C₅	1	1	yes	characteristic
132	#901	—	2	1	no	—
133	#901	—	2	1	no	—
134	#901	—	2	1	no	—
135	#901	—	2	1	no	—
136	C₂×ΓL(1,𝔽₂₅)	C₄×C₅	1	2	yes	complemented
137	C₂×D₃×C₈	C₄×C₅	1	2	yes	complemented
138	C₃×#97	—	2	1	no	—
139	C₃×C₄×C₈	—	2	1	no	—
140	#824	C₄×C₅	1	2	yes	complemented
141	#823	C₄×C₅	1	2	yes	complemented
142	#815	—	2	1	no	—
143	C₈×Dic₃	—	2	1	no	—
144	#806	C₄×C₅	1	4	yes	—
145	C₅×#41	—	6	1	no	—
146	C₅×#41	—	6	1	no	—
147	C₅×#41	—	6	1	no	—
148	C₅×#41	—	6	1	no	—
149	C₂×C₅×Q₈	—	3	1	no	—
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	3	1	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₅×M₁₆	—	2	1	no	—
155	C₅×M₁₆	—	3	2	no	—
156	C₅×M₁₆	—	6	1	no	—
157	C₅×M₁₆	—	6	1	no	—
158	C₅×M₁₆	—	6	1	no	—
159	C₅×M₁₆	—	6	2	no	—
160	C₅×M₁₆	—	6	2	no	—
161	C₅×M₁₆	C₄×D₃	1	2	yes	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	3	2	no	—
164	C₂×C₅×C₈	—	6	1	no	—
165	C₂×C₅×C₈	—	6	2	no	—
166	C₂×C₅×C₈	—	6	2	no	—
167	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
168	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
169	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
170	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
171	C₂×C₅×C₈	#67	1	1	yes	characteristic
172	C₂×C₅×C₈	#67	1	1	yes	characteristic
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	6	1	no	—
175	C₅×C₂²⋊C₄	—	3	2	no	—
176	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	6	1	no	—
179	C₂×#131	—	3	1	no	—
180	#413	—	3	1	no	—
181	#410	—	3	1	no	—
182	#405	—	3	1	no	—
183	#405	C₅×D₃	1	1	yes	characteristic, complemented
184	#344	—	3	1	no	—
185	#344	—	3	1	no	—
186	C₂²×C₃×C₅	—	4	1	no	—
187	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂×C₅×D₃	—	2	2	no	—
191	C₂×C₅×D₃	—	4	2	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₃×C₄×C₅	#117	1	1	yes	characteristic
195	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	—	4	2	no	—
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂×#67	C₂×C₄×C₅	1	2	yes	—
201	#235	—	2	1	no	—
202	#235	—	2	1	no	—
203	#235	—	2	1	no	—
204	#235	—	2	1	no	—
205	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
207	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
208	C₃×M₁₆	—	2	1	no	—
209	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
214	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
215	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
216	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
217	C₃×C₄⋊C₄	—	2	1	no	—
218	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
219	C₃×C₄²	—	2	1	no	—
220	#217	C₂×C₄×C₅	1	2	yes	—
221	C₄⋊Dic₃	—	2	1	no	—
222	C₄×Dic₃	—	2	1	no	—
223	#208	—	2	1	no	—
224	#208	—	2	1	no	—
225	#208	—	2	1	no	—
226	#208	C₂×C₄×C₅	1	2	yes	—
227	C₂×C₃⋊C₈	—	2	1	no	—
228	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
229	ΓL(1,𝔽₂₅)	—	2	2	no	—
230	ΓL(1,𝔽₂₅)	—	2	2	no	—
231	D₃×C₈	—	2	2	no	—
232	D₃×C₈	—	2	2	no	—
233	C₂³×C₅	—	3	2	no	—
234	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
235	C₅×Q₈	—	6	1	no	—
236	C₅×Q₈	—	6	1	no	—
237	C₅×D₄	—	6	2	no	—
238	C₅×D₄	—	6	2	no	—
239	C₅×D₄	—	6	1	no	—
240	C₅×D₄	—	6	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	3	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	6	2	no	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
249	C₂×C₄×C₅	#235	1	1	yes	characteristic
250	C₂×C₄×C₅	#235	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	6	2	no	—
254	C₅×C₈	—	6	2	no	—
255	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
256	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
257	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
258	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
259	C₂×#41	—	3	1	no	—
260	#131	—	6	1	no	—
261	#131	—	6	1	no	—
262	#131	—	6	1	no	—
263	#131	—	6	1	no	—
264	C₂×M₁₆	—	3	1	no	—
265	C₂×M₁₆	—	3	2	no	—
266	C₂×M₁₆	—	3	1	no	—
267	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂²×C₈	—	3	2	no	—
269	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
270	#117	—	3	1	no	—
271	#117	C₂×C₅×D₃	1	1	yes	characteristic
272	#101	—	3	2	no	—
273	#100	—	3	2	no	—
274	#99	—	3	4	no	—
275	#97	—	2	1	no	—
276	#97	—	6	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	6	1	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
283	C₅×D₃	—	4	2	no	—
284	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂²×D₃	C₄²×C₅	1	2	yes	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
292	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
293	#67	—	2	2	no	—
294	#67	—	2	2	no	—
295	C₂×Dic₃	—	2	2	no	—
296	C₂×Dic₃	C₄²×C₅	1	2	yes	—
297	D₁₂	—	2	1	no	—
298	D₁₂	—	2	1	no	—
299	C₄×D₃	—	2	2	no	—
300	C₄×D₃	—	2	2	no	—
301	Dic₆	—	2	1	no	—
302	Dic₆	—	2	1	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
306	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
307	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₃⋊C₈	—	2	2	no	—
309	C₃⋊C₈	—	2	2	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	6	2	no	—
312	C₂²×C₅	—	12	2	no	—
313	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
314	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
315	C₂²×C₅	C₄×#67	1	1	yes	characteristic
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	6	2	no	—
318	C₄×C₅	—	12	2	no	—
319	C₄×C₅	#872	1	1	yes	characteristic
320	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
321	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
322	C₄×C₅	C₄×#67	1	1	yes	characteristic
323	#41	—	6	1	no	—
324	#41	—	6	1	no	—
325	#41	—	6	1	no	—
326	#41	—	6	1	no	—
327	C₂×Q₈	—	3	1	no	—
328	C₂×D₄	—	3	2	no	—
329	C₂×D₄	—	3	1	no	—
330	C₂²×C₄	—	3	2	no	—
331	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
332	M₁₆	—	2	1	no	—
333	M₁₆	—	3	2	no	—
334	M₁₆	—	6	1	no	—
335	M₁₆	—	6	1	no	—
336	M₁₆	—	6	1	no	—
337	M₁₆	—	6	2	no	—
338	M₁₆	—	6	2	no	—
339	M₁₆	C₄×C₅×D₃	1	2	yes	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	3	2	no	—
342	C₂×C₈	—	6	1	no	—
343	C₂×C₈	—	6	2	no	—
344	C₂×C₈	—	6	2	no	—
345	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
346	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
347	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
348	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
349	C₂×C₈	C₅×#67	1	1	yes	characteristic
350	C₂×C₈	C₅×#67	1	1	yes	characteristic
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	6	1	no	—
353	C₂²⋊C₄	—	3	2	no	—
354	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
355	C₄²	—	2	1	no	—
356	C₄²	—	6	1	no	—
357	C₃×C₅	#1757	1	1	yes	characteristic, complemented, Hall
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
360	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
362	C₂×D₃	—	2	2	no	—
363	C₂×D₃	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₃×C₄	C₅×#117	1	1	yes	characteristic
367	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
368	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
369	Dic₃	—	2	2	no	—
370	Dic₃	—	4	2	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	2	1	no	—
373	C₂×C₅	—	2	1	no	—
374	C₂×C₅	—	12	2	no	—
375	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
376	C₂³	—	3	2	no	—
377	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
378	Q₈	—	6	1	no	—
379	Q₈	—	6	1	no	—
380	D₄	—	6	2	no	—
381	D₄	—	6	2	no	—
382	D₄	—	6	1	no	—
383	D₄	—	6	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	3	2	no	—
386	C₂×C₄	—	6	2	no	—
387	C₂×C₄	—	6	2	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
391	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
392	C₂×C₄	C₅×#235	1	1	yes	characteristic
393	C₂×C₄	C₅×#235	1	1	yes	characteristic
394	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	6	2	no	—
397	C₈	—	6	2	no	—
398	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
399	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
400	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
401	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
406	D₃	—	4	2	no	—
407	C₅	#69898	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²	—	4	1	no	—
409	C₂²	—	6	2	no	—
410	C₂²	—	12	2	no	—
411	C₂²	C₄²×C₅×D₃	1	1	yes	characteristic
412	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
413	C₂²	C₄×C₅×#67	1	1	yes	characteristic
414	C₄	—	4	2	no	—
415	C₄	—	6	2	no	—
416	C₄	—	12	2	no	—
417	C₄	C₅×#872	1	1	yes	characteristic
418	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
419	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
420	C₄	C₄×C₅×#67	1	1	yes	characteristic
421	C₃	C₅×#1757	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	12	2	no	—
426	C₂	C₄×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₈	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂×C₃×C₅	C₄×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#1757
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂²×C₅×C₈ ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#405	C₂	semidirect
4. C₅×#5101	C₂	semidirect
6. C₅×#4559	C₂	semidirect
7. C₅×#4533	C₂	semidirect
20. C₂×C₅×ΓL(1,𝔽₂₅)	C₄	semidirect
21. C₂×C₅×D₃×C₈	C₄	semidirect
24. C₅×#824	C₄	semidirect
25. C₅×#823	C₄	semidirect
29. #69898	C₅	direct (N × H)
34. C₅×#405	D₃	semidirect
72. C₃×#405	C₂×C₅	semidirect
74. #5101	C₂×C₅	semidirect
76. #4559	C₂×C₅	semidirect
77. #4533	C₂×C₅	semidirect
136. C₂×ΓL(1,𝔽₂₅)	C₄×C₅	semidirect
137. C₂×D₃×C₈	C₄×C₅	semidirect
140. #824	C₄×C₅	semidirect
141. #823	C₄×C₅	semidirect
183. #405	C₅×D₃	semidirect
357. C₃×C₅	#1757	semidirect
407. C₅	#69898	direct (N × H)
421. C₃	C₅×#1757	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#901	2
C₃×C₅×#405	2
C₅×#5132	2
C₅×#5101	2
C₅×#5006	2
C₅×#4559	2
C₅×#4533	2
C₅×#1757	3
#69898	5

Subgroups — C5×#69898 #14295505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69898 #14295505