Subgroups — C₂×#11756589 #14480367

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#11756589	C₂	1	16	yes	maximal, direct product factor
4	C₂×#91836	C₂	1	2	yes	maximal, complemented
5	C₂×#91829	C₂	1	2	yes	maximal, complemented
6	C₂×#91826	C₂	1	4	yes	maximal, complemented
7	C₂×#91819	C₂	1	4	yes	maximal, complemented
8	C₂×#91815	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66164	—	3	1	no	maximal, Hall
10	C₂⁴×D₁₅	C₂²	1	2	yes	—
11	C₂×C₃×C₅×#41	—	2	8	no	—
12	C₂×C₃×C₅×#41	C₂²	1	8	yes	complemented
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
18	C₂²×#1220	C₂²	1	8	yes	complemented
19	C₂²×D₆₀	—	2	8	no	—
20	C₂²×D₆₀	C₂²	1	2	yes	—
21	C₂²×D₆₀	C₂²	1	2	yes	—
22	C₂²×D₆₀	C₂²	1	8	yes	complemented
23	C₂×#6719	C₂²	1	2	yes	—
24	#91836	C₂²	1	16	yes	complemented
25	#91829	C₂²	1	16	yes	complemented
26	#91826	C₂²	1	32	yes	complemented
27	#91819	C₂²	1	32	yes	complemented
28	C₂×#6714	C₂²	1	8	yes	complemented
29	#91815	C₂²	1	8	yes	complemented
30	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	complemented
31	C₂×C₄×Dic₁₅	C₂²	1	2	yes	complemented
32	C₂×#5830	—	5	1	no	maximal, Hall
33	C₂²×C₅×#41	D₃	1	1	yes	characteristic, complemented
34	C₂³×D₂₀	—	3	1	no	—
35	#66164	—	3	16	no	—
36	C₂×#4093	—	3	2	no	—
37	C₂×#4086	—	3	2	no	—
38	C₂×#4083	—	3	4	no	—
39	C₂×#4076	—	3	4	no	—
40	C₂×#4072	—	3	1	no	—
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂³×D₁₅	—	2	8	no	—
44	C₂³×D₁₅	—	4	8	no	—
45	C₂³×D₁₅	C₂³	1	4	yes	—
46	C₂³×D₁₅	C₂³	1	8	yes	—
47	C₃×C₅×#41	—	2	32	no	—
48	C₂×C₃×C₅×Q₈	—	2	4	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
50	C₂×C₃×C₅×D₄	—	2	8	no	—
51	C₂×C₃×C₅×D₄	—	2	4	no	—
52	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
53	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
54	C₂²×C₃×C₄×C₅	—	2	8	no	—
55	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	complemented
61	C₂×#1220	—	4	16	no	—
62	C₂×#1220	C₂³	1	32	yes	complemented
63	C₂²×Dic₁₅	C₂³	1	4	yes	—
64	C₂×D₆₀	—	2	8	no	—
65	C₂×D₆₀	—	2	8	no	—
66	C₂×D₆₀	—	2	32	no	—
67	C₂×D₆₀	C₂³	1	8	yes	—
68	C₂×D₆₀	C₂³	1	8	yes	—
69	#6719	C₂³	1	8	yes	—
70	#6714	C₂³	1	32	yes	complemented
71	C₄⋊Dic₁₅	C₂³	1	8	yes	complemented
72	C₄×Dic₁₅	C₂³	1	8	yes	complemented
73	C₂²×C₃×#41	D₅	1	1	yes	characteristic, complemented
74	C₂³×D₁₂	—	5	1	no	—
75	#5830	—	5	16	no	—
76	C₂×#947	—	5	2	no	—
77	C₂×#940	—	5	2	no	—
78	C₂×#937	—	5	4	no	—
79	C₂×#930	—	5	4	no	—
80	C₂×#926	—	5	1	no	—
81	C₂⁴×D₅	—	3	2	no	—
82	C₂×C₅×#41	—	2	8	no	—
83	C₂×C₅×#41	C₂×D₃	1	8	yes	complemented
84	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
85	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
86	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
87	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂×D₃	1	2	yes	complemented
89	C₂²×C₂²⋊D₅	—	3	8	no	—
90	C₂²×D₂₀	—	3	2	no	—
91	C₂²×D₂₀	—	3	2	no	—
92	C₂²×D₂₀	—	3	8	no	—
93	C₂²×D₂₀	—	6	8	no	—
94	C₂×C₂²⋊Dic₅	—	3	2	no	—
95	#4093	—	3	16	no	—
96	#4086	—	3	16	no	—
97	#4083	—	3	32	no	—
98	#4076	—	3	32	no	—
99	C₂×#685	—	3	8	no	—
100	#4072	—	3	8	no	—
101	C₂×C₄⋊Dic₅	—	3	2	no	—
102	C₂×C₄×Dic₅	—	3	2	no	—
103	C₂×#535	—	15	1	no	Sylow
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	4	no	—
106	C₂³×C₃×C₅	—	2	8	no	—
107	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
108	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
109	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
110	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
111	C₂²×D₁₅	—	2	16	no	—
112	C₂²×D₁₅	—	2	8	no	—
113	C₂²×D₁₅	—	2	16	no	—
114	C₂²×D₁₅	—	4	16	no	—
115	C₂²×D₁₅	—	4	32	no	—
116	C₂²×D₁₅	C₂⁴	1	8	yes	—
117	C₃×C₅×Q₈	—	2	8	no	—
118	C₃×C₅×D₄	—	2	16	no	—
119	C₃×C₅×D₄	—	2	8	no	—
120	C₂×C₃×C₄×C₅	—	2	4	no	—
121	C₂×C₃×C₄×C₅	—	2	16	no	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
125	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
128	#1220	—	4	32	no	—
129	C₂×Dic₁₅	—	2	8	no	—
130	C₂×Dic₁₅	C₂⁴	1	8	yes	—
131	D₆₀	—	2	16	no	—
132	D₆₀	—	2	16	no	—
133	C₂⁴×D₃	—	5	2	no	—
134	C₂×C₃×#41	—	2	8	no	—
135	C₂×C₃×#41	C₂×D₅	1	8	yes	complemented
136	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
137	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
138	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
139	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂×D₅	1	2	yes	complemented
141	C₂²×#67	—	5	8	no	—
142	C₂²×D₁₂	—	5	2	no	—
143	C₂²×D₁₂	—	5	2	no	—
144	C₂²×D₁₂	—	5	8	no	—
145	C₂²×D₁₂	—	10	8	no	—
146	C₂×#217	—	5	2	no	—
147	#947	—	5	16	no	—
148	#940	—	5	16	no	—
149	#937	—	5	32	no	—
150	#930	—	5	32	no	—
151	C₂×(C₂×D₃)⋊C₄	—	5	8	no	—
152	#926	—	5	8	no	—
153	C₂×C₄⋊Dic₃	—	5	2	no	—
154	C₂×C₄×Dic₃	—	5	2	no	—
155	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
156	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₂³×D₅	—	3	4	no	—
158	C₂³×D₅	—	3	8	no	—
159	C₂³×D₅	—	6	8	no	—
160	C₂³×D₅	—	12	8	no	—
161	C₅×#41	—	2	32	no	—
162	C₂×C₅×Q₈	—	2	4	no	—
163	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
164	C₂×C₅×D₄	—	2	8	no	—
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
167	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
168	C₂²×C₄×C₅	—	2	8	no	—
169	C₂²×C₄×C₅	#67	1	8	yes	complemented
170	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
174	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	complemented
175	C₂×C₂²⋊D₅	—	3	32	no	—
176	C₂×C₂²⋊D₅	—	12	16	no	—
177	C₂²×Dic₅	—	3	4	no	—
178	C₂×D₂₀	—	3	8	no	—
179	C₂×D₂₀	—	3	8	no	—
180	C₂×D₂₀	—	6	8	no	—
181	C₂×D₂₀	—	6	8	no	—
182	C₂×D₂₀	—	6	32	no	—
183	C₂²⋊Dic₅	—	3	8	no	—
184	#685	—	3	32	no	—
185	C₄⋊Dic₅	—	3	8	no	—
186	C₄×Dic₅	—	3	8	no	—
187	C₂²×#41	D₁₅	1	1	yes	characteristic, complemented
188	C₂³×D₄	—	15	1	no	—
189	#535	—	15	16	no	—
190	C₂×#127	—	15	2	no	—
191	C₂×#124	—	15	2	no	—
192	C₂×#121	—	15	4	no	—
193	C₂×#120	—	15	4	no	—
194	C₂×#117	—	15	1	no	—
195	C₂²×C₃×C₅	—	2	8	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	—	2	4	no	—
198	C₂²×C₃×C₅	—	2	8	no	—
199	C₂²×C₃×C₅	—	4	8	no	—
200	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
201	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
202	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
203	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
204	C₂×D₁₅	—	2	8	no	—
205	C₂×D₁₅	—	2	16	no	—
206	C₂×D₁₅	—	4	32	no	—
207	C₂×D₁₅	—	4	16	no	—
208	C₃×C₄×C₅	—	2	4	no	—
209	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
211	Dic₁₅	—	2	8	no	—
212	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
213	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
214	C₂³×D₃	—	5	4	no	—
215	C₂³×D₃	—	5	8	no	—
216	C₂³×D₃	—	10	8	no	—
217	C₂³×D₃	—	20	8	no	—
218	C₃×#41	—	2	32	no	—
219	C₂×C₃×Q₈	—	2	4	no	—
220	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	complemented
221	C₂×C₃×D₄	—	2	8	no	—
222	C₂×C₃×D₄	—	2	4	no	—
223	C₂×C₃×D₄	C₂²×D₅	1	8	yes	—
224	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
225	C₂²×C₃×C₄	—	2	8	no	—
226	C₂²×C₃×C₄	C₂²⋊D₅	1	8	yes	complemented
227	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
231	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	complemented
232	C₂×#67	—	5	32	no	—
233	C₂×#67	—	20	16	no	—
234	C₂²×Dic₃	—	5	4	no	—
235	C₂×D₁₂	—	5	8	no	—
236	C₂×D₁₂	—	5	8	no	—
237	C₂×D₁₂	—	10	8	no	—
238	C₂×D₁₂	—	10	8	no	—
239	C₂×D₁₂	—	10	32	no	—
240	#217	—	5	8	no	—
241	(C₂×D₃)⋊C₄	—	5	32	no	—
242	C₄⋊Dic₃	—	5	8	no	—
243	C₄×Dic₃	—	5	8	no	—
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	—	2	8	no	—
246	C₂³×C₅	—	2	4	no	—
247	C₂³×C₅	C₂×#67	1	4	yes	—
248	C₂³×C₅	C₂³×D₃	1	4	yes	—
249	C₂³×C₅	C₂³×D₃	1	2	yes	—
250	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
251	C₂²×D₅	—	3	8	no	—
252	C₂²×D₅	—	6	16	no	—
253	C₂²×D₅	—	6	16	no	—
254	C₂²×D₅	—	6	8	no	—
255	C₂²×D₅	—	12	16	no	—
256	C₂²×D₅	—	12	32	no	—
257	C₅×Q₈	—	2	8	no	—
258	C₅×D₄	—	2	16	no	—
259	C₅×D₄	—	2	8	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	16	no	—
262	C₂×C₄×C₅	C₂×#67	1	4	yes	—
263	C₂×C₄×C₅	C₂×#67	1	4	yes	—
264	C₂×C₄×C₅	C₂×#67	1	16	yes	complemented
265	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
266	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
267	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
268	C₂²⋊D₅	—	12	32	no	—
269	C₂×Dic₅	—	3	8	no	—
270	C₂×Dic₅	—	6	8	no	—
271	D₂₀	—	6	16	no	—
272	D₂₀	—	6	16	no	—
273	C₂⁵	—	15	2	no	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	C₂×D₁₅	1	8	yes	complemented
276	C₂²×Q₈	C₂×D₁₅	1	1	yes	characteristic, complemented
277	C₂²×D₄	—	15	8	no	—
278	C₂²×D₄	—	15	2	no	—
279	C₂²×D₄	—	15	2	no	—
280	C₂²×D₄	—	15	8	no	—
281	C₂²×D₄	—	30	8	no	—
282	C₂²×D₄	C₂×D₁₅	1	2	yes	—
283	C₂²×D₄	C₂×D₁₅	1	1	yes	characteristic, complemented
284	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
285	C₂³×C₄	C₂×D₁₅	1	2	yes	complemented
286	#127	—	15	16	no	—
287	#124	—	15	16	no	—
288	#121	—	15	32	no	—
289	#120	—	15	32	no	—
290	#117	—	15	8	no	—
291	C₂×C₄⋊C₄	—	15	2	no	—
292	C₂×C₂²⋊C₄	—	15	2	no	—
293	C₂×C₂²⋊C₄	—	15	8	no	—
294	C₂×C₄²	—	15	2	no	—
295	C₂×C₃×C₅	—	2	4	no	—
296	C₂×C₃×C₅	—	4	4	no	—
297	C₂×C₃×C₅	#535	1	4	yes	complemented
298	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
300	D₁₅	—	4	8	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	2	8	no	—
303	C₂³×C₃	—	2	4	no	—
304	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
305	C₂³×C₃	C₂³×D₅	1	4	yes	—
306	C₂³×C₃	C₂³×D₅	1	2	yes	—
307	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
308	C₂²×D₃	—	5	8	no	—
309	C₂²×D₃	—	10	16	no	—
310	C₂²×D₃	—	10	16	no	—
311	C₂²×D₃	—	10	8	no	—
312	C₂²×D₃	—	20	16	no	—
313	C₂²×D₃	—	20	32	no	—
314	C₃×Q₈	—	2	8	no	—
315	C₃×D₄	—	2	16	no	—
316	C₃×D₄	—	2	8	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	16	no	—
319	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
320	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
321	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	16	yes	complemented
322	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
323	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
324	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
325	#67	—	20	32	no	—
326	C₂×Dic₃	—	5	8	no	—
327	C₂×Dic₃	—	10	8	no	—
328	D₁₂	—	10	16	no	—
329	D₁₂	—	10	16	no	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	2	8	no	—
332	C₂²×C₅	—	2	8	no	—
333	C₂²×C₅	—	2	4	no	—
334	C₂²×C₅	—	4	8	no	—
335	C₂²×C₅	#1009	1	4	yes	—
336	C₂²×C₅	C₂²×#67	1	4	yes	—
337	C₂²×C₅	C₂²×#67	1	2	yes	—
338	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
339	C₂×D₅	—	6	16	no	—
340	C₂×D₅	—	6	8	no	—
341	C₂×D₅	—	12	32	no	—
342	C₂×D₅	—	12	16	no	—
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	C₂²×#67	1	4	yes	—
345	C₄×C₅	C₂²×#67	1	4	yes	—
346	Dic₅	—	6	8	no	—
347	C₂⁴	—	15	4	no	—
348	C₂⁴	—	15	8	no	—
349	C₂⁴	—	30	8	no	—
350	C₂⁴	—	60	8	no	—
351	C₂⁴	C₂²×D₁₅	1	2	yes	—
352	C₂⁴	C₂²×D₁₅	1	1	yes	characteristic
353	#41	—	2	32	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	C₂²×D₁₅	1	4	yes	complemented
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	15	32	no	—
359	C₂×D₄	—	15	8	no	—
360	C₂×D₄	—	15	8	no	—
361	C₂×D₄	—	30	8	no	—
362	C₂×D₄	—	30	8	no	—
363	C₂×D₄	—	30	32	no	—
364	C₂×D₄	—	60	16	no	—
365	C₂×D₄	C₂²×D₁₅	1	8	yes	—
366	C₂×D₄	C₂²×D₁₅	1	4	yes	complemented
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	15	4	no	—
369	C₂²×C₄	#1220	1	8	yes	complemented
370	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
371	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
372	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
373	C₂²×C₄	C₂²×D₁₅	1	4	yes	—
374	C₂²×C₄	C₂²×D₁₅	1	8	yes	complemented
375	C₄⋊C₄	—	15	8	no	—
376	C₂²⋊C₄	—	15	8	no	—
377	C₂²⋊C₄	—	15	32	no	—
378	C₄²	—	15	8	no	—
379	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	8	no	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	—	4	8	no	—
385	C₂²×C₃	#4149	1	4	yes	—
386	C₂²×C₃	C₂²×C₂²⋊D₅	1	4	yes	—
387	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
388	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
389	C₂×D₃	—	10	16	no	—
390	C₂×D₃	—	10	8	no	—
391	C₂×D₃	—	20	32	no	—
392	C₂×D₃	—	20	16	no	—
393	C₃×C₄	—	2	4	no	—
394	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
395	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
396	Dic₃	—	10	8	no	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	4	4	no	—
399	C₂×C₅	#5830	1	4	yes	complemented
400	C₂×C₅	C₂×#1009	1	2	yes	—
401	C₂×C₅	C₂³×#67	1	1	yes	characteristic
402	D₅	—	12	8	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	8	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	15	8	no	—
407	C₂³	—	30	16	no	—
408	C₂³	—	30	16	no	—
409	C₂³	—	30	8	no	—
410	C₂³	—	60	16	no	—
411	C₂³	—	60	32	no	—
412	C₂³	C₂×#1220	1	4	yes	—
413	C₂³	C₂³×D₁₅	1	4	yes	—
414	C₂³	C₂³×D₁₅	1	2	yes	—
415	C₂³	C₂³×D₁₅	1	1	yes	characteristic
416	Q₈	—	2	8	no	—
417	D₄	—	2	16	no	—
418	D₄	—	2	8	no	—
419	D₄	—	30	16	no	—
420	D₄	—	30	16	no	—
421	D₄	—	60	32	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	16	no	—
424	C₂×C₄	—	15	8	no	—
425	C₂×C₄	—	30	8	no	—
426	C₂×C₄	C₂×#1220	1	4	yes	—
427	C₂×C₄	C₂×#1220	1	4	yes	—
428	C₂×C₄	C₂×#1220	1	16	yes	complemented
429	C₂×C₄	C₂³×D₁₅	1	4	yes	—
430	C₂×C₄	C₂³×D₁₅	1	2	yes	—
431	C₂×C₄	C₂³×D₁₅	1	2	yes	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	4	4	no	—
434	C₂×C₃	#66164	1	4	yes	complemented
435	C₂×C₃	C₂×#4149	1	2	yes	—
436	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
437	D₃	—	20	8	no	—
438	C₅	C₂×#5830	1	1	yes	characteristic, complemented, Sylow
439	C₂²	—	2	8	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	8	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	8	no	—
444	C₂²	—	30	16	no	—
445	C₂²	—	30	8	no	—
446	C₂²	—	60	32	no	—
447	C₂²	—	60	16	no	—
448	C₂²	#92100	1	4	yes	—
449	C₂²	C₂²×#1220	1	4	yes	—
450	C₂²	C₂²×#1220	1	2	yes	—
451	C₂²	C₂⁴×D₁₅	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	30	8	no	—
454	C₄	C₂²×#1220	1	4	yes	—
455	C₄	C₂²×#1220	1	4	yes	—
456	C₃	C₂×#66164	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	4	no	—
458	C₂	—	4	4	no	—
459	C₂	—	60	8	no	—
460	C₂	#11756589	1	4	yes	direct product factor
461	C₂	C₂×#92100	1	2	yes	—
462	C₂	C₂³×#1220	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₅
commutator, cosocle	C₂²×C₃×C₅	C₂⁵
Frattini	C₂²	C₂⁴×D₁₅
Fitting	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×#41	D₁₅
hypocenter	C₃×C₅	C₂×#535
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂³×D₆₀	C₂	semidirect
3. #11756589	C₂	direct (N × H)
4. C₂×#91836	C₂	semidirect
5. C₂×#91829	C₂	semidirect
6. C₂×#91826	C₂	semidirect
7. C₂×#91819	C₂	semidirect
8. C₂×#91815	C₂	semidirect
12. C₂×C₃×C₅×#41	C₂²	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂³×C₃×C₄×C₅	C₂²	semidirect
18. C₂²×#1220	C₂²	semidirect
22. C₂²×D₆₀	C₂²	semidirect
24. #91836	C₂²	semidirect
25. #91829	C₂²	semidirect
26. #91826	C₂²	semidirect
27. #91819	C₂²	semidirect
28. C₂×#6714	C₂²	semidirect
29. #91815	C₂²	semidirect
30. C₂×C₄⋊Dic₁₅	C₂²	semidirect
31. C₂×C₄×Dic₁₅	C₂²	semidirect
33. C₂²×C₅×#41	D₃	semidirect
49. C₂×C₃×C₅×Q₈	C₂³	semidirect
53. C₂×C₃×C₅×D₄	C₂³	semidirect
55. C₂²×C₃×C₄×C₅	D₄	semidirect
60. C₂²×C₃×C₄×C₅	C₂³	semidirect
62. C₂×#1220	C₂³	semidirect
70. #6714	C₂³	semidirect
71. C₄⋊Dic₁₅	C₂³	semidirect
72. C₄×Dic₁₅	C₂³	semidirect
73. C₂²×C₃×#41	D₅	semidirect
83. C₂×C₅×#41	C₂×D₃	semidirect
84. C₂²×C₅×Q₈	C₂×D₃	semidirect
86. C₂²×C₅×D₄	C₂×D₃	semidirect
88. C₂³×C₄×C₅	C₂×D₃	semidirect
124. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
135. C₂×C₃×#41	C₂×D₅	semidirect
136. C₂²×C₃×Q₈	C₂×D₅	semidirect
138. C₂²×C₃×D₄	C₂×D₅	semidirect
140. C₂³×C₃×C₄	C₂×D₅	semidirect
163. C₂×C₅×Q₈	C₂²×D₃	semidirect
167. C₂×C₅×D₄	C₂²×D₃	semidirect
169. C₂²×C₄×C₅	#67	semidirect
174. C₂²×C₄×C₅	C₂²×D₃	semidirect
187. C₂²×#41	D₁₅	semidirect
220. C₂×C₃×Q₈	C₂²×D₅	semidirect
224. C₂×C₃×D₄	C₂²×D₅	semidirect
226. C₂²×C₃×C₄	C₂²⋊D₅	semidirect
231. C₂²×C₃×C₄	C₂²×D₅	semidirect
264. C₂×C₄×C₅	C₂×#67	semidirect
275. C₂×#41	C₂×D₁₅	semidirect
276. C₂²×Q₈	C₂×D₁₅	semidirect
283. C₂²×D₄	C₂×D₁₅	semidirect
285. C₂³×C₄	C₂×D₁₅	semidirect
297. C₂×C₃×C₅	#535	semidirect
321. C₂×C₃×C₄	C₂×C₂²⋊D₅	semidirect
355. C₂×Q₈	C₂²×D₁₅	semidirect
366. C₂×D₄	C₂²×D₁₅	semidirect
369. C₂²×C₄	#1220	semidirect
374. C₂²×C₄	C₂²×D₁₅	semidirect
379. C₃×C₅	C₂×#535	semidirect
399. C₂×C₅	#5830	semidirect
428. C₂×C₄	C₂×#1220	semidirect
434. C₂×C₃	#66164	semidirect
438. C₅	C₂×#5830	semidirect
456. C₃	C₂×#66164	semidirect
460. C₂	#11756589	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×#41	2
C₂³×D₆₀	2
#11756589	2
C₂×#91836	2
C₂×#91829	2
C₂×#91826	2
C₂×#91819	2
C₂×#91815	2
C₂×#66164	3
C₂×#5830	5

Subgroups — C2×#11756589 #14480367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11756589 #14480367