Subgroups — C₅×#68239 #14282319

Order 1920.

504 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	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#4835	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4535	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×#1491	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
12	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
13	C₅×D₃×C₄⋊C₄	—	2	1	no	—
14	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₅×#887	—	2	1	no	—
16	C₅×#887	C₄	1	1	yes	characteristic
17	C₄²×C₅×D₃	—	2	1	no	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₄×C₅×Dic₆	—	2	1	no	—
20	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×#815	—	2	1	no	—
25	C₅×#815	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	#68239	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×Q₈	—	3	1	no	—
30	C₅×#432	—	3	1	no	—
31	C₄×C₅×M₁₆	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×Q₈⋊C₈	—	3	1	no	—
34	C₅×Q₈⋊C₈	—	3	1	no	—
35	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₅×D₃×Q₈	—	2	2	no	—
38	C₅×D₃×Q₈	—	2	2	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
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	1	no	—
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	1	no	—
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	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
66	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic
67	#4835	C₂×C₅	1	1	yes	characteristic
68	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic
69	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
70	#4535	C₂×C₅	1	1	yes	characteristic, complemented
71	#4484	C₂×C₅	1	1	yes	characteristic, complemented
72	#4456	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×C₅×Q₈	—	3	1	no	—
74	C₂×C₅×M₁₆	—	6	1	no	—
75	C₄×C₅×Q₈	—	3	1	no	—
76	C₄×C₅×Q₈	—	3	1	no	—
77	C₄×C₅×Q₈	—	3	1	no	—
78	C₄×C₅×Q₈	—	6	1	no	—
79	C₄×C₅×Q₈	—	6	1	no	—
80	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	—	3	1	no	—
82	C₂×C₅×C₄⋊C₄	—	6	1	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×C₄²×C₅	—	6	1	no	—
85	C₅×C₄⋊C₈	—	3	1	no	—
86	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
87	C₅×C₂²⋊C₈	—	6	1	no	—
88	C₅×#97	—	6	1	no	—
89	C₅×#97	—	6	1	no	—
90	C₄×C₅×C₈	—	3	1	no	—
91	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
92	#1491	—	3	1	no	Sylow
93	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	M₁₆	1	2	yes	complemented
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	—	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	4	no	—
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	2	1	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	—	4	2	no	—
113	C₅×Dic₆	—	2	4	no	—
114	C₅×Dic₆	—	2	1	no	—
115	C₅×Dic₆	M₁₆	1	2	yes	complemented
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₅×C₃⋊C₈	—	4	1	no	—
120	C₂×D₃×Q₈	C₄×C₅	1	1	yes	characteristic
121	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
122	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic
123	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
124	D₃×C₄⋊C₄	—	2	1	no	—
125	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
126	#887	—	2	1	no	—
127	#887	C₄×C₅	1	1	yes	characteristic
128	C₄²×D₃	—	2	1	no	—
129	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
130	C₄×Dic₆	—	2	1	no	—
131	C₄×Dic₆	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	(C₂×D₃)⋊C₈	—	2	1	no	—
135	#815	—	2	1	no	—
136	#815	—	2	1	no	—
137	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
138	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₅×Q₈	—	3	1	no	—
140	C₂×C₅×Q₈	—	6	1	no	—
141	C₂×C₅×Q₈	—	6	2	no	—
142	C₂×C₅×Q₈	—	6	2	no	—
143	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	3	1	no	—
145	C₂²×C₄×C₅	—	3	1	no	—
146	C₂²×C₄×C₅	—	3	1	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂²×C₄×C₅	—	6	1	no	—
149	C₅×M₁₆	—	6	4	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	6	1	no	—
153	C₂×C₅×C₈	—	6	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	3	1	no	—
156	C₅×C₄⋊C₄	—	6	1	no	—
157	C₅×C₄⋊C₄	—	6	1	no	—
158	C₅×C₄⋊C₄	—	6	1	no	—
159	C₅×C₄⋊C₄	—	6	1	no	—
160	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	3	1	no	—
164	C₄²×C₅	—	3	1	no	—
165	C₄²×C₅	—	6	1	no	—
166	C₄²×C₅	—	6	1	no	—
167	C₄²×C₅	—	6	1	no	—
168	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₄×Q₈	—	3	1	no	—
170	#432	—	3	1	no	—
171	C₄×M₁₆	—	3	1	no	—
172	Q₈⋊C₈	—	3	1	no	—
173	Q₈⋊C₈	—	3	1	no	—
174	Q₈⋊C₈	—	3	1	no	—
175	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
176	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₅×D₃	—	2	1	no	—
178	C₂×C₅×D₃	—	2	1	no	—
179	C₂×C₅×D₃	#104	1	2	yes	—
180	C₃×C₄×C₅	—	2	2	no	—
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	—	4	1	no	—
183	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
185	C₃×C₄×C₅	#137	1	1	yes	characteristic
186	C₃×C₄×C₅	#137	1	1	yes	characteristic
187	C₅×Dic₃	—	2	1	no	—
188	C₅×Dic₃	—	2	2	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	D₃×Q₈	—	2	2	no	—
194	D₃×Q₈	—	2	2	no	—
195	C₂×C₄×D₃	—	2	1	no	—
196	C₂×C₄×D₃	—	2	1	no	—
197	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
199	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
200	C₂×Dic₆	—	2	1	no	—
201	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₃×C₄⋊C₄	—	2	1	no	—
205	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
206	C₃×C₄²	—	2	1	no	—
207	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
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	1	no	—
214	C₄×Dic₃	—	2	1	no	—
215	C₄×Dic₃	—	2	1	no	—
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	C₂×C₃⋊C₈	—	2	1	no	—
221	ΓL(1,𝔽₂₅)	—	2	4	no	—
222	C₂³×C₅	—	3	1	no	—
223	C₅×Q₈	—	2	1	no	—
224	C₅×Q₈	—	3	2	no	—
225	C₅×Q₈	—	6	4	no	—
226	C₅×Q₈	—	6	1	no	—
227	C₅×Q₈	ΓL(1,𝔽₂₅)	1	2	yes	complemented
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	4	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	—	6	1	no	—
240	C₂×C₄×C₅	—	6	1	no	—
241	C₂×C₄×C₅	—	12	2	no	—
242	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	4	1	no	—
247	C₅×C₈	—	6	2	no	—
248	C₅×C₈	—	12	1	no	—
249	C₂²×Q₈	—	3	1	no	—
250	C₂×M₁₆	—	6	1	no	—
251	C₄×Q₈	—	3	1	no	—
252	C₄×Q₈	—	3	1	no	—
253	C₄×Q₈	—	3	1	no	—
254	C₄×Q₈	—	6	1	no	—
255	C₄×Q₈	—	6	1	no	—
256	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	—	3	1	no	—
258	C₂×C₄⋊C₄	—	6	1	no	—
259	C₂×C₄²	—	3	1	no	—
260	C₂×C₄²	—	6	1	no	—
261	C₄⋊C₈	—	3	1	no	—
262	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂²⋊C₈	—	6	1	no	—
264	#97	—	6	1	no	—
265	#97	—	6	1	no	—
266	C₄×C₈	—	3	1	no	—
267	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂×C₃×C₅	#407	1	1	yes	characteristic
269	C₂×C₃×C₅	#419	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
271	C₅×D₃	—	2	2	no	—
272	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₃×Q₈	—	2	1	no	—
274	C₃×Q₈	C₅×M₁₆	1	2	yes	complemented
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂×Dic₃	—	2	1	no	—
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	C₄×D₃	—	2	4	no	—
286	C₄×D₃	—	2	2	no	—
287	C₄×D₃	—	2	1	no	—
288	C₄×D₃	—	2	1	no	—
289	C₄×D₃	—	2	1	no	—
290	C₄×D₃	—	2	1	no	—
291	C₄×D₃	—	4	2	no	—
292	Dic₆	—	2	4	no	—
293	Dic₆	—	2	1	no	—
294	Dic₆	C₅×M₁₆	1	2	yes	complemented
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	D₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	4	1	no	—
306	C₄×C₅	—	6	1	no	—
307	C₄×C₅	—	6	2	no	—
308	C₄×C₅	—	6	1	no	—
309	C₄×C₅	—	6	1	no	—
310	C₄×C₅	—	12	1	no	—
311	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
312	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
313	C₄×C₅	#915	1	1	yes	characteristic
314	C₄×C₅	#918	1	1	yes	characteristic
315	C₂×Q₈	—	3	1	no	—
316	C₂×Q₈	—	6	1	no	—
317	C₂×Q₈	—	6	2	no	—
318	C₂×Q₈	—	6	2	no	—
319	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
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	C₂²×C₄	—	6	1	no	—
325	M₁₆	—	6	4	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	6	1	no	—
329	C₂×C₈	—	6	1	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	—	6	1	no	—
336	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
337	C₄²	—	2	1	no	—
338	C₄²	—	3	1	no	—
339	C₄²	—	3	1	no	—
340	C₄²	—	3	1	no	—
341	C₄²	—	6	1	no	—
342	C₄²	—	6	1	no	—
343	C₄²	—	6	1	no	—
344	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₃×C₅	#1491	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×D₃	—	2	1	no	—
348	C₂×D₃	—	2	1	no	—
349	C₂×D₃	C₅×#104	1	2	yes	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	4	1	no	—
353	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
354	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
355	C₃×C₄	C₅×#137	1	1	yes	characteristic
356	C₃×C₄	C₅×#137	1	1	yes	characteristic
357	Dic₃	—	2	1	no	—
358	Dic₃	—	2	2	no	—
359	Dic₃	—	2	1	no	—
360	Dic₃	—	2	1	no	—
361	Dic₃	—	4	1	no	—
362	C₂×C₅	—	6	2	no	—
363	C₂×C₅	#4726	1	1	yes	characteristic
364	C₂×C₅	#4802	1	1	yes	characteristic
365	C₂×C₅	D₃×#104	1	1	yes	characteristic
366	C₂³	—	3	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	3	2	no	—
369	Q₈	—	6	4	no	—
370	Q₈	—	6	1	no	—
371	Q₈	C₅×ΓL(1,𝔽₂₅)	1	2	yes	complemented
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	3	1	no	—
375	C₂×C₄	—	3	1	no	—
376	C₂×C₄	—	3	1	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	6	4	no	—
379	C₂×C₄	—	6	1	no	—
380	C₂×C₄	—	6	1	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	12	2	no	—
386	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
387	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
388	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	4	1	no	—
391	C₈	—	6	2	no	—
392	C₈	—	12	1	no	—
393	C₂×C₃	C₅×#407	1	1	yes	characteristic
394	C₂×C₃	C₅×#419	1	1	yes	characteristic
395	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
396	D₃	—	2	2	no	—
397	C₅	#68239	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	3	2	no	—
399	C₂²	—	6	1	no	—
400	C₂²	—	6	1	no	—
401	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	6	2	no	—
407	C₄	—	6	1	no	—
408	C₄	—	6	1	no	—
409	C₄	—	12	1	no	—
410	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
411	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
412	C₄	C₅×#915	1	1	yes	characteristic
413	C₄	C₅×#918	1	1	yes	characteristic
414	C₃	C₅×#1491	1	1	yes	characteristic, complemented, Sylow
415	C₂	—	6	2	no	—
416	C₂	C₅×#4726	1	1	yes	characteristic
417	C₂	C₅×#4802	1	1	yes	characteristic
418	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	C₂²×C₅×D₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1491
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
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. C₅×#4535	C₂	semidirect
6. C₅×#4484	C₂	semidirect
7. C₅×#4456	C₂	semidirect
28. #68239	C₅	direct (N × H)
35. C₅×Q₈⋊C₈	D₃	semidirect
69. C₃×Q₈⋊C₈	C₂×C₅	semidirect
70. #4535	C₂×C₅	semidirect
71. #4484	C₂×C₅	semidirect
72. #4456	C₂×C₅	semidirect
95. C₃×C₅×Q₈	M₁₆	semidirect
115. C₅×Dic₆	M₁₆	semidirect
175. Q₈⋊C₈	C₅×D₃	semidirect
227. C₅×Q₈	ΓL(1,𝔽₂₅)	semidirect
274. C₃×Q₈	C₅×M₁₆	semidirect
294. Dic₆	C₅×M₁₆	semidirect
345. C₃×C₅	#1491	semidirect
371. Q₈	C₅×ΓL(1,𝔽₂₅)	semidirect
397. C₅	#68239	direct (N × H)
414. C₃	C₅×#1491	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₃×Q₈	2
C₅×#4835	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4484	2
C₅×#4456	2
C₅×#1491	3
#68239	5

Subgroups — C5×#68239 #14282319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68239 #14282319