Subgroups — C₃×#10600647 #14282226

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	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64679	C₂	1	2	yes	maximal, complemented
5	C₃×#64676	C₂	1	2	yes	maximal, complemented
6	#10600647	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#709	C₄	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
11	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
12	C₃×#4072	C₄	1	1	yes	characteristic
13	C₂×C₃×#681	—	2	1	no	—
14	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
15	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
16	C₃×#4018	—	2	1	no	—
17	C₃×C₄²×D₅	—	2	1	no	—
18	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
19	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
20	C₃×C₅×#97	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₃×C₄⋊#168	—	2	1	no	—
23	C₃×C₄⋊#168	C₂²	1	2	yes	—
24	C₃×#1489	—	5	1	no	maximal, Hall
25	C₄×#709	C₂×C₃	1	1	yes	characteristic
26	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
27	#65213	C₂×C₃	1	1	yes	characteristic, complemented
28	#64679	C₂×C₃	1	2	yes	complemented
29	#64676	C₂×C₃	1	2	yes	complemented
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×C₃×C₂²⋊D₅	—	2	1	no	—
34	C₃×#709	—	2	2	no	—
35	C₃×#709	—	2	2	no	—
36	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	—	2	1	no	—
38	C₂×C₃×C₄×D₅	—	2	1	no	—
39	C₂×C₃×C₄×D₅	—	2	1	no	—
40	C₂×C₃×Dic₁₀	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	C₃×C₂²⋊Dic₅	—	2	1	no	—
48	C₃×#685	—	2	1	no	—
49	C₃×#685	—	2	1	no	—
50	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
52	C₃×#683	—	2	1	no	—
53	C₃×#683	—	2	1	no	—
54	C₃×C₄×Dic₅	—	2	1	no	—
55	C₃×C₄×Dic₅	—	2	1	no	—
56	C₃×C₄×Dic₅	—	2	1	no	—
57	C₃×#681	—	4	2	no	—
58	C₂×C₃×#168	—	2	2	no	—
59	C₃×C₄×#41	—	5	1	no	—
60	C₃×#423	—	5	1	no	—
61	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
62	C₃×Q₈⋊C₈	—	5	2	no	—
63	C₃×D₄⋊C₈	—	5	2	no	—
64	C₂×#709	C₃×C₄	1	1	yes	characteristic
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₄×C₂²⋊D₅	—	2	1	no	—
68	C₄×C₂²⋊D₅	—	2	1	no	—
69	#4072	C₃×C₄	1	1	yes	characteristic
70	C₂×#681	—	2	1	no	—
71	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic
72	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
73	#4018	—	2	1	no	—
74	C₄²×D₅	—	2	1	no	—
75	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
76	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
77	C₅×#97	—	2	1	no	—
78	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
79	C₄⋊#168	—	2	1	no	—
80	C₄⋊#168	C₂²×C₃	1	2	yes	—
81	#1489	—	5	1	no	Sylow
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₃×D₅	—	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	C₃×C₂²⋊D₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	1	no	—
97	C₂×C₃×Dic₅	—	2	1	no	—
98	C₂×C₃×Dic₅	—	2	1	no	—
99	C₃×D₂₀	—	2	1	no	—
100	C₃×D₂₀	M₁₆	1	2	yes	complemented
101	C₃×C₄×D₅	—	2	4	no	—
102	C₃×C₄×D₅	—	4	2	no	—
103	C₃×C₄×D₅	—	4	1	no	—
104	C₃×C₄×D₅	—	4	1	no	—
105	C₃×Dic₁₀	—	2	1	no	—
106	C₃×Dic₁₀	M₁₆	1	2	yes	complemented
107	C₃×C₅×C₈	—	2	4	no	—
108	C₃×#168	—	4	2	no	—
109	C₂×C₃×#41	—	5	1	no	—
110	C₂×C₃×M₁₆	—	2	1	no	—
111	C₂×C₃×M₁₆	—	10	1	no	—
112	C₃×C₄×Q₈	—	5	1	no	—
113	C₃×C₄×Q₈	—	5	1	no	—
114	C₃×C₄×D₄	—	5	1	no	—
115	C₃×C₄×D₄	—	5	1	no	—
116	C₃×C₄×D₄	—	10	1	no	—
117	C₃×C₄×D₄	—	10	1	no	—
118	C₃×#117	—	5	1	no	—
119	C₃×#117	—	10	1	no	—
120	C₂×C₃×C₄²	—	10	1	no	—
121	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄⋊C₈	—	5	2	no	—
123	C₃×C₄⋊C₈	—	10	1	no	—
124	C₃×#97	—	2	1	no	—
125	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
126	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	—	2	1	no	—
130	#709	—	2	2	no	—
131	#709	—	2	2	no	—
132	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂×C₄×D₅	—	2	1	no	—
134	C₂×C₄×D₅	—	2	1	no	—
135	C₂×C₄×D₅	—	2	1	no	—
136	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
137	C₅×M₁₆	—	2	4	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
140	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
141	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
142	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂²⋊Dic₅	—	2	1	no	—
144	#685	—	2	1	no	—
145	#685	—	2	1	no	—
146	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
148	#683	—	2	1	no	—
149	#683	—	2	1	no	—
150	C₄×Dic₅	—	2	1	no	—
151	C₄×Dic₅	—	2	1	no	—
152	C₄×Dic₅	—	2	1	no	—
153	#681	—	4	2	no	—
154	C₂×#168	—	2	2	no	—
155	C₄×#41	—	5	1	no	—
156	#423	—	5	1	no	—
157	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
158	Q₈⋊C₈	—	5	2	no	—
159	D₄⋊C₈	—	5	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×C₃×D₅	—	2	2	no	—
165	C₂×C₃×D₅	—	4	1	no	—
166	C₂×C₃×D₅	—	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	C₃×Dic₅	—	2	2	no	—
176	C₃×Dic₅	—	4	1	no	—
177	C₃×Dic₅	—	4	1	no	—
178	C₃×#41	—	10	2	no	—
179	C₃×#41	—	10	2	no	—
180	C₂×C₃×Q₈	—	5	1	no	—
181	C₂×C₃×D₄	—	5	1	no	—
182	C₂×C₃×D₄	—	10	1	no	—
183	C₂²×C₃×C₄	—	10	1	no	—
184	C₂²×C₃×C₄	—	10	1	no	—
185	C₂²×C₃×C₄	—	10	1	no	—
186	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
189	C₃×M₁₆	—	2	4	no	—
190	C₃×M₁₆	—	20	2	no	—
191	C₂×C₃×C₈	—	2	2	no	—
192	C₂×C₃×C₈	—	10	2	no	—
193	C₃×C₄⋊C₄	—	5	1	no	—
194	C₃×C₄⋊C₄	—	5	1	no	—
195	C₃×C₄⋊C₄	—	10	1	no	—
196	C₃×C₄⋊C₄	—	10	1	no	—
197	C₃×C₂²⋊C₄	—	10	1	no	—
198	C₃×C₂²⋊C₄	—	10	1	no	—
199	C₃×C₂²⋊C₄	—	10	1	no	—
200	C₃×C₄²	—	10	1	no	—
201	C₃×C₄²	—	10	1	no	—
202	C₃×C₄²	—	10	1	no	—
203	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
204	C₃×C₄²	D₂₀	1	1	yes	characteristic
205	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
206	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
207	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×D₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂²⋊D₅	—	2	4	no	—
221	C₂×Dic₅	—	2	1	no	—
222	C₂×Dic₅	—	2	1	no	—
223	C₂×Dic₅	—	2	1	no	—
224	D₂₀	—	2	1	no	—
225	D₂₀	C₃×M₁₆	1	2	yes	complemented
226	C₄×D₅	—	2	4	no	—
227	C₄×D₅	—	4	2	no	—
228	C₄×D₅	—	4	1	no	—
229	C₄×D₅	—	4	1	no	—
230	Dic₁₀	—	2	1	no	—
231	Dic₁₀	C₃×M₁₆	1	2	yes	complemented
232	C₅×C₈	—	2	4	no	—
233	#168	—	4	2	no	—
234	C₂×#41	—	5	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	10	1	no	—
237	C₄×Q₈	—	5	1	no	—
238	C₄×Q₈	—	5	1	no	—
239	C₄×D₄	—	5	1	no	—
240	C₄×D₄	—	5	1	no	—
241	C₄×D₄	—	10	1	no	—
242	C₄×D₄	—	10	1	no	—
243	#117	—	5	1	no	—
244	#117	—	10	1	no	—
245	C₂×C₄²	—	10	1	no	—
246	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
247	C₄⋊C₈	—	5	2	no	—
248	C₄⋊C₈	—	10	1	no	—
249	#97	—	2	1	no	—
250	C₄×C₈	C₂×C₃×D₅	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	C₃×D₅	—	4	2	no	—
256	C₂³×C₃	—	10	1	no	—
257	C₂³×C₃	#685	1	1	yes	characteristic
258	C₃×Q₈	—	5	2	no	—
259	C₃×Q₈	—	10	1	no	—
260	C₃×D₄	—	5	2	no	—
261	C₃×D₄	—	10	4	no	—
262	C₃×D₄	—	10	1	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	10	4	no	—
269	C₂×C₃×C₄	—	10	1	no	—
270	C₂×C₃×C₄	—	10	1	no	—
271	C₂×C₃×C₄	—	10	1	no	—
272	C₂×C₃×C₄	—	20	2	no	—
273	C₂×C₃×C₄	—	20	1	no	—
274	C₂×C₃×C₄	—	20	1	no	—
275	C₂×C₃×C₄	#685	1	1	yes	characteristic
276	C₂×C₃×C₄	#685	1	1	yes	characteristic
277	C₂×C₃×C₄	#685	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
281	C₃×C₈	—	2	4	no	—
282	C₃×C₈	—	20	2	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×D₅	—	2	2	no	—
288	C₂×D₅	—	4	1	no	—
289	C₂×D₅	—	4	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	C₃×#104	1	2	yes	—
294	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
295	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
296	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₄×C₅	C₃×#137	1	1	yes	characteristic
298	Dic₅	—	2	2	no	—
299	Dic₅	—	4	1	no	—
300	Dic₅	—	4	1	no	—
301	#41	—	10	2	no	—
302	#41	—	10	2	no	—
303	C₂×Q₈	—	5	1	no	—
304	C₂×D₄	—	5	1	no	—
305	C₂×D₄	—	10	1	no	—
306	C₂²×C₄	—	10	1	no	—
307	C₂²×C₄	—	10	1	no	—
308	C₂²×C₄	—	10	1	no	—
309	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
310	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
311	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
312	M₁₆	—	2	4	no	—
313	M₁₆	—	20	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	10	2	no	—
316	C₄⋊C₄	—	5	1	no	—
317	C₄⋊C₄	—	5	1	no	—
318	C₄⋊C₄	—	10	1	no	—
319	C₄⋊C₄	—	10	1	no	—
320	C₂²⋊C₄	—	10	1	no	—
321	C₂²⋊C₄	—	10	1	no	—
322	C₂²⋊C₄	—	10	1	no	—
323	C₄²	—	10	1	no	—
324	C₄²	—	10	1	no	—
325	C₄²	—	10	1	no	—
326	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
327	C₄²	C₃×D₂₀	1	1	yes	characteristic
328	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
329	C₄²	C₂²×C₃×D₅	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	—	10	2	no	—
335	C₂²×C₃	—	20	1	no	—
336	C₂²×C₃	—	20	1	no	—
337	C₂²×C₃	C₂×#685	1	1	yes	characteristic
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	10	2	no	—
342	C₃×C₄	—	20	1	no	—
343	C₃×C₄	—	20	1	no	—
344	C₃×C₄	#3937	1	2	yes	—
345	C₃×C₄	D₅×M₁₆	1	1	yes	characteristic
346	C₃×C₄	D₅×M₁₆	1	1	yes	characteristic
347	C₃×C₄	#4054	1	1	yes	characteristic
348	C₃×C₄	#4055	1	1	yes	characteristic
349	C₂×C₅	—	4	1	no	—
350	C₂×C₅	C₃×#407	1	1	yes	characteristic
351	C₂×C₅	C₃×#417	1	1	yes	characteristic
352	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
353	D₅	—	4	2	no	—
354	C₂³	—	10	1	no	—
355	C₂³	C₃×#685	1	1	yes	characteristic
356	Q₈	—	5	2	no	—
357	Q₈	—	10	1	no	—
358	D₄	—	5	2	no	—
359	D₄	—	10	4	no	—
360	D₄	—	10	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	10	1	no	—
368	C₂×C₄	—	10	1	no	—
369	C₂×C₄	—	10	1	no	—
370	C₂×C₄	—	20	2	no	—
371	C₂×C₄	—	20	1	no	—
372	C₂×C₄	—	20	1	no	—
373	C₂×C₄	C₃×#685	1	1	yes	characteristic
374	C₂×C₄	C₃×#685	1	1	yes	characteristic
375	C₂×C₄	C₃×#685	1	1	yes	characteristic
376	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
377	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
378	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	20	2	no	—
381	C₂×C₃	—	4	1	no	—
382	C₂×C₃	—	20	2	no	—
383	C₂×C₃	C₂×#3937	1	1	yes	characteristic
384	C₂×C₃	#65415	1	1	yes	characteristic
385	C₂×C₃	#65422	1	1	yes	characteristic
386	C₅	C₃×#1489	1	1	yes	characteristic, complemented, Sylow
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	10	2	no	—
391	C₂²	—	20	1	no	—
392	C₂²	—	20	1	no	—
393	C₂²	C₂×C₃×#685	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	10	2	no	—
398	C₄	—	20	1	no	—
399	C₄	—	20	1	no	—
400	C₄	C₃×#3937	1	2	yes	—
401	C₄	C₃×D₅×M₁₆	1	1	yes	characteristic
402	C₄	C₃×D₅×M₁₆	1	1	yes	characteristic
403	C₄	C₃×#4054	1	1	yes	characteristic
404	C₄	C₃×#4055	1	1	yes	characteristic
405	C₃	#10600647	1	1	yes	characteristic, direct product factor, Sylow
406	C₂	—	4	1	no	—
407	C₂	—	20	2	no	—
408	C₂	C₂×C₃×#3937	1	1	yes	characteristic
409	C₂	C₃×#65415	1	1	yes	characteristic
410	C₂	C₃×#65422	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×#1489
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×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. C₃×#65213	C₂	semidirect
4. C₃×#64679	C₂	semidirect
5. C₃×#64676	C₂	semidirect
6. #10600647	C₃	direct (N × H)
26. C₄×C₅×M₁₆	C₂×C₃	semidirect
27. #65213	C₂×C₃	semidirect
28. #64679	C₂×C₃	semidirect
29. #64676	C₂×C₃	semidirect
61. C₃×C₄×M₁₆	D₅	semidirect
100. C₃×D₂₀	M₁₆	semidirect
106. C₃×Dic₁₀	M₁₆	semidirect
157. C₄×M₁₆	C₃×D₅	semidirect
225. D₂₀	C₃×M₁₆	semidirect
231. Dic₁₀	C₃×M₁₆	semidirect
330. C₃×C₅	#1489	semidirect
386. C₅	C₃×#1489	semidirect
405. C₃	#10600647	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#709	2
C₃×C₄×C₅×M₁₆	2
C₃×#65213	2
C₃×#64679	2
C₃×#64676	2
#10600647	3
C₃×#1489	5

Subgroups — C3×#10600647 #14282226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600647 #14282226