Subgroups — C₂×#11751215 #14427599

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#91819	C₂	1	1	yes	maximal, characteristic
3	C₂×#91813	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#6706	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751215	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91105	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#91100	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65403	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×#1220	—	2	1	no	—
12	C₂²×D₆₀	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₀	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	—	2	4	no	—
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	complemented
18	C₂×#6719	—	2	1	no	—
19	#91819	—	2	2	no	—
20	#91819	C₂²	1	4	yes	—
21	C₂×#6714	—	2	1	no	—
22	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
24	#91813	—	2	2	no	—
25	#91813	C₂²	1	4	yes	complemented
26	C₂×#6712	—	2	1	no	—
27	C₂×#6706	—	2	4	no	—
28	C₂×#6706	C₂²	1	4	yes	complemented
29	#91105	C₂²	1	4	yes	complemented
30	#91101	C₂²	1	4	yes	complemented
31	#91100	C₂²	1	4	yes	complemented
32	C₂×#5114	—	5	1	no	maximal, Hall
33	C₂³×C₅×C₈	D₃	1	1	yes	characteristic, complemented
34	C₂×#4076	—	3	1	no	—
35	C₂×#4070	—	3	1	no	—
36	C₂²×#677	—	3	1	no	—
37	#65403	—	3	8	no	—
38	C₂×#3953	—	3	1	no	—
39	C₂×#3949	—	3	1	no	—
40	C₂×#3948	—	3	1	no	—
41	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
42	C₂³×D₁₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×#1220	—	2	4	no	—
50	C₂×#1220	—	4	4	no	—
51	C₂²×Dic₁₅	—	2	1	no	—
52	C₂²×Dic₁₅	—	2	1	no	—
53	C₂²×Dic₁₅	—	2	1	no	—
54	C₂×D₆₀	—	2	2	no	—
55	C₂×D₆₀	—	2	2	no	—
56	C₂×D₆₀	—	2	1	no	—
57	C₂×D₆₀	C₂³	1	2	yes	—
58	C₂×Dic₃₀	—	2	2	no	—
59	C₂×Dic₃₀	—	2	2	no	—
60	C₂×Dic₃₀	—	2	1	no	—
61	C₂×Dic₃₀	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	—	2	2	no	—
63	C₂×C₃×C₅×C₈	—	2	8	no	—
64	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	#6719	—	2	4	no	—
68	#6714	—	2	4	no	—
69	C₄⋊Dic₁₅	—	2	1	no	—
70	C₄⋊Dic₁₅	—	2	1	no	—
71	C₄⋊Dic₁₅	C₂³	1	2	yes	—
72	C₄⋊Dic₁₅	C₂³	1	2	yes	—
73	#6712	—	2	4	no	—
74	#6706	—	2	8	no	—
75	C₂³×C₃×C₈	D₅	1	1	yes	characteristic, complemented
76	C₂×#930	—	5	1	no	—
77	C₂×#924	—	5	1	no	—
78	C₂²×#204	—	5	1	no	—
79	#5114	—	5	8	no	—
80	C₂×#821	—	5	1	no	—
81	C₂×#817	—	5	1	no	—
82	C₂×#816	—	5	1	no	—
83	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₂²⋊D₅	—	6	1	no	—
85	C₂²×D₂₀	—	3	1	no	—
86	C₂²×Dic₁₀	—	3	1	no	—
87	C₂²×C₅×C₈	—	2	4	no	—
88	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂×D₃	1	4	yes	complemented
91	C₂×C₂²⋊Dic₅	—	6	1	no	—
92	#4076	—	3	4	no	—
93	#4076	—	6	2	no	—
94	C₂×#685	—	6	1	no	—
95	C₂×C₄⋊Dic₅	—	3	1	no	—
96	C₂×C₄⋊Dic₅	—	3	1	no	—
97	#4070	—	3	4	no	—
98	#4070	—	6	2	no	—
99	C₂×#683	—	6	1	no	—
100	C₂×#677	—	3	4	no	—
101	C₂×#677	—	6	4	no	—
102	#3953	—	3	4	no	—
103	#3949	—	3	4	no	—
104	#3948	—	3	4	no	—
105	C₂×#465	—	15	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	SD₁₆	1	4	yes	complemented
109	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
110	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×D₁₅	—	2	2	no	—
112	C₂²×D₁₅	—	4	2	no	—
113	C₂²×D₁₅	—	4	2	no	—
114	C₂²×D₁₅	—	4	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	#1220	—	4	8	no	—
125	C₂×Dic₁₅	—	2	2	no	—
126	C₂×Dic₁₅	—	2	2	no	—
127	C₂×Dic₁₅	—	2	2	no	—
128	C₂×Dic₁₅	—	4	2	no	—
129	C₂×Dic₁₅	—	4	2	no	—
130	C₂×Dic₁₅	—	4	2	no	—
131	D₆₀	—	2	2	no	—
132	D₆₀	—	2	2	no	—
133	D₆₀	—	4	2	no	—
134	Dic₃₀	—	2	2	no	—
135	Dic₃₀	—	2	2	no	—
136	Dic₃₀	—	4	2	no	—
137	C₃×C₅×C₈	—	2	2	no	—
138	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
139	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
140	C₂²×#67	—	10	1	no	—
141	C₂²×D₁₂	—	5	1	no	—
142	C₂²×Dic₆	—	5	1	no	—
143	C₂²×C₃×C₈	—	2	4	no	—
144	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
145	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
146	C₂²×C₃×C₈	C₂×D₅	1	4	yes	complemented
147	C₂×#217	—	10	1	no	—
148	#930	—	5	4	no	—
149	#930	—	10	2	no	—
150	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
151	C₂×C₄⋊Dic₃	—	5	1	no	—
152	C₂×C₄⋊Dic₃	—	5	1	no	—
153	#924	—	5	4	no	—
154	#924	—	10	2	no	—
155	C₂×Dic₃⋊C₄	—	10	1	no	—
156	C₂×#204	—	5	4	no	—
157	C₂×#204	—	10	4	no	—
158	#821	—	5	4	no	—
159	#817	—	5	4	no	—
160	#816	—	5	4	no	—
161	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
162	C₂³×D₅	—	6	1	no	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
166	C₂²×C₄×C₅	D₁₂	1	2	yes	—
167	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₂²⋊D₅	—	6	4	no	—
170	C₂×C₂²⋊D₅	—	12	4	no	—
171	C₂²×Dic₅	—	6	1	no	—
172	C₂²×Dic₅	—	6	1	no	—
173	C₂²×Dic₅	—	6	1	no	—
174	C₂×D₂₀	—	3	2	no	—
175	C₂×D₂₀	—	6	2	no	—
176	C₂×D₂₀	—	6	2	no	—
177	C₂×D₂₀	—	6	1	no	—
178	C₂×Dic₁₀	—	3	2	no	—
179	C₂×Dic₁₀	—	6	2	no	—
180	C₂×Dic₁₀	—	6	2	no	—
181	C₂×Dic₁₀	—	6	1	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	2	8	no	—
184	C₂×C₅×C₈	#67	1	4	yes	complemented
185	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
186	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
187	C₂²⋊Dic₅	—	6	4	no	—
188	#685	—	6	4	no	—
189	C₄⋊Dic₅	—	3	2	no	—
190	C₄⋊Dic₅	—	3	2	no	—
191	C₄⋊Dic₅	—	6	1	no	—
192	C₄⋊Dic₅	—	6	1	no	—
193	#683	—	6	4	no	—
194	#677	—	6	8	no	—
195	C₂²×SD₁₆	—	15	1	no	—
196	C₂³×C₈	D₁₅	1	1	yes	characteristic, complemented
197	C₂×C₂²⋊Q₈	—	15	1	no	—
198	C₂×#121	—	15	1	no	—
199	#465	—	15	8	no	—
200	C₂×#106	—	15	1	no	—
201	C₂×#103	—	15	1	no	—
202	C₂×#102	—	15	1	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	8	no	—
206	C₂²×C₃×C₅	#121	1	2	yes	—
207	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
208	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
209	C₂²×C₃×C₅	#135	1	2	yes	—
210	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₂×D₁₅	—	4	2	no	—
212	C₂×D₁₅	—	4	2	no	—
213	C₂×D₁₅	—	4	2	no	—
214	C₂×D₁₅	—	8	4	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	#121	1	2	yes	—
217	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	Dic₁₅	—	4	2	no	—
220	Dic₁₅	—	4	2	no	—
221	Dic₁₅	—	4	2	no	—
222	C₂⁴×C₃	D₂₀	1	1	yes	characteristic
223	C₂³×D₃	—	10	1	no	—
224	C₂²×C₃×C₄	—	2	2	no	—
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
227	C₂²×C₃×C₄	D₂₀	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
230	C₂×#67	—	10	4	no	—
231	C₂×#67	—	20	4	no	—
232	C₂²×Dic₃	—	10	1	no	—
233	C₂²×Dic₃	—	10	1	no	—
234	C₂²×Dic₃	—	10	1	no	—
235	C₂×D₁₂	—	5	2	no	—
236	C₂×D₁₂	—	10	2	no	—
237	C₂×D₁₂	—	10	2	no	—
238	C₂×D₁₂	—	10	1	no	—
239	C₂×Dic₆	—	5	2	no	—
240	C₂×Dic₆	—	10	2	no	—
241	C₂×Dic₆	—	10	2	no	—
242	C₂×Dic₆	—	10	1	no	—
243	C₂×C₃×C₈	—	2	2	no	—
244	C₂×C₃×C₈	—	2	8	no	—
245	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
246	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
247	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
248	#217	—	10	4	no	—
249	(C₂×D₃)⋊C₄	—	10	4	no	—
250	C₄⋊Dic₃	—	5	2	no	—
251	C₄⋊Dic₃	—	5	2	no	—
252	C₄⋊Dic₃	—	10	1	no	—
253	C₄⋊Dic₃	—	10	1	no	—
254	Dic₃⋊C₄	—	10	4	no	—
255	#204	—	10	8	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	#204	1	4	yes	complemented
259	C₂³×C₅	C₂×D₁₂	1	2	yes	—
260	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
261	C₂²×D₅	—	6	2	no	—
262	C₂²×D₅	—	12	2	no	—
263	C₂²×D₅	—	12	2	no	—
264	C₂²×D₅	—	12	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	4	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
270	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
271	C₂×C₄×C₅	#235	1	2	yes	—
272	C₂×C₄×C₅	C₂×#67	1	2	yes	—
273	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
274	C₂²⋊D₅	—	12	8	no	—
275	C₂×Dic₅	—	6	2	no	—
276	C₂×Dic₅	—	6	2	no	—
277	C₂×Dic₅	—	6	2	no	—
278	C₂×Dic₅	—	12	2	no	—
279	C₂×Dic₅	—	12	2	no	—
280	C₂×Dic₅	—	12	2	no	—
281	D₂₀	—	6	2	no	—
282	D₂₀	—	6	2	no	—
283	D₂₀	—	12	2	no	—
284	Dic₁₀	—	6	2	no	—
285	Dic₁₀	—	6	2	no	—
286	Dic₁₀	—	12	2	no	—
287	C₅×C₈	—	2	2	no	—
288	C₅×C₈	C₂×#67	1	4	yes	complemented
289	C₂²×Q₈	—	15	1	no	—
290	C₂²×D₄	—	15	1	no	—
291	C₂²×D₄	—	30	1	no	—
292	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
293	C₂×SD₁₆	—	15	4	no	—
294	C₂×SD₁₆	—	30	4	no	—
295	C₂²×C₈	—	2	4	no	—
296	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
297	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
298	C₂²×C₈	C₂×D₁₅	1	4	yes	complemented
299	C₂²⋊Q₈	—	15	4	no	—
300	C₂²⋊Q₈	—	30	2	no	—
301	#121	—	15	4	no	—
302	#121	—	30	2	no	—
303	C₂×C₄⋊C₄	—	15	1	no	—
304	C₂×C₄⋊C₄	—	15	1	no	—
305	C₂×C₄⋊C₄	—	30	1	no	—
306	C₂×C₂²⋊C₄	—	30	1	no	—
307	C₂×C₂²⋊C₄	—	30	1	no	—
308	#106	—	15	4	no	—
309	#103	—	15	4	no	—
310	#102	—	15	4	no	—
311	C₂×C₃×C₅	—	2	4	no	—
312	C₂×C₃×C₅	#465	1	4	yes	complemented
313	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
316	D₁₅	—	8	2	no	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	2	2	no	—
319	C₂³×C₃	#677	1	4	yes	complemented
320	C₂³×C₃	C₂×D₂₀	1	2	yes	—
321	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
322	C₂²×D₃	—	10	2	no	—
323	C₂²×D₃	—	20	2	no	—
324	C₂²×D₃	—	20	2	no	—
325	C₂²×D₃	—	20	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
331	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
332	C₂×C₃×C₄	#709	1	2	yes	—
333	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
334	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
335	#67	—	20	8	no	—
336	C₂×Dic₃	—	10	2	no	—
337	C₂×Dic₃	—	10	2	no	—
338	C₂×Dic₃	—	10	2	no	—
339	C₂×Dic₃	—	20	2	no	—
340	C₂×Dic₃	—	20	2	no	—
341	C₂×Dic₃	—	20	2	no	—
342	D₁₂	—	10	2	no	—
343	D₁₂	—	10	2	no	—
344	D₁₂	—	20	2	no	—
345	Dic₆	—	10	2	no	—
346	Dic₆	—	10	2	no	—
347	Dic₆	—	20	2	no	—
348	C₃×C₈	—	2	2	no	—
349	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	—	2	2	no	—
352	C₂²×C₅	—	2	8	no	—
353	C₂²×C₅	C₂×#204	1	2	yes	—
354	C₂²×C₅	C₂×#204	1	4	yes	complemented
355	C₂²×C₅	#904	1	2	yes	—
356	C₂²×C₅	#930	1	2	yes	—
357	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
358	C₂×D₅	—	12	2	no	—
359	C₂×D₅	—	12	2	no	—
360	C₂×D₅	—	12	2	no	—
361	C₂×D₅	—	24	4	no	—
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	#930	1	2	yes	—
364	C₄×C₅	C₂×#235	1	1	yes	characteristic
365	C₄×C₅	C₂²×#67	1	1	yes	characteristic
366	Dic₅	—	12	2	no	—
367	Dic₅	—	12	2	no	—
368	Dic₅	—	12	2	no	—
369	C₂⁴	—	30	1	no	—
370	C₂⁴	D₆₀	1	1	yes	characteristic
371	C₂×Q₈	—	15	2	no	—
372	C₂×Q₈	—	30	1	no	—
373	C₂×Q₈	—	30	2	no	—
374	C₂×Q₈	—	30	2	no	—
375	C₂×D₄	—	15	2	no	—
376	C₂×D₄	—	30	4	no	—
377	C₂×D₄	—	30	1	no	—
378	C₂×D₄	—	30	2	no	—
379	C₂×D₄	—	30	2	no	—
380	C₂×D₄	—	60	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	30	1	no	—
384	C₂²×C₄	—	30	1	no	—
385	C₂²×C₄	—	30	1	no	—
386	C₂²×C₄	D₆₀	1	2	yes	—
387	C₂²×C₄	D₆₀	1	1	yes	characteristic
388	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
389	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
390	SD₁₆	—	30	8	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	8	no	—
393	C₂×C₈	#1220	1	4	yes	complemented
394	C₂×C₈	C₂²×D₁₅	1	2	yes	—
395	C₂×C₈	C₂²×D₁₅	1	2	yes	—
396	C₄⋊C₄	—	15	2	no	—
397	C₄⋊C₄	—	15	2	no	—
398	C₄⋊C₄	—	30	1	no	—
399	C₄⋊C₄	—	30	1	no	—
400	C₄⋊C₄	—	30	4	no	—
401	C₂²⋊C₄	—	30	4	no	—
402	C₂²⋊C₄	—	30	4	no	—
403	C₃×C₅	C₂×#465	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	8	no	—
407	C₂²×C₃	C₂×#677	1	2	yes	—
408	C₂²×C₃	C₂×#677	1	4	yes	complemented
409	C₂²×C₃	#4050	1	2	yes	—
410	C₂²×C₃	#4076	1	2	yes	—
411	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
412	C₂×D₃	—	20	2	no	—
413	C₂×D₃	—	20	2	no	—
414	C₂×D₃	—	20	2	no	—
415	C₂×D₃	—	40	4	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	#4076	1	2	yes	—
418	C₃×C₄	C₂×#709	1	1	yes	characteristic
419	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
420	Dic₃	—	20	2	no	—
421	Dic₃	—	20	2	no	—
422	Dic₃	—	20	2	no	—
423	C₂×C₅	—	2	4	no	—
424	C₂×C₅	#5114	1	4	yes	complemented
425	C₂×C₅	C₂²×#204	1	1	yes	characteristic
426	C₂×C₅	C₂×#904	1	1	yes	characteristic
427	C₂×C₅	C₂×#930	1	1	yes	characteristic
428	D₅	—	24	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	30	2	no	—
432	C₂³	—	60	2	no	—
433	C₂³	—	60	2	no	—
434	C₂³	—	60	2	no	—
435	C₂³	#6706	1	4	yes	complemented
436	C₂³	C₂×D₆₀	1	2	yes	—
437	C₂³	C₂×D₆₀	1	1	yes	characteristic
438	Q₈	—	30	2	no	—
439	Q₈	—	30	2	no	—
440	Q₈	—	60	2	no	—
441	D₄	—	30	2	no	—
442	D₄	—	30	2	no	—
443	D₄	—	60	8	no	—
444	D₄	—	60	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	30	2	no	—
450	C₂×C₄	—	30	2	no	—
451	C₂×C₄	—	30	2	no	—
452	C₂×C₄	—	60	2	no	—
453	C₂×C₄	—	60	2	no	—
454	C₂×C₄	—	60	2	no	—
455	C₂×C₄	C₂×D₆₀	1	2	yes	—
456	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
457	C₂×C₄	#6817	1	2	yes	—
458	C₂×C₄	C₂×#1220	1	2	yes	—
459	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	C₂×#1220	1	4	yes	complemented
462	C₂×C₃	—	2	4	no	—
463	C₂×C₃	#65403	1	4	yes	complemented
464	C₂×C₃	C₂²×#677	1	1	yes	characteristic
465	C₂×C₃	C₂×#4050	1	1	yes	characteristic
466	C₂×C₃	C₂×#4076	1	1	yes	characteristic
467	D₃	—	40	2	no	—
468	C₅	C₂×#5114	1	1	yes	characteristic, complemented, Sylow
469	C₂²	—	2	2	no	—
470	C₂²	—	2	8	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	60	2	no	—
473	C₂²	—	60	2	no	—
474	C₂²	—	60	2	no	—
475	C₂²	—	120	4	no	—
476	C₂²	C₂×#6706	1	2	yes	—
477	C₂²	C₂×#6706	1	4	yes	complemented
478	C₂²	#91793	1	2	yes	—
479	C₂²	#91819	1	2	yes	—
480	C₂²	C₂²×D₆₀	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	60	2	no	—
483	C₄	—	60	2	no	—
484	C₄	—	60	2	no	—
485	C₄	#91819	1	2	yes	—
486	C₄	C₂×#6817	1	1	yes	characteristic
487	C₄	C₂²×#1220	1	1	yes	characteristic
488	C₃	C₂×#65403	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	4	no	—
490	C₂	—	120	2	no	—
491	C₂	#11751215	1	4	yes	direct product factor
492	C₂	C₂²×#6706	1	1	yes	characteristic
493	C₂	C₂×#91793	1	1	yes	characteristic
494	C₂	C₂×#91819	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₆₀
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂³×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×#91819	C₂
hypercenter	C₂³×C₈	D₁₅
hypocenter	C₃×C₅	C₂×#465
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×C₈	C₂	semidirect
3. C₂×#91813	C₂	semidirect
4. C₂²×#6706	C₂	semidirect
5. #11751215	C₂	direct (N × H)
6. C₂×#91105	C₂	semidirect
7. C₂×#91101	C₂	semidirect
8. C₂×#91100	C₂	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. #91813	C₂²	semidirect
28. C₂×#6706	C₂²	semidirect
29. #91105	C₂²	semidirect
30. #91101	C₂²	semidirect
31. #91100	C₂²	semidirect
33. C₂³×C₅×C₈	D₃	semidirect
64. C₂×C₃×C₅×C₈	D₄	semidirect
75. C₂³×C₃×C₈	D₅	semidirect
90. C₂²×C₅×C₈	C₂×D₃	semidirect
108. C₂³×C₃×C₅	SD₁₆	semidirect
138. C₃×C₅×C₈	C₂×D₄	semidirect
146. C₂²×C₃×C₈	C₂×D₅	semidirect
184. C₂×C₅×C₈	#67	semidirect
196. C₂³×C₈	D₁₅	semidirect
208. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
245. C₂×C₃×C₈	C₂²⋊D₅	semidirect
258. C₂³×C₅	#204	semidirect
288. C₅×C₈	C₂×#67	semidirect
298. C₂²×C₈	C₂×D₁₅	semidirect
312. C₂×C₃×C₅	#465	semidirect
319. C₂³×C₃	#677	semidirect
349. C₃×C₈	C₂×C₂²⋊D₅	semidirect
354. C₂²×C₅	C₂×#204	semidirect
393. C₂×C₈	#1220	semidirect
403. C₃×C₅	C₂×#465	semidirect
408. C₂²×C₃	C₂×#677	semidirect
424. C₂×C₅	#5114	semidirect
435. C₂³	#6706	semidirect
461. C₈	C₂×#1220	semidirect
463. C₂×C₃	#65403	semidirect
468. C₅	C₂×#5114	semidirect
477. C₂²	C₂×#6706	semidirect
488. C₃	C₂×#65403	semidirect
491. C₂	#11751215	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×C₈	2
C₂×#91819	2
C₂×#91813	2
C₂²×#6706	2
#11751215	2
C₂×#91105	2
C₂×#91101	2
C₂×#91100	2
C₂×#65403	3
C₂×#5114	5

Subgroups — C2×#11751215 #14427599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751215 #14427599