Subgroups — C₂×C₄×#6715 #14415984

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6715	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91116	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6715	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91091	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×#686	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₂²×D₆₀	C₂²	1	1	yes	characteristic
13	C₂²×C₄×D₁₅	—	2	1	no	—
14	C₃×C₄×C₅×D₄	—	2	2	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×#6715	C₄	1	8	yes	direct product factor
20	C₂×#6715	C₂²	1	4	yes	—
21	C₂×#6714	—	2	1	no	—
22	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
25	C₄×D₆₀	—	2	2	no	—
26	C₄×D₆₀	C₂²	1	4	yes	complemented
27	#91116	C₂²	1	4	yes	complemented
28	#91093	C₂²	1	4	yes	complemented
29	#91091	C₂²	1	4	yes	complemented
30	C₄×C₃⋊#168	C₂²	1	4	yes	complemented
31	C₂×C₄×#213	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
33	C₂²×#686	—	3	1	no	—
34	C₂×C₄×D₂₀	—	3	1	no	—
35	C₂×#3964	—	3	1	no	—
36	C₄×#686	—	3	8	no	—
37	C₂×#3941	—	3	1	no	—
38	C₂×#3939	—	3	1	no	—
39	C₂×C₄×#168	—	3	1	no	—
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₂³×D₁₅	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	4	4	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×Dic₁₅	—	2	1	no	—
53	C₂×D₆₀	—	2	1	no	—
54	C₂×D₆₀	—	2	2	no	—
55	C₂×D₆₀	C₂×C₄	1	4	yes	complemented
56	C₂×D₆₀	C₂³	1	2	yes	—
57	C₂×C₄×D₁₅	—	2	4	no	—
58	C₂×C₄×D₁₅	—	4	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₄²×C₅	D₄	1	2	yes	—
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	#6715	C₂×C₄	1	16	yes	direct product factor
65	#6714	—	2	4	no	—
66	C₄⋊Dic₁₅	—	2	1	no	—
67	C₄⋊Dic₁₅	C₂³	1	2	yes	—
68	C₂×C₃⋊#168	—	2	2	no	—
69	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
70	C₂×C₃⋊#168	C₂³	1	2	yes	—
71	C₂×C₃⋊#168	C₂³	1	2	yes	—
72	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
73	C₂²×#213	—	5	1	no	—
74	C₂×C₄×D₁₂	—	5	1	no	—
75	C₂×#832	—	5	1	no	—
76	C₄×#213	—	5	8	no	—
77	C₂×#809	—	5	1	no	—
78	C₂×#807	—	5	1	no	—
79	C₂×C₄×C₃⋊C₈	—	5	1	no	—
80	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
81	C₂³×C₄×C₅	—	2	1	no	—
82	C₂²×D₂₀	—	3	1	no	—
83	C₂²×C₄×D₅	—	6	1	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	C₂×D₃	1	4	yes	complemented
86	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
89	C₂×#686	—	3	8	no	—
90	C₂×#686	—	3	4	no	—
91	C₂×#685	—	6	1	no	—
92	C₂×C₄⋊Dic₅	—	3	1	no	—
93	C₂²×#168	—	3	1	no	—
94	C₂²×#168	—	3	1	no	—
95	C₄×D₂₀	—	3	4	no	—
96	C₄×D₂₀	—	6	2	no	—
97	#3964	—	3	4	no	—
98	#3941	—	3	4	no	—
99	#3939	—	3	4	no	—
100	C₄×#168	—	3	4	no	—
101	C₂×C₄×D₈	—	15	1	no	Sylow
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	4	2	no	—
105	C₂³×C₃×C₅	—	4	2	no	—
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×D₁₅	—	2	4	no	—
108	C₂²×D₁₅	—	2	2	no	—
109	C₂²×D₁₅	—	4	2	no	—
110	C₂²×D₁₅	—	4	2	no	—
111	C₃×C₅×D₄	—	2	4	no	—
112	C₃×C₅×D₄	—	2	2	no	—
113	C₃×C₅×D₄	C₂²×C₄	1	4	yes	complemented
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	4	2	no	—
117	C₂×C₃×C₄×C₅	—	4	8	no	—
118	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	#41	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₂×Dic₁₅	—	2	2	no	—
126	C₂×Dic₁₅	—	4	2	no	—
127	D₆₀	—	2	4	no	—
128	D₆₀	—	2	2	no	—
129	D₆₀	C₂²×C₄	1	4	yes	complemented
130	C₄×D₁₅	—	4	8	no	—
131	C₃⋊#168	—	2	2	no	—
132	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
133	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
134	C₂³×C₃×C₄	—	2	1	no	—
135	C₂²×D₁₂	—	5	1	no	—
136	C₂²×C₄×D₃	—	10	1	no	—
137	C₃×C₄×D₄	—	2	2	no	—
138	C₃×C₄×D₄	C₂×D₅	1	4	yes	complemented
139	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
142	C₂×#213	—	5	8	no	—
143	C₂×#213	—	5	4	no	—
144	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
145	C₂×C₄⋊Dic₃	—	5	1	no	—
146	C₂²×C₃⋊C₈	—	5	1	no	—
147	C₂²×C₃⋊C₈	—	5	1	no	—
148	C₄×D₁₂	—	5	4	no	—
149	C₄×D₁₂	—	10	2	no	—
150	#832	—	5	4	no	—
151	#809	—	5	4	no	—
152	#807	—	5	4	no	—
153	C₄×C₃⋊C₈	—	5	4	no	—
154	C₂⁴×C₅	—	2	1	no	—
155	C₂³×D₅	—	6	1	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
159	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	—	4	4	no	—
163	C₂²×C₄×C₅	#67	1	1	yes	characteristic
164	C₂²×C₄×C₅	#67	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₂²×Dic₅	—	6	1	no	—
167	C₂×D₂₀	—	3	4	no	—
168	C₂×D₂₀	—	3	2	no	—
169	C₂×D₂₀	—	6	2	no	—
170	C₂×D₂₀	—	6	1	no	—
171	C₂×C₄×D₅	—	6	4	no	—
172	C₂×C₄×D₅	—	12	4	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₄²×C₅	#67	1	2	yes	—
177	C₄²×C₅	C₂²×D₃	1	2	yes	—
178	#686	—	3	16	no	—
179	#685	—	6	4	no	—
180	C₄⋊Dic₅	—	3	2	no	—
181	C₄⋊Dic₅	—	6	1	no	—
182	C₂×#168	—	3	4	no	—
183	C₂×#168	—	3	2	no	—
184	C₂×#168	—	3	2	no	—
185	C₂×#168	—	6	2	no	—
186	C₂²×D₈	—	15	1	no	—
187	C₂×C₄×D₄	—	15	1	no	—
188	C₂×C₄×D₄	D₁₅	1	1	yes	characteristic, complemented
189	C₄×D₈	—	15	8	no	—
190	C₂×#107	—	15	1	no	—
191	C₂×#102	—	15	1	no	—
192	C₂×#102	—	15	1	no	—
193	C₂×C₄×C₈	—	15	1	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	4	8	no	—
198	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
199	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
200	C₂²×C₃×C₅	#135	1	2	yes	—
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂×D₁₅	—	2	4	no	—
203	C₂×D₁₅	—	4	2	no	—
204	C₂×D₁₅	—	4	2	no	—
205	C₂×D₁₅	—	4	8	no	—
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
209	C₃×C₄×C₅	C₂×D₈	1	4	yes	complemented
210	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	Dic₁₅	—	4	2	no	—
213	C₂⁴×C₃	—	2	1	no	—
214	C₂³×D₃	—	10	1	no	—
215	C₂×C₃×D₄	—	2	2	no	—
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	C₄×D₅	1	4	yes	complemented
218	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
219	C₂²×C₃×C₄	—	2	1	no	—
220	C₂²×C₃×C₄	—	2	4	no	—
221	C₂²×C₃×C₄	—	4	4	no	—
222	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
225	C₂²×Dic₃	—	10	1	no	—
226	C₂×D₁₂	—	5	4	no	—
227	C₂×D₁₂	—	5	2	no	—
228	C₂×D₁₂	—	10	2	no	—
229	C₂×D₁₂	—	10	1	no	—
230	C₂×C₄×D₃	—	10	4	no	—
231	C₂×C₄×D₃	—	20	4	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
234	C₃×C₂²⋊C₄	—	2	4	no	—
235	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
236	C₃×C₄²	C₂²×D₅	1	2	yes	—
237	#213	—	5	16	no	—
238	(C₂×D₃)⋊C₄	—	10	4	no	—
239	C₄⋊Dic₃	—	5	2	no	—
240	C₄⋊Dic₃	—	10	1	no	—
241	C₂×C₃⋊C₈	—	5	4	no	—
242	C₂×C₃⋊C₈	—	5	2	no	—
243	C₂×C₃⋊C₈	—	5	2	no	—
244	C₂×C₃⋊C₈	—	10	2	no	—
245	C₂³×C₅	—	2	4	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	4	2	no	—
248	C₂³×C₅	—	4	2	no	—
249	C₂³×C₅	C₂×#67	1	1	yes	characteristic
250	C₂²×D₅	—	6	4	no	—
251	C₂²×D₅	—	6	2	no	—
252	C₂²×D₅	—	12	2	no	—
253	C₂²×D₅	—	12	2	no	—
254	C₅×D₄	—	2	4	no	—
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	C₂×C₄×D₃	1	4	yes	complemented
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	—	4	8	no	—
261	C₂×C₄×C₅	#213	1	4	yes	complemented
262	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
263	C₂×C₄×C₅	#235	1	2	yes	—
264	C₂×C₄×C₅	C₂×#67	1	2	yes	—
265	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×#67	1	2	yes	—
267	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
268	C₂×Dic₅	—	6	2	no	—
269	C₂×Dic₅	—	12	2	no	—
270	D₂₀	—	3	4	no	—
271	D₂₀	—	6	4	no	—
272	D₂₀	—	6	2	no	—
273	C₄×D₅	—	12	8	no	—
274	#168	—	3	4	no	—
275	#168	—	6	2	no	—
276	C₂²×D₄	—	15	1	no	—
277	C₂²×D₄	C₂×D₁₅	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	30	1	no	—
280	C₂×D₈	—	15	8	no	—
281	C₂×D₈	—	15	4	no	—
282	C₂²×C₈	—	15	1	no	—
283	C₂²×C₈	—	15	1	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	15	4	no	—
286	C₄×D₄	—	30	2	no	—
287	C₄×D₄	C₂×D₁₅	1	4	yes	complemented
288	C₂×C₄⋊C₄	—	15	1	no	—
289	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	30	1	no	—
292	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
293	#107	—	15	4	no	—
294	#102	—	15	4	no	—
295	#102	—	15	4	no	—
296	C₄×C₈	—	15	4	no	—
297	C₂×C₃×C₅	—	4	4	no	—
298	C₂×C₃×C₅	C₄×D₈	1	4	yes	complemented
299	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
302	D₁₅	—	4	4	no	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	—	4	2	no	—
306	C₂³×C₃	—	4	2	no	—
307	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
308	C₂²×D₃	—	10	2	no	—
309	C₂²×D₃	—	10	4	no	—
310	C₂²×D₃	—	20	2	no	—
311	C₂²×D₃	—	20	2	no	—
312	C₃×D₄	—	2	2	no	—
313	C₃×D₄	—	2	4	no	—
314	C₃×D₄	C₂×C₄×D₅	1	4	yes	complemented
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	4	2	no	—
318	C₂×C₃×C₄	—	4	8	no	—
319	C₂×C₃×C₄	#686	1	4	yes	complemented
320	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
321	C₂×C₃×C₄	#709	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
326	C₂×Dic₃	—	10	2	no	—
327	C₂×Dic₃	—	20	2	no	—
328	D₁₂	—	5	4	no	—
329	D₁₂	—	10	2	no	—
330	D₁₂	—	10	4	no	—
331	C₄×D₃	—	20	8	no	—
332	C₃⋊C₈	—	5	4	no	—
333	C₃⋊C₈	—	10	2	no	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	4	8	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	C₄×#67	1	2	yes	—
339	C₂²×C₅	C₂×#213	1	2	yes	—
340	C₂²×C₅	#950	1	2	yes	—
341	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
342	C₂×D₅	—	6	4	no	—
343	C₂×D₅	—	12	8	no	—
344	C₂×D₅	—	12	2	no	—
345	C₂×D₅	—	12	2	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	C₄×#67	1	2	yes	—
349	C₄×C₅	C₂×#213	1	4	yes	complemented
350	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
351	C₄×C₅	C₂×#235	1	1	yes	characteristic
352	Dic₅	—	12	2	no	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	30	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	15	4	no	—
358	C₂×D₄	—	15	2	no	—
359	C₂×D₄	—	30	2	no	—
360	C₂×D₄	—	30	1	no	—
361	C₂×D₄	C₄×D₁₅	1	4	yes	complemented
362	C₂×D₄	C₂²×D₁₅	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	30	1	no	—
367	C₂²×C₄	—	30	4	no	—
368	C₂²×C₄	—	60	4	no	—
369	C₂²×C₄	#1220	1	1	yes	characteristic
370	C₂²×C₄	#1220	1	1	yes	characteristic
371	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
372	D₈	—	15	16	no	—
373	C₂×C₈	—	15	4	no	—
374	C₂×C₈	—	15	2	no	—
375	C₂×C₈	—	15	2	no	—
376	C₂×C₈	—	30	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	15	2	no	—
379	C₄⋊C₄	—	30	1	no	—
380	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	30	4	no	—
383	C₄²	#1220	1	2	yes	—
384	C₄²	C₂²×D₁₅	1	2	yes	—
385	C₃×C₅	C₂×C₄×D₈	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	—	4	8	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
391	C₂²×C₃	C₂×#686	1	2	yes	—
392	C₂²×C₃	#4096	1	2	yes	—
393	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
394	C₂×D₃	—	10	4	no	—
395	C₂×D₃	—	20	8	no	—
396	C₂×D₃	—	20	2	no	—
397	C₂×D₃	—	20	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
401	C₃×C₄	C₂×#686	1	4	yes	complemented
402	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
403	C₃×C₄	C₂×#709	1	1	yes	characteristic
404	Dic₃	—	20	2	no	—
405	C₂×C₅	—	4	4	no	—
406	C₂×C₅	C₄×#213	1	4	yes	complemented
407	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
408	C₂×C₅	C₂²×#213	1	1	yes	characteristic
409	C₂×C₅	C₂×#950	1	1	yes	characteristic
410	D₅	—	12	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	30	4	no	—
416	C₂³	—	30	2	no	—
417	C₂³	—	60	2	no	—
418	C₂³	—	60	2	no	—
419	C₂³	C₂×#1220	1	1	yes	characteristic
420	D₄	—	2	4	no	—
421	D₄	—	2	2	no	—
422	D₄	—	15	4	no	—
423	D₄	—	30	4	no	—
424	D₄	—	30	2	no	—
425	D₄	C₂×C₄×D₁₅	1	4	yes	complemented
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	30	2	no	—
431	C₂×C₄	—	60	2	no	—
432	C₂×C₄	—	60	8	no	—
433	C₂×C₄	#6715	1	4	yes	direct product factor
434	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
435	C₂×C₄	#6817	1	2	yes	—
436	C₂×C₄	C₂×#1220	1	2	yes	—
437	C₂×C₄	C₂×#1220	1	1	yes	characteristic
438	C₂×C₄	C₂×#1220	1	2	yes	—
439	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
440	C₈	—	15	4	no	—
441	C₈	—	30	2	no	—
442	C₂×C₃	—	4	4	no	—
443	C₂×C₃	C₄×#686	1	4	yes	complemented
444	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
445	C₂×C₃	C₂²×#686	1	1	yes	characteristic
446	C₂×C₃	C₂×#4096	1	1	yes	characteristic
447	D₃	—	20	4	no	—
448	C₅	C₂×C₄×#213	1	1	yes	characteristic, complemented, Sylow
449	C₂²	—	2	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	30	4	no	—
454	C₂²	—	60	2	no	—
455	C₂²	—	60	2	no	—
456	C₂²	—	60	8	no	—
457	C₂²	C₄×#1220	1	2	yes	—
458	C₂²	C₂×#6715	1	2	yes	—
459	C₂²	#91839	1	2	yes	—
460	C₂²	C₂²×#1220	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	60	2	no	—
464	C₄	C₄×#1220	1	2	yes	—
465	C₄	C₂×#6715	1	4	yes	direct product factor
466	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
467	C₄	C₂×#6817	1	1	yes	characteristic
468	C₃	C₂×C₄×#686	1	1	yes	characteristic, complemented, Sylow
469	C₂	—	4	4	no	—
470	C₂	—	60	4	no	—
471	C₂	C₄×#6715	1	4	yes	direct product factor
472	C₂	C₂×C₄×#1220	1	1	yes	characteristic
473	C₂	C₂²×#6715	1	1	yes	characteristic
474	C₂	C₂×#91839	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#1220
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×#6715	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄×D₄	D₁₅
hypocenter	C₃×C₅	C₂×C₄×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₄×D₆₀	C₂	semidirect
4. C₂×#91116	C₂	semidirect
5. C₄×#6715	C₂	direct (N × H)
6. C₂×#91093	C₂	semidirect
7. C₂×#91091	C₂	semidirect
8. C₂×C₄×C₃⋊#168	C₂	semidirect
15. C₃×C₄×C₅×D₄	C₂²	semidirect
19. C₂×#6715	C₄	direct (N × H)
26. C₄×D₆₀	C₂²	semidirect
27. #91116	C₂²	semidirect
28. #91093	C₂²	semidirect
29. #91091	C₂²	semidirect
30. C₄×C₃⋊#168	C₂²	semidirect
32. C₂×C₄×C₅×D₄	D₃	semidirect
44. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
55. C₂×D₆₀	C₂×C₄	semidirect
64. #6715	C₂×C₄	direct (N × H)
69. C₂×C₃⋊#168	C₂×C₄	semidirect
72. C₂×C₃×C₄×D₄	D₅	semidirect
85. C₄×C₅×D₄	C₂×D₃	semidirect
113. C₃×C₅×D₄	C₂²×C₄	semidirect
118. C₂×C₃×C₄×C₅	D₈	semidirect
129. D₆₀	C₂²×C₄	semidirect
132. C₃⋊#168	C₂²×C₄	semidirect
138. C₃×C₄×D₄	C₂×D₅	semidirect
158. C₂×C₅×D₄	C₄×D₃	semidirect
188. C₂×C₄×D₄	D₁₅	semidirect
209. C₃×C₄×C₅	C₂×D₈	semidirect
217. C₂×C₃×D₄	C₄×D₅	semidirect
256. C₅×D₄	C₂×C₄×D₃	semidirect
261. C₂×C₄×C₅	#213	semidirect
287. C₄×D₄	C₂×D₁₅	semidirect
298. C₂×C₃×C₅	C₄×D₈	semidirect
314. C₃×D₄	C₂×C₄×D₅	semidirect
319. C₂×C₃×C₄	#686	semidirect
349. C₄×C₅	C₂×#213	semidirect
361. C₂×D₄	C₄×D₁₅	semidirect
385. C₃×C₅	C₂×C₄×D₈	semidirect
401. C₃×C₄	C₂×#686	semidirect
406. C₂×C₅	C₄×#213	semidirect
425. D₄	C₂×C₄×D₁₅	semidirect
433. C₂×C₄	#6715	direct (N × H)
443. C₂×C₃	C₄×#686	semidirect
448. C₅	C₂×C₄×#213	semidirect
465. C₄	C₂×#6715	direct (N × H)
468. C₃	C₂×C₄×#686	semidirect
471. C₂	C₄×#6715	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×C₄×C₅×D₄	2
C₂²×#6715	2
C₂×C₄×D₆₀	2
C₂×#91116	2
C₄×#6715	2
C₂×#91093	2
C₂×#91091	2
C₂×C₄×C₃⋊#168	2
C₂×C₄×#686	3
C₂×C₄×#213	5

Subgroups — C2×C4×#6715 #14415984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6715 #14415984