Subgroups — C₂×#11754509 #14479088

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91559	C₂	1	4	yes	maximal, complemented
5	#11754509	C₂	1	16	yes	maximal, direct product factor
6	C₂×Dic₃×D₂₀	C₂	1	2	yes	maximal, complemented
7	C₂×D₅×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
8	C₂×#91358	C₂	1	2	yes	maximal, complemented
9	C₂×Dic₃×Dic₁₀	C₂	1	2	yes	maximal, complemented
10	C₂×#65857	—	3	1	no	maximal, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×Dic₁₅	C₂²	1	2	yes	—
13	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
14	C₂×C₃×#709	C₄	1	16	yes	complemented
15	C₂×C₃×#709	C₂²	1	8	yes	—
16	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
19	C₂²×D₅×Dic₃	C₂²	1	4	yes	—
20	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
21	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
22	C₂×C₄⋊Dic₁₅	C₂²	1	8	yes	complemented
23	C₂×C₅×#217	C₂²	1	2	yes	—
24	C₅×#926	C₂²	1	8	yes	complemented
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
28	#91559	C₂²	1	32	yes	complemented
29	C₂×#6668	C₂²	1	4	yes	—
30	C₂×#6665	C₂²	1	4	yes	—
31	C₂×Dic₃×Dic₅	C₂²	1	4	yes	—
32	Dic₃×D₂₀	C₂²	1	16	yes	complemented
33	D₅×C₄⋊Dic₃	C₂²	1	16	yes	complemented
34	#91358	C₂²	1	16	yes	complemented
35	Dic₃×Dic₁₀	C₂²	1	16	yes	complemented
36	C₂×#5827	—	5	1	no	maximal, Hall
37	C₂²×#709	D₃	1	1	yes	characteristic
38	C₂×C₅×#117	—	3	1	no	—
39	C₂²×C₄⋊Dic₅	—	3	1	no	—
40	#65857	—	3	16	no	—
41	C₂×#4038	—	3	2	no	—
42	C₂×D₅×C₄⋊C₄	—	3	2	no	—
43	C₂×#4027	—	3	4	no	—
44	C₂×C₄×D₂₀	—	3	2	no	—
45	C₂×C₄×Dic₁₀	—	3	2	no	—
46	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂³×C₃×D₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
52	C₂²×Dic₁₅	—	4	4	no	—
53	C₂²×Dic₁₅	C₂³	1	4	yes	—
54	C₂²×Dic₁₅	C₂³	1	8	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	16	yes	complemented
58	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
59	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
60	C₃×#709	C₂×C₄	1	64	yes	complemented
61	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
62	C₂×C₃×D₂₀	C₂³	1	4	yes	—
63	C₂×C₃×C₄×D₅	C₂×C₄	1	16	yes	complemented
64	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
65	C₂×C₃×Dic₁₀	C₂×C₄	1	8	yes	complemented
66	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
67	C₂×D₅×Dic₃	—	4	8	no	—
68	C₂×D₅×Dic₃	C₂³	1	16	yes	—
69	C₄⋊Dic₁₅	C₂³	1	8	yes	—
70	C₄⋊Dic₁₅	C₂³	1	8	yes	—
71	C₅×#217	C₂³	1	8	yes	—
72	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
73	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
74	C₄×C₅×Dic₃	C₂³	1	8	yes	—
75	#6668	C₂³	1	16	yes	—
76	#6665	C₂³	1	16	yes	—
77	Dic₃×Dic₅	C₂³	1	16	yes	—
78	C₂²×C₃×#41	—	5	1	no	—
79	#5827	—	5	16	no	—
80	C₂×Q₈×Dic₃	—	5	2	no	—
81	C₂×D₄×Dic₃	—	5	4	no	—
82	C₂×D₄×Dic₃	—	5	2	no	—
83	C₂×#926	—	5	2	no	—
84	C₂×#926	D₅	1	1	yes	characteristic, complemented
85	C₂²×C₄⋊Dic₃	—	5	1	no	—
86	C₂²×C₄⋊Dic₃	—	5	2	no	—
87	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₂²⋊D₅	C₂×D₃	1	2	yes	—
89	C₂³×Dic₅	—	3	2	no	—
90	C₂×#709	Dic₃	1	16	yes	complemented
91	C₂×#709	C₂×D₃	1	8	yes	—
92	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₄×D₅	—	3	4	no	—
94	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
95	C₂²×Dic₁₀	C₂×D₃	1	1	yes	characteristic
96	C₅×#117	—	3	8	no	—
97	C₂×C₅×C₄⋊C₄	—	3	1	no	—
98	C₂×C₅×C₄⋊C₄	—	3	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
100	C₂×C₄²×C₅	—	3	2	no	—
101	C₂×#685	—	3	4	no	—
102	C₂×C₄⋊Dic₅	—	3	2	no	—
103	C₂×C₄⋊Dic₅	—	3	2	no	—
104	C₂×C₄⋊Dic₅	—	3	8	no	—
105	C₂×#683	—	3	4	no	—
106	C₂×C₄×Dic₅	—	3	4	no	—
107	#4038	—	3	16	no	—
108	D₅×C₄⋊C₄	—	3	16	no	—
109	#4027	—	3	32	no	—
110	C₄×D₂₀	—	3	16	no	—
111	C₄×Dic₁₀	—	3	16	no	—
112	C₂×#520	—	15	1	no	Sylow
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
116	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₂²×C₃×D₅	—	2	4	no	—
119	C₂²×C₃×D₅	—	2	4	no	—
120	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
121	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	16	yes	complemented
125	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
127	C₂×Dic₁₅	—	2	8	no	—
128	C₂×Dic₁₅	—	4	8	no	—
129	C₂×Dic₁₅	C₂⁴	1	8	yes	—
130	C₂×C₅×Dic₃	—	2	4	no	—
131	C₂×C₅×Dic₃	—	2	4	no	—
132	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
133	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
134	C₃×C₂²⋊D₅	C₂²×C₄	1	32	yes	complemented
135	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
136	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
137	C₃×D₂₀	C₂²×C₄	1	16	yes	complemented
138	C₃×C₄×D₅	C₂²×C₄	1	32	yes	complemented
139	C₃×Dic₁₀	C₂²×C₄	1	16	yes	complemented
140	D₅×Dic₃	—	4	16	no	—
141	C₂×C₃×#41	—	5	16	no	—
142	C₂×C₃×#41	—	5	8	no	—
143	C₂²×C₃×Q₈	—	5	1	no	—
144	C₂²×C₃×D₄	—	5	2	no	—
145	C₂²×C₃×D₄	—	5	1	no	—
146	C₂³×C₃×C₄	—	5	2	no	—
147	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
148	C₂³×Dic₃	—	5	2	no	—
149	C₂³×Dic₃	—	5	4	no	—
150	C₂×#217	—	5	4	no	—
151	C₂×#217	C₂×D₅	1	2	yes	—
152	Q₈×Dic₃	—	5	16	no	—
153	D₄×Dic₃	—	5	32	no	—
154	D₄×Dic₃	—	5	16	no	—
155	#926	—	5	16	no	—
156	#926	C₂×D₅	1	8	yes	complemented
157	C₂×C₄⋊Dic₃	—	5	2	no	—
158	C₂×C₄⋊Dic₃	—	5	2	no	—
159	C₂×C₄⋊Dic₃	—	5	8	no	—
160	C₂×C₄⋊Dic₃	—	5	4	no	—
161	C₂×C₄⋊Dic₃	—	5	16	no	—
162	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
163	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
164	C₂×C₄×Dic₃	—	5	4	no	—
165	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	—
166	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₂³×D₅	C₂²×D₃	1	2	yes	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	—	3	2	no	—
170	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	complemented
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	C₂×C₂²⋊D₅	C₂×Dic₃	1	16	yes	complemented
175	C₂×C₂²⋊D₅	C₂²×D₃	1	8	yes	—
176	C₂²×Dic₅	—	3	4	no	—
177	C₂²×Dic₅	—	3	8	no	—
178	C₂²×Dic₅	—	12	4	no	—
179	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
180	#709	C₂×Dic₃	1	64	yes	complemented
181	C₂×D₂₀	C₂×Dic₃	1	8	yes	complemented
182	C₂×D₂₀	C₂²×D₃	1	4	yes	—
183	C₂×C₄×D₅	—	3	16	no	—
184	C₂×C₄×D₅	—	12	8	no	—
185	C₂×C₄×D₅	C₂×Dic₃	1	16	yes	complemented
186	C₂×C₄×D₅	C₂²×D₃	1	8	yes	—
187	C₂×Dic₁₀	C₂×Dic₃	1	8	yes	complemented
188	C₂×Dic₁₀	C₂²×D₃	1	4	yes	—
189	C₅×C₄⋊C₄	—	3	4	no	—
190	C₅×C₄⋊C₄	—	3	4	no	—
191	C₅×C₂²⋊C₄	—	3	8	no	—
192	C₄²×C₅	—	3	8	no	—
193	#685	—	3	16	no	—
194	C₄⋊Dic₅	—	3	8	no	—
195	C₄⋊Dic₅	—	3	8	no	—
196	#683	—	3	16	no	—
197	C₄×Dic₅	—	3	16	no	—
198	C₂²×#41	—	5	1	no	—
199	#520	—	15	16	no	—
200	C₂×C₄×Q₈	—	15	2	no	—
201	C₂×C₄×D₄	—	15	2	no	—
202	C₂×C₄×D₄	—	15	4	no	—
203	C₂×#117	—	3	1	no	—
204	C₂×#117	—	15	2	no	—
205	C₂²×C₄⋊C₄	—	15	2	no	—
206	C₂²×C₄⋊C₄	—	15	1	no	—
207	C₂²×C₃×C₅	—	2	8	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	C₂³×C₄	1	4	yes	—
211	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
212	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
213	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
214	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
215	C₂×C₃×D₅	—	2	16	no	—
216	C₂×C₃×D₅	—	2	4	no	—
217	C₂×C₃×D₅	—	2	4	no	—
218	C₂×C₃×D₅	C₂³×C₄	1	8	yes	—
219	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
220	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
221	Dic₁₅	—	2	8	no	—
222	C₃×Dic₅	C₂³×C₄	1	8	yes	—
223	C₅×Dic₃	—	2	4	no	—
224	C₅×Dic₃	—	2	4	no	—
225	C₂⁴×C₃	—	5	2	no	—
226	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
227	C₃×#41	—	5	64	no	—
228	C₂×C₃×Q₈	—	5	8	no	—
229	C₂×C₃×Q₈	—	5	4	no	—
230	C₂×C₃×D₄	—	5	16	no	—
231	C₂×C₃×D₄	—	5	8	no	—
232	C₂×C₃×D₄	—	5	8	no	—
233	C₂×C₃×D₄	—	5	4	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	5	16	no	—
236	C₂²×C₃×C₄	—	5	8	no	—
237	C₂²×C₃×C₄	C₄×D₅	1	8	yes	complemented
238	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
241	C₂²×Dic₃	—	5	4	no	—
242	C₂²×Dic₃	—	5	8	no	—
243	C₂²×Dic₃	—	5	16	no	—
244	C₂²×Dic₃	—	20	8	no	—
245	C₂²×Dic₃	—	20	4	no	—
246	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
247	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
248	#217	—	5	16	no	—
249	#217	C₂²×D₅	1	8	yes	—
250	C₄⋊Dic₃	—	5	8	no	—
251	C₄⋊Dic₃	—	5	8	no	—
252	C₄⋊Dic₃	—	5	16	no	—
253	C₄⋊Dic₃	C₂²×D₅	1	4	yes	—
254	C₄⋊Dic₃	C₂²×D₅	1	4	yes	—
255	C₄×Dic₃	—	5	16	no	—
256	C₄×Dic₃	C₂²×D₅	1	8	yes	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
260	C₂³×C₅	C₂³×D₃	1	2	yes	—
261	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
262	C₂²×D₅	—	2	4	no	—
263	C₂²×D₅	—	2	4	no	—
264	C₂²×D₅	C₂²×Dic₃	1	8	yes	—
265	C₂²×D₅	C₂³×D₃	1	4	yes	—
266	C₂×C₄×C₅	—	3	4	no	—
267	C₂×C₄×C₅	—	3	4	no	—
268	C₂×C₄×C₅	—	6	4	no	—
269	C₂×C₄×C₅	—	6	4	no	—
270	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
271	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
272	C₂×C₄×C₅	C₂²×Dic₃	1	16	yes	complemented
273	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
274	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
275	C₂²⋊D₅	C₂²×Dic₃	1	32	yes	complemented
276	C₂×Dic₅	—	3	8	no	—
277	C₂×Dic₅	—	6	8	no	—
278	C₂×Dic₅	—	12	8	no	—
279	C₂×Dic₅	C₂²×Dic₃	1	8	yes	—
280	C₂×Dic₅	C₂³×D₃	1	4	yes	—
281	D₂₀	C₂²×Dic₃	1	16	yes	complemented
282	C₄×D₅	—	12	16	no	—
283	C₄×D₅	C₂²×Dic₃	1	32	yes	complemented
284	Dic₁₀	C₂²×Dic₃	1	16	yes	complemented
285	C₂×#41	—	5	16	no	—
286	C₂×#41	—	5	8	no	—
287	C₂²×Q₈	—	5	1	no	—
288	C₂²×D₄	—	5	2	no	—
289	C₂²×D₄	—	5	1	no	—
290	C₂³×C₄	—	5	2	no	—
291	C₂³×C₄	—	15	4	no	—
292	C₂³×C₄	—	15	2	no	—
293	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
294	C₄×Q₈	—	15	16	no	—
295	C₄×D₄	—	15	16	no	—
296	C₄×D₄	—	15	32	no	—
297	#117	—	3	8	no	—
298	#117	—	15	16	no	—
299	C₂×C₄⋊C₄	—	3	1	no	—
300	C₂×C₄⋊C₄	—	3	1	no	—
301	C₂×C₄⋊C₄	—	15	16	no	—
302	C₂×C₄⋊C₄	—	15	4	no	—
303	C₂×C₄⋊C₄	—	15	2	no	—
304	C₂×C₄⋊C₄	—	15	2	no	—
305	C₂×C₄⋊C₄	—	15	8	no	—
306	C₂×C₂²⋊C₄	—	3	2	no	—
307	C₂×C₂²⋊C₄	—	15	4	no	—
308	C₂×C₄²	—	3	2	no	—
309	C₂×C₄²	—	15	4	no	—
310	C₂×C₃×C₅	—	2	4	no	—
311	C₂×C₃×C₅	#520	1	4	yes	complemented
312	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₃×D₅	—	2	8	no	—
316	C₂³×C₃	—	2	2	no	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	5	8	no	—
319	C₂³×C₃	—	5	4	no	—
320	C₂³×C₃	—	10	4	no	—
321	C₂³×C₃	—	10	4	no	—
322	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
323	C₂³×C₃	C₂³×D₅	1	2	yes	—
324	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
325	C₃×Q₈	—	5	16	no	—
326	C₃×D₄	—	5	32	no	—
327	C₃×D₄	—	5	16	no	—
328	C₂×C₃×C₄	—	5	8	no	—
329	C₂×C₃×C₄	—	5	4	no	—
330	C₂×C₃×C₄	—	5	32	no	—
331	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
333	C₂×C₃×C₄	C₂×C₄×D₅	1	16	yes	complemented
334	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
335	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
336	C₂×Dic₃	—	2	4	no	—
337	C₂×Dic₃	—	2	4	no	—
338	C₂×Dic₃	—	5	8	no	—
339	C₂×Dic₃	—	10	8	no	—
340	C₂×Dic₃	—	20	16	no	—
341	C₂×Dic₃	—	20	8	no	—
342	C₂×Dic₃	C₂³×D₅	1	4	yes	—
343	C₂×Dic₃	C₂³×D₅	1	4	yes	—
344	C₂²×C₅	—	2	2	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	8	no	—
347	C₂²×C₅	#1009	1	2	yes	—
348	C₂²×C₅	#1010	1	2	yes	—
349	C₂²×C₅	C₂³×Dic₃	1	4	yes	—
350	C₂²×C₅	C₂³×Dic₃	1	2	yes	—
351	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
352	C₂×D₅	—	2	4	no	—
353	C₂×D₅	—	2	4	no	—
354	C₂×D₅	—	2	16	no	—
355	C₂×D₅	C₂³×Dic₃	1	8	yes	—
356	C₄×C₅	—	6	4	no	—
357	C₄×C₅	—	6	4	no	—
358	C₄×C₅	C₂³×Dic₃	1	4	yes	—
359	C₄×C₅	C₂³×Dic₃	1	4	yes	—
360	Dic₅	—	6	8	no	—
361	Dic₅	C₂³×Dic₃	1	8	yes	—
362	C₂⁴	—	5	2	no	—
363	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
364	#41	—	5	64	no	—
365	C₂×Q₈	—	5	8	no	—
366	C₂×Q₈	—	5	4	no	—
367	C₂×D₄	—	5	16	no	—
368	C₂×D₄	—	5	8	no	—
369	C₂×D₄	—	5	8	no	—
370	C₂×D₄	—	5	4	no	—
371	C₂²×C₄	—	3	2	no	—
372	C₂²×C₄	—	3	2	no	—
373	C₂²×C₄	—	5	2	no	—
374	C₂²×C₄	—	5	16	no	—
375	C₂²×C₄	—	5	8	no	—
376	C₂²×C₄	—	15	16	no	—
377	C₂²×C₄	—	15	4	no	—
378	C₂²×C₄	—	15	8	no	—
379	C₂²×C₄	—	60	8	no	—
380	C₂²×C₄	—	60	4	no	—
381	C₂²×C₄	D₅×Dic₃	1	8	yes	complemented
382	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₃×D₅	1	4	yes	—
385	C₄⋊C₄	—	3	4	no	—
386	C₄⋊C₄	—	3	4	no	—
387	C₄⋊C₄	—	15	16	no	—
388	C₄⋊C₄	—	15	8	no	—
389	C₄⋊C₄	—	15	8	no	—
390	C₂²⋊C₄	—	3	8	no	—
391	C₂²⋊C₄	—	15	16	no	—
392	C₄²	—	3	8	no	—
393	C₄²	—	15	16	no	—
394	C₃×C₅	C₂×#520	1	1	yes	characteristic, complemented, Hall
395	C₂²×C₃	—	2	8	no	—
396	C₂²×C₃	—	2	2	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	5	8	no	—
399	C₂²×C₃	—	10	16	no	—
400	C₂²×C₃	—	10	4	no	—
401	C₂²×C₃	—	10	4	no	—
402	C₂²×C₃	C₂²×C₄×D₅	1	4	yes	—
403	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
404	C₂²×C₃	#4149	1	2	yes	—
405	C₂²×C₃	#4150	1	2	yes	—
406	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
407	C₃×C₄	—	5	8	no	—
408	C₃×C₄	C₂²×C₄×D₅	1	4	yes	—
409	C₃×C₄	C₂²×C₄×D₅	1	4	yes	—
410	Dic₃	—	2	4	no	—
411	Dic₃	—	2	4	no	—
412	Dic₃	—	10	8	no	—
413	C₂×C₅	—	2	4	no	—
414	C₂×C₅	#5827	1	4	yes	complemented
415	C₂×C₅	C₂×#1009	1	1	yes	characteristic
416	C₂×C₅	C₂×#1010	1	1	yes	characteristic
417	C₂×C₅	C₂⁴×Dic₃	1	1	yes	characteristic
418	D₅	—	2	8	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	5	8	no	—
422	C₂³	—	5	4	no	—
423	C₂³	—	10	4	no	—
424	C₂³	—	10	4	no	—
425	C₂³	C₂×D₅×Dic₃	1	4	yes	—
426	C₂³	C₂²×D₃×D₅	1	2	yes	—
427	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
428	Q₈	—	5	16	no	—
429	D₄	—	5	32	no	—
430	D₄	—	5	16	no	—
431	C₂×C₄	—	3	4	no	—
432	C₂×C₄	—	3	4	no	—
433	C₂×C₄	—	5	8	no	—
434	C₂×C₄	—	5	4	no	—
435	C₂×C₄	—	5	32	no	—
436	C₂×C₄	—	6	4	no	—
437	C₂×C₄	—	6	4	no	—
438	C₂×C₄	—	15	8	no	—
439	C₂×C₄	—	30	8	no	—
440	C₂×C₄	—	60	16	no	—
441	C₂×C₄	—	60	8	no	—
442	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
443	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
444	C₂×C₄	C₂×D₅×Dic₃	1	16	yes	complemented
445	C₂×C₄	C₂²×D₃×D₅	1	2	yes	—
446	C₂×C₄	C₂²×D₃×D₅	1	2	yes	—
447	C₂×C₃	—	2	4	no	—
448	C₂×C₃	—	10	8	no	—
449	C₂×C₃	#65857	1	4	yes	complemented
450	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
451	C₂×C₃	C₂×#4149	1	1	yes	characteristic
452	C₂×C₃	C₂×#4150	1	1	yes	characteristic
453	C₅	C₂×#5827	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	2	8	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	5	8	no	—
458	C₂²	—	10	16	no	—
459	C₂²	—	10	4	no	—
460	C₂²	—	10	4	no	—
461	C₂²	#92001	1	2	yes	—
462	C₂²	#92019	1	2	yes	—
463	C₂²	C₂²×D₅×Dic₃	1	4	yes	—
464	C₂²	C₂²×D₅×Dic₃	1	2	yes	—
465	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
466	C₄	—	5	8	no	—
467	C₄	—	6	4	no	—
468	C₄	—	6	4	no	—
469	C₄	—	30	8	no	—
470	C₄	C₂²×D₅×Dic₃	1	4	yes	—
471	C₄	C₂²×D₅×Dic₃	1	4	yes	—
472	C₃	C₂×#65857	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	2	4	no	—
474	C₂	—	10	8	no	—
475	C₂	#11754509	1	4	yes	direct product factor
476	C₂	C₂×#92001	1	1	yes	characteristic
477	C₂	C₂×#92019	1	1	yes	characteristic
478	C₂	C₂³×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×#709	C₂
cosocle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#520
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Dic₁₅	C₂	semidirect
3. C₂×C₅×#926	C₂	semidirect
4. C₂×#91559	C₂	semidirect
5. #11754509	C₂	direct (N × H)
6. C₂×Dic₃×D₂₀	C₂	semidirect
7. C₂×D₅×C₄⋊Dic₃	C₂	semidirect
8. C₂×#91358	C₂	semidirect
9. C₂×Dic₃×Dic₁₀	C₂	semidirect
14. C₂×C₃×#709	C₄	semidirect
22. C₂×C₄⋊Dic₁₅	C₂²	semidirect
24. C₅×#926	C₂²	semidirect
28. #91559	C₂²	semidirect
32. Dic₃×D₂₀	C₂²	semidirect
33. D₅×C₄⋊Dic₃	C₂²	semidirect
34. #91358	C₂²	semidirect
35. Dic₃×Dic₁₀	C₂²	semidirect
48. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
57. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
60. C₃×#709	C₂×C₄	semidirect
61. C₂×C₃×D₂₀	C₂×C₄	semidirect
63. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
65. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
84. C₂×#926	D₅	semidirect
90. C₂×#709	Dic₃	semidirect
124. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
134. C₃×C₂²⋊D₅	C₂²×C₄	semidirect
137. C₃×D₂₀	C₂²×C₄	semidirect
138. C₃×C₄×D₅	C₂²×C₄	semidirect
139. C₃×Dic₁₀	C₂²×C₄	semidirect
156. #926	C₂×D₅	semidirect
170. C₂²×C₄×C₅	C₂×Dic₃	semidirect
174. C₂×C₂²⋊D₅	C₂×Dic₃	semidirect
180. #709	C₂×Dic₃	semidirect
181. C₂×D₂₀	C₂×Dic₃	semidirect
185. C₂×C₄×D₅	C₂×Dic₃	semidirect
187. C₂×Dic₁₀	C₂×Dic₃	semidirect
237. C₂²×C₃×C₄	C₄×D₅	semidirect
272. C₂×C₄×C₅	C₂²×Dic₃	semidirect
275. C₂²⋊D₅	C₂²×Dic₃	semidirect
281. D₂₀	C₂²×Dic₃	semidirect
283. C₄×D₅	C₂²×Dic₃	semidirect
284. Dic₁₀	C₂²×Dic₃	semidirect
311. C₂×C₃×C₅	#520	semidirect
333. C₂×C₃×C₄	C₂×C₄×D₅	semidirect
381. C₂²×C₄	D₅×Dic₃	semidirect
394. C₃×C₅	C₂×#520	semidirect
414. C₂×C₅	#5827	semidirect
444. C₂×C₄	C₂×D₅×Dic₃	semidirect
449. C₂×C₃	#65857	semidirect
453. C₅	C₂×#5827	semidirect
472. C₃	C₂×#65857	semidirect
475. C₂	#11754509	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×#709	2
C₂²×C₄⋊Dic₁₅	2
C₂×C₅×#926	2
C₂×#91559	2
#11754509	2
C₂×Dic₃×D₂₀	2
C₂×D₅×C₄⋊Dic₃	2
C₂×#91358	2
C₂×Dic₃×Dic₁₀	2
C₂×#65857	3
C₂×#5827	5

Subgroups — C2×#11754509 #14479088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11754509 #14479088