Subgroups — C₃×#10615016 #14438890

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4096	C₂	1	4	yes	maximal, complemented
3	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65348	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615016	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂×C₃×#709	C₂²	1	2	yes	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×#121	—	2	2	no	—
17	C₃×C₄×C₅×D₄	—	2	2	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×#4096	—	2	16	no	—
20	C₂×C₃×#689	C₂²	1	4	yes	—
21	C₂×C₃×#688	C₂²	1	4	yes	—
22	C₂×C₃×#687	C₂²	1	4	yes	—
23	C₂×C₃×#686	C₂²	1	4	yes	—
24	C₃×#4076	—	2	2	no	—
25	C₂²×C₃×#168	C₂²	1	2	yes	—
26	C₃×#4021	C₂²	1	2	yes	—
27	C₃×#4020	C₂²	1	1	yes	characteristic
28	C₃×C₄×D₂₀	—	2	2	no	—
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×C₄×#168	C₂²	1	2	yes	—
31	C₃×C₄×#168	C₂²	1	1	yes	characteristic
32	C₃×C₄×#168	C₂²	1	1	yes	characteristic
33	C₃×#3147	—	5	1	no	maximal, Hall
34	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#4096	C₂×C₃	1	4	yes	complemented
36	#65811	C₂×C₃	1	1	yes	characteristic, complemented
37	#65381	C₂×C₃	1	1	yes	characteristic, complemented
38	#65374	C₂×C₃	1	1	yes	characteristic, complemented
39	#65365	C₂×C₃	1	1	yes	characteristic, complemented
40	#65362	C₂×C₃	1	1	yes	characteristic, complemented
41	#65348	C₂×C₃	1	4	yes	complemented
42	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×C₅×#41	—	2	8	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
52	C₃×#709	—	2	8	no	—
53	C₂×C₃×D₂₀	—	2	2	no	—
54	C₂×C₃×D₂₀	C₂³	1	2	yes	—
55	C₂×C₃×C₄×D₅	—	2	2	no	—
56	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₄²×C₅	D₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₃×#689	—	2	8	no	—
63	C₃×#688	—	2	8	no	—
64	C₃×#687	—	2	8	no	—
65	C₃×#686	—	2	8	no	—
66	C₃×#685	—	2	4	no	—
67	C₃×C₄⋊Dic₅	—	2	2	no	—
68	C₂×C₃×#168	D₄	1	8	yes	complemented
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₂×C₃×#168	C₂³	1	2	yes	—
71	C₂×C₃×#135	—	5	4	no	—
72	C₃×#532	—	5	1	no	—
73	C₃×#532	D₅	1	1	yes	characteristic, complemented
74	C₃×#495	—	5	4	no	—
75	C₃×#494	—	5	1	no	—
76	C₃×#493	—	5	1	no	—
77	C₃×#492	—	5	1	no	—
78	C₃×#492	—	5	1	no	—
79	C₂×C₃×C₄×C₈	—	5	1	no	—
80	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
81	C₂×#709	C₂²×C₃	1	2	yes	—
82	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
83	C₅×#127	C₂²×C₃	1	1	yes	characteristic
84	C₅×#124	C₂²×C₃	1	2	yes	—
85	C₅×#121	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	#4096	—	2	16	no	—
89	C₂×#689	C₂²×C₃	1	4	yes	—
90	C₂×#688	C₂²×C₃	1	4	yes	—
91	C₂×#687	C₂²×C₃	1	4	yes	—
92	C₂×#686	C₂²×C₃	1	4	yes	—
93	#4076	—	2	2	no	—
94	C₂²×#168	C₂²×C₃	1	2	yes	—
95	#4021	C₂²×C₃	1	2	yes	—
96	#4020	C₂²×C₃	1	1	yes	characteristic
97	C₄×D₂₀	—	2	2	no	—
98	#4015	C₂²×C₃	1	1	yes	characteristic
99	C₄×#168	C₂²×C₃	1	2	yes	—
100	C₄×#168	C₂²×C₃	1	1	yes	characteristic
101	C₄×#168	C₂²×C₃	1	1	yes	characteristic
102	#3147	—	5	1	no	Sylow
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×D₄	—	2	4	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₃×C₅×D₄	—	4	4	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	4	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₂²⋊D₅	—	4	4	no	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₃×D₂₀	—	2	4	no	—
121	C₃×D₂₀	—	4	4	no	—
122	C₃×C₄×D₅	—	4	4	no	—
123	C₃×Dic₁₀	—	2	4	no	—
124	C₃×#168	C₂×D₄	1	4	yes	—
125	C₃×#168	C₂×D₄	1	4	yes	—
126	C₂×C₃×#41	—	5	2	no	—
127	C₂×C₃×#41	C₂×D₅	1	2	yes	—
128	C₃×#135	—	10	16	no	—
129	C₂×C₃×Q₁₆	—	5	4	no	—
130	C₂×C₃×SD₁₆	—	5	4	no	—
131	C₂×C₃×SD₁₆	—	5	4	no	—
132	C₂×C₃×D₈	—	5	4	no	—
133	C₂²×C₃×C₈	—	5	2	no	—
134	C₃×C₄⋊Q₈	—	5	1	no	—
135	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
136	C₃×#127	—	5	1	no	—
137	C₃×#127	C₂×D₅	1	1	yes	characteristic
138	C₃×#124	—	5	2	no	—
139	C₃×#124	C₂×D₅	1	2	yes	—
140	C₃×#121	—	2	2	no	—
141	C₃×#121	—	10	2	no	—
142	C₃×C₄×D₄	—	2	2	no	—
143	C₃×C₄×D₄	—	10	2	no	—
144	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
145	C₃×C₄×C₈	—	5	1	no	—
146	C₃×C₄×C₈	—	5	1	no	—
147	C₃×C₄×C₈	—	5	2	no	—
148	C₅×#41	—	2	8	no	—
149	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
150	C₂×C₅×D₄	—	2	2	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₂²⋊D₅	—	2	2	no	—
157	#709	—	2	8	no	—
158	C₂×D₂₀	—	2	2	no	—
159	C₂×D₂₀	C₂³×C₃	1	2	yes	—
160	C₂×C₄×D₅	—	2	2	no	—
161	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₄²×C₅	C₃×D₄	1	2	yes	—
165	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
167	#689	—	2	8	no	—
168	#688	—	2	8	no	—
169	#687	—	2	8	no	—
170	#686	—	2	8	no	—
171	#685	—	2	4	no	—
172	C₄⋊Dic₅	—	2	2	no	—
173	C₂×#168	C₃×D₄	1	8	yes	complemented
174	C₂×#168	C₂³×C₃	1	2	yes	—
175	C₂×#168	C₂³×C₃	1	2	yes	—
176	C₂×#135	—	5	4	no	—
177	#532	—	5	1	no	—
178	#532	C₃×D₅	1	1	yes	characteristic, complemented
179	#495	—	5	4	no	—
180	#494	—	5	1	no	—
181	#493	—	5	1	no	—
182	#492	—	5	1	no	—
183	#492	—	5	1	no	—
184	C₂×C₄×C₈	—	5	1	no	—
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	4	2	no	—
187	C₂²×C₃×C₅	—	4	4	no	—
188	C₂²×C₃×C₅	#127	1	2	yes	—
189	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₃×D₅	—	4	2	no	—
191	C₂×C₃×D₅	—	4	4	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	#127	1	2	yes	—
195	C₃×C₄×C₅	#135	1	4	yes	complemented
196	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
197	C₃×Dic₅	—	4	2	no	—
198	C₃×#41	—	2	8	no	—
199	C₃×#41	—	10	8	no	—
200	C₂×C₃×Q₈	—	5	2	no	—
201	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
202	C₂×C₃×D₄	—	2	2	no	—
203	C₂×C₃×D₄	—	2	2	no	—
204	C₂×C₃×D₄	—	5	2	no	—
205	C₂×C₃×D₄	—	10	2	no	—
206	C₂×C₃×D₄	—	10	2	no	—
207	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
208	C₂²×C₃×C₄	—	2	2	no	—
209	C₂²×C₃×C₄	—	10	2	no	—
210	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
212	C₃×Q₁₆	—	10	8	no	—
213	C₃×SD₁₆	—	10	8	no	—
214	C₃×SD₁₆	—	10	8	no	—
215	C₃×D₈	—	10	8	no	—
216	C₂×C₃×C₈	—	5	8	no	—
217	C₂×C₃×C₈	—	5	2	no	—
218	C₂×C₃×C₈	—	5	2	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	—	10	2	no	—
221	C₃×C₂²⋊C₄	—	2	4	no	—
222	C₃×C₂²⋊C₄	—	10	4	no	—
223	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
224	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
225	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂²×D₅	—	2	2	no	—
229	C₅×Q₈	—	2	4	no	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	4	4	no	—
232	C₅×D₄	—	4	4	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	4	4	no	—
236	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
237	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
238	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
240	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
241	C₂²⋊D₅	—	4	4	no	—
242	C₂×Dic₅	—	2	2	no	—
243	D₂₀	—	2	4	no	—
244	D₂₀	—	4	4	no	—
245	C₄×D₅	—	4	4	no	—
246	Dic₁₀	—	2	4	no	—
247	#168	C₂×C₃×D₄	1	4	yes	—
248	#168	C₂×C₃×D₄	1	4	yes	—
249	C₂×#41	—	5	2	no	—
250	C₂×#41	C₂×C₃×D₅	1	2	yes	—
251	#135	—	10	16	no	—
252	C₂×Q₁₆	—	5	4	no	—
253	C₂×SD₁₆	—	5	4	no	—
254	C₂×SD₁₆	—	5	4	no	—
255	C₂×D₈	—	5	4	no	—
256	C₂²×C₈	—	5	2	no	—
257	C₄⋊Q₈	—	5	1	no	—
258	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
259	#127	—	5	1	no	—
260	#127	C₂×C₃×D₅	1	1	yes	characteristic
261	#124	—	5	2	no	—
262	#124	C₂×C₃×D₅	1	2	yes	—
263	#121	—	2	2	no	—
264	#121	—	10	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	10	2	no	—
267	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
268	C₄×C₈	—	5	1	no	—
269	C₄×C₈	—	5	1	no	—
270	C₄×C₈	—	5	2	no	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	—	8	2	no	—
273	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#135	1	2	yes	—
275	C₃×D₅	—	8	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	10	2	no	—
278	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
279	C₃×Q₈	—	2	4	no	—
280	C₃×Q₈	—	10	4	no	—
281	C₃×D₄	—	2	4	no	—
282	C₃×D₄	—	4	4	no	—
283	C₃×D₄	—	4	4	no	—
284	C₃×D₄	—	10	4	no	—
285	C₃×D₄	—	20	4	no	—
286	C₃×D₄	—	20	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	4	4	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	20	4	no	—
292	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
293	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
297	C₃×C₈	—	5	4	no	—
298	C₃×C₈	—	5	4	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	4	4	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	C₃×#127	1	2	yes	—
303	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
304	C₂×D₅	—	4	4	no	—
305	C₂×D₅	—	4	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	C₃×#127	1	2	yes	—
309	C₄×C₅	C₃×#135	1	4	yes	complemented
310	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
311	Dic₅	—	4	2	no	—
312	#41	—	2	8	no	—
313	#41	—	10	8	no	—
314	C₂×Q₈	—	5	2	no	—
315	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	5	2	no	—
319	C₂×D₄	—	10	2	no	—
320	C₂×D₄	—	10	2	no	—
321	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	10	2	no	—
324	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	Q₁₆	—	10	8	no	—
327	SD₁₆	—	10	8	no	—
328	SD₁₆	—	10	8	no	—
329	D₈	—	10	8	no	—
330	C₂×C₈	—	5	8	no	—
331	C₂×C₈	—	5	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	10	2	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	10	4	no	—
337	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
338	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
339	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
340	C₃×C₅	#3147	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	—	20	2	no	—
345	C₂²×C₃	—	20	4	no	—
346	C₂²×C₃	#4086	1	2	yes	—
347	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	—	20	2	no	—
351	C₃×C₄	#4086	1	2	yes	—
352	C₃×C₄	#4096	1	4	yes	complemented
353	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
354	C₂×C₅	—	2	2	no	—
355	C₂×C₅	—	8	2	no	—
356	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
357	C₂×C₅	C₂×C₃×#135	1	2	yes	—
358	D₅	—	8	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	10	2	no	—
361	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	10	4	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	10	4	no	—
368	D₄	—	20	4	no	—
369	D₄	—	20	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	20	4	no	—
375	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
376	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
377	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
378	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
379	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
380	C₈	—	5	4	no	—
381	C₈	—	5	4	no	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	8	2	no	—
384	C₂×C₃	—	40	2	no	—
385	C₂×C₃	C₂×#4086	1	1	yes	characteristic
386	C₂×C₃	C₂×#4096	1	2	yes	—
387	C₅	C₃×#3147	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	20	2	no	—
392	C₂²	—	20	4	no	—
393	C₂²	C₃×#4086	1	2	yes	—
394	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	20	2	no	—
398	C₄	C₃×#4086	1	2	yes	—
399	C₄	C₃×#4096	1	4	yes	complemented
400	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
401	C₃	#10615016	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	8	2	no	—
404	C₂	—	40	2	no	—
405	C₂	C₂×C₃×#4086	1	1	yes	characteristic
406	C₂	C₂×C₃×#4096	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#3147
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₂×C₃×#4096	C₂	semidirect
3. C₃×#65811	C₂	semidirect
4. C₃×#65381	C₂	semidirect
5. C₃×#65374	C₂	semidirect
6. C₃×#65365	C₂	semidirect
7. C₃×#65362	C₂	semidirect
8. C₃×#65348	C₂	semidirect
9. C₂×C₃×C₄×#168	C₂	semidirect
10. #10615016	C₃	direct (N × H)
34. C₅×#532	C₂×C₃	semidirect
35. C₂×#4096	C₂×C₃	semidirect
36. #65811	C₂×C₃	semidirect
37. #65381	C₂×C₃	semidirect
38. #65374	C₂×C₃	semidirect
39. #65365	C₂×C₃	semidirect
40. #65362	C₂×C₃	semidirect
41. #65348	C₂×C₃	semidirect
42. C₂×C₄×#168	C₂×C₃	semidirect
68. C₂×C₃×#168	D₄	semidirect
73. C₃×#532	D₅	semidirect
173. C₂×#168	C₃×D₄	semidirect
178. #532	C₃×D₅	semidirect
195. C₃×C₄×C₅	#135	semidirect
309. C₄×C₅	C₃×#135	semidirect
340. C₃×C₅	#3147	semidirect
352. C₃×C₄	#4096	semidirect
387. C₅	C₃×#3147	semidirect
399. C₄	C₃×#4096	semidirect
401. C₃	#10615016	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×C₅×#532	2
C₂×C₃×#4096	2
C₃×#65811	2
C₃×#65381	2
C₃×#65374	2
C₃×#65365	2
C₃×#65362	2
C₃×#65348	2
C₂×C₃×C₄×#168	2
#10615016	3
C₃×#3147	5

Subgroups — C3×#10615016 #14438890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615016 #14438890