Subgroups — C₂×C₃×#65200 #14478321

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3958	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65200	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#3932	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65200	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#711	—	2	1	no	—
11	C₂×C₃×D₄×D₅	—	2	1	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×#687	—	2	1	no	—
15	C₂×C₃×#686	—	2	1	no	—
16	C₃×#4058	—	2	2	no	—
17	C₃×#4058	C₂²	1	4	yes	complemented
18	C₃×D₅×D₈	—	2	2	no	—
19	C₃×D₅×D₈	C₂²	1	4	yes	complemented
20	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×D₁₆	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×#3959	C₂²	1	4	yes	complemented
26	C₃×#3958	C₂²	1	4	yes	complemented
27	C₂×C₃×#672	C₂²	1	1	yes	characteristic, complemented
28	C₃×#3932	C₂²	1	4	yes	complemented
29	C₃×#3930	C₂²	1	4	yes	complemented
30	C₂×C₃×#509	—	5	1	no	maximal, Hall
31	C₂×#4058	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×D₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3959	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3958	C₂×C₃	1	1	yes	characteristic, complemented
36	#65200	C₂×C₃	1	8	yes	direct product factor
37	C₂×#3932	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#3930	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	—	4	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
43	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
44	C₂²×C₃×Dic₅	—	4	1	no	—
45	C₃×#711	—	2	4	no	—
46	C₃×#711	—	4	2	no	—
47	C₃×D₄×D₅	—	2	4	no	—
48	C₃×D₄×D₅	—	4	2	no	—
49	C₂×C₃×D₂₀	—	2	1	no	—
50	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
51	C₂×C₃×Dic₁₀	—	2	1	no	—
52	C₃×C₅×D₈	—	2	1	no	—
53	C₃×C₅×D₈	—	2	1	no	—
54	C₃×C₅×D₈	C₂³	1	2	yes	—
55	C₃×C₅×D₈	C₂³	1	2	yes	complemented
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₃×#687	—	2	4	no	—
58	C₃×#686	—	2	4	no	—
59	C₂×C₃×#168	D₄	1	1	yes	characteristic
60	C₃×Dic₂₀	—	2	1	no	—
61	C₃×Dic₂₀	C₂³	1	2	yes	complemented
62	C₃×D₄₀	—	2	1	no	—
63	C₃×D₄₀	C₂³	1	2	yes	—
64	C₃×C₈×D₅	D₄	1	2	yes	—
65	C₃×C₈×D₅	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	complemented
67	C₃×#672	C₂³	1	2	yes	complemented
68	C₂×C₃×#135	—	5	1	no	—
69	C₂²×C₃×D₈	—	5	1	no	—
70	C₃×#509	—	5	8	no	—
71	C₂×C₃×SD₃₂	—	5	1	no	—
72	C₂×C₃×SD₃₂	—	5	1	no	—
73	C₂×C₃×D₁₆	—	5	1	no	—
74	C₂×C₃×D₁₆	D₅	1	1	yes	characteristic, complemented
75	C₂×C₃×M₃₂	—	5	1	no	—
76	C₂×#711	—	2	1	no	—
77	C₂×D₄×D₅	—	2	1	no	—
78	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂×#687	—	2	1	no	—
81	C₂×#686	—	2	1	no	—
82	#4058	—	2	2	no	—
83	#4058	C₂²×C₃	1	4	yes	complemented
84	D₅×D₈	—	2	2	no	—
85	D₅×D₈	C₂²×C₃	1	4	yes	complemented
86	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×D₁₆	C₂²×C₃	1	4	yes	complemented
90	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
91	#3959	C₂²×C₃	1	4	yes	complemented
92	#3958	C₂²×C₃	1	4	yes	complemented
93	C₂×#672	C₂²×C₃	1	1	yes	characteristic, complemented
94	#3932	C₂²×C₃	1	4	yes	complemented
95	#3930	C₂²×C₃	1	4	yes	complemented
96	C₂×#509	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂³×C₃×C₅	—	4	1	no	—
99	C₂²×C₃×D₅	—	4	1	no	—
100	C₂²×C₃×D₅	—	4	4	no	—
101	C₂²×C₃×D₅	—	8	4	no	—
102	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
103	C₃×C₅×D₄	—	2	2	no	—
104	C₃×C₅×D₄	—	2	2	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₃×C₅×D₄	—	4	1	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₂²⋊D₅	—	4	4	no	—
109	C₃×C₂²⋊D₅	—	4	4	no	—
110	C₂×C₃×Dic₅	—	4	1	no	—
111	C₂×C₃×Dic₅	—	4	4	no	—
112	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
113	C₃×D₂₀	—	2	2	no	—
114	C₃×D₂₀	—	4	1	no	—
115	C₃×C₄×D₅	D₈	1	2	yes	—
116	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
117	C₃×Dic₁₀	—	2	2	no	—
118	C₃×Dic₁₀	—	4	1	no	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₃×#168	C₂×D₄	1	2	yes	—
122	C₂×C₃×#41	—	10	1	no	—
123	C₂²×C₃×D₄	—	10	1	no	—
124	C₃×#135	—	5	4	no	—
125	C₃×#135	—	10	2	no	—
126	C₂×C₃×Q₁₆	—	5	1	no	—
127	C₂×C₃×SD₁₆	—	10	1	no	—
128	C₂×C₃×D₈	—	5	4	no	—
129	C₂×C₃×D₈	—	5	1	no	—
130	C₂×C₃×D₈	—	10	2	no	—
131	C₂×C₃×D₈	—	10	1	no	—
132	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₃×SD₃₂	—	5	4	no	—
136	C₃×SD₃₂	—	5	4	no	—
137	C₃×D₁₆	—	5	4	no	—
138	C₃×D₁₆	C₂×D₅	1	4	yes	complemented
139	C₃×M₃₂	—	5	4	no	—
140	C₂×C₃×C₁₆	—	5	1	no	—
141	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
142	C₂³×D₅	—	4	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₂²⋊D₅	—	4	1	no	—
146	C₂×C₂²⋊D₅	—	4	1	no	—
147	C₂²×Dic₅	—	4	1	no	—
148	#711	—	2	4	no	—
149	#711	—	4	2	no	—
150	D₄×D₅	—	2	4	no	—
151	D₄×D₅	—	4	2	no	—
152	C₂×D₂₀	—	2	1	no	—
153	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
154	C₂×Dic₁₀	—	2	1	no	—
155	C₅×D₈	—	2	1	no	—
156	C₅×D₈	—	2	1	no	—
157	C₅×D₈	C₂³×C₃	1	2	yes	—
158	C₅×D₈	C₂³×C₃	1	2	yes	complemented
159	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
160	#687	—	2	4	no	—
161	#686	—	2	4	no	—
162	C₂×#168	C₃×D₄	1	1	yes	characteristic
163	Dic₂₀	—	2	1	no	—
164	Dic₂₀	C₂³×C₃	1	2	yes	complemented
165	D₄₀	—	2	1	no	—
166	D₄₀	C₂³×C₃	1	2	yes	—
167	C₈×D₅	C₃×D₄	1	2	yes	—
168	C₈×D₅	C₂³×C₃	1	2	yes	—
169	C₅×C₁₆	C₂³×C₃	1	2	yes	complemented
170	#672	C₂³×C₃	1	2	yes	complemented
171	C₂×#135	—	5	1	no	—
172	C₂²×D₈	—	5	1	no	—
173	#509	—	5	8	no	—
174	C₂×SD₃₂	—	5	1	no	—
175	C₂×SD₃₂	—	5	1	no	—
176	C₂×D₁₆	—	5	1	no	—
177	C₂×D₁₆	C₃×D₅	1	1	yes	characteristic, complemented
178	C₂×M₃₂	—	5	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	8	2	no	—
182	C₂²×C₃×C₅	—	8	2	no	—
183	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
184	C₂×C₃×D₅	—	2	2	no	—
185	C₂×C₃×D₅	—	4	2	no	—
186	C₂×C₃×D₅	—	8	8	no	—
187	C₂×C₃×D₅	—	8	2	no	—
188	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
189	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
190	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₃×Dic₅	—	4	2	no	—
192	C₃×Dic₅	C₂×D₈	1	2	yes	—
193	C₂⁴×C₃	—	20	1	no	—
194	C₃×#41	—	10	4	no	—
195	C₃×#41	—	20	2	no	—
196	C₂×C₃×Q₈	—	10	1	no	—
197	C₂×C₃×D₄	—	2	1	no	—
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	—	10	4	no	—
200	C₂×C₃×D₄	—	10	1	no	—
201	C₂×C₃×D₄	—	20	2	no	—
202	C₂×C₃×D₄	—	20	1	no	—
203	C₂×C₃×D₄	—	20	1	no	—
204	C₂²×C₃×C₄	—	5	1	no	—
205	C₂²×C₃×C₄	—	20	1	no	—
206	C₃×Q₁₆	—	5	2	no	—
207	C₃×Q₁₆	—	10	1	no	—
208	C₃×SD₁₆	—	10	4	no	—
209	C₃×D₈	—	2	1	no	—
210	C₃×D₈	—	2	1	no	—
211	C₃×D₈	—	5	2	no	—
212	C₃×D₈	—	10	4	no	—
213	C₃×D₈	—	10	1	no	—
214	C₃×D₈	C₂²×D₅	1	2	yes	—
215	C₃×D₈	C₂²×D₅	1	2	yes	complemented
216	C₂×C₃×C₈	—	5	1	no	—
217	C₂×C₃×C₈	—	5	2	no	—
218	C₂×C₃×C₈	—	5	2	no	—
219	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
220	C₃×C₁₆	—	5	2	no	—
221	C₃×C₁₆	C₂²×D₅	1	2	yes	complemented
222	C₂³×C₅	—	4	1	no	—
223	C₂³×C₅	—	4	1	no	—
224	C₂²×D₅	—	4	1	no	—
225	C₂²×D₅	—	4	4	no	—
226	C₂²×D₅	—	8	4	no	—
227	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	2	2	no	—
230	C₅×D₄	—	4	1	no	—
231	C₅×D₄	—	4	1	no	—
232	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂²⋊D₅	—	4	4	no	—
234	C₂²⋊D₅	—	4	4	no	—
235	C₂×Dic₅	—	4	1	no	—
236	C₂×Dic₅	—	4	4	no	—
237	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
238	D₂₀	—	2	2	no	—
239	D₂₀	—	4	1	no	—
240	C₄×D₅	C₃×D₈	1	2	yes	—
241	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
242	Dic₁₀	—	2	2	no	—
243	Dic₁₀	—	4	1	no	—
244	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
245	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
246	#168	C₂×C₃×D₄	1	2	yes	—
247	C₂×#41	—	10	1	no	—
248	C₂²×D₄	—	10	1	no	—
249	#135	—	5	4	no	—
250	#135	—	10	2	no	—
251	C₂×Q₁₆	—	5	1	no	—
252	C₂×SD₁₆	—	10	1	no	—
253	C₂×D₈	—	5	4	no	—
254	C₂×D₈	—	5	1	no	—
255	C₂×D₈	—	10	2	no	—
256	C₂×D₈	—	10	1	no	—
257	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
258	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
259	C₂²×C₈	—	5	1	no	—
260	SD₃₂	—	5	4	no	—
261	SD₃₂	—	5	4	no	—
262	D₁₆	—	5	4	no	—
263	D₁₆	C₂×C₃×D₅	1	4	yes	complemented
264	M₃₂	—	5	4	no	—
265	C₂×C₁₆	—	5	1	no	—
266	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
267	C₂×C₃×C₅	—	8	2	no	—
268	C₂×C₃×C₅	—	8	2	no	—
269	C₂×C₃×C₅	#509	1	2	yes	complemented
270	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
271	C₃×D₅	—	2	2	no	—
272	C₃×D₅	—	8	2	no	—
273	C₂³×C₃	—	4	1	no	—
274	C₂³×C₃	—	4	1	no	—
275	C₂³×C₃	—	5	1	no	—
276	C₂³×C₃	—	20	4	no	—
277	C₂³×C₃	—	20	1	no	—
278	C₂³×C₃	—	40	4	no	—
279	C₃×Q₈	—	10	2	no	—
280	C₃×Q₈	—	20	1	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	2	no	—
283	C₃×D₄	—	4	1	no	—
284	C₃×D₄	—	4	1	no	—
285	C₃×D₄	—	10	2	no	—
286	C₃×D₄	—	20	4	no	—
287	C₃×D₄	—	20	4	no	—
288	C₃×D₄	—	20	1	no	—
289	C₂×C₃×C₄	—	5	1	no	—
290	C₂×C₃×C₄	—	5	2	no	—
291	C₂×C₃×C₄	—	5	2	no	—
292	C₂×C₃×C₄	—	20	4	no	—
293	C₂×C₃×C₄	—	20	1	no	—
294	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
295	C₃×C₈	—	5	2	no	—
296	C₃×C₈	D₄×D₅	1	1	yes	characteristic
297	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	—	8	2	no	—
301	C₂²×C₅	—	8	2	no	—
302	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
303	C₂×D₅	—	2	2	no	—
304	C₂×D₅	—	4	2	no	—
305	C₂×D₅	—	8	8	no	—
306	C₂×D₅	—	8	2	no	—
307	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
308	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
309	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	Dic₅	—	4	2	no	—
311	Dic₅	C₂×C₃×D₈	1	2	yes	—
312	C₂⁴	—	20	1	no	—
313	#41	—	10	4	no	—
314	#41	—	20	2	no	—
315	C₂×Q₈	—	10	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	10	4	no	—
319	C₂×D₄	—	10	1	no	—
320	C₂×D₄	—	20	2	no	—
321	C₂×D₄	—	20	1	no	—
322	C₂×D₄	—	20	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	20	1	no	—
325	Q₁₆	—	5	2	no	—
326	Q₁₆	—	10	1	no	—
327	SD₁₆	—	10	4	no	—
328	D₈	—	2	1	no	—
329	D₈	—	2	1	no	—
330	D₈	—	5	2	no	—
331	D₈	—	10	4	no	—
332	D₈	—	10	1	no	—
333	D₈	C₂²×C₃×D₅	1	2	yes	—
334	D₈	C₂²×C₃×D₅	1	2	yes	complemented
335	C₂×C₈	—	5	1	no	—
336	C₂×C₈	—	5	2	no	—
337	C₂×C₈	—	5	2	no	—
338	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
339	C₁₆	—	5	2	no	—
340	C₁₆	C₂²×C₃×D₅	1	2	yes	complemented
341	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	5	2	no	—
345	C₂²×C₃	—	8	2	no	—
346	C₂²×C₃	—	8	2	no	—
347	C₂²×C₃	—	10	2	no	—
348	C₂²×C₃	—	20	2	no	—
349	C₂²×C₃	—	40	8	no	—
350	C₂²×C₃	—	40	2	no	—
351	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
352	C₃×C₄	—	5	2	no	—
353	C₃×C₄	—	20	2	no	—
354	C₃×C₄	D₅×D₈	1	1	yes	characteristic
355	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
356	C₂×C₅	—	8	2	no	—
357	C₂×C₅	—	8	2	no	—
358	C₂×C₅	C₃×#509	1	2	yes	complemented
359	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
360	D₅	—	2	2	no	—
361	D₅	—	8	2	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	5	1	no	—
365	C₂³	—	20	4	no	—
366	C₂³	—	20	1	no	—
367	C₂³	—	40	4	no	—
368	Q₈	—	10	2	no	—
369	Q₈	—	20	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	10	2	no	—
375	D₄	—	20	4	no	—
376	D₄	—	20	4	no	—
377	D₄	—	20	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	2	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	20	4	no	—
382	C₂×C₄	—	20	1	no	—
383	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
384	C₈	—	5	2	no	—
385	C₈	C₃×D₄×D₅	1	1	yes	characteristic
386	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
387	C₂×C₃	—	8	2	no	—
388	C₂×C₃	—	8	2	no	—
389	C₂×C₃	—	10	2	no	—
390	C₂×C₃	—	40	2	no	—
391	C₂×C₃	#65200	1	2	yes	direct product factor
392	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
393	C₅	C₂×C₃×#509	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	5	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	10	2	no	—
400	C₂²	—	20	2	no	—
401	C₂²	—	40	8	no	—
402	C₂²	—	40	2	no	—
403	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
404	C₄	—	5	2	no	—
405	C₄	—	20	2	no	—
406	C₄	C₃×D₅×D₈	1	1	yes	characteristic
407	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
408	C₃	C₂×#65200	1	1	yes	characteristic, direct product factor, Sylow
409	C₂	—	8	2	no	—
410	C₂	—	8	2	no	—
411	C₂	—	10	2	no	—
412	C₂	—	40	2	no	—
413	C₂	C₃×#65200	1	2	yes	direct product factor
414	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×D₁₆	C₂
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×C₃×D₁₆	D₅
hypocenter	C₅	C₂×C₃×#509
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4058	C₂	semidirect
2. C₂×C₃×D₅×D₈	C₂	semidirect
3. C₂×C₃×C₅×D₁₆	C₂	semidirect
4. C₂×C₃×#3959	C₂	semidirect
5. C₂×C₃×#3958	C₂	semidirect
6. C₃×#65200	C₂	direct (N × H)
7. C₂×C₃×#3932	C₂	semidirect
8. C₂×C₃×#3930	C₂	semidirect
9. C₂×#65200	C₃	direct (N × H)
13. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₃×#4058	C₂²	semidirect
19. C₃×D₅×D₈	C₂²	semidirect
20. C₂×C₃×Dic₂₀	C₂²	semidirect
23. C₃×C₅×D₁₆	C₂²	semidirect
24. C₂×C₃×C₅×C₁₆	C₂²	semidirect
25. C₃×#3959	C₂²	semidirect
26. C₃×#3958	C₂²	semidirect
27. C₂×C₃×#672	C₂²	semidirect
28. C₃×#3932	C₂²	semidirect
29. C₃×#3930	C₂²	semidirect
31. C₂×#4058	C₂×C₃	semidirect
32. C₂×D₅×D₈	C₂×C₃	semidirect
33. C₂×C₅×D₁₆	C₂×C₃	semidirect
34. C₂×#3959	C₂×C₃	semidirect
35. C₂×#3958	C₂×C₃	semidirect
36. #65200	C₂×C₃	direct (N × H)
37. C₂×#3932	C₂×C₃	semidirect
38. C₂×#3930	C₂×C₃	semidirect
55. C₃×C₅×D₈	C₂³	semidirect
61. C₃×Dic₂₀	C₂³	semidirect
66. C₃×C₅×C₁₆	C₂³	semidirect
67. C₃×#672	C₂³	semidirect
74. C₂×C₃×D₁₆	D₅	semidirect
79. C₂×C₅×D₈	C₂²×C₃	semidirect
83. #4058	C₂²×C₃	semidirect
85. D₅×D₈	C₂²×C₃	semidirect
86. C₂×Dic₂₀	C₂²×C₃	semidirect
89. C₅×D₁₆	C₂²×C₃	semidirect
90. C₂×C₅×C₁₆	C₂²×C₃	semidirect
91. #3959	C₂²×C₃	semidirect
92. #3958	C₂²×C₃	semidirect
93. C₂×#672	C₂²×C₃	semidirect
94. #3932	C₂²×C₃	semidirect
95. #3930	C₂²×C₃	semidirect
133. C₂×C₃×D₈	C₂×D₅	semidirect
138. C₃×D₁₆	C₂×D₅	semidirect
141. C₂×C₃×C₁₆	C₂×D₅	semidirect
158. C₅×D₈	C₂³×C₃	semidirect
164. Dic₂₀	C₂³×C₃	semidirect
169. C₅×C₁₆	C₂³×C₃	semidirect
170. #672	C₂³×C₃	semidirect
177. C₂×D₁₆	C₃×D₅	semidirect
215. C₃×D₈	C₂²×D₅	semidirect
221. C₃×C₁₆	C₂²×D₅	semidirect
258. C₂×D₈	C₂×C₃×D₅	semidirect
263. D₁₆	C₂×C₃×D₅	semidirect
266. C₂×C₁₆	C₂×C₃×D₅	semidirect
269. C₂×C₃×C₅	#509	semidirect
334. D₈	C₂²×C₃×D₅	semidirect
340. C₁₆	C₂²×C₃×D₅	semidirect
341. C₃×C₅	C₂×#509	semidirect
358. C₂×C₅	C₃×#509	semidirect
391. C₂×C₃	#65200	direct (N × H)
393. C₅	C₂×C₃×#509	semidirect
408. C₃	C₂×#65200	direct (N × H)
413. C₂	C₃×#65200	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×#4058	2
C₂×C₃×D₅×D₈	2
C₂×C₃×C₅×D₁₆	2
C₂×C₃×#3959	2
C₂×C₃×#3958	2
C₃×#65200	2
C₂×C₃×#3932	2
C₂×C₃×#3930	2
C₂×#65200	3
C₂×C₃×#509	5

Subgroups — C2×C3×#65200 #14478321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65200 #14478321