Subgroups — C₂×C₃×#65516 #14423296

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#688	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic
4	C₃×#65516	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3967	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65516	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	—	2	8	no	—
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₂²×C₃×C₅×Q₈	—	2	2	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	4	yes	complemented
13	C₂³×C₃×C₄×C₅	—	2	1	no	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
16	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
17	C₂×C₃×#688	—	2	8	no	—
18	C₂×C₃×#688	C₂²	1	8	yes	complemented
19	C₃×#4076	—	2	2	no	—
20	C₃×#4076	C₂²	1	4	yes	—
21	C₂×C₃×#685	—	2	1	no	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	2	yes	—
24	C₃×#3967	C₂²	1	8	yes	complemented
25	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
26	C₂×C₃×#448	—	5	1	no	maximal, Hall
27	C₂³×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×#688	C₂×C₃	1	2	yes	complemented
29	C₂×#4076	C₂×C₃	1	1	yes	characteristic
30	#65516	C₂×C₃	1	8	yes	direct product factor
31	C₂×#3967	C₂×C₃	1	2	yes	complemented
32	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂³×C₃×D₅	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	—	2	16	no	—
36	C₂×C₃×C₅×Q₈	—	2	8	no	—
37	C₂×C₃×C₅×Q₈	—	2	16	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	4	no	—
41	C₂×C₃×C₅×Q₈	D₄	1	8	yes	complemented
42	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	—	2	8	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
52	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
53	C₂²×C₃×Dic₅	—	2	1	no	—
54	C₂×C₃×D₂₀	—	2	4	no	—
55	C₂×C₃×D₂₀	—	2	1	no	—
56	C₂×C₃×D₂₀	C₂³	1	2	yes	—
57	C₃×#688	—	2	16	no	—
58	C₃×#685	—	2	4	no	—
59	C₃×C₄⋊Dic₅	—	2	1	no	—
60	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
61	C₂×C₃×#168	—	2	4	no	—
62	C₂×C₃×#168	C₂³	1	4	yes	—
63	C₂³×C₃×Q₈	D₅	1	1	yes	characteristic, complemented
64	C₂²×C₃×SD₁₆	—	5	2	no	—
65	C₂×C₃×#121	—	5	1	no	—
66	C₃×#448	—	5	8	no	—
67	C₂×C₃×#103	—	5	2	no	—
68	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
69	C₂²×C₅×Q₈	—	2	8	no	—
70	C₂²×C₅×Q₈	—	2	1	no	—
71	C₂²×C₅×Q₈	—	2	2	no	—
72	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
73	C₂²×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₂²⋊D₅	—	2	1	no	—
77	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
78	C₂×#688	—	2	8	no	—
79	C₂×#688	C₂²×C₃	1	8	yes	complemented
80	#4076	—	2	2	no	—
81	#4076	C₂²×C₃	1	4	yes	—
82	C₂×#685	—	2	1	no	—
83	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂²×#168	C₂²×C₃	1	2	yes	—
85	#3967	C₂²×C₃	1	8	yes	complemented
86	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
87	C₂×#448	—	5	1	no	Sylow
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	SD₁₆	1	4	yes	complemented
91	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₃×D₅	—	2	2	no	—
94	C₂²×C₃×D₅	—	4	2	no	—
95	C₂²×C₃×D₅	—	4	2	no	—
96	C₂²×C₃×D₅	—	4	2	no	—
97	C₃×C₅×Q₈	—	2	16	no	—
98	C₃×C₅×Q₈	—	2	8	no	—
99	C₃×C₅×Q₈	—	2	4	no	—
100	C₃×C₅×Q₈	C₂×D₄	1	8	yes	complemented
101	C₂×C₃×C₄×C₅	—	2	16	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₃×C₂²⋊D₅	—	4	8	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	4	2	no	—
114	C₃×D₂₀	—	2	4	no	—
115	C₃×D₂₀	—	4	2	no	—
116	C₃×#168	—	2	4	no	—
117	C₂²×C₃×Q₈	—	2	8	no	—
118	C₂²×C₃×Q₈	—	2	2	no	—
119	C₂²×C₃×Q₈	—	2	1	no	—
120	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
121	C₂²×C₃×Q₈	C₂×D₅	1	4	yes	complemented
122	C₂²×C₃×D₄	—	5	1	no	—
123	C₂²×C₃×D₄	—	10	1	no	—
124	C₂³×C₃×C₄	—	2	1	no	—
125	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
126	C₂×C₃×SD₁₆	—	5	8	no	—
127	C₂×C₃×SD₁₆	—	10	8	no	—
128	C₂²×C₃×C₈	—	5	2	no	—
129	C₃×#121	—	5	4	no	—
130	C₃×#121	—	10	2	no	—
131	C₂×C₃×C₄⋊C₄	—	5	1	no	—
132	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
133	C₃×#103	—	5	8	no	—
134	C₃×C₂²⋊C₈	—	5	4	no	—
135	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
136	C₂³×D₅	—	2	1	no	—
137	C₂×C₅×Q₈	—	2	16	no	—
138	C₂×C₅×Q₈	—	2	8	no	—
139	C₂×C₅×Q₈	—	2	16	no	—
140	C₂×C₅×Q₈	—	2	4	no	—
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	2	4	no	—
143	C₂×C₅×Q₈	C₃×D₄	1	8	yes	complemented
144	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
145	C₂²×C₄×C₅	—	2	8	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₂²⋊D₅	—	2	4	no	—
154	C₂×C₂²⋊D₅	—	4	4	no	—
155	C₂²×Dic₅	—	2	1	no	—
156	C₂×D₂₀	—	2	4	no	—
157	C₂×D₂₀	—	2	1	no	—
158	C₂×D₂₀	C₂³×C₃	1	2	yes	—
159	#688	—	2	16	no	—
160	#685	—	2	4	no	—
161	C₄⋊Dic₅	—	2	1	no	—
162	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
163	C₂×#168	—	2	4	no	—
164	C₂×#168	C₂³×C₃	1	4	yes	—
165	C₂³×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
166	C₂²×SD₁₆	—	5	2	no	—
167	C₂×#121	—	5	1	no	—
168	#448	—	5	8	no	—
169	C₂×#103	—	5	2	no	—
170	C₂×C₂²⋊C₈	—	5	1	no	—
171	C₂²×C₃×C₅	—	2	2	no	—
172	C₂²×C₃×C₅	—	2	2	no	—
173	C₂²×C₃×C₅	—	2	8	no	—
174	C₂²×C₃×C₅	#120	1	2	yes	—
175	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
176	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
177	C₂²×C₃×C₅	#137	1	2	yes	—
178	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₃×D₅	—	4	2	no	—
180	C₂×C₃×D₅	—	4	2	no	—
181	C₂×C₃×D₅	—	4	2	no	—
182	C₂×C₃×D₅	—	8	4	no	—
183	C₃×C₄×C₅	—	2	8	no	—
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	#120	1	2	yes	—
186	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
187	C₃×Dic₅	—	4	2	no	—
188	C₂⁴×C₃	—	10	1	no	—
189	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
190	C₂×C₃×Q₈	—	2	16	no	—
191	C₂×C₃×Q₈	—	2	8	no	—
192	C₂×C₃×Q₈	—	2	16	no	—
193	C₂×C₃×Q₈	—	2	4	no	—
194	C₂×C₃×Q₈	—	2	2	no	—
195	C₂×C₃×Q₈	—	2	4	no	—
196	C₂×C₃×Q₈	C₂²⋊D₅	1	8	yes	complemented
197	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
198	C₂×C₃×D₄	—	5	2	no	—
199	C₂×C₃×D₄	—	10	4	no	—
200	C₂×C₃×D₄	—	10	4	no	—
201	C₂×C₃×D₄	—	10	1	no	—
202	C₂×C₃×D₄	—	20	4	no	—
203	C₂²×C₃×C₄	—	2	8	no	—
204	C₂²×C₃×C₄	—	2	4	no	—
205	C₂²×C₃×C₄	—	2	2	no	—
206	C₂²×C₃×C₄	—	2	4	no	—
207	C₂²×C₃×C₄	—	10	1	no	—
208	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
212	C₃×SD₁₆	—	10	16	no	—
213	C₂×C₃×C₈	—	5	4	no	—
214	C₂×C₃×C₈	—	10	4	no	—
215	C₃×C₄⋊C₄	—	5	2	no	—
216	C₃×C₄⋊C₄	—	10	1	no	—
217	C₃×C₂²⋊C₄	—	10	4	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	C₃×SD₁₆	1	4	yes	complemented
221	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
222	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂²×D₅	—	2	2	no	—
224	C₂²×D₅	—	4	2	no	—
225	C₂²×D₅	—	4	2	no	—
226	C₂²×D₅	—	4	2	no	—
227	C₅×Q₈	—	2	16	no	—
228	C₅×Q₈	—	2	8	no	—
229	C₅×Q₈	—	2	4	no	—
230	C₅×Q₈	C₂×C₃×D₄	1	8	yes	complemented
231	C₂×C₄×C₅	—	2	16	no	—
232	C₂×C₄×C₅	—	2	8	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	4	no	—
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	4	yes	—
240	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
241	C₂²⋊D₅	—	4	8	no	—
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	4	2	no	—
244	D₂₀	—	2	4	no	—
245	D₂₀	—	4	2	no	—
246	#168	—	2	4	no	—
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
251	C₂²×Q₈	C₂×C₃×D₅	1	4	yes	complemented
252	C₂²×D₄	—	5	1	no	—
253	C₂²×D₄	—	10	1	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
256	C₂×SD₁₆	—	5	8	no	—
257	C₂×SD₁₆	—	10	8	no	—
258	C₂²×C₈	—	5	2	no	—
259	#121	—	5	4	no	—
260	#121	—	10	2	no	—
261	C₂×C₄⋊C₄	—	5	1	no	—
262	C₂×C₂²⋊C₄	—	10	1	no	—
263	#103	—	5	8	no	—
264	C₂²⋊C₈	—	5	4	no	—
265	C₂×C₃×C₅	—	2	4	no	—
266	C₂×C₃×C₅	#448	1	4	yes	complemented
267	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
270	C₃×D₅	—	8	2	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	10	2	no	—
274	C₂³×C₃	—	20	2	no	—
275	C₂³×C₃	—	20	2	no	—
276	C₂³×C₃	—	20	2	no	—
277	C₂³×C₃	#688	1	4	yes	complemented
278	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
279	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
280	C₃×Q₈	—	2	16	no	—
281	C₃×Q₈	—	2	8	no	—
282	C₃×Q₈	—	2	4	no	—
283	C₃×Q₈	C₂×C₂²⋊D₅	1	8	yes	complemented
284	C₃×D₄	—	10	4	no	—
285	C₃×D₄	—	20	8	no	—
286	C₃×D₄	—	20	2	no	—
287	C₂×C₃×C₄	—	2	16	no	—
288	C₂×C₃×C₄	—	2	8	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	20	2	no	—
295	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
298	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
299	C₃×C₈	—	10	4	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	8	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	C₃×#120	1	2	yes	—
304	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
305	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
306	C₂²×C₅	C₃×#137	1	2	yes	—
307	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
308	C₂×D₅	—	4	2	no	—
309	C₂×D₅	—	4	2	no	—
310	C₂×D₅	—	4	2	no	—
311	C₂×D₅	—	8	4	no	—
312	C₄×C₅	—	2	8	no	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	C₃×#120	1	2	yes	—
315	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
316	Dic₅	—	4	2	no	—
317	C₂⁴	—	10	1	no	—
318	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
319	C₂×Q₈	—	2	16	no	—
320	C₂×Q₈	—	2	8	no	—
321	C₂×Q₈	—	2	16	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	C₃×C₂²⋊D₅	1	8	yes	complemented
326	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
327	C₂×D₄	—	5	2	no	—
328	C₂×D₄	—	10	4	no	—
329	C₂×D₄	—	10	4	no	—
330	C₂×D₄	—	10	1	no	—
331	C₂×D₄	—	20	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	10	1	no	—
337	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
338	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
339	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
340	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
341	SD₁₆	—	10	16	no	—
342	C₂×C₈	—	5	4	no	—
343	C₂×C₈	—	10	4	no	—
344	C₄⋊C₄	—	5	2	no	—
345	C₄⋊C₄	—	10	1	no	—
346	C₂²⋊C₄	—	10	4	no	—
347	C₃×C₅	C₂×#448	1	1	yes	characteristic, complemented, Hall
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	8	no	—
351	C₂²×C₃	—	20	2	no	—
352	C₂²×C₃	—	20	2	no	—
353	C₂²×C₃	—	20	2	no	—
354	C₂²×C₃	—	40	4	no	—
355	C₂²×C₃	C₂×#688	1	2	yes	—
356	C₂²×C₃	C₂×#688	1	4	yes	complemented
357	C₂²×C₃	#4088	1	2	yes	—
358	C₂²×C₃	#4099	1	2	yes	—
359	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
360	C₃×C₄	—	2	8	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	20	2	no	—
363	C₃×C₄	#4099	1	2	yes	—
364	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
365	C₂×C₅	—	2	4	no	—
366	C₂×C₅	C₃×#448	1	4	yes	complemented
367	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
368	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
369	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
370	D₅	—	8	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	10	2	no	—
374	C₂³	—	20	2	no	—
375	C₂³	—	20	2	no	—
376	C₂³	—	20	2	no	—
377	C₂³	C₃×#688	1	4	yes	complemented
378	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
379	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
380	Q₈	—	2	16	no	—
381	Q₈	—	2	8	no	—
382	Q₈	—	2	4	no	—
383	Q₈	C₂×C₃×C₂²⋊D₅	1	8	yes	complemented
384	D₄	—	10	4	no	—
385	D₄	—	20	8	no	—
386	D₄	—	20	2	no	—
387	C₂×C₄	—	2	16	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	20	2	no	—
395	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
396	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
397	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
398	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
399	C₈	—	10	4	no	—
400	C₂×C₃	—	2	4	no	—
401	C₂×C₃	—	40	2	no	—
402	C₂×C₃	#65516	1	4	yes	direct product factor
403	C₂×C₃	C₂²×#688	1	1	yes	characteristic
404	C₂×C₃	C₂×#4088	1	1	yes	characteristic
405	C₂×C₃	C₂×#4099	1	1	yes	characteristic
406	C₅	C₂×C₃×#448	1	1	yes	characteristic, complemented, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	8	no	—
410	C₂²	—	20	2	no	—
411	C₂²	—	20	2	no	—
412	C₂²	—	20	2	no	—
413	C₂²	—	40	4	no	—
414	C₂²	C₂×C₃×#688	1	2	yes	—
415	C₂²	C₂×C₃×#688	1	4	yes	complemented
416	C₂²	C₃×#4088	1	2	yes	—
417	C₂²	C₃×#4099	1	2	yes	—
418	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
419	C₄	—	2	8	no	—
420	C₄	—	2	2	no	—
421	C₄	—	20	2	no	—
422	C₄	C₃×#4099	1	2	yes	—
423	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
424	C₃	C₂×#65516	1	1	yes	characteristic, direct product factor, Sylow
425	C₂	—	2	4	no	—
426	C₂	—	40	2	no	—
427	C₂	C₃×#65516	1	4	yes	direct product factor
428	C₂	C₂²×C₃×#688	1	1	yes	characteristic
429	C₂	C₂×C₃×#4088	1	1	yes	characteristic
430	C₂	C₂×C₃×#4099	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂³×C₃×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×#4076	C₂
hypercenter	C₂³×C₃×Q₈	D₅
hypocenter	C₅	C₂×C₃×#448
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×Q₈	C₂	semidirect
2. C₂²×C₃×#688	C₂	semidirect
4. C₃×#65516	C₂	direct (N × H)
5. C₂×C₃×#3967	C₂	semidirect
6. C₂×C₃×C₂²⋊#168	C₂	semidirect
7. C₂×#65516	C₃	direct (N × H)
12. C₂²×C₃×C₅×Q₈	C₂²	semidirect
18. C₂×C₃×#688	C₂²	semidirect
24. C₃×#3967	C₂²	semidirect
25. C₃×C₂²⋊#168	C₂²	semidirect
27. C₂³×C₅×Q₈	C₂×C₃	semidirect
28. C₂²×#688	C₂×C₃	semidirect
30. #65516	C₂×C₃	direct (N × H)
31. C₂×#3967	C₂×C₃	semidirect
32. C₂×C₂²⋊#168	C₂×C₃	semidirect
41. C₂×C₃×C₅×Q₈	D₄	semidirect
63. C₂³×C₃×Q₈	D₅	semidirect
73. C₂²×C₅×Q₈	C₂²×C₃	semidirect
79. C₂×#688	C₂²×C₃	semidirect
85. #3967	C₂²×C₃	semidirect
86. C₂²⋊#168	C₂²×C₃	semidirect
90. C₂³×C₃×C₅	SD₁₆	semidirect
100. C₃×C₅×Q₈	C₂×D₄	semidirect
121. C₂²×C₃×Q₈	C₂×D₅	semidirect
143. C₂×C₅×Q₈	C₃×D₄	semidirect
165. C₂³×Q₈	C₃×D₅	semidirect
176. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
196. C₂×C₃×Q₈	C₂²⋊D₅	semidirect
220. C₂³×C₅	C₃×SD₁₆	semidirect
230. C₅×Q₈	C₂×C₃×D₄	semidirect
251. C₂²×Q₈	C₂×C₃×D₅	semidirect
266. C₂×C₃×C₅	#448	semidirect
277. C₂³×C₃	#688	semidirect
283. C₃×Q₈	C₂×C₂²⋊D₅	semidirect
305. C₂²×C₅	C₂×C₃×SD₁₆	semidirect
325. C₂×Q₈	C₃×C₂²⋊D₅	semidirect
347. C₃×C₅	C₂×#448	semidirect
356. C₂²×C₃	C₂×#688	semidirect
366. C₂×C₅	C₃×#448	semidirect
377. C₂³	C₃×#688	semidirect
383. Q₈	C₂×C₃×C₂²⋊D₅	semidirect
402. C₂×C₃	#65516	direct (N × H)
406. C₅	C₂×C₃×#448	semidirect
415. C₂²	C₂×C₃×#688	semidirect
424. C₃	C₂×#65516	direct (N × H)
427. C₂	C₃×#65516	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×Q₈	2
C₂²×C₃×#688	2
C₂×C₃×#4076	2
C₃×#65516	2
C₂×C₃×#3967	2
C₂×C₃×C₂²⋊#168	2
C₂×#65516	3
C₂×C₃×#448	5

Subgroups — C2×C3×#65516 #14423296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65516 #14423296