Subgroups — C₅×#69854 #14282225

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4459	C₂	1	2	yes	maximal, complemented
5	C₅×#4456	C₂	1	2	yes	maximal, complemented
6	C₅×#1489	—	3	1	no	maximal, Hall
7	C₂×C₅×#235	C₄	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄×C₅×#67	—	2	1	no	—
11	C₄×C₅×#67	—	2	1	no	—
12	C₅×#926	C₄	1	1	yes	characteristic
13	C₂×C₅×#208	—	2	1	no	—
14	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
15	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₅×#872	—	2	1	no	—
17	C₄²×C₅×D₃	—	2	1	no	—
18	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
19	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×#97	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
24	#69854	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	—	3	1	no	—
26	C₅×#423	—	3	1	no	—
27	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×#67	—	2	1	no	—
34	C₅×#235	—	2	2	no	—
35	C₅×#235	—	2	2	no	—
36	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
41	C₃×C₅×M₁₆	—	2	4	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
47	C₅×#217	—	2	1	no	—
48	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₄×C₅×Dic₃	—	2	1	no	—
57	C₅×#208	—	4	2	no	—
58	C₂×C₅×C₃⋊C₈	—	2	2	no	—
59	C₄×#235	C₂×C₅	1	1	yes	characteristic
60	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
61	#4924	C₂×C₅	1	1	yes	characteristic, complemented
62	#4459	C₂×C₅	1	2	yes	complemented
63	#4456	C₂×C₅	1	2	yes	complemented
64	C₂×C₅×#41	—	3	1	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	—	6	1	no	—
67	C₄×C₅×Q₈	—	3	1	no	—
68	C₄×C₅×Q₈	—	3	1	no	—
69	C₄×C₅×D₄	—	3	1	no	—
70	C₄×C₅×D₄	—	3	1	no	—
71	C₄×C₅×D₄	—	6	1	no	—
72	C₄×C₅×D₄	—	6	1	no	—
73	C₅×#117	—	3	1	no	—
74	C₅×#117	—	6	1	no	—
75	C₂×C₄²×C₅	—	6	1	no	—
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	C₅×C₄⋊C₈	—	3	2	no	—
78	C₅×C₄⋊C₈	—	6	1	no	—
79	C₅×#97	—	2	1	no	—
80	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
81	#1489	—	3	1	no	Sylow
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₅×D₃	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₅×#67	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	1	no	—
97	C₂×C₅×Dic₃	—	2	1	no	—
98	C₂×C₅×Dic₃	—	2	1	no	—
99	C₅×D₁₂	—	2	1	no	—
100	C₅×D₁₂	M₁₆	1	2	yes	complemented
101	C₄×C₅×D₃	—	2	4	no	—
102	C₄×C₅×D₃	—	4	2	no	—
103	C₄×C₅×D₃	—	4	1	no	—
104	C₄×C₅×D₃	—	4	1	no	—
105	C₅×Dic₆	—	2	1	no	—
106	C₅×Dic₆	M₁₆	1	2	yes	complemented
107	C₃×C₅×C₈	—	2	4	no	—
108	C₅×C₃⋊C₈	—	4	2	no	—
109	C₂×#235	C₄×C₅	1	1	yes	characteristic
110	C₂×C₃×M₁₆	—	2	1	no	—
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₄×#67	—	2	1	no	—
113	C₄×#67	—	2	1	no	—
114	#926	C₄×C₅	1	1	yes	characteristic
115	C₂×#208	—	2	1	no	—
116	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
117	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
118	#872	—	2	1	no	—
119	C₄²×D₃	—	2	1	no	—
120	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
121	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
122	C₃×#97	—	2	1	no	—
123	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
124	C₄⋊(C₃⋊C₈)	—	2	1	no	—
125	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
126	C₅×#41	—	6	2	no	—
127	C₅×#41	—	6	2	no	—
128	C₂×C₅×Q₈	—	3	1	no	—
129	C₂×C₅×D₄	—	3	1	no	—
130	C₂×C₅×D₄	—	6	1	no	—
131	C₂²×C₄×C₅	—	6	1	no	—
132	C₂²×C₄×C₅	—	6	1	no	—
133	C₂²×C₄×C₅	—	6	1	no	—
134	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
136	C₂²×C₄×C₅	#67	1	1	yes	characteristic
137	C₅×M₁₆	—	2	4	no	—
138	C₅×M₁₆	—	12	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	6	2	no	—
141	C₅×C₄⋊C₄	—	3	1	no	—
142	C₅×C₄⋊C₄	—	3	1	no	—
143	C₅×C₄⋊C₄	—	6	1	no	—
144	C₅×C₄⋊C₄	—	6	1	no	—
145	C₅×C₂²⋊C₄	—	6	1	no	—
146	C₅×C₂²⋊C₄	—	6	1	no	—
147	C₅×C₂²⋊C₄	—	6	1	no	—
148	C₄²×C₅	—	6	1	no	—
149	C₄²×C₅	—	6	1	no	—
150	C₄²×C₅	—	6	1	no	—
151	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
152	C₄²×C₅	D₁₂	1	1	yes	characteristic
153	C₄²×C₅	#67	1	1	yes	characteristic
154	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
155	C₄×#41	—	3	1	no	—
156	#423	—	3	1	no	—
157	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
158	Q₈⋊C₈	—	3	2	no	—
159	D₄⋊C₈	—	3	2	no	—
160	C₂²×C₃×C₅	—	2	1	no	—
161	C₂²×C₃×C₅	—	2	1	no	—
162	C₂²×C₃×C₅	—	2	1	no	—
163	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₅×D₃	—	2	2	no	—
165	C₂×C₅×D₃	—	4	1	no	—
166	C₂×C₅×D₃	—	4	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	#104	1	2	yes	—
171	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
173	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₃×C₄×C₅	#137	1	1	yes	characteristic
175	C₅×Dic₃	—	2	2	no	—
176	C₅×Dic₃	—	4	1	no	—
177	C₅×Dic₃	—	4	1	no	—
178	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
181	C₂×#67	—	2	1	no	—
182	#235	—	2	2	no	—
183	#235	—	2	2	no	—
184	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂×C₄×D₃	—	2	1	no	—
186	C₂×C₄×D₃	—	2	1	no	—
187	C₂×C₄×D₃	—	2	1	no	—
188	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
189	C₃×M₁₆	—	2	4	no	—
190	C₂×C₃×C₈	—	2	2	no	—
191	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
192	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
193	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
194	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
195	#217	—	2	1	no	—
196	(C₂×D₃)⋊C₄	—	2	1	no	—
197	(C₂×D₃)⋊C₄	—	2	1	no	—
198	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
199	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
200	Dic₃⋊C₄	—	2	1	no	—
201	Dic₃⋊C₄	—	2	1	no	—
202	C₄×Dic₃	—	2	1	no	—
203	C₄×Dic₃	—	2	1	no	—
204	C₄×Dic₃	—	2	1	no	—
205	#208	—	4	2	no	—
206	C₂×C₃⋊C₈	—	2	2	no	—
207	C₂³×C₅	—	6	1	no	—
208	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
209	C₅×Q₈	—	3	2	no	—
210	C₅×Q₈	—	6	1	no	—
211	C₅×D₄	—	3	2	no	—
212	C₅×D₄	—	6	4	no	—
213	C₅×D₄	—	6	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	6	4	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	6	1	no	—
222	C₂×C₄×C₅	—	6	1	no	—
223	C₂×C₄×C₅	—	12	2	no	—
224	C₂×C₄×C₅	—	12	1	no	—
225	C₂×C₄×C₅	—	12	1	no	—
226	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
232	C₅×C₈	—	2	4	no	—
233	C₅×C₈	—	12	2	no	—
234	C₂×#41	—	3	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	6	1	no	—
237	C₄×Q₈	—	3	1	no	—
238	C₄×Q₈	—	3	1	no	—
239	C₄×D₄	—	3	1	no	—
240	C₄×D₄	—	3	1	no	—
241	C₄×D₄	—	6	1	no	—
242	C₄×D₄	—	6	1	no	—
243	#117	—	3	1	no	—
244	#117	—	6	1	no	—
245	C₂×C₄²	—	6	1	no	—
246	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
247	C₄⋊C₈	—	3	2	no	—
248	C₄⋊C₈	—	6	1	no	—
249	#97	—	2	1	no	—
250	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
251	C₂×C₃×C₅	—	4	1	no	—
252	C₂×C₃×C₅	#407	1	1	yes	characteristic
253	C₂×C₃×C₅	#417	1	1	yes	characteristic
254	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
255	C₅×D₃	—	4	2	no	—
256	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×D₃	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	#67	—	2	4	no	—
270	C₂×Dic₃	—	2	1	no	—
271	C₂×Dic₃	—	2	1	no	—
272	C₂×Dic₃	—	2	1	no	—
273	D₁₂	—	2	1	no	—
274	D₁₂	C₅×M₁₆	1	2	yes	complemented
275	C₄×D₃	—	2	4	no	—
276	C₄×D₃	—	4	1	no	—
277	C₄×D₃	—	4	1	no	—
278	C₄×D₃	—	4	2	no	—
279	Dic₆	—	2	1	no	—
280	Dic₆	C₅×M₁₆	1	2	yes	complemented
281	C₃×C₈	—	2	4	no	—
282	C₃⋊C₈	—	4	2	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	6	2	no	—
287	C₂²×C₅	—	12	1	no	—
288	C₂²×C₅	—	12	1	no	—
289	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	6	2	no	—
294	C₄×C₅	—	12	1	no	—
295	C₄×C₅	—	12	1	no	—
296	C₄×C₅	#805	1	2	yes	—
297	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
298	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
299	C₄×C₅	#908	1	1	yes	characteristic
300	C₄×C₅	#909	1	1	yes	characteristic
301	#41	—	6	2	no	—
302	#41	—	6	2	no	—
303	C₂×Q₈	—	3	1	no	—
304	C₂×D₄	—	3	1	no	—
305	C₂×D₄	—	6	1	no	—
306	C₂²×C₄	—	6	1	no	—
307	C₂²×C₄	—	6	1	no	—
308	C₂²×C₄	—	6	1	no	—
309	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
310	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
311	C₂²×C₄	C₅×#67	1	1	yes	characteristic
312	M₁₆	—	2	4	no	—
313	M₁₆	—	12	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	6	2	no	—
316	C₄⋊C₄	—	3	1	no	—
317	C₄⋊C₄	—	3	1	no	—
318	C₄⋊C₄	—	6	1	no	—
319	C₄⋊C₄	—	6	1	no	—
320	C₂²⋊C₄	—	6	1	no	—
321	C₂²⋊C₄	—	6	1	no	—
322	C₂²⋊C₄	—	6	1	no	—
323	C₄²	—	6	1	no	—
324	C₄²	—	6	1	no	—
325	C₄²	—	6	1	no	—
326	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
327	C₄²	C₅×D₁₂	1	1	yes	characteristic
328	C₄²	C₅×#67	1	1	yes	characteristic
329	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
330	C₃×C₅	#1489	1	1	yes	characteristic, complemented, Hall
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×D₃	—	2	2	no	—
336	C₂×D₃	—	4	1	no	—
337	C₂×D₃	—	4	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	C₅×#104	1	2	yes	—
342	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
343	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
344	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₃×C₄	C₅×#137	1	1	yes	characteristic
346	Dic₃	—	2	2	no	—
347	Dic₃	—	4	1	no	—
348	Dic₃	—	4	1	no	—
349	C₂×C₅	—	4	1	no	—
350	C₂×C₅	—	12	2	no	—
351	C₂×C₅	C₂×#805	1	1	yes	characteristic
352	C₂×C₅	#5126	1	1	yes	characteristic
353	C₂×C₅	#5133	1	1	yes	characteristic
354	C₂³	—	6	1	no	—
355	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
356	Q₈	—	3	2	no	—
357	Q₈	—	6	1	no	—
358	D₄	—	3	2	no	—
359	D₄	—	6	4	no	—
360	D₄	—	6	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	—	6	1	no	—
368	C₂×C₄	—	6	1	no	—
369	C₂×C₄	—	6	1	no	—
370	C₂×C₄	—	12	1	no	—
371	C₂×C₄	—	12	1	no	—
372	C₂×C₄	—	12	2	no	—
373	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
374	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
375	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	12	2	no	—
381	C₂×C₃	—	4	1	no	—
382	C₂×C₃	C₅×#407	1	1	yes	characteristic
383	C₂×C₃	C₅×#417	1	1	yes	characteristic
384	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
385	D₃	—	4	2	no	—
386	C₅	#69854	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	6	2	no	—
391	C₂²	—	12	1	no	—
392	C₂²	—	12	1	no	—
393	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	6	2	no	—
398	C₄	—	12	1	no	—
399	C₄	—	12	1	no	—
400	C₄	C₅×#805	1	2	yes	—
401	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
402	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
403	C₄	C₅×#908	1	1	yes	characteristic
404	C₄	C₅×#909	1	1	yes	characteristic
405	C₃	C₅×#1489	1	1	yes	characteristic, complemented, Sylow
406	C₂	—	4	1	no	—
407	C₂	—	12	2	no	—
408	C₂	C₂×C₅×#805	1	1	yes	characteristic
409	C₂	C₅×#5126	1	1	yes	characteristic
410	C₂	C₅×#5133	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#1489
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
3. C₅×#4924	C₂	semidirect
4. C₅×#4459	C₂	semidirect
5. C₅×#4456	C₂	semidirect
24. #69854	C₅	direct (N × H)
27. C₄×C₅×M₁₆	D₃	semidirect
60. C₃×C₄×M₁₆	C₂×C₅	semidirect
61. #4924	C₂×C₅	semidirect
62. #4459	C₂×C₅	semidirect
63. #4456	C₂×C₅	semidirect
100. C₅×D₁₂	M₁₆	semidirect
106. C₅×Dic₆	M₁₆	semidirect
157. C₄×M₁₆	C₅×D₃	semidirect
274. D₁₂	C₅×M₁₆	semidirect
280. Dic₆	C₅×M₁₆	semidirect
330. C₃×C₅	#1489	semidirect
386. C₅	#69854	direct (N × H)
405. 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×#235	2
C₃×C₄×C₅×M₁₆	2
C₅×#4924	2
C₅×#4459	2
C₅×#4456	2
C₅×#1489	3
#69854	5

Subgroups — C5×#69854 #14282225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69854 #14282225