Subgroups — C₅×#68238 #14282219

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	C₅×#4837	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×#1489	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	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	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
14	C₅×#893	—	2	1	no	—
15	C₅×#893	C₄	1	1	yes	characteristic
16	C₅×#892	—	2	1	no	—
17	C₅×#892	C₄	1	1	yes	characteristic
18	C₄×C₅×D₁₂	—	2	1	no	—
19	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₄²×C₅×D₃	—	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	#68238	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₄×C₅×#41	—	3	1	no	—
30	C₅×#423	—	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	C₅×#239	—	2	2	no	—
38	C₅×#239	—	2	2	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
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	C₅×ΓL(1,𝔽₂₅)	—	4	2	no	—
67	C₄×#239	C₂×C₅	1	1	yes	characteristic
68	#4837	C₂×C₅	1	1	yes	characteristic, complemented
69	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
71	#4535	C₂×C₅	1	1	yes	characteristic, complemented
72	#4483	C₂×C₅	1	1	yes	characteristic, complemented
73	#4459	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₅×#41	—	3	1	no	—
75	C₂×C₅×M₁₆	—	6	1	no	—
76	C₂×C₅×M₁₆	—	6	1	no	—
77	C₄×C₅×Q₈	—	3	1	no	—
78	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₄×C₅×D₄	—	3	1	no	—
80	C₄×C₅×D₄	—	3	1	no	—
81	C₄×C₅×D₄	—	6	1	no	—
82	C₄×C₅×D₄	—	6	1	no	—
83	C₅×#117	—	3	1	no	—
84	C₅×#117	—	6	1	no	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×C₄²×C₅	—	6	1	no	—
87	C₅×C₄⋊C₈	—	3	1	no	—
88	C₅×C₄⋊C₈	—	6	1	no	—
89	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
90	C₅×#97	—	6	1	no	—
91	C₄×C₅×C₈	—	3	1	no	—
92	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
93	#1489	—	3	1	no	Sylow
94	C₂²×C₅×D₃	—	2	1	no	—
95	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	2	1	no	—
97	C₃×C₅×Q₈	M₁₆	1	2	yes	complemented
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₅×D₁₂	—	2	4	no	—
108	C₅×D₁₂	—	2	1	no	—
109	C₅×D₁₂	M₁₆	1	2	yes	complemented
110	C₄×C₅×D₃	—	2	4	no	—
111	C₄×C₅×D₃	—	2	1	no	—
112	C₄×C₅×D₃	—	2	1	no	—
113	C₄×C₅×D₃	—	2	1	no	—
114	C₄×C₅×D₃	—	2	1	no	—
115	C₄×C₅×D₃	—	2	2	no	—
116	C₄×C₅×D₃	—	4	1	no	—
117	C₄×C₅×D₃	—	4	1	no	—
118	C₄×C₅×D₃	—	4	2	no	—
119	C₃×C₅×C₈	—	2	2	no	—
120	C₃×C₅×C₈	—	4	1	no	—
121	C₅×C₃⋊C₈	—	2	2	no	—
122	C₅×C₃⋊C₈	—	4	1	no	—
123	C₂×#239	C₄×C₅	1	1	yes	characteristic
124	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
125	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic
126	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
127	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
128	#893	—	2	1	no	—
129	#893	C₄×C₅	1	1	yes	characteristic
130	#892	—	2	1	no	—
131	#892	C₄×C₅	1	1	yes	characteristic
132	C₄×D₁₂	—	2	1	no	—
133	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
134	C₄²×D₃	—	2	1	no	—
135	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
136	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
138	#815	—	2	1	no	—
139	Dic₃⋊C₈	—	2	1	no	—
140	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
141	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
142	C₅×#41	—	6	2	no	—
143	C₅×#41	—	6	2	no	—
144	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
145	C₂×C₅×D₄	—	3	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	3	1	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂²×C₄×C₅	—	6	1	no	—
153	C₅×M₁₆	—	6	4	no	—
154	C₅×M₁₆	—	12	2	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	6	1	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	3	1	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
163	C₅×C₂²⋊C₄	—	6	1	no	—
164	C₅×C₂²⋊C₄	—	6	1	no	—
165	C₅×C₂²⋊C₄	—	6	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	1	no	—
169	C₄²×C₅	—	3	1	no	—
170	C₄²×C₅	—	6	1	no	—
171	C₄²×C₅	—	6	1	no	—
172	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₄×#41	—	3	1	no	—
174	#423	—	3	1	no	—
175	C₄×M₁₆	—	3	1	no	—
176	Q₈⋊C₈	—	3	1	no	—
177	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
178	D₄⋊C₈	—	3	1	no	—
179	D₄⋊C₈	—	3	1	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	1	no	—
182	C₂×C₅×D₃	—	2	2	no	—
183	C₂×C₅×D₃	—	2	1	no	—
184	C₂×C₅×D₃	—	2	1	no	—
185	C₂×C₅×D₃	—	4	1	no	—
186	C₂×C₅×D₃	—	4	1	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	2	1	no	—
189	C₃×C₄×C₅	—	4	1	no	—
190	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
192	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₃×C₄×C₅	#137	1	1	yes	characteristic
194	C₅×Dic₃	—	2	1	no	—
195	C₅×Dic₃	—	2	1	no	—
196	C₅×Dic₃	—	4	1	no	—
197	C₅×Dic₃	#104	1	2	yes	—
198	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
199	#239	—	2	2	no	—
200	#239	—	2	2	no	—
201	C₂×D₁₂	—	2	1	no	—
202	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×C₄×D₃	—	2	1	no	—
205	C₂×C₄×D₃	—	2	1	no	—
206	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
208	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₃×C₄⋊C₄	—	2	1	no	—
212	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	—	2	1	no	—
216	(C₂×D₃)⋊C₄	—	2	1	no	—
217	(C₂×D₃)⋊C₄	—	2	1	no	—
218	C₄⋊Dic₃	—	2	1	no	—
219	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
220	C₄×Dic₃	—	2	1	no	—
221	C₄×Dic₃	—	2	1	no	—
222	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
223	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
224	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
225	C₂×C₃⋊C₈	—	2	1	no	—
226	C₂×C₃⋊C₈	—	2	1	no	—
227	ΓL(1,𝔽₂₅)	—	2	4	no	—
228	ΓL(1,𝔽₂₅)	—	4	2	no	—
229	C₂³×C₅	—	3	1	no	—
230	C₂³×C₅	—	6	1	no	—
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	ΓL(1,𝔽₂₅)	1	2	yes	complemented
233	C₅×D₄	—	3	2	no	—
234	C₅×D₄	—	6	4	no	—
235	C₅×D₄	—	6	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	3	1	no	—
239	C₂×C₄×C₅	—	3	1	no	—
240	C₂×C₄×C₅	—	3	1	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	4	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	—	6	1	no	—
246	C₂×C₄×C₅	—	6	1	no	—
247	C₂×C₄×C₅	—	6	1	no	—
248	C₂×C₄×C₅	—	12	2	no	—
249	C₂×C₄×C₅	—	12	1	no	—
250	C₂×C₄×C₅	—	12	1	no	—
251	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
252	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	—	4	1	no	—
256	C₅×C₈	—	6	2	no	—
257	C₅×C₈	—	12	1	no	—
258	C₂×#41	—	3	1	no	—
259	C₂×M₁₆	—	6	1	no	—
260	C₂×M₁₆	—	6	1	no	—
261	C₄×Q₈	—	3	1	no	—
262	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
263	C₄×D₄	—	3	1	no	—
264	C₄×D₄	—	3	1	no	—
265	C₄×D₄	—	6	1	no	—
266	C₄×D₄	—	6	1	no	—
267	#117	—	3	1	no	—
268	#117	—	6	1	no	—
269	C₂×C₄²	—	3	1	no	—
270	C₂×C₄²	—	6	1	no	—
271	C₄⋊C₈	—	3	1	no	—
272	C₄⋊C₈	—	6	1	no	—
273	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
274	#97	—	6	1	no	—
275	C₄×C₈	—	3	1	no	—
276	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
277	C₂×C₃×C₅	#407	1	1	yes	characteristic
278	C₂×C₃×C₅	#417	1	1	yes	characteristic
279	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
280	C₅×D₃	—	4	1	no	—
281	C₅×D₃	—	4	2	no	—
282	C₂²×D₃	—	2	1	no	—
283	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₅×M₁₆	1	2	yes	complemented
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
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×Dic₃	—	2	1	no	—
292	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	D₁₂	—	2	4	no	—
296	D₁₂	—	2	1	no	—
297	D₁₂	C₅×M₁₆	1	2	yes	complemented
298	C₄×D₃	—	2	4	no	—
299	C₄×D₃	—	2	1	no	—
300	C₄×D₃	—	2	1	no	—
301	C₄×D₃	—	2	1	no	—
302	C₄×D₃	—	2	1	no	—
303	C₄×D₃	—	2	2	no	—
304	C₄×D₃	—	4	1	no	—
305	C₄×D₃	—	4	1	no	—
306	C₄×D₃	—	4	2	no	—
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	—	4	1	no	—
309	C₃⋊C₈	—	2	2	no	—
310	C₃⋊C₈	—	4	1	no	—
311	C₂²×C₅	—	6	2	no	—
312	C₂²×C₅	—	6	1	no	—
313	C₂²×C₅	—	6	1	no	—
314	C₂²×C₅	—	6	1	no	—
315	C₂²×C₅	—	12	1	no	—
316	C₂²×C₅	—	12	1	no	—
317	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	3	2	no	—
321	C₄×C₅	—	4	1	no	—
322	C₄×C₅	—	6	1	no	—
323	C₄×C₅	—	6	1	no	—
324	C₄×C₅	—	12	1	no	—
325	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
326	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
327	C₄×C₅	#914	1	1	yes	characteristic
328	C₄×C₅	#918	1	1	yes	characteristic
329	#41	—	6	2	no	—
330	#41	—	6	2	no	—
331	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
332	C₂×D₄	—	3	1	no	—
333	C₂×D₄	—	6	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	6	1	no	—
338	C₂²×C₄	—	6	1	no	—
339	C₂²×C₄	—	6	1	no	—
340	M₁₆	—	6	4	no	—
341	M₁₆	—	12	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	6	1	no	—
345	C₂×C₈	—	6	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	3	1	no	—
348	C₄⋊C₄	—	6	1	no	—
349	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
350	C₂²⋊C₄	—	6	1	no	—
351	C₂²⋊C₄	—	6	1	no	—
352	C₂²⋊C₄	—	6	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	3	1	no	—
355	C₄²	—	3	1	no	—
356	C₄²	—	3	1	no	—
357	C₄²	—	6	1	no	—
358	C₄²	—	6	1	no	—
359	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
360	C₃×C₅	#1489	1	1	yes	characteristic, complemented, Hall
361	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×D₃	—	2	1	no	—
363	C₂×D₃	—	2	2	no	—
364	C₂×D₃	—	2	1	no	—
365	C₂×D₃	—	2	1	no	—
366	C₂×D₃	—	4	1	no	—
367	C₂×D₃	—	4	1	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
372	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
373	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₃×C₄	C₅×#137	1	1	yes	characteristic
375	Dic₃	—	2	1	no	—
376	Dic₃	—	2	1	no	—
377	Dic₃	—	4	1	no	—
378	Dic₃	C₅×#104	1	2	yes	—
379	C₂×C₅	—	12	1	no	—
380	C₂×C₅	—	12	2	no	—
381	C₂×C₅	#4726	1	1	yes	characteristic
382	C₂×C₅	#4803	1	1	yes	characteristic
383	C₂×C₅	D₃×#104	1	1	yes	characteristic
384	C₂³	—	3	1	no	—
385	C₂³	—	6	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	C₅×ΓL(1,𝔽₂₅)	1	2	yes	complemented
388	D₄	—	3	2	no	—
389	D₄	—	6	4	no	—
390	D₄	—	6	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	3	1	no	—
395	C₂×C₄	—	3	1	no	—
396	C₂×C₄	—	6	2	no	—
397	C₂×C₄	—	6	4	no	—
398	C₂×C₄	—	6	1	no	—
399	C₂×C₄	—	6	1	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	—	6	1	no	—
402	C₂×C₄	—	6	1	no	—
403	C₂×C₄	—	12	2	no	—
404	C₂×C₄	—	12	1	no	—
405	C₂×C₄	—	12	1	no	—
406	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
407	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
408	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	6	2	no	—
412	C₈	—	12	1	no	—
413	C₂×C₃	C₅×#407	1	1	yes	characteristic
414	C₂×C₃	C₅×#417	1	1	yes	characteristic
415	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
416	D₃	—	4	1	no	—
417	D₃	—	4	2	no	—
418	C₅	#68238	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	6	2	no	—
420	C₂²	—	6	1	no	—
421	C₂²	—	6	1	no	—
422	C₂²	—	6	1	no	—
423	C₂²	—	12	1	no	—
424	C₂²	—	12	1	no	—
425	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	1	no	—
428	C₄	—	3	2	no	—
429	C₄	—	4	1	no	—
430	C₄	—	6	1	no	—
431	C₄	—	6	1	no	—
432	C₄	—	12	1	no	—
433	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
434	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
435	C₄	C₅×#914	1	1	yes	characteristic
436	C₄	C₅×#918	1	1	yes	characteristic
437	C₃	C₅×#1489	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	12	1	no	—
439	C₂	—	12	2	no	—
440	C₂	C₅×#4726	1	1	yes	characteristic
441	C₂	C₅×#4803	1	1	yes	characteristic
442	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	C₂×C₅×#239	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1489
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×#4837	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. #68238	C₅	direct (N × H)
33. C₅×Q₈⋊C₈	D₃	semidirect
68. #4837	C₂×C₅	semidirect
69. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
70. C₃×Q₈⋊C₈	C₂×C₅	semidirect
71. #4535	C₂×C₅	semidirect
72. #4483	C₂×C₅	semidirect
73. #4459	C₂×C₅	semidirect
97. C₃×C₅×Q₈	M₁₆	semidirect
109. C₅×D₁₂	M₁₆	semidirect
177. Q₈⋊C₈	C₅×D₃	semidirect
232. C₅×Q₈	ΓL(1,𝔽₂₅)	semidirect
285. C₃×Q₈	C₅×M₁₆	semidirect
297. D₁₂	C₅×M₁₆	semidirect
360. C₃×C₅	#1489	semidirect
387. Q₈	C₅×ΓL(1,𝔽₂₅)	semidirect
418. C₅	#68238	direct (N × H)
437. C₃	C₅×#1489	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#239	2
C₅×#4837	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4535	2
C₅×#4483	2
C₅×#4459	2
C₅×#1489	3
#68238	5

Subgroups — C5×#68238 #14282219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68238 #14282219