Subgroups — C₅×#68169 #14281852

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×#5557	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×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1482	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₅×#938	C₄	1	1	yes	characteristic
11	C₅×#936	C₄	1	1	yes	characteristic
12	C₄×C₅×#67	—	2	1	no	—
13	C₅×#926	—	2	1	no	—
14	C₅×#897	C₄	1	1	yes	characteristic
15	C₅×#890	C₄	1	1	yes	characteristic
16	C₅×#883	—	2	1	no	—
17	C₅×#879	—	2	1	no	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₄×C₅×Dic₆	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	#68169	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	—	3	1	no	—
34	C₅×D₄⋊C₈	—	3	1	no	—
35	C₅×D₄⋊C₈	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂×C₅×#67	—	2	1	no	—
39	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
42	C₂×C₅×Dic₆	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×#217	—	2	1	no	—
49	C₅×#217	—	2	1	no	—
50	C₅×#217	—	2	1	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	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	#5557	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×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
68	#4484	C₂×C₅	1	1	yes	characteristic, complemented
69	#4456	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	—	3	1	no	—
77	C₄×C₅×D₄	—	6	1	no	—
78	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
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	C₂³×C₃×C₅	—	2	1	no	—
91	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₅×#67	—	4	2	no	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₅×Dic₆	—	2	1	no	—
112	C₅×Dic₆	—	2	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×D₄	C₂²×C₅	1	1	yes	characteristic
118	#938	C₄×C₅	1	1	yes	characteristic
119	#936	C₄×C₅	1	1	yes	characteristic
120	C₄×#67	—	2	1	no	—
121	#926	—	2	1	no	—
122	#897	C₄×C₅	1	1	yes	characteristic
123	#890	C₄×C₅	1	1	yes	characteristic
124	#883	—	2	1	no	—
125	#879	—	2	1	no	—
126	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
127	C₄×Dic₆	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	—	3	1	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	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	—	3	1	no	—
148	C₅×C₄⋊C₄	—	6	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	—	2	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	—	3	1	no	—
159	C₄²×C₅	—	3	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	6	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	—	3	1	no	—
168	D₄⋊C₈	—	3	1	no	—
169	D₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
170	C₂²×C₃×C₅	—	4	1	no	—
171	C₂²×C₃×C₅	—	4	1	no	—
172	C₂²×C₃×C₅	—	4	1	no	—
173	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₅×D₃	—	2	1	no	—
175	C₂×C₅×D₃	—	2	1	no	—
176	C₂×C₅×D₃	—	2	1	no	—
177	C₃×C₄×C₅	—	2	1	no	—
178	C₃×C₄×C₅	—	4	1	no	—
179	C₃×C₄×C₅	#131	1	1	yes	characteristic
180	C₃×C₄×C₅	#131	1	1	yes	characteristic
181	C₃×C₄×C₅	#135	1	1	yes	characteristic
182	C₃×C₄×C₅	#135	1	1	yes	characteristic
183	C₅×Dic₃	—	2	1	no	—
184	C₅×Dic₃	—	2	1	no	—
185	C₅×Dic₃	—	2	1	no	—
186	C₅×Dic₃	—	4	1	no	—
187	C₅×Dic₃	—	4	1	no	—
188	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂×#67	—	2	1	no	—
191	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
193	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
194	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
195	C₂×C₃×C₈	—	2	1	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	—	2	1	no	—
199	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
200	#217	—	2	1	no	—
201	#217	—	2	1	no	—
202	#217	—	2	1	no	—
203	(C₂×D₃)⋊C₄	—	2	1	no	—
204	C₄⋊Dic₃	—	2	1	no	—
205	C₄⋊Dic₃	—	2	1	no	—
206	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
207	Dic₃⋊C₄	—	2	1	no	—
208	Dic₃⋊C₄	—	2	1	no	—
209	C₄×Dic₃	—	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	—	2	1	no	—
216	C₂³×C₅	—	3	1	no	—
217	C₅×Q₈	—	6	1	no	—
218	C₅×Q₈	—	6	1	no	—
219	C₅×D₄	—	2	1	no	—
220	C₅×D₄	—	2	1	no	—
221	C₅×D₄	—	12	2	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	3	1	no	—
224	C₂×C₄×C₅	—	3	1	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	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	—	6	1	no	—
233	C₂×C₄×C₅	—	6	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	—	3	1	no	—
249	C₄×D₄	—	6	1	no	—
250	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
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	—	8	1	no	—
262	C₂×C₃×C₅	#408	1	1	yes	characteristic
263	C₂×C₃×C₅	#416	1	1	yes	characteristic
264	C₂×C₃×C₅	#421	1	1	yes	characteristic
265	C₅×D₃	—	4	1	no	—
266	C₂³×C₃	—	2	1	no	—
267	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
268	C₃×D₄	—	2	1	no	—
269	C₃×D₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	4	1	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	#67	—	4	2	no	—
277	C₂×Dic₃	—	2	1	no	—
278	C₂×Dic₃	—	2	1	no	—
279	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
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	Dic₆	—	2	1	no	—
288	Dic₆	—	2	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	—	4	1	no	—
294	C₂²×C₅	—	4	1	no	—
295	C₂²×C₅	—	4	1	no	—
296	C₂²×C₅	—	6	1	no	—
297	C₂²×C₅	—	6	1	no	—
298	C₂²×C₅	—	6	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	—	6	1	no	—
303	C₄×C₅	—	6	1	no	—
304	C₄×C₅	—	6	1	no	—
305	C₄×C₅	—	12	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	#912	1	1	yes	characteristic
310	C₄×C₅	#916	1	1	yes	characteristic
311	C₂×Q₈	—	3	1	no	—
312	C₂×D₄	—	6	1	no	—
313	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	3	1	no	—
316	C₂²×C₄	—	3	1	no	—
317	C₂²×C₄	—	3	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	—	3	1	no	—
323	C₄⋊C₄	—	6	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	—	2	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	—	3	1	no	—
334	C₄²	—	3	1	no	—
335	C₄²	—	3	1	no	—
336	C₄²	—	6	1	no	—
337	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
338	C₃×C₅	#1482	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	—	4	1	no	—
340	C₂²×C₃	—	4	1	no	—
341	C₂²×C₃	—	4	1	no	—
342	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×D₃	—	2	1	no	—
344	C₂×D₃	—	2	1	no	—
345	C₂×D₃	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	4	1	no	—
348	C₃×C₄	C₅×#131	1	1	yes	characteristic
349	C₃×C₄	C₅×#131	1	1	yes	characteristic
350	C₃×C₄	C₅×#135	1	1	yes	characteristic
351	C₃×C₄	C₅×#135	1	1	yes	characteristic
352	Dic₃	—	2	1	no	—
353	Dic₃	—	2	1	no	—
354	Dic₃	—	2	1	no	—
355	Dic₃	—	4	1	no	—
356	Dic₃	—	4	1	no	—
357	C₂×C₅	—	8	1	no	—
358	C₂×C₅	—	12	1	no	—
359	C₂×C₅	#4727	1	1	yes	characteristic
360	C₂×C₅	#4772	1	1	yes	characteristic
361	C₂×C₅	#4821	1	1	yes	characteristic
362	C₂³	—	2	1	no	—
363	C₂³	—	3	1	no	—
364	Q₈	—	6	1	no	—
365	Q₈	—	6	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	12	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	3	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	3	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	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	—	6	1	no	—
380	C₂×C₄	—	6	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	—	8	1	no	—
390	C₂×C₃	C₅×#408	1	1	yes	characteristic
391	C₂×C₃	C₅×#416	1	1	yes	characteristic
392	C₂×C₃	C₅×#421	1	1	yes	characteristic
393	D₃	—	4	1	no	—
394	C₅	#68169	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	6	1	no	—
399	C₂²	—	6	1	no	—
400	C₂²	—	6	1	no	—
401	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	6	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	6	1	no	—
407	C₄	—	12	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×#912	1	1	yes	characteristic
412	C₄	C₅×#916	1	1	yes	characteristic
413	C₃	C₅×#1482	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	8	1	no	—
415	C₂	—	12	1	no	—
416	C₂	C₅×#4727	1	1	yes	characteristic
417	C₂	C₅×#4772	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×D₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#938	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×D₄⋊C₈	D₃
hypocenter	C₃	C₅×#1482
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×D₄⋊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×D₄⋊C₈	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4484	C₂	semidirect
7. C₅×#4456	C₂	semidirect
28. #68169	C₅	direct (N × H)
35. C₅×D₄⋊C₈	D₃	semidirect
64. #4833	C₂×C₅	semidirect
65. #4685	C₂×C₅	semidirect
66. C₃×D₄⋊C₈	C₂×C₅	semidirect
67. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
68. #4484	C₂×C₅	semidirect
69. #4456	C₂×C₅	semidirect
169. D₄⋊C₈	C₅×D₃	semidirect
338. C₃×C₅	#1482	semidirect
394. C₅	#68169	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×#5557	2
C₅×#4833	2
C₅×#4685	2
C₃×C₅×D₄⋊C₈	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#4484	2
C₅×#4456	2
C₅×#1482	3
#68169	5

Subgroups — C5×#68169 #14281852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68169 #14281852