Subgroups — C₃×#10615637 #14439553

Order 1920.

1192 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	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66164	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4095	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65480	C₂	1	2	yes	maximal, complemented
6	C₃×#65465	C₂	1	4	yes	maximal, complemented
7	C₃×#65440	C₂	1	2	yes	maximal, complemented
8	C₃×#65390	C₂	1	1	yes	maximal, characteristic, complemented
9	#10615637	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×#4095	—	2	8	no	—
18	C₃×#4093	C₂²	1	4	yes	complemented
19	C₂×C₃×#688	C₂²	1	4	yes	complemented
20	C₃×#4086	C₂²	1	4	yes	complemented
21	C₃×#4083	—	2	4	no	—
22	C₂×C₃×#686	C₂²	1	4	yes	complemented
23	C₃×#4076	—	2	4	no	—
24	C₃×#4072	C₂²	1	1	yes	characteristic
25	C₂×C₃×#681	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₄₀	—	2	4	no	—
27	C₂×C₃×D₄₀	C₂²	1	2	yes	—
28	C₂×C₃×D₄₀	C₂²	1	2	yes	—
29	C₃×#3947	C₂²	1	2	yes	complemented
30	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
31	C₃×#3155	—	5	1	no	maximal, Hall
32	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
33	#66164	C₂×C₃	1	2	yes	complemented
34	C₂×#4095	C₂×C₃	1	2	yes	complemented
35	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
36	#65480	C₂×C₃	1	2	yes	complemented
37	#65465	C₂×C₃	1	4	yes	complemented
38	#65440	C₂×C₃	1	2	yes	complemented
39	#65390	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×D₅	—	2	2	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
49	C₂×C₃×D₂₀	—	2	4	no	—
50	C₂×C₃×D₂₀	—	2	4	no	—
51	C₂×C₃×D₂₀	—	2	2	no	—
52	C₂×C₃×D₂₀	C₂³	1	4	yes	—
53	C₃×C₅×Q₁₆	—	2	2	no	—
54	C₃×C₅×SD₁₆	—	2	4	no	—
55	C₃×C₅×D₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
60	C₃×#688	—	2	8	no	—
61	C₃×#686	—	2	8	no	—
62	C₃×#685	—	2	8	no	—
63	C₃×C₄⋊Dic₅	D₄	1	2	yes	—
64	C₃×C₄×Dic₅	C₂³	1	2	yes	—
65	C₃×#681	D₄	1	4	yes	complemented
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₃×D₄₀	—	2	4	no	—
68	C₃×D₄₀	—	2	4	no	—
69	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
70	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
71	C₂²×C₃×D₈	—	5	1	no	—
72	C₃×#535	—	5	2	no	—
73	C₃×#496	—	5	4	no	—
74	C₃×#495	—	5	2	no	—
75	C₃×#493	—	5	2	no	—
76	C₃×#405	—	5	1	no	—
77	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
78	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
79	C₅×#135	—	2	4	no	—
80	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
82	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
84	#4095	—	2	8	no	—
85	#4093	C₂²×C₃	1	4	yes	complemented
86	C₂×#688	C₂²×C₃	1	4	yes	complemented
87	#4086	C₂²×C₃	1	4	yes	complemented
88	#4083	—	2	4	no	—
89	C₂×#686	C₂²×C₃	1	4	yes	complemented
90	#4076	—	2	4	no	—
91	#4072	C₂²×C₃	1	1	yes	characteristic
92	C₂×#681	C₂²×C₃	1	1	yes	characteristic
93	C₂×D₄₀	—	2	4	no	—
94	C₂×D₄₀	C₂²×C₃	1	2	yes	—
95	C₂×D₄₀	C₂²×C₃	1	2	yes	—
96	#3947	C₂²×C₃	1	2	yes	complemented
97	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
98	#3155	—	5	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×D₅	—	2	4	no	—
102	C₂²×C₃×D₅	—	4	4	no	—
103	C₂²×C₃×D₅	—	8	4	no	—
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×D₄	—	2	2	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	4	4	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₃×C₂²⋊D₅	—	8	8	no	—
116	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
117	C₃×D₂₀	—	2	4	no	—
118	C₃×D₂₀	—	2	4	no	—
119	C₃×D₂₀	—	4	4	no	—
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
122	C₃×#168	C₂×D₄	1	4	yes	—
123	C₂×C₃×#41	C₂×D₅	1	2	yes	—
124	C₂²×C₃×D₄	—	5	2	no	—
125	C₃×AGL(1,ℤ/8)	—	10	8	no	—
126	C₃×#135	—	2	4	no	—
127	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
128	C₂×C₃×SD₁₆	—	5	4	no	—
129	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
130	C₂×C₃×D₈	—	5	4	no	—
131	C₂×C₃×D₈	—	5	2	no	—
132	C₂×C₃×D₈	—	5	2	no	—
133	C₂×C₃×D₈	—	10	4	no	—
134	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
135	C₂×C₃×M₁₆	—	5	1	no	—
136	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
137	C₃×#127	—	5	4	no	—
138	C₃×#124	—	5	4	no	—
139	C₃×#121	—	10	4	no	—
140	C₃×#120	—	10	4	no	—
141	C₃×#117	—	5	1	no	—
142	C₃×#97	—	5	2	no	—
143	C₃×C₄×C₈	—	5	2	no	—
144	C₂³×D₅	—	2	2	no	—
145	C₅×#41	—	2	4	no	—
146	C₅×#41	—	2	4	no	—
147	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₂²⋊D₅	—	2	8	no	—
153	C₂×D₂₀	—	2	4	no	—
154	C₂×D₂₀	—	2	4	no	—
155	C₂×D₂₀	—	2	2	no	—
156	C₂×D₂₀	C₂³×C₃	1	4	yes	—
157	C₅×Q₁₆	—	2	2	no	—
158	C₅×SD₁₆	—	2	4	no	—
159	C₅×D₈	—	2	2	no	—
160	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
161	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
163	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
164	#688	—	2	8	no	—
165	#686	—	2	8	no	—
166	#685	—	2	8	no	—
167	C₄⋊Dic₅	C₃×D₄	1	2	yes	—
168	C₄×Dic₅	C₂³×C₃	1	2	yes	—
169	#681	C₃×D₄	1	4	yes	complemented
170	C₂×#168	C₂³×C₃	1	2	yes	—
171	D₄₀	—	2	4	no	—
172	D₄₀	—	2	4	no	—
173	C₂×AGL(1,ℤ/8)	—	5	2	no	—
174	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
175	C₂²×D₈	—	5	1	no	—
176	#535	—	5	2	no	—
177	#496	—	5	4	no	—
178	#495	—	5	2	no	—
179	#493	—	5	2	no	—
180	#405	—	5	1	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	4	no	—
184	C₂²×C₃×C₅	#127	1	2	yes	—
185	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₃×D₅	—	4	4	no	—
187	C₂×C₃×D₅	—	4	8	no	—
188	C₂×C₃×D₅	—	8	8	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	#127	1	2	yes	—
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₃×Dic₅	—	2	4	no	—
194	C₂⁴×C₃	—	10	2	no	—
195	C₃×#41	—	2	4	no	—
196	C₃×#41	—	2	4	no	—
197	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂×C₃×D₄	—	5	4	no	—
200	C₂×C₃×D₄	—	10	8	no	—
201	C₂×C₃×D₄	—	10	4	no	—
202	C₂×C₃×D₄	—	10	2	no	—
203	C₂×C₃×D₄	—	10	4	no	—
204	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
205	C₂²×C₃×C₄	—	2	2	no	—
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₃×Q₁₆	—	2	2	no	—
208	C₃×SD₁₆	—	2	4	no	—
209	C₃×SD₁₆	—	10	8	no	—
210	C₃×D₈	—	2	2	no	—
211	C₃×D₈	—	10	8	no	—
212	C₃×D₈	—	10	4	no	—
213	C₃×D₈	—	10	4	no	—
214	C₃×M₁₆	—	5	4	no	—
215	C₂×C₃×C₈	—	5	2	no	—
216	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
217	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
219	C₃×C₄⋊C₄	—	5	2	no	—
220	C₃×C₂²⋊C₄	—	5	2	no	—
221	C₃×C₂²⋊C₄	—	10	8	no	—
222	C₃×C₄²	—	5	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
225	C₂²×D₅	—	2	4	no	—
226	C₂²×D₅	—	4	4	no	—
227	C₂²×D₅	—	8	4	no	—
228	C₅×Q₈	—	2	2	no	—
229	C₅×Q₈	—	2	2	no	—
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	4	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	4	4	no	—
235	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
237	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
238	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
239	C₂²⋊D₅	—	8	8	no	—
240	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
241	D₂₀	—	2	4	no	—
242	D₂₀	—	2	4	no	—
243	D₂₀	—	4	4	no	—
244	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
245	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
246	#168	C₂×C₃×D₄	1	4	yes	—
247	C₂×#41	C₂×C₃×D₅	1	2	yes	—
248	C₂²×D₄	—	5	2	no	—
249	AGL(1,ℤ/8)	—	10	8	no	—
250	#135	—	2	4	no	—
251	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	—	5	4	no	—
253	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
254	C₂×D₈	—	5	4	no	—
255	C₂×D₈	—	5	2	no	—
256	C₂×D₈	—	5	2	no	—
257	C₂×D₈	—	10	4	no	—
258	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
259	C₂×M₁₆	—	5	1	no	—
260	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
261	#127	—	5	4	no	—
262	#124	—	5	4	no	—
263	#121	—	10	4	no	—
264	#120	—	10	4	no	—
265	#117	—	5	1	no	—
266	#97	—	5	2	no	—
267	C₄×C₈	—	5	2	no	—
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	—	8	2	no	—
270	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
271	C₂×C₃×C₅	#576	1	2	yes	—
272	C₃×D₅	—	8	4	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	10	4	no	—
275	C₂³×C₃	—	20	4	no	—
276	C₂³×C₃	—	40	4	no	—
277	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	—	2	2	no	—
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	4	4	no	—
283	C₃×D₄	—	10	4	no	—
284	C₃×D₄	—	10	4	no	—
285	C₃×D₄	—	20	4	no	—
286	C₃×D₄	—	40	8	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	4	no	—
289	C₂×C₃×C₄	—	5	4	no	—
290	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
291	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
293	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
294	C₃×C₈	—	5	4	no	—
295	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
296	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	4	4	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	C₃×#127	1	2	yes	—
301	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
302	C₂×D₅	—	4	8	no	—
303	C₂×D₅	—	4	4	no	—
304	C₂×D₅	—	8	8	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	C₃×#127	1	2	yes	—
307	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
308	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	Dic₅	—	2	4	no	—
310	C₂⁴	—	10	2	no	—
311	#41	—	2	4	no	—
312	#41	—	2	4	no	—
313	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	5	4	no	—
316	C₂×D₄	—	10	8	no	—
317	C₂×D₄	—	10	4	no	—
318	C₂×D₄	—	10	2	no	—
319	C₂×D₄	—	10	4	no	—
320	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
323	Q₁₆	—	2	2	no	—
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	10	8	no	—
326	D₈	—	2	2	no	—
327	D₈	—	10	8	no	—
328	D₈	—	10	4	no	—
329	D₈	—	10	4	no	—
330	M₁₆	—	5	4	no	—
331	C₂×C₈	—	5	2	no	—
332	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
333	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
334	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
335	C₄⋊C₄	—	5	2	no	—
336	C₂²⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	10	8	no	—
338	C₄²	—	5	2	no	—
339	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	4	4	no	—
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	20	8	no	—
344	C₂²×C₃	—	20	4	no	—
345	C₂²×C₃	—	40	8	no	—
346	C₂²×C₃	#4086	1	2	yes	—
347	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
348	C₃×C₄	—	4	2	no	—
349	C₃×C₄	—	10	4	no	—
350	C₃×C₄	#4086	1	2	yes	—
351	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
352	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	—	8	2	no	—
355	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
356	C₂×C₅	C₃×#576	1	2	yes	—
357	D₅	—	8	4	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	10	4	no	—
360	C₂³	—	20	4	no	—
361	C₂³	—	40	4	no	—
362	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	4	no	—
368	D₄	—	10	4	no	—
369	D₄	—	10	4	no	—
370	D₄	—	20	4	no	—
371	D₄	—	40	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	5	4	no	—
375	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
376	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
377	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
378	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
379	C₈	—	5	4	no	—
380	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
381	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	8	2	no	—
384	C₂×C₃	—	40	4	no	—
385	C₂×C₃	#66103	1	2	yes	—
386	C₂×C₃	C₂×#4086	1	1	yes	characteristic
387	C₅	C₃×#3155	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	20	8	no	—
392	C₂²	—	20	4	no	—
393	C₂²	—	40	8	no	—
394	C₂²	C₃×#4086	1	2	yes	—
395	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
396	C₄	—	4	2	no	—
397	C₄	—	10	4	no	—
398	C₄	C₃×#4086	1	2	yes	—
399	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
400	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
401	C₃	#10615637	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	8	2	no	—
404	C₂	—	40	4	no	—
405	C₂	C₃×#66103	1	2	yes	—
406	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₃×#3155
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₃×#66164	C₂	semidirect
3. C₂×C₃×#4095	C₂	semidirect
4. C₂²×C₃×D₄₀	C₂	semidirect
5. C₃×#65480	C₂	semidirect
6. C₃×#65465	C₂	semidirect
7. C₃×#65440	C₂	semidirect
8. C₃×#65390	C₂	semidirect
9. #10615637	C₃	direct (N × H)
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
18. C₃×#4093	C₂²	semidirect
19. C₂×C₃×#688	C₂²	semidirect
20. C₃×#4086	C₂²	semidirect
22. C₂×C₃×#686	C₂²	semidirect
29. C₃×#3947	C₂²	semidirect
30. C₃×C₈×Dic₅	C₂²	semidirect
32. C₂×C₅×#135	C₂×C₃	semidirect
33. #66164	C₂×C₃	semidirect
34. C₂×#4095	C₂×C₃	semidirect
35. C₂²×D₄₀	C₂×C₃	semidirect
36. #65480	C₂×C₃	semidirect
37. #65465	C₂×C₃	semidirect
38. #65440	C₂×C₃	semidirect
39. #65390	C₂×C₃	semidirect
56. C₂×C₃×C₅×C₈	D₄	semidirect
65. C₃×#681	D₄	semidirect
70. C₂×C₃×#135	D₅	semidirect
80. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
81. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
82. C₂×C₅×D₈	C₂²×C₃	semidirect
85. #4093	C₂²×C₃	semidirect
86. C₂×#688	C₂²×C₃	semidirect
87. #4086	C₂²×C₃	semidirect
89. C₂×#686	C₂²×C₃	semidirect
96. #3947	C₂²×C₃	semidirect
97. C₈×Dic₅	C₂²×C₃	semidirect
127. C₂×C₃×Q₁₆	C₂×D₅	semidirect
129. C₂×C₃×SD₁₆	C₂×D₅	semidirect
134. C₂×C₃×D₈	C₂×D₅	semidirect
160. C₂×C₅×C₈	C₃×D₄	semidirect
169. #681	C₃×D₄	semidirect
174. C₂×#135	C₃×D₅	semidirect
216. C₂×C₃×C₈	C₂²⋊D₅	semidirect
251. C₂×Q₁₆	C₂×C₃×D₅	semidirect
253. C₂×SD₁₆	C₂×C₃×D₅	semidirect
258. C₂×D₈	C₂×C₃×D₅	semidirect
332. C₂×C₈	C₃×C₂²⋊D₅	semidirect
339. C₃×C₅	#3155	semidirect
387. C₅	C₃×#3155	semidirect
401. C₃	#10615637	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₃×#66164	2
C₂×C₃×#4095	2
C₂²×C₃×D₄₀	2
C₃×#65480	2
C₃×#65465	2
C₃×#65440	2
C₃×#65390	2
#10615637	3
C₃×#3155	5

Subgroups — C3×#10615637 #14439553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615637 #14439553