Subgroups — C₂×#11754513 #14479090

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×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#67⋊Dic₅	C₂	1	4	yes	maximal, complemented
5	#11754513	C₂	1	16	yes	maximal, direct product factor
6	C₂×D₃×C₄⋊Dic₅	C₂	1	2	yes	maximal, complemented
7	C₂×Dic₅×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₂×#91338	C₂	1	2	yes	maximal, complemented
9	C₂×Dic₅×Dic₆	C₂	1	2	yes	maximal, complemented
10	C₂×#66161	—	3	1	no	maximal, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×Dic₁₅	C₂²	1	2	yes	—
13	C₂²×C₅×#67	C₂²	1	2	yes	—
14	C₂×C₅×#235	C₄	1	16	yes	complemented
15	C₂×C₅×#235	C₂²	1	8	yes	—
16	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₂²×D₃×Dic₅	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×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
24	C₃×#4072	C₂²	1	8	yes	complemented
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
28	#67⋊Dic₅	C₂²	1	32	yes	complemented
29	C₂×Dic₃⋊Dic₅	C₂²	1	4	yes	—
30	C₂×(C₂×D₃)⋊Dic₅	C₂²	1	4	yes	—
31	C₂×Dic₃×Dic₅	C₂²	1	4	yes	—
32	D₃×C₄⋊Dic₅	C₂²	1	16	yes	complemented
33	Dic₅×D₁₂	C₂²	1	16	yes	complemented
34	#91338	C₂²	1	16	yes	complemented
35	Dic₅×Dic₆	C₂²	1	16	yes	complemented
36	C₂×#5523	—	5	1	no	maximal, Hall
37	C₂²×C₅×#41	—	3	1	no	—
38	#66161	—	3	16	no	—
39	C₂×Q₈×Dic₅	—	3	2	no	—
40	C₂×D₄×Dic₅	—	3	2	no	—
41	C₂×D₄×Dic₅	—	3	4	no	—
42	C₂×#4072	—	3	2	no	—
43	C₂×#4072	D₃	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊Dic₅	—	3	2	no	—
45	C₂²×C₄⋊Dic₅	—	3	1	no	—
46	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂³×C₅×D₃	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	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
56	C₂×C₅×#67	C₂³	1	8	yes	—
57	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
58	C₅×#235	C₂×C₄	1	64	yes	complemented
59	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
60	C₂×C₅×D₁₂	C₂³	1	4	yes	—
61	C₂×C₄×C₅×D₃	C₂×C₄	1	16	yes	complemented
62	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
63	C₂×C₅×Dic₆	C₂×C₄	1	8	yes	complemented
64	C₂×C₅×Dic₆	C₂³	1	4	yes	—
65	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
66	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
67	C₂×D₃×Dic₅	—	4	8	no	—
68	C₂×D₃×Dic₅	C₂³	1	16	yes	—
69	C₄⋊Dic₁₅	C₂³	1	8	yes	—
70	C₄⋊Dic₁₅	C₂³	1	8	yes	—
71	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
72	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
73	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
74	C₃×C₄×Dic₅	C₂³	1	8	yes	—
75	Dic₃⋊Dic₅	C₂³	1	16	yes	—
76	(C₂×D₃)⋊Dic₅	C₂³	1	16	yes	—
77	Dic₃×Dic₅	C₂³	1	16	yes	—
78	C₂²×#235	D₅	1	1	yes	characteristic
79	C₂×C₃×#117	—	5	1	no	—
80	C₂²×C₄⋊Dic₃	—	5	1	no	—
81	#5523	—	5	16	no	—
82	C₂×#892	—	5	2	no	—
83	C₂×D₃×C₄⋊C₄	—	5	2	no	—
84	C₂×#67⋊C₄	—	5	4	no	—
85	C₂×C₄×D₁₂	—	5	2	no	—
86	C₂×C₄×Dic₆	—	5	2	no	—
87	C₂×C₅×#41	—	3	16	no	—
88	C₂×C₅×#41	—	3	8	no	—
89	C₂²×C₅×Q₈	—	3	1	no	—
90	C₂²×C₅×D₄	—	3	2	no	—
91	C₂²×C₅×D₄	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	2	no	—
93	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
94	C₂³×Dic₅	—	3	2	no	—
95	C₂³×Dic₅	—	3	4	no	—
96	C₂×C₂²⋊Dic₅	—	3	4	no	—
97	C₂×C₂²⋊Dic₅	C₂×D₃	1	2	yes	—
98	Q₈×Dic₅	—	3	16	no	—
99	D₄×Dic₅	—	3	32	no	—
100	D₄×Dic₅	—	3	16	no	—
101	#4072	—	3	16	no	—
102	#4072	C₂×D₃	1	8	yes	complemented
103	C₂×C₄⋊Dic₅	—	3	2	no	—
104	C₂×C₄⋊Dic₅	—	3	2	no	—
105	C₂×C₄⋊Dic₅	—	3	8	no	—
106	C₂×C₄⋊Dic₅	—	3	4	no	—
107	C₂×C₄⋊Dic₅	—	3	16	no	—
108	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
109	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
110	C₂×C₄×Dic₅	—	3	4	no	—
111	C₂×C₄×Dic₅	C₂×D₃	1	2	yes	—
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×C₅×D₃	—	2	4	no	—
119	C₂²×C₅×D₃	—	2	4	no	—
120	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
121	C₂²×C₅×D₃	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	C₅×#67	C₂²×C₄	1	32	yes	complemented
131	C₂×C₅×Dic₃	C₂²×C₄	1	8	yes	—
132	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
133	C₅×D₁₂	C₂²×C₄	1	16	yes	complemented
134	C₄×C₅×D₃	C₂²×C₄	1	32	yes	complemented
135	C₅×Dic₆	C₂²×C₄	1	16	yes	complemented
136	C₂×C₃×Dic₅	—	2	4	no	—
137	C₂×C₃×Dic₅	—	2	4	no	—
138	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
139	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
140	D₃×Dic₅	—	4	16	no	—
141	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
142	C₂²×#67	C₂×D₅	1	2	yes	—
143	C₂³×Dic₃	—	5	2	no	—
144	C₂×#235	Dic₅	1	16	yes	complemented
145	C₂×#235	C₂×D₅	1	8	yes	—
146	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
147	C₂²×C₄×D₃	—	5	4	no	—
148	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
149	C₂²×Dic₆	C₂×D₅	1	1	yes	characteristic
150	C₃×#117	—	5	8	no	—
151	C₂×C₃×C₄⋊C₄	—	5	1	no	—
152	C₂×C₃×C₄⋊C₄	—	5	1	no	—
153	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
154	C₂×C₃×C₄²	—	5	2	no	—
155	C₂×(C₂×D₃)⋊C₄	—	5	4	no	—
156	C₂×C₄⋊Dic₃	—	5	2	no	—
157	C₂×C₄⋊Dic₃	—	5	2	no	—
158	C₂×C₄⋊Dic₃	—	5	8	no	—
159	C₂×Dic₃⋊C₄	—	5	4	no	—
160	C₂×C₄×Dic₃	—	5	4	no	—
161	#892	—	5	16	no	—
162	D₃×C₄⋊C₄	—	5	16	no	—
163	#67⋊C₄	—	5	32	no	—
164	C₄×D₁₂	—	5	16	no	—
165	C₄×Dic₆	—	5	16	no	—
166	C₂⁴×C₅	—	3	2	no	—
167	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₅×#41	—	3	64	no	—
169	C₂×C₅×Q₈	—	3	8	no	—
170	C₂×C₅×Q₈	—	3	4	no	—
171	C₂×C₅×D₄	—	3	16	no	—
172	C₂×C₅×D₄	—	3	8	no	—
173	C₂×C₅×D₄	—	3	8	no	—
174	C₂×C₅×D₄	—	3	4	no	—
175	C₂²×C₄×C₅	—	3	2	no	—
176	C₂²×C₄×C₅	—	3	16	no	—
177	C₂²×C₄×C₅	—	3	8	no	—
178	C₂²×C₄×C₅	C₄×D₃	1	8	yes	complemented
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
182	C₂²×Dic₅	—	3	4	no	—
183	C₂²×Dic₅	—	3	8	no	—
184	C₂²×Dic₅	—	3	16	no	—
185	C₂²×Dic₅	—	12	8	no	—
186	C₂²×Dic₅	—	12	4	no	—
187	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
188	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
189	C₂²⋊Dic₅	—	3	16	no	—
190	C₂²⋊Dic₅	C₂²×D₃	1	8	yes	—
191	C₄⋊Dic₅	—	3	8	no	—
192	C₄⋊Dic₅	—	3	8	no	—
193	C₄⋊Dic₅	—	3	16	no	—
194	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
195	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
196	C₄×Dic₅	—	3	16	no	—
197	C₄×Dic₅	C₂²×D₃	1	8	yes	—
198	C₂²×#41	—	3	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	—	5	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×C₅×D₃	—	2	16	no	—
216	C₂×C₅×D₃	—	2	4	no	—
217	C₂×C₅×D₃	—	2	4	no	—
218	C₂×C₅×D₃	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	—	2	4	no	—
223	C₃×Dic₅	—	2	4	no	—
224	C₅×Dic₃	C₂³×C₄	1	8	yes	—
225	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
226	C₂³×D₃	C₂²×D₅	1	2	yes	—
227	C₂²×C₃×C₄	—	5	2	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	C₂×Dic₅	1	8	yes	complemented
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
233	C₂×#67	C₂×Dic₅	1	16	yes	complemented
234	C₂×#67	C₂²×D₅	1	8	yes	—
235	C₂²×Dic₃	—	5	4	no	—
236	C₂²×Dic₃	—	5	8	no	—
237	C₂²×Dic₃	—	20	4	no	—
238	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
239	#235	C₂×Dic₅	1	64	yes	complemented
240	C₂×D₁₂	C₂×Dic₅	1	8	yes	complemented
241	C₂×D₁₂	C₂²×D₅	1	4	yes	—
242	C₂×C₄×D₃	—	5	16	no	—
243	C₂×C₄×D₃	—	20	8	no	—
244	C₂×C₄×D₃	C₂×Dic₅	1	16	yes	complemented
245	C₂×C₄×D₃	C₂²×D₅	1	8	yes	—
246	C₂×Dic₆	C₂×Dic₅	1	8	yes	complemented
247	C₂×Dic₆	C₂²×D₅	1	4	yes	—
248	C₃×C₄⋊C₄	—	5	4	no	—
249	C₃×C₄⋊C₄	—	5	4	no	—
250	C₃×C₂²⋊C₄	—	5	8	no	—
251	C₃×C₄²	—	5	8	no	—
252	(C₂×D₃)⋊C₄	—	5	16	no	—
253	C₄⋊Dic₃	—	5	8	no	—
254	C₄⋊Dic₃	—	5	8	no	—
255	Dic₃⋊C₄	—	5	16	no	—
256	C₄×Dic₃	—	5	16	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	3	8	no	—
260	C₂³×C₅	—	3	4	no	—
261	C₂³×C₅	—	6	4	no	—
262	C₂³×C₅	—	6	4	no	—
263	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
264	C₂³×C₅	C₂³×D₃	1	2	yes	—
265	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
266	C₅×Q₈	—	3	16	no	—
267	C₅×D₄	—	3	32	no	—
268	C₅×D₄	—	3	16	no	—
269	C₂×C₄×C₅	—	3	8	no	—
270	C₂×C₄×C₅	—	3	4	no	—
271	C₂×C₄×C₅	—	3	32	no	—
272	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
273	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
274	C₂×C₄×C₅	C₂×C₄×D₃	1	16	yes	complemented
275	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
276	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
277	C₂×Dic₅	—	2	4	no	—
278	C₂×Dic₅	—	2	4	no	—
279	C₂×Dic₅	—	3	8	no	—
280	C₂×Dic₅	—	6	8	no	—
281	C₂×Dic₅	—	12	16	no	—
282	C₂×Dic₅	—	12	8	no	—
283	C₂×Dic₅	C₂³×D₃	1	4	yes	—
284	C₂×Dic₅	C₂³×D₃	1	4	yes	—
285	C₂×#41	—	3	16	no	—
286	C₂×#41	—	3	8	no	—
287	C₂²×Q₈	—	3	1	no	—
288	C₂²×D₄	—	3	2	no	—
289	C₂²×D₄	—	3	1	no	—
290	C₂³×C₄	—	3	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	—	5	8	no	—
298	#117	—	15	16	no	—
299	C₂×C₄⋊C₄	—	5	1	no	—
300	C₂×C₄⋊C₄	—	5	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	—	5	2	no	—
307	C₂×C₂²⋊C₄	—	15	4	no	—
308	C₂×C₄²	—	5	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	C₅×D₃	—	2	8	no	—
316	C₂³×C₃	—	2	2	no	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
319	C₂³×C₃	C₂³×D₅	1	2	yes	—
320	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
321	C₂²×D₃	—	2	4	no	—
322	C₂²×D₃	—	2	4	no	—
323	C₂²×D₃	C₂²×Dic₅	1	8	yes	—
324	C₂²×D₃	C₂³×D₅	1	4	yes	—
325	C₂×C₃×C₄	—	5	4	no	—
326	C₂×C₃×C₄	—	5	4	no	—
327	C₂×C₃×C₄	—	10	4	no	—
328	C₂×C₃×C₄	—	10	4	no	—
329	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
330	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
331	C₂×C₃×C₄	C₂²×Dic₅	1	16	yes	complemented
332	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
333	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
334	#67	C₂²×Dic₅	1	32	yes	complemented
335	C₂×Dic₃	—	5	8	no	—
336	C₂×Dic₃	—	10	8	no	—
337	C₂×Dic₃	—	20	8	no	—
338	C₂×Dic₃	C₂²×Dic₅	1	8	yes	—
339	C₂×Dic₃	C₂³×D₅	1	4	yes	—
340	D₁₂	C₂²×Dic₅	1	16	yes	complemented
341	C₄×D₃	—	20	16	no	—
342	C₄×D₃	C₂²×Dic₅	1	32	yes	complemented
343	Dic₆	C₂²×Dic₅	1	16	yes	complemented
344	C₂²×C₅	—	2	2	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	8	no	—
347	C₂²×C₅	—	3	8	no	—
348	C₂²×C₅	—	6	4	no	—
349	C₂²×C₅	—	6	4	no	—
350	C₂²×C₅	—	6	16	no	—
351	C₂²×C₅	C₂²×C₄×D₃	1	4	yes	—
352	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
353	C₂²×C₅	#1009	1	2	yes	—
354	C₂²×C₅	#1010	1	2	yes	—
355	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
356	C₄×C₅	—	3	8	no	—
357	C₄×C₅	C₂²×C₄×D₃	1	4	yes	—
358	C₄×C₅	C₂²×C₄×D₃	1	4	yes	—
359	Dic₅	—	2	4	no	—
360	Dic₅	—	2	4	no	—
361	Dic₅	—	6	8	no	—
362	C₂⁴	—	3	2	no	—
363	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
364	#41	—	3	64	no	—
365	C₂×Q₈	—	3	8	no	—
366	C₂×Q₈	—	3	4	no	—
367	C₂×D₄	—	3	16	no	—
368	C₂×D₄	—	3	8	no	—
369	C₂×D₄	—	3	8	no	—
370	C₂×D₄	—	3	4	no	—
371	C₂²×C₄	—	3	2	no	—
372	C₂²×C₄	—	3	16	no	—
373	C₂²×C₄	—	3	8	no	—
374	C₂²×C₄	—	5	2	no	—
375	C₂²×C₄	—	5	2	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	D₃×Dic₅	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	—	5	4	no	—
386	C₄⋊C₄	—	5	4	no	—
387	C₄⋊C₄	—	15	16	no	—
388	C₄⋊C₄	—	15	8	no	—
389	C₄⋊C₄	—	15	8	no	—
390	C₂²⋊C₄	—	5	8	no	—
391	C₂²⋊C₄	—	15	16	no	—
392	C₄²	—	5	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	#4149	1	2	yes	—
399	C₂²×C₃	#4150	1	2	yes	—
400	C₂²×C₃	C₂³×Dic₅	1	4	yes	—
401	C₂²×C₃	C₂³×Dic₅	1	2	yes	—
402	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
403	C₂×D₃	—	2	16	no	—
404	C₂×D₃	—	2	4	no	—
405	C₂×D₃	—	2	4	no	—
406	C₂×D₃	C₂³×Dic₅	1	8	yes	—
407	C₃×C₄	—	10	4	no	—
408	C₃×C₄	—	10	4	no	—
409	C₃×C₄	C₂³×Dic₅	1	4	yes	—
410	C₃×C₄	C₂³×Dic₅	1	4	yes	—
411	Dic₃	—	10	8	no	—
412	Dic₃	C₂³×Dic₅	1	8	yes	—
413	C₂×C₅	—	2	4	no	—
414	C₂×C₅	—	6	8	no	—
415	C₂×C₅	#5523	1	4	yes	complemented
416	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
417	C₂×C₅	C₂×#1009	1	1	yes	characteristic
418	C₂×C₅	C₂×#1010	1	1	yes	characteristic
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	3	8	no	—
422	C₂³	—	3	4	no	—
423	C₂³	—	6	4	no	—
424	C₂³	—	6	4	no	—
425	C₂³	C₂×D₃×Dic₅	1	4	yes	—
426	C₂³	C₂²×D₃×D₅	1	2	yes	—
427	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
428	Q₈	—	3	16	no	—
429	D₄	—	3	32	no	—
430	D₄	—	3	16	no	—
431	C₂×C₄	—	3	8	no	—
432	C₂×C₄	—	3	4	no	—
433	C₂×C₄	—	3	32	no	—
434	C₂×C₄	—	5	4	no	—
435	C₂×C₄	—	5	4	no	—
436	C₂×C₄	—	10	4	no	—
437	C₂×C₄	—	10	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×D₃×Dic₅	1	4	yes	—
443	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
444	C₂×C₄	C₂×D₃×Dic₅	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	#66161	1	4	yes	complemented
449	C₂×C₃	C₂×#4149	1	1	yes	characteristic
450	C₂×C₃	C₂×#4150	1	1	yes	characteristic
451	C₂×C₃	C₂⁴×Dic₅	1	1	yes	characteristic
452	D₃	—	2	8	no	—
453	C₅	C₂×#5523	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	2	8	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	3	8	no	—
458	C₂²	—	6	16	no	—
459	C₂²	—	6	4	no	—
460	C₂²	—	6	4	no	—
461	C₂²	#92001	1	2	yes	—
462	C₂²	#92019	1	2	yes	—
463	C₂²	C₂²×D₃×Dic₅	1	4	yes	—
464	C₂²	C₂²×D₃×Dic₅	1	2	yes	—
465	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
466	C₄	—	3	8	no	—
467	C₄	—	10	4	no	—
468	C₄	—	10	4	no	—
469	C₄	—	30	8	no	—
470	C₄	C₂²×D₃×Dic₅	1	4	yes	—
471	C₄	C₂²×D₃×Dic₅	1	4	yes	—
472	C₃	C₂×#66161	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	2	4	no	—
474	C₂	—	6	8	no	—
475	C₂	#11754513	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×D₃×Dic₅	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×C₅×#235	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×C₃×#4072	C₂	semidirect
4. C₂×#67⋊Dic₅	C₂	semidirect
5. #11754513	C₂	direct (N × H)
6. C₂×D₃×C₄⋊Dic₅	C₂	semidirect
7. C₂×Dic₅×D₁₂	C₂	semidirect
8. C₂×#91338	C₂	semidirect
9. C₂×Dic₅×Dic₆	C₂	semidirect
14. C₂×C₅×#235	C₄	semidirect
22. C₂×C₄⋊Dic₁₅	C₂²	semidirect
24. C₃×#4072	C₂²	semidirect
28. #67⋊Dic₅	C₂²	semidirect
32. D₃×C₄⋊Dic₅	C₂²	semidirect
33. Dic₅×D₁₂	C₂²	semidirect
34. #91338	C₂²	semidirect
35. Dic₅×Dic₆	C₂²	semidirect
43. C₂×#4072	D₃	semidirect
48. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
55. C₂×C₅×#67	C₂×C₄	semidirect
58. C₅×#235	C₂×C₄	semidirect
59. C₂×C₅×D₁₂	C₂×C₄	semidirect
61. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
63. C₂×C₅×Dic₆	C₂×C₄	semidirect
102. #4072	C₂×D₃	semidirect
124. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
130. C₅×#67	C₂²×C₄	semidirect
133. C₅×D₁₂	C₂²×C₄	semidirect
134. C₄×C₅×D₃	C₂²×C₄	semidirect
135. C₅×Dic₆	C₂²×C₄	semidirect
144. C₂×#235	Dic₅	semidirect
178. C₂²×C₄×C₅	C₄×D₃	semidirect
229. C₂²×C₃×C₄	C₂×Dic₅	semidirect
233. C₂×#67	C₂×Dic₅	semidirect
239. #235	C₂×Dic₅	semidirect
240. C₂×D₁₂	C₂×Dic₅	semidirect
244. C₂×C₄×D₃	C₂×Dic₅	semidirect
246. C₂×Dic₆	C₂×Dic₅	semidirect
274. C₂×C₄×C₅	C₂×C₄×D₃	semidirect
311. C₂×C₃×C₅	#520	semidirect
331. C₂×C₃×C₄	C₂²×Dic₅	semidirect
334. #67	C₂²×Dic₅	semidirect
340. D₁₂	C₂²×Dic₅	semidirect
342. C₄×D₃	C₂²×Dic₅	semidirect
343. Dic₆	C₂²×Dic₅	semidirect
381. C₂²×C₄	D₃×Dic₅	semidirect
394. C₃×C₅	C₂×#520	semidirect
415. C₂×C₅	#5523	semidirect
444. C₂×C₄	C₂×D₃×Dic₅	semidirect
448. C₂×C₃	#66161	semidirect
453. C₅	C₂×#5523	semidirect
472. C₃	C₂×#66161	semidirect
475. C₂	#11754513	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×C₅×#235	2
C₂²×C₄⋊Dic₁₅	2
C₂×C₃×#4072	2
C₂×#67⋊Dic₅	2
#11754513	2
C₂×D₃×C₄⋊Dic₅	2
C₂×Dic₅×D₁₂	2
C₂×#91338	2
C₂×Dic₅×Dic₆	2
C₂×#66161	3
C₂×#5523	5

Subgroups — C2×#11754513 #14479090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11754513 #14479090