Subgroups — C₅×#68233 #14281858

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 420 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×#4833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4685	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×#1482	—	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	C₅×#898	—	2	1	no	—
13	C₅×#895	C₄	1	1	yes	characteristic
14	C₅×#894	—	2	1	no	—
15	C₅×#890	C₄	1	1	yes	characteristic
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₅×#872	—	2	1	no	—
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#68233	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#529	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₅×#431	—	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	#5580	C₂×C₅	1	1	yes	characteristic
64	#4833	C₂×C₅	1	1	yes	characteristic, complemented
65	#4685	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	#4535	C₂×C₅	1	1	yes	characteristic, complemented
68	#4483	C₂×C₅	1	1	yes	characteristic, complemented
69	#4459	C₂×C₅	1	1	yes	characteristic, complemented
70	C₅×#126	—	6	1	no	—
71	C₅×#125	—	3	1	no	—
72	C₅×#124	—	3	1	no	—
73	C₅×#123	—	6	1	no	—
74	C₅×C₂²⋊Q₈	—	3	1	no	—
75	C₅×#121	—	3	1	no	—
76	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×D₄	—	3	1	no	—
78	C₄×C₅×D₄	—	6	1	no	—
79	C₅×#117	—	6	1	no	—
80	C₂×C₄²×C₅	—	3	1	no	—
81	C₅×C₄⋊C₈	—	3	1	no	—
82	C₅×C₄⋊C₈	—	6	1	no	—
83	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
84	C₅×C₂²⋊C₈	—	6	1	no	—
85	C₅×C₂²⋊C₈	—	6	1	no	—
86	C₄×C₅×C₈	—	3	1	no	—
87	C₄×C₅×C₈	—	6	1	no	—
88	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	#1482	—	3	1	no	Sylow
90	C₂²×C₅×D₃	—	2	1	no	—
91	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	1	no	—
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	2	1	no	—
100	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₅×D₁₂	—	2	1	no	—
104	C₅×D₁₂	—	2	1	no	—
105	C₅×D₁₂	—	4	2	no	—
106	C₄×C₅×D₃	—	2	1	no	—
107	C₄×C₅×D₃	—	2	1	no	—
108	C₄×C₅×D₃	—	2	1	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	4	1	no	—
111	C₄×C₅×D₃	—	4	1	no	—
112	C₄×C₅×D₃	—	4	1	no	—
113	C₃×C₅×C₈	—	4	1	no	—
114	C₃×C₅×C₈	—	4	1	no	—
115	C₅×C₃⋊C₈	—	4	1	no	—
116	C₅×C₃⋊C₈	—	4	1	no	—
117	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
118	#947	C₄×C₅	1	1	yes	characteristic
119	#946	C₄×C₅	1	1	yes	characteristic
120	#898	—	2	1	no	—
121	#895	C₄×C₅	1	1	yes	characteristic
122	#894	—	2	1	no	—
123	#890	C₄×C₅	1	1	yes	characteristic
124	C₄×D₁₂	—	2	1	no	—
125	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
126	#872	—	2	1	no	—
127	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
128	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
130	(C₂×D₃)⋊C₈	—	2	1	no	—
131	(C₂×D₃)⋊C₈	—	2	1	no	—
132	Dic₃⋊C₈	—	2	1	no	—
133	C₈×Dic₃	—	2	1	no	—
134	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
135	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
137	C₂×C₅×D₄	—	3	1	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂²×C₄×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	6	1	no	—
146	C₂×C₅×C₈	—	6	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	3	1	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
153	C₅×C₂²⋊C₄	—	6	1	no	—
154	C₅×C₂²⋊C₄	—	6	1	no	—
155	C₅×C₂²⋊C₄	—	6	1	no	—
156	C₅×C₂²⋊C₄	—	6	1	no	—
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	3	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
163	#529	—	3	1	no	—
164	#431	—	3	1	no	—
165	#431	—	3	1	no	—
166	Q₈⋊C₈	—	3	1	no	—
167	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
168	D₄⋊C₈	—	3	1	no	—
169	D₄⋊C₈	—	3	1	no	—
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₅×D₃	—	2	1	no	—
172	C₂×C₅×D₃	—	2	1	no	—
173	C₂×C₅×D₃	—	2	1	no	—
174	C₂×C₅×D₃	—	4	1	no	—
175	C₂×C₅×D₃	—	4	1	no	—
176	C₂×C₅×D₃	—	4	1	no	—
177	C₃×C₄×C₅	—	2	1	no	—
178	C₃×C₄×C₅	—	4	1	no	—
179	C₃×C₄×C₅	—	4	1	no	—
180	C₃×C₄×C₅	#131	1	1	yes	characteristic
181	C₃×C₄×C₅	#131	1	1	yes	characteristic
182	C₃×C₄×C₅	#135	1	1	yes	characteristic
183	C₃×C₄×C₅	#135	1	1	yes	characteristic
184	C₅×Dic₃	—	2	1	no	—
185	C₅×Dic₃	—	2	1	no	—
186	C₅×Dic₃	—	2	1	no	—
187	C₅×Dic₃	—	4	1	no	—
188	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂×D₁₂	—	2	1	no	—
190	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	1	no	—
192	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
194	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
195	C₂×C₃×C₈	—	2	1	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₃×C₄⋊C₄	—	2	1	no	—
198	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
201	(C₂×D₃)⋊C₄	—	2	1	no	—
202	(C₂×D₃)⋊C₄	—	2	1	no	—
203	(C₂×D₃)⋊C₄	—	2	1	no	—
204	(C₂×D₃)⋊C₄	—	2	1	no	—
205	(C₂×D₃)⋊C₄	—	2	1	no	—
206	C₄⋊Dic₃	—	2	1	no	—
207	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
208	Dic₃⋊C₄	—	2	1	no	—
209	Dic₃⋊C₄	—	2	1	no	—
210	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
211	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
212	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
213	C₂×C₃⋊C₈	—	2	1	no	—
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂³×C₅	—	3	1	no	—
216	C₂³×C₅	—	6	1	no	—
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	2	1	no	—
219	C₅×D₄	—	6	1	no	—
220	C₅×D₄	—	6	1	no	—
221	C₅×D₄	—	12	2	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	3	1	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	3	1	no	—
227	C₂×C₄×C₅	—	6	1	no	—
228	C₂×C₄×C₅	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	6	1	no	—
231	C₂×C₄×C₅	—	6	1	no	—
232	C₂×C₄×C₅	—	12	1	no	—
233	C₂×C₄×C₅	—	12	1	no	—
234	C₂×C₄×C₅	—	12	1	no	—
235	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	C₅×C₈	—	4	1	no	—
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	12	1	no	—
241	C₅×C₈	—	12	1	no	—
242	#126	—	6	1	no	—
243	#125	—	3	1	no	—
244	#124	—	3	1	no	—
245	#123	—	6	1	no	—
246	C₂²⋊Q₈	—	3	1	no	—
247	#121	—	3	1	no	—
248	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
249	C₄×D₄	—	3	1	no	—
250	C₄×D₄	—	6	1	no	—
251	#117	—	6	1	no	—
252	C₂×C₄²	—	3	1	no	—
253	C₄⋊C₈	—	3	1	no	—
254	C₄⋊C₈	—	6	1	no	—
255	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
256	C₂²⋊C₈	—	6	1	no	—
257	C₂²⋊C₈	—	6	1	no	—
258	C₄×C₈	—	3	1	no	—
259	C₄×C₈	—	6	1	no	—
260	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
261	C₂×C₃×C₅	#408	1	1	yes	characteristic
262	C₂×C₃×C₅	#416	1	1	yes	characteristic
263	C₂×C₃×C₅	#421	1	1	yes	characteristic
264	C₅×D₃	—	4	1	no	—
265	C₅×D₃	—	8	1	no	—
266	C₂²×D₃	—	2	1	no	—
267	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
268	C₃×Q₈	—	2	1	no	—
269	C₃×Q₈	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×Dic₃	—	2	1	no	—
276	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
279	D₁₂	—	2	1	no	—
280	D₁₂	—	2	1	no	—
281	D₁₂	—	4	2	no	—
282	C₄×D₃	—	2	1	no	—
283	C₄×D₃	—	2	1	no	—
284	C₄×D₃	—	2	1	no	—
285	C₄×D₃	—	2	1	no	—
286	C₄×D₃	—	4	1	no	—
287	C₄×D₃	—	4	1	no	—
288	C₄×D₃	—	4	1	no	—
289	C₃×C₈	—	4	1	no	—
290	C₃×C₈	—	4	1	no	—
291	C₃⋊C₈	—	4	1	no	—
292	C₃⋊C₈	—	4	1	no	—
293	C₂²×C₅	—	6	1	no	—
294	C₂²×C₅	—	6	1	no	—
295	C₂²×C₅	—	6	1	no	—
296	C₂²×C₅	—	12	1	no	—
297	C₂²×C₅	—	12	1	no	—
298	C₂²×C₅	—	12	1	no	—
299	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	4	1	no	—
302	C₄×C₅	—	4	1	no	—
303	C₄×C₅	—	6	1	no	—
304	C₄×C₅	—	6	1	no	—
305	C₄×C₅	—	6	1	no	—
306	C₄×C₅	—	12	1	no	—
307	C₄×C₅	#901	1	1	yes	characteristic
308	C₄×C₅	#907	1	1	yes	characteristic
309	C₄×C₅	#916	1	1	yes	characteristic
310	C₄×C₅	#919	1	1	yes	characteristic
311	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
312	C₂×D₄	—	3	1	no	—
313	C₂×D₄	—	6	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	3	1	no	—
316	C₂²×C₄	—	3	1	no	—
317	C₂²×C₄	—	6	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	6	1	no	—
321	C₂×C₈	—	6	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	3	1	no	—
324	C₄⋊C₄	—	6	1	no	—
325	C₄⋊C₄	—	6	1	no	—
326	C₄⋊C₄	—	6	1	no	—
327	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
328	C₂²⋊C₄	—	6	1	no	—
329	C₂²⋊C₄	—	6	1	no	—
330	C₂²⋊C₄	—	6	1	no	—
331	C₂²⋊C₄	—	6	1	no	—
332	C₂²⋊C₄	—	6	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	3	1	no	—
335	C₄²	—	3	1	no	—
336	C₄²	—	3	1	no	—
337	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
338	C₃×C₅	#1482	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×D₃	—	2	1	no	—
341	C₂×D₃	—	2	1	no	—
342	C₂×D₃	—	2	1	no	—
343	C₂×D₃	—	4	1	no	—
344	C₂×D₃	—	4	1	no	—
345	C₂×D₃	—	4	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	4	1	no	—
348	C₃×C₄	—	4	1	no	—
349	C₃×C₄	C₅×#131	1	1	yes	characteristic
350	C₃×C₄	C₅×#131	1	1	yes	characteristic
351	C₃×C₄	C₅×#135	1	1	yes	characteristic
352	C₃×C₄	C₅×#135	1	1	yes	characteristic
353	Dic₃	—	2	1	no	—
354	Dic₃	—	2	1	no	—
355	Dic₃	—	2	1	no	—
356	Dic₃	—	4	1	no	—
357	C₂×C₅	—	12	1	no	—
358	C₂×C₅	—	24	1	no	—
359	C₂×C₅	#4727	1	1	yes	characteristic
360	C₂×C₅	#4804	1	1	yes	characteristic
361	C₂×C₅	#4821	1	1	yes	characteristic
362	C₂³	—	3	1	no	—
363	C₂³	—	6	1	no	—
364	Q₈	—	2	1	no	—
365	Q₈	—	2	1	no	—
366	D₄	—	6	1	no	—
367	D₄	—	6	1	no	—
368	D₄	—	12	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	3	1	no	—
373	C₂×C₄	—	3	1	no	—
374	C₂×C₄	—	6	1	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	6	1	no	—
377	C₂×C₄	—	6	1	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	12	1	no	—
380	C₂×C₄	—	12	1	no	—
381	C₂×C₄	—	12	1	no	—
382	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
383	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
384	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₈	—	12	1	no	—
388	C₈	—	12	1	no	—
389	C₂×C₃	C₅×#408	1	1	yes	characteristic
390	C₂×C₃	C₅×#416	1	1	yes	characteristic
391	C₂×C₃	C₅×#421	1	1	yes	characteristic
392	D₃	—	4	1	no	—
393	D₃	—	8	1	no	—
394	C₅	#68233	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	6	1	no	—
396	C₂²	—	6	1	no	—
397	C₂²	—	6	1	no	—
398	C₂²	—	12	1	no	—
399	C₂²	—	12	1	no	—
400	C₂²	—	12	1	no	—
401	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	6	1	no	—
407	C₄	—	6	1	no	—
408	C₄	—	12	1	no	—
409	C₄	C₅×#901	1	1	yes	characteristic
410	C₄	C₅×#907	1	1	yes	characteristic
411	C₄	C₅×#916	1	1	yes	characteristic
412	C₄	C₅×#919	1	1	yes	characteristic
413	C₃	C₅×#1482	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	12	1	no	—
415	C₂	—	24	1	no	—
416	C₂	C₅×#4727	1	1	yes	characteristic
417	C₂	C₅×#4804	1	1	yes	characteristic
418	C₂	C₅×#4821	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×#1482
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×#4833	C₂	semidirect
3. C₅×#4685	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. #68233	C₅	direct (N × H)
33. C₅×Q₈⋊C₈	D₃	semidirect
64. #4833	C₂×C₅	semidirect
65. #4685	C₂×C₅	semidirect
66. C₃×Q₈⋊C₈	C₂×C₅	semidirect
67. #4535	C₂×C₅	semidirect
68. #4483	C₂×C₅	semidirect
69. #4459	C₂×C₅	semidirect
167. Q₈⋊C₈	C₅×D₃	semidirect
338. C₃×C₅	#1482	semidirect
394. C₅	#68233	direct (N × H)
413. C₃	C₅×#1482	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×#4833	2
C₅×#4685	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4483	2
C₅×#4459	2
C₅×#1482	3
#68233	5

Subgroups — C5×#68233 #14281858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68233 #14281858