Subgroups — C₅×#68234 #14281921

Order 1920.

468 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	C₅×#5580	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1483	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₅×#947	C₄	1	1	yes	characteristic
11	C₅×#946	C₄	1	1	yes	characteristic
12	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
13	C₂×C₅×D₃×C₈	—	2	1	no	—
14	C₅×#898	—	2	1	no	—
15	C₅×#895	C₄	1	1	yes	characteristic
16	C₅×#894	—	2	1	no	—
17	C₅×#890	C₄	1	1	yes	characteristic
18	C₄×C₅×D₁₂	—	2	1	no	—
19	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₅×#872	—	2	1	no	—
21	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₅×#815	—	2	1	no	—
25	C₅×Dic₃⋊C₈	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#68234	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#529	—	3	1	no	—
30	C₂×C₅×C₄⋊C₈	—	3	1	no	—
31	C₄×C₅×M₁₆	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
34	C₅×D₄⋊C₈	—	3	1	no	—
35	C₅×D₄⋊C₈	—	3	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₅×Dic₃⋊C₄	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
64	C₅×D₃×C₈	—	4	2	no	—
65	#5580	C₂×C₅	1	1	yes	characteristic
66	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
69	#4535	C₂×C₅	1	1	yes	characteristic, complemented
70	#4483	C₂×C₅	1	1	yes	characteristic, complemented
71	#4459	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₅×M₁₆	—	6	1	no	—
73	C₂²×C₅×C₈	—	6	1	no	—
74	C₅×#126	—	6	1	no	—
75	C₅×#125	—	3	1	no	—
76	C₅×#124	—	3	1	no	—
77	C₅×#123	—	6	1	no	—
78	C₅×C₂²⋊Q₈	—	3	1	no	—
79	C₅×#121	—	3	1	no	—
80	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
81	C₄×C₅×D₄	—	3	1	no	—
82	C₄×C₅×D₄	—	6	1	no	—
83	C₅×#117	—	6	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₅×C₄⋊C₈	—	3	1	no	—
86	C₅×C₄⋊C₈	—	6	1	no	—
87	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
88	C₅×#97	—	6	1	no	—
89	C₄×C₅×C₈	—	3	1	no	—
90	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
91	#1483	—	3	1	no	Sylow
92	C₂²×C₅×D₃	—	2	1	no	—
93	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₅×D₁₂	—	2	1	no	—
106	C₅×D₁₂	—	2	1	no	—
107	C₅×D₁₂	—	4	2	no	—
108	C₄×C₅×D₃	—	2	2	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	2	1	no	—
111	C₄×C₅×D₃	—	2	1	no	—
112	C₄×C₅×D₃	—	2	1	no	—
113	C₄×C₅×D₃	—	4	1	no	—
114	C₄×C₅×D₃	—	4	1	no	—
115	C₃×C₅×C₈	—	2	2	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₅×C₃⋊C₈	—	2	2	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
120	#947	C₄×C₅	1	1	yes	characteristic
121	#946	C₄×C₅	1	1	yes	characteristic
122	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
123	C₂×D₃×C₈	—	2	1	no	—
124	#898	—	2	1	no	—
125	#895	C₄×C₅	1	1	yes	characteristic
126	#894	—	2	1	no	—
127	#890	C₄×C₅	1	1	yes	characteristic
128	C₄×D₁₂	—	2	1	no	—
129	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	#872	—	2	1	no	—
131	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
132	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
133	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
134	#815	—	2	1	no	—
135	Dic₃⋊C₈	—	2	1	no	—
136	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
137	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
139	C₂×C₅×D₄	—	3	1	no	—
140	C₂×C₅×D₄	—	6	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₅×M₁₆	—	6	4	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	—	12	2	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	3	1	no	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₅×C₂²⋊C₄	—	6	1	no	—
159	C₅×C₂²⋊C₄	—	6	1	no	—
160	C₅×C₂²⋊C₄	—	6	1	no	—
161	C₅×C₂²⋊C₄	—	6	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	3	1	no	—
164	C₄²×C₅	—	3	1	no	—
165	C₄²×C₅	—	3	1	no	—
166	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
167	#529	—	3	1	no	—
168	C₂×C₄⋊C₈	—	3	1	no	—
169	C₄×M₁₆	—	3	1	no	—
170	Q₈⋊C₈	—	3	1	no	—
171	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
172	D₄⋊C₈	—	3	1	no	—
173	D₄⋊C₈	—	3	1	no	—
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₅×D₃	—	2	1	no	—
176	C₂×C₅×D₃	—	2	1	no	—
177	C₂×C₅×D₃	—	4	1	no	—
178	C₂×C₅×D₃	—	4	1	no	—
179	C₂×C₅×D₃	—	4	1	no	—
180	C₂×C₅×D₃	#104	1	2	yes	—
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	—	4	1	no	—
183	C₃×C₄×C₅	—	4	1	no	—
184	C₃×C₄×C₅	#131	1	1	yes	characteristic
185	C₃×C₄×C₅	#131	1	1	yes	characteristic
186	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₃×C₄×C₅	#137	1	1	yes	characteristic
188	C₅×Dic₃	—	2	1	no	—
189	C₅×Dic₃	—	2	1	no	—
190	C₅×Dic₃	—	2	1	no	—
191	C₅×Dic₃	—	4	1	no	—
192	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂×D₁₂	—	2	1	no	—
194	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
195	C₂×C₄×D₃	—	2	1	no	—
196	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
198	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
199	C₂×C₃×C₈	—	2	1	no	—
200	C₂×C₃×C₈	—	2	1	no	—
201	C₃×C₄⋊C₄	—	2	1	no	—
202	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
203	C₃×C₄²	—	2	1	no	—
204	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	—	2	1	no	—
206	(C₂×D₃)⋊C₄	—	2	1	no	—
207	(C₂×D₃)⋊C₄	—	2	1	no	—
208	(C₂×D₃)⋊C₄	—	2	1	no	—
209	(C₂×D₃)⋊C₄	—	2	1	no	—
210	C₄⋊Dic₃	—	2	1	no	—
211	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
212	Dic₃⋊C₄	—	2	1	no	—
213	Dic₃⋊C₄	—	2	1	no	—
214	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
215	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
216	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
217	C₂×C₃⋊C₈	—	2	1	no	—
218	C₂×C₃⋊C₈	—	2	1	no	—
219	ΓL(1,𝔽₂₅)	—	2	4	no	—
220	D₃×C₈	—	4	2	no	—
221	C₂³×C₅	—	3	1	no	—
222	C₂³×C₅	—	6	1	no	—
223	C₅×Q₈	—	2	1	no	—
224	C₅×Q₈	—	2	1	no	—
225	C₅×D₄	—	6	1	no	—
226	C₅×D₄	—	6	1	no	—
227	C₅×D₄	—	12	2	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	3	1	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	3	1	no	—
233	C₂×C₄×C₅	—	6	2	no	—
234	C₂×C₄×C₅	—	6	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	1	no	—
239	C₂×C₄×C₅	—	12	1	no	—
240	C₂×C₄×C₅	—	12	1	no	—
241	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	4	1	no	—
246	C₅×C₈	—	6	2	no	—
247	C₅×C₈	—	12	1	no	—
248	C₂×M₁₆	—	6	1	no	—
249	C₂²×C₈	—	6	1	no	—
250	#126	—	6	1	no	—
251	#125	—	3	1	no	—
252	#124	—	3	1	no	—
253	#123	—	6	1	no	—
254	C₂²⋊Q₈	—	3	1	no	—
255	#121	—	3	1	no	—
256	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
257	C₄×D₄	—	3	1	no	—
258	C₄×D₄	—	6	1	no	—
259	#117	—	6	1	no	—
260	C₂×C₄²	—	3	1	no	—
261	C₄⋊C₈	—	3	1	no	—
262	C₄⋊C₈	—	6	1	no	—
263	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
264	#97	—	6	1	no	—
265	C₄×C₈	—	3	1	no	—
266	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
267	C₂×C₃×C₅	#408	1	1	yes	characteristic
268	C₂×C₃×C₅	#417	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
270	C₅×D₃	—	2	2	no	—
271	C₅×D₃	—	8	1	no	—
272	C₂²×D₃	—	2	1	no	—
273	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
274	C₃×Q₈	—	2	1	no	—
275	C₃×Q₈	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂×Dic₃	—	2	1	no	—
282	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
285	D₁₂	—	2	1	no	—
286	D₁₂	—	2	1	no	—
287	D₁₂	—	4	2	no	—
288	C₄×D₃	—	2	2	no	—
289	C₄×D₃	—	2	1	no	—
290	C₄×D₃	—	2	1	no	—
291	C₄×D₃	—	2	1	no	—
292	C₄×D₃	—	2	1	no	—
293	C₄×D₃	—	4	1	no	—
294	C₄×D₃	—	4	1	no	—
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	4	1	no	—
297	C₃⋊C₈	—	2	2	no	—
298	C₃⋊C₈	—	4	1	no	—
299	C₂²×C₅	—	3	2	no	—
300	C₂²×C₅	—	6	1	no	—
301	C₂²×C₅	—	6	1	no	—
302	C₂²×C₅	—	12	1	no	—
303	C₂²×C₅	—	12	1	no	—
304	C₂²×C₅	—	12	1	no	—
305	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	4	1	no	—
308	C₄×C₅	—	4	1	no	—
309	C₄×C₅	—	6	1	no	—
310	C₄×C₅	—	6	1	no	—
311	C₄×C₅	—	6	1	no	—
312	C₄×C₅	—	12	1	no	—
313	C₄×C₅	#901	1	1	yes	characteristic
314	C₄×C₅	#907	1	1	yes	characteristic
315	C₄×C₅	#914	1	1	yes	characteristic
316	C₄×C₅	#918	1	1	yes	characteristic
317	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
318	C₂×D₄	—	3	1	no	—
319	C₂×D₄	—	6	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	3	1	no	—
322	C₂²×C₄	—	3	1	no	—
323	C₂²×C₄	—	6	1	no	—
324	M₁₆	—	6	4	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	6	1	no	—
328	C₂×C₈	—	6	1	no	—
329	C₂×C₈	—	12	2	no	—
330	C₄⋊C₄	—	2	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	C₄×C₅×D₃	1	1	yes	characteristic
336	C₂²⋊C₄	—	6	1	no	—
337	C₂²⋊C₄	—	6	1	no	—
338	C₂²⋊C₄	—	6	1	no	—
339	C₂²⋊C₄	—	6	1	no	—
340	C₂²⋊C₄	—	6	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	3	1	no	—
343	C₄²	—	3	1	no	—
344	C₄²	—	3	1	no	—
345	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₃×C₅	#1483	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×D₃	—	2	1	no	—
349	C₂×D₃	—	2	1	no	—
350	C₂×D₃	—	4	1	no	—
351	C₂×D₃	—	4	1	no	—
352	C₂×D₃	—	4	1	no	—
353	C₂×D₃	C₅×#104	1	2	yes	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	4	1	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	C₅×#131	1	1	yes	characteristic
358	C₃×C₄	C₅×#131	1	1	yes	characteristic
359	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₃×C₄	C₅×#137	1	1	yes	characteristic
361	Dic₃	—	2	1	no	—
362	Dic₃	—	2	1	no	—
363	Dic₃	—	2	1	no	—
364	Dic₃	—	4	1	no	—
365	C₂×C₅	—	6	2	no	—
366	C₂×C₅	—	24	1	no	—
367	C₂×C₅	#4727	1	1	yes	characteristic
368	C₂×C₅	#4803	1	1	yes	characteristic
369	C₂×C₅	D₃×#104	1	1	yes	characteristic
370	C₂³	—	3	1	no	—
371	C₂³	—	6	1	no	—
372	Q₈	—	2	1	no	—
373	Q₈	—	2	1	no	—
374	D₄	—	6	1	no	—
375	D₄	—	6	1	no	—
376	D₄	—	12	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	3	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	6	2	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	6	1	no	—
386	C₂×C₄	—	6	1	no	—
387	C₂×C₄	—	6	1	no	—
388	C₂×C₄	—	12	1	no	—
389	C₂×C₄	—	12	1	no	—
390	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
391	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
392	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	6	2	no	—
396	C₈	—	12	1	no	—
397	C₂×C₃	C₅×#408	1	1	yes	characteristic
398	C₂×C₃	C₅×#417	1	1	yes	characteristic
399	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
400	D₃	—	2	2	no	—
401	D₃	—	8	1	no	—
402	C₅	#68234	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	—	3	2	no	—
404	C₂²	—	6	1	no	—
405	C₂²	—	6	1	no	—
406	C₂²	—	12	1	no	—
407	C₂²	—	12	1	no	—
408	C₂²	—	12	1	no	—
409	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	6	1	no	—
414	C₄	—	6	1	no	—
415	C₄	—	6	1	no	—
416	C₄	—	12	1	no	—
417	C₄	C₅×#901	1	1	yes	characteristic
418	C₄	C₅×#907	1	1	yes	characteristic
419	C₄	C₅×#914	1	1	yes	characteristic
420	C₄	C₅×#918	1	1	yes	characteristic
421	C₃	C₅×#1483	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	6	2	no	—
423	C₂	—	24	1	no	—
424	C₂	C₅×#4727	1	1	yes	characteristic
425	C₂	C₅×#4803	1	1	yes	characteristic
426	C₂	C₅×D₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#895	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1483
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₅×D₃×C₄⋊C₈	C₂	semidirect
3. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. C₅×#4535	C₂	semidirect
6. C₅×#4483	C₂	semidirect
7. C₅×#4459	C₂	semidirect
28. #68234	C₅	direct (N × H)
33. C₅×Q₈⋊C₈	D₃	semidirect
66. D₃×C₄⋊C₈	C₂×C₅	semidirect
67. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
68. C₃×Q₈⋊C₈	C₂×C₅	semidirect
69. #4535	C₂×C₅	semidirect
70. #4483	C₂×C₅	semidirect
71. #4459	C₂×C₅	semidirect
171. Q₈⋊C₈	C₅×D₃	semidirect
346. C₃×C₅	#1483	semidirect
402. C₅	#68234	direct (N × H)
421. C₃	C₅×#1483	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5580	2
C₅×D₃×C₄⋊C₈	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4483	2
C₅×#4459	2
C₅×#1483	3
#68234	5

Subgroups — C5×#68234 #14281921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68234 #14281921