Subgroups — C₂×C₃×#65050 #14429866

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4034	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3964	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#3949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65050	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65050	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×Dic₅	—	2	1	no	—
12	C₂²×C₃×Dic₁₀	—	2	1	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
16	C₃×D₄×Dic₅	—	2	2	no	—
17	C₃×D₄×Dic₅	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×#683	—	2	1	no	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	C₃×#4034	—	2	2	no	—
24	C₃×#4034	C₂²	1	4	yes	complemented
25	C₃×C₅×#102	C₂²	1	4	yes	—
26	C₃×#3964	C₂²	1	4	yes	—
27	C₃×#3949	C₂²	1	4	yes	complemented
28	C₃×#3946	C₂²	1	4	yes	complemented
29	C₃×#3940	C₂²	1	4	yes	complemented
30	C₂×C₃×#476	—	5	1	no	maximal, Hall
31	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic
32	C₂×#4034	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic
34	C₂×#3964	C₂×C₃	1	1	yes	characteristic
35	C₂×#3949	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#3940	C₂×C₃	1	1	yes	characteristic, complemented
38	#65050	C₂×C₃	1	8	yes	direct product factor
39	C₂⁴×C₃×C₅	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	—	2	1	no	—
47	C₂²×C₃×Dic₅	—	2	1	no	—
48	C₂²×C₃×Dic₅	—	2	4	no	—
49	C₂²×C₃×Dic₅	—	4	4	no	—
50	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
52	C₂×C₃×Dic₁₀	—	2	4	no	—
53	C₂×C₃×Dic₁₀	—	4	4	no	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₂²⋊Dic₅	—	2	4	no	—
59	C₃×C₄⋊Dic₅	—	2	1	no	—
60	C₃×C₄⋊Dic₅	—	2	1	no	—
61	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
62	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
63	C₃×#683	—	2	4	no	—
64	C₃×C₄×Dic₅	D₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂³	1	2	yes	—
66	C₂×C₃×#168	—	2	2	no	—
67	C₂×C₃×#168	C₂³	1	2	yes	—
68	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
69	C₂×C₃×C₄×D₄	—	5	1	no	—
70	C₃×#476	—	5	8	no	—
71	C₂×C₃×#106	—	5	1	no	—
72	C₂×C₃×#106	—	5	1	no	—
73	C₂×C₃×C₄⋊C₈	—	5	1	no	—
74	C₂×C₃×#102	—	5	1	no	—
75	C₂×C₃×#102	D₅	1	1	yes	characteristic
76	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂³×Dic₅	—	2	1	no	—
78	C₂²×Dic₁₀	—	2	1	no	—
79	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₂²⋊Dic₅	—	2	1	no	—
82	D₄×Dic₅	—	2	2	no	—
83	D₄×Dic₅	C₂²×C₃	1	4	yes	—
84	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×#683	—	2	1	no	—
87	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
88	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
89	#4034	—	2	2	no	—
90	#4034	C₂²×C₃	1	4	yes	complemented
91	C₅×#102	C₂²×C₃	1	4	yes	—
92	#3964	C₂²×C₃	1	4	yes	—
93	#3949	C₂²×C₃	1	4	yes	complemented
94	#3946	C₂²×C₃	1	4	yes	complemented
95	#3940	C₂²×C₃	1	4	yes	complemented
96	C₂×#476	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	2	4	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	4	2	no	—
100	C₂³×C₃×C₅	—	4	2	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₃×C₅×D₄	—	2	4	no	—
103	C₃×C₅×D₄	—	2	2	no	—
104	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	4	2	no	—
115	C₂×C₃×Dic₅	—	4	2	no	—
116	C₂×C₃×Dic₅	—	4	8	no	—
117	C₂×C₃×Dic₅	SD₁₆	1	4	yes	—
118	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
120	C₃×Dic₁₀	—	4	8	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×#168	—	2	2	no	—
123	C₂²×C₃×Q₈	—	10	1	no	—
124	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
125	C₂³×C₃×C₄	—	10	1	no	—
126	C₂²×C₃×C₈	—	5	1	no	—
127	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	—	5	4	no	—
129	C₃×C₄⋊Q₈	—	10	2	no	—
130	C₃×C₄×D₄	—	5	4	no	—
131	C₃×C₄×D₄	—	10	2	no	—
132	C₂×C₃×C₄⋊C₄	—	5	1	no	—
133	C₂×C₃×C₄⋊C₄	—	5	1	no	—
134	C₂×C₃×C₄⋊C₄	—	10	1	no	—
135	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
137	C₂×C₃×C₄²	—	5	1	no	—
138	C₃×#106	—	5	4	no	—
139	C₃×#106	—	5	4	no	—
140	C₃×C₄⋊C₈	—	5	4	no	—
141	C₃×#102	—	5	4	no	—
142	C₃×#102	C₂×D₅	1	4	yes	—
143	C₂⁴×C₅	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
147	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×Dic₅	—	2	1	no	—
151	C₂²×Dic₅	—	2	1	no	—
152	C₂²×Dic₅	—	2	4	no	—
153	C₂²×Dic₅	—	4	4	no	—
154	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
155	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
156	C₂×Dic₁₀	—	2	4	no	—
157	C₂×Dic₁₀	—	4	4	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
162	C₂²⋊Dic₅	—	2	4	no	—
163	C₄⋊Dic₅	—	2	1	no	—
164	C₄⋊Dic₅	—	2	1	no	—
165	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
166	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
167	#683	—	2	4	no	—
168	C₄×Dic₅	C₃×D₄	1	2	yes	—
169	C₄×Dic₅	C₂³×C₃	1	2	yes	—
170	C₂×#168	—	2	2	no	—
171	C₂×#168	C₂³×C₃	1	2	yes	—
172	C₂×C₄⋊Q₈	—	5	1	no	—
173	C₂×C₄×D₄	—	5	1	no	—
174	#476	—	5	8	no	—
175	C₂×#106	—	5	1	no	—
176	C₂×#106	—	5	1	no	—
177	C₂×C₄⋊C₈	—	5	1	no	—
178	C₂×#102	—	5	1	no	—
179	C₂×#102	C₃×D₅	1	1	yes	characteristic
180	C₂²×C₃×C₅	—	2	4	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	8	no	—
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
185	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
186	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
190	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₃×Dic₅	—	2	2	no	—
193	C₃×Dic₅	—	4	2	no	—
194	C₃×Dic₅	—	4	2	no	—
195	C₃×Dic₅	C₂×SD₁₆	1	4	yes	—
196	C₂⁴×C₃	—	2	1	no	—
197	C₂×C₃×Q₈	—	10	4	no	—
198	C₂×C₃×Q₈	—	20	4	no	—
199	C₂×C₃×D₄	—	2	1	no	—
200	C₂×C₃×D₄	—	2	2	no	—
201	C₂×C₃×D₄	Dic₁₀	1	4	yes	complemented
202	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	5	1	no	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	10	4	no	—
207	C₂²×C₃×C₄	—	10	1	no	—
208	C₂²×C₃×C₄	—	10	1	no	—
209	C₂²×C₃×C₄	—	20	4	no	—
210	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	10	2	no	—
214	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
215	C₃×C₄⋊C₄	—	2	1	no	—
216	C₃×C₄⋊C₄	—	5	2	no	—
217	C₃×C₄⋊C₄	—	5	2	no	—
218	C₃×C₄⋊C₄	—	10	4	no	—
219	C₃×C₄⋊C₄	—	10	1	no	—
220	C₃×C₄⋊C₄	—	10	1	no	—
221	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
222	C₃×C₂²⋊C₄	—	10	4	no	—
223	C₃×C₄²	—	5	2	no	—
224	C₃×C₄²	—	5	2	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	—	4	2	no	—
229	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	C₂×C₃×Q₈	1	4	yes	complemented
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
237	C₂×C₄×C₅	C₃×#41	1	2	yes	—
238	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
239	C₂×Dic₅	—	2	2	no	—
240	C₂×Dic₅	—	2	2	no	—
241	C₂×Dic₅	—	2	2	no	—
242	C₂×Dic₅	—	4	2	no	—
243	C₂×Dic₅	—	4	2	no	—
244	C₂×Dic₅	—	4	8	no	—
245	C₂×Dic₅	C₃×SD₁₆	1	4	yes	—
246	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
247	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
248	Dic₁₀	—	4	8	no	—
249	C₅×C₈	—	2	2	no	—
250	#168	—	2	2	no	—
251	C₂²×Q₈	—	10	1	no	—
252	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
253	C₂³×C₄	—	10	1	no	—
254	C₂²×C₈	—	5	1	no	—
255	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
256	C₄⋊Q₈	—	5	4	no	—
257	C₄⋊Q₈	—	10	2	no	—
258	C₄×D₄	—	5	4	no	—
259	C₄×D₄	—	10	2	no	—
260	C₂×C₄⋊C₄	—	5	1	no	—
261	C₂×C₄⋊C₄	—	5	1	no	—
262	C₂×C₄⋊C₄	—	10	1	no	—
263	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	10	1	no	—
265	C₂×C₄²	—	5	1	no	—
266	#106	—	5	4	no	—
267	#106	—	5	4	no	—
268	C₄⋊C₈	—	5	4	no	—
269	#102	—	5	4	no	—
270	#102	C₂×C₃×D₅	1	4	yes	—
271	C₂×C₃×C₅	—	4	4	no	—
272	C₂×C₃×C₅	#476	1	4	yes	complemented
273	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	4	2	no	—
279	C₂³×C₃	—	4	2	no	—
280	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
281	C₃×Q₈	—	20	8	no	—
282	C₃×D₄	—	2	2	no	—
283	C₃×D₄	—	2	4	no	—
284	C₃×D₄	C₂×Dic₁₀	1	4	yes	complemented
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	5	4	no	—
289	C₂×C₃×C₄	—	5	2	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	2	no	—
293	C₂×C₃×C₄	—	20	8	no	—
294	C₂×C₃×C₄	—	20	2	no	—
295	C₂×C₃×C₄	—	20	2	no	—
296	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
297	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	#711	1	2	yes	—
299	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
300	C₃×C₈	—	2	2	no	—
301	C₃×C₈	—	10	2	no	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	8	no	—
306	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
307	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
308	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
309	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
312	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
313	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
314	Dic₅	—	2	2	no	—
315	Dic₅	—	4	2	no	—
316	Dic₅	—	4	2	no	—
317	Dic₅	C₂×C₃×SD₁₆	1	4	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	—	10	4	no	—
320	C₂×Q₈	—	20	4	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	C₃×Dic₁₀	1	4	yes	complemented
324	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	10	4	no	—
329	C₂²×C₄	—	10	1	no	—
330	C₂²×C₄	—	10	1	no	—
331	C₂²×C₄	—	20	4	no	—
332	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	5	2	no	—
335	C₂×C₈	—	10	2	no	—
336	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	5	2	no	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	10	4	no	—
341	C₄⋊C₄	—	10	1	no	—
342	C₄⋊C₄	—	10	1	no	—
343	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
344	C₂²⋊C₄	—	10	4	no	—
345	C₄²	—	5	2	no	—
346	C₄²	—	5	2	no	—
347	C₃×C₅	C₂×#476	1	1	yes	characteristic, complemented, Hall
348	C₂²×C₃	—	2	4	no	—
349	C₂²×C₃	—	4	8	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	#4024	1	2	yes	—
353	C₂²×C₃	#4057	1	2	yes	—
354	C₂²×C₃	D₅×SD₁₆	1	2	yes	—
355	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	—	5	4	no	—
358	C₃×C₄	—	10	2	no	—
359	C₃×C₄	—	20	2	no	—
360	C₃×C₄	—	20	2	no	—
361	C₃×C₄	#4024	1	2	yes	—
362	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
363	C₃×C₄	C₂×#711	1	1	yes	characteristic
364	C₂×C₅	—	4	4	no	—
365	C₂×C₅	C₃×#476	1	4	yes	complemented
366	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
367	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
368	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂³	—	2	2	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
374	Q₈	—	20	8	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	4	no	—
377	D₄	C₂×C₃×Dic₁₀	1	4	yes	complemented
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	4	no	—
382	C₂×C₄	—	5	2	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	20	8	no	—
387	C₂×C₄	—	20	2	no	—
388	C₂×C₄	—	20	2	no	—
389	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
390	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
391	C₂×C₄	C₃×#711	1	2	yes	—
392	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	10	2	no	—
395	C₂×C₃	—	4	4	no	—
396	C₂×C₃	#65050	1	4	yes	direct product factor
397	C₂×C₃	C₂×#4024	1	1	yes	characteristic
398	C₂×C₃	C₂×#4057	1	1	yes	characteristic
399	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
400	C₅	C₂×C₃×#476	1	1	yes	characteristic, complemented, Sylow
401	C₂²	—	2	4	no	—
402	C₂²	—	4	8	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	C₃×#4024	1	2	yes	—
406	C₂²	C₃×#4057	1	2	yes	—
407	C₂²	C₃×D₅×SD₁₆	1	2	yes	—
408	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
409	C₄	—	4	2	no	—
410	C₄	—	5	4	no	—
411	C₄	—	10	2	no	—
412	C₄	—	20	2	no	—
413	C₄	—	20	2	no	—
414	C₄	C₃×#4024	1	2	yes	—
415	C₄	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
416	C₄	C₂×C₃×#711	1	1	yes	characteristic
417	C₃	C₂×#65050	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	4	4	no	—
419	C₂	C₃×#65050	1	4	yes	direct product factor
420	C₂	C₂×C₃×#4024	1	1	yes	characteristic
421	C₂	C₂×C₃×#4057	1	1	yes	characteristic
422	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₃×#102	D₅
hypocenter	C₅	C₂×C₃×#476
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4034	C₂	semidirect
5. C₂×C₃×#3949	C₂	semidirect
6. C₂×C₃×#3946	C₂	semidirect
7. C₂×C₃×#3940	C₂	semidirect
8. C₃×#65050	C₂	direct (N × H)
9. C₂×#65050	C₃	direct (N × H)
24. C₃×#4034	C₂²	semidirect
27. C₃×#3949	C₂²	semidirect
28. C₃×#3946	C₂²	semidirect
29. C₃×#3940	C₂²	semidirect
32. C₂×#4034	C₂×C₃	semidirect
35. C₂×#3949	C₂×C₃	semidirect
36. C₂×#3946	C₂×C₃	semidirect
37. C₂×#3940	C₂×C₃	semidirect
38. #65050	C₂×C₃	direct (N × H)
42. C₂×C₃×C₅×D₄	Q₈	semidirect
90. #4034	C₂²×C₃	semidirect
93. #3949	C₂²×C₃	semidirect
94. #3946	C₂²×C₃	semidirect
95. #3940	C₂²×C₃	semidirect
104. C₃×C₅×D₄	C₂×Q₈	semidirect
146. C₂×C₅×D₄	C₃×Q₈	semidirect
201. C₂×C₃×D₄	Dic₁₀	semidirect
232. C₅×D₄	C₂×C₃×Q₈	semidirect
272. C₂×C₃×C₅	#476	semidirect
284. C₃×D₄	C₂×Dic₁₀	semidirect
323. C₂×D₄	C₃×Dic₁₀	semidirect
347. C₃×C₅	C₂×#476	semidirect
365. C₂×C₅	C₃×#476	semidirect
377. D₄	C₂×C₃×Dic₁₀	semidirect
396. C₂×C₃	#65050	direct (N × H)
400. C₅	C₂×C₃×#476	semidirect
417. C₃	C₂×#65050	direct (N × H)
419. C₂	C₃×#65050	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×D₄×Dic₅	2
C₂×C₃×#4034	2
C₂×C₃×C₅×#102	2
C₂×C₃×#3964	2
C₂×C₃×#3949	2
C₂×C₃×#3946	2
C₂×C₃×#3940	2
C₃×#65050	2
C₂×#65050	3
C₂×C₃×#476	5

Subgroups — C2×C3×#65050 #14429866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65050 #14429866