Subgroups — C₂×C₅×#5507 #14482679

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 656 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	2	yes	maximal, complemented
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#929	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
7	C₅×#5507	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#547	—	3	1	no	maximal, Hall
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂×C₅×#235	—	2	16	no	—
19	C₂×C₅×#235	C₂²	1	16	yes	complemented
20	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
21	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
23	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
24	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₅×#930	C₂²	1	8	yes	complemented
32	C₅×#929	C₂²	1	16	yes	complemented
33	C₄×C₅×#67	C₂²	1	8	yes	complemented
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
43	C₅×#896	C₂²	1	16	yes	complemented
44	C₅×#895	C₂²	1	8	yes	complemented
45	C₅×#894	C₂²	1	16	yes	complemented
46	C₅×#893	C₂²	1	8	yes	complemented
47	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
48	C₅×#888	C₂²	1	8	yes	complemented
49	C₂×#5507	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
50	C₂²×C₅×#41	—	3	2	no	—
51	C₅×#547	—	3	16	no	—
52	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
53	C₂×C₅×#123	—	3	2	no	—
54	C₂×C₅×#123	—	3	2	no	—
55	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
56	C₂×C₅×#121	—	3	1	no	—
57	C₂×C₅×#121	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	1	no	—
60	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
61	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
62	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
63	C₂³×C₅×D₃	C₂³	1	2	yes	—
64	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	8	no	—
66	C₂²×C₃×C₄×C₅	—	2	4	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₅×#67	—	2	8	no	—
74	C₂×C₅×#67	D₄	1	8	yes	complemented
75	C₂×C₅×#67	C₂³	1	8	yes	—
76	C₂×C₅×#67	C₂³	1	4	yes	—
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₅×#235	—	2	64	no	—
82	C₂×C₅×D₁₂	—	2	8	no	—
83	C₂×C₅×D₁₂	—	2	4	no	—
84	C₂×C₅×D₁₂	C₂³	1	4	yes	—
85	C₂×C₅×D₁₂	C₂³	1	8	yes	—
86	C₂×C₄×C₅×D₃	—	2	8	no	—
87	C₂×C₄×C₅×D₃	—	2	4	no	—
88	C₂×C₄×C₅×D₃	—	2	8	no	—
89	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
90	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
91	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
92	C₂×C₅×Dic₆	—	2	8	no	—
93	C₂×C₅×Dic₆	C₂³	1	8	yes	—
94	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
95	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
97	C₅×#217	C₂³	1	4	yes	—
98	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
99	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
100	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
101	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
102	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
103	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
104	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
105	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
106	C₄×C₅×Dic₃	C₂³	1	4	yes	—
107	C₂²×#235	C₂×C₅	1	2	yes	complemented
108	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×#929	C₂×C₅	1	2	yes	complemented
111	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#896	C₂×C₅	1	2	yes	complemented
113	#5507	C₂×C₅	1	16	yes	direct product factor
114	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#894	C₂×C₅	1	2	yes	complemented
116	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×#888	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×C₅×#41	—	3	16	no	—
120	C₂×C₅×#41	—	6	16	no	—
121	C₂²×C₅×Q₈	—	3	2	no	—
122	C₂²×C₅×D₄	—	3	1	no	—
123	C₂²×C₅×D₄	—	3	2	no	—
124	C₂²×C₅×D₄	—	3	1	no	—
125	C₂²×C₅×D₄	—	3	2	no	—
126	C₂³×C₄×C₅	—	3	1	no	—
127	C₂³×C₄×C₅	—	3	2	no	—
128	C₂³×C₄×C₅	—	3	2	no	—
129	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
131	C₅×C₄⋊Q₈	—	3	8	no	—
132	C₅×#123	—	3	16	no	—
133	C₅×#123	—	3	16	no	—
134	C₅×C₂²⋊Q₈	—	3	16	no	—
135	C₅×#121	—	3	8	no	—
136	C₅×#121	—	3	8	no	—
137	C₄×C₅×D₄	—	3	8	no	—
138	C₄×C₅×D₄	—	3	8	no	—
139	C₂×C₅×C₄⋊C₄	—	3	2	no	—
140	C₂×C₅×C₄⋊C₄	—	3	1	no	—
141	C₂×C₅×C₄⋊C₄	—	3	2	no	—
142	C₂×C₅×C₄⋊C₄	—	3	1	no	—
143	C₂×C₅×C₄⋊C₄	—	3	8	no	—
144	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
148	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
149	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
150	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
153	C₂×C₄²×C₅	—	3	1	no	—
154	C₂×#547	—	3	1	no	Sylow
155	C₂³×C₃×C₅	—	2	2	no	—
156	C₂³×C₃×C₅	—	2	2	no	—
157	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
158	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
159	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
160	C₂²×C₅×D₃	—	2	2	no	—
161	C₂²×C₅×D₃	—	2	2	no	—
162	C₂²×C₅×D₃	—	2	4	no	—
163	C₂²×C₅×D₃	—	2	4	no	—
164	C₂²×C₅×D₃	—	2	4	no	—
165	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
166	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
167	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
168	C₂×C₃×C₄×C₅	—	2	4	no	—
169	C₂×C₃×C₄×C₅	—	2	4	no	—
170	C₂×C₃×C₄×C₅	—	2	16	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	2	8	no	—
173	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
174	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
177	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
178	C₅×#67	—	2	16	no	—
179	C₅×#67	C₂×D₄	1	16	yes	complemented
180	C₂×C₅×Dic₃	—	2	4	no	—
181	C₂×C₅×Dic₃	—	2	2	no	—
182	C₂×C₅×Dic₃	—	2	2	no	—
183	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
184	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
185	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
186	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
187	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
188	C₅×D₁₂	—	2	16	no	—
189	C₅×D₁₂	—	2	8	no	—
190	C₄×C₅×D₃	—	2	16	no	—
191	C₄×C₅×D₃	—	2	8	no	—
192	C₄×C₅×D₃	—	2	16	no	—
193	C₅×Dic₆	—	2	16	no	—
194	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
195	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂²×#67	C₂²×C₅	1	2	yes	—
197	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
198	C₂×#235	—	2	16	no	—
199	C₂×#235	C₂²×C₅	1	16	yes	complemented
200	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
201	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
202	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
203	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
204	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
205	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
210	C₂×#217	C₂²×C₅	1	1	yes	characteristic
211	#930	C₂²×C₅	1	8	yes	complemented
212	#929	C₂²×C₅	1	16	yes	complemented
213	C₄×#67	C₂²×C₅	1	8	yes	complemented
214	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
215	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
217	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
218	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
219	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
220	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
221	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
223	#896	C₂²×C₅	1	16	yes	complemented
224	#895	C₂²×C₅	1	8	yes	complemented
225	#894	C₂²×C₅	1	16	yes	complemented
226	#893	C₂²×C₅	1	8	yes	complemented
227	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
228	#888	C₂²×C₅	1	8	yes	complemented
229	C₂⁴×C₅	—	3	1	no	—
230	C₂⁴×C₅	—	3	2	no	—
231	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₅×#41	—	6	64	no	—
233	C₂×C₅×Q₈	—	3	8	no	—
234	C₂×C₅×Q₈	—	6	8	no	—
235	C₂×C₅×D₄	—	3	8	no	—
236	C₂×C₅×D₄	—	3	4	no	—
237	C₂×C₅×D₄	—	3	8	no	—
238	C₂×C₅×D₄	—	3	4	no	—
239	C₂×C₅×D₄	—	3	8	no	—
240	C₂×C₅×D₄	—	6	8	no	—
241	C₂×C₅×D₄	—	6	8	no	—
242	C₂×C₅×D₄	—	6	4	no	—
243	C₂²×C₄×C₅	—	2	8	no	—
244	C₂²×C₄×C₅	—	2	4	no	—
245	C₂²×C₄×C₅	—	3	1	no	—
246	C₂²×C₄×C₅	—	3	1	no	—
247	C₂²×C₄×C₅	—	3	1	no	—
248	C₂²×C₄×C₅	—	3	2	no	—
249	C₂²×C₄×C₅	—	3	4	no	—
250	C₂²×C₄×C₅	—	3	8	no	—
251	C₂²×C₄×C₅	—	3	8	no	—
252	C₂²×C₄×C₅	—	6	8	no	—
253	C₂²×C₄×C₅	—	6	8	no	—
254	C₂²×C₄×C₅	—	6	4	no	—
255	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
256	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
257	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
259	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
260	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
261	C₅×C₄⋊C₄	—	3	4	no	—
262	C₅×C₄⋊C₄	—	3	8	no	—
263	C₅×C₄⋊C₄	—	3	4	no	—
264	C₅×C₄⋊C₄	—	3	8	no	—
265	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
266	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
267	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
268	C₅×C₂²⋊C₄	—	3	4	no	—
269	C₅×C₂²⋊C₄	—	3	4	no	—
270	C₅×C₂²⋊C₄	—	3	8	no	—
271	C₅×C₂²⋊C₄	—	3	8	no	—
272	C₅×C₂²⋊C₄	—	3	8	no	—
273	C₄²×C₅	—	3	4	no	—
274	C₂²×#41	—	3	2	no	—
275	#547	—	3	16	no	—
276	C₂×C₄⋊Q₈	—	3	1	no	—
277	C₂×#123	—	3	2	no	—
278	C₂×#123	—	3	2	no	—
279	C₂×C₂²⋊Q₈	—	3	2	no	—
280	C₂×#121	—	3	1	no	—
281	C₂×#121	—	3	1	no	—
282	C₂×C₄×D₄	—	3	1	no	—
283	C₂×C₄×D₄	—	3	1	no	—
284	C₂²×C₄⋊C₄	—	3	1	no	—
285	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
286	C₂²×C₃×C₅	—	2	8	no	—
287	C₂²×C₃×C₅	—	2	2	no	—
288	C₂²×C₃×C₅	—	2	2	no	—
289	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
290	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
291	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
292	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
293	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
294	C₂×C₅×D₃	—	2	8	no	—
295	C₂×C₅×D₃	—	2	2	no	—
296	C₂×C₅×D₃	—	2	2	no	—
297	C₂×C₅×D₃	—	2	4	no	—
298	C₂×C₅×D₃	—	2	4	no	—
299	C₂×C₅×D₃	—	2	4	no	—
300	C₂×C₅×D₃	—	4	8	no	—
301	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
302	C₃×C₄×C₅	—	2	4	no	—
303	C₃×C₄×C₅	—	2	4	no	—
304	C₃×C₄×C₅	—	2	2	no	—
305	C₃×C₄×C₅	C₂×#41	1	4	yes	complemented
306	C₅×Dic₃	—	2	4	no	—
307	C₅×Dic₃	—	2	2	no	—
308	C₅×Dic₃	—	2	2	no	—
309	C₅×Dic₃	C₂²×D₄	1	4	yes	—
310	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
311	C₂³×D₃	C₂³×C₅	1	2	yes	—
312	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₃×C₄	—	2	8	no	—
314	C₂²×C₃×C₄	—	2	4	no	—
315	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
317	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
318	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
319	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
320	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
321	C₂×#67	—	2	8	no	—
322	C₂×#67	C₅×D₄	1	8	yes	complemented
323	C₂×#67	C₂³×C₅	1	8	yes	—
324	C₂×#67	C₂³×C₅	1	4	yes	—
325	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
326	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
327	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
328	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
329	#235	—	2	64	no	—
330	C₂×D₁₂	—	2	8	no	—
331	C₂×D₁₂	—	2	4	no	—
332	C₂×D₁₂	C₂³×C₅	1	4	yes	—
333	C₂×D₁₂	C₂³×C₅	1	8	yes	—
334	C₂×C₄×D₃	—	2	8	no	—
335	C₂×C₄×D₃	—	2	4	no	—
336	C₂×C₄×D₃	—	2	8	no	—
337	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
338	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
339	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
340	C₂×Dic₆	—	2	8	no	—
341	C₂×Dic₆	C₂³×C₅	1	8	yes	—
342	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
343	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
344	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
345	#217	C₂³×C₅	1	4	yes	—
346	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
347	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
348	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
349	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
350	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
351	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
352	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
353	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
354	C₄×Dic₃	C₂³×C₅	1	4	yes	—
355	C₂³×C₅	—	2	2	no	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	3	4	no	—
358	C₂³×C₅	—	3	2	no	—
359	C₂³×C₅	—	3	4	no	—
360	C₂³×C₅	—	6	2	no	—
361	C₂³×C₅	—	6	2	no	—
362	C₂³×C₅	—	6	4	no	—
363	C₂³×C₅	—	6	4	no	—
364	C₂³×C₅	—	6	4	no	—
365	C₂³×C₅	D₃×D₄	1	4	yes	—
366	C₂³×C₅	C₂³×D₃	1	2	yes	—
367	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
368	C₅×Q₈	—	6	16	no	—
369	C₅×D₄	—	3	16	no	—
370	C₅×D₄	—	6	16	no	—
371	C₅×D₄	—	6	16	no	—
372	C₅×D₄	—	6	8	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	4	no	—
375	C₂×C₄×C₅	—	2	4	no	—
376	C₂×C₄×C₅	—	2	16	no	—
377	C₂×C₄×C₅	—	2	8	no	—
378	C₂×C₄×C₅	—	3	4	no	—
379	C₂×C₄×C₅	—	3	2	no	—
380	C₂×C₄×C₅	—	3	2	no	—
381	C₂×C₄×C₅	—	3	2	no	—
382	C₂×C₄×C₅	—	3	4	no	—
383	C₂×C₄×C₅	—	6	16	no	—
384	C₂×C₄×C₅	—	6	16	no	—
385	C₂×C₄×C₅	—	6	2	no	—
386	C₂×C₄×C₅	—	6	4	no	—
387	C₂×C₄×C₅	—	6	2	no	—
388	C₂×C₄×C₅	—	6	8	no	—
389	C₂×C₄×C₅	#235	1	4	yes	complemented
390	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
391	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
392	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
393	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
394	C₂×#41	—	3	16	no	—
395	C₂×#41	—	6	16	no	—
396	C₂²×Q₈	—	3	2	no	—
397	C₂²×D₄	—	3	1	no	—
398	C₂²×D₄	—	3	2	no	—
399	C₂²×D₄	—	3	1	no	—
400	C₂²×D₄	—	3	2	no	—
401	C₂³×C₄	—	3	1	no	—
402	C₂³×C₄	—	3	2	no	—
403	C₂³×C₄	—	3	2	no	—
404	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
405	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
406	C₄⋊Q₈	—	3	8	no	—
407	#123	—	3	16	no	—
408	#123	—	3	16	no	—
409	C₂²⋊Q₈	—	3	16	no	—
410	#121	—	3	8	no	—
411	#121	—	3	8	no	—
412	C₄×D₄	—	3	8	no	—
413	C₄×D₄	—	3	8	no	—
414	C₂×C₄⋊C₄	—	3	1	no	—
415	C₂×C₄⋊C₄	—	3	2	no	—
416	C₂×C₄⋊C₄	—	3	1	no	—
417	C₂×C₄⋊C₄	—	3	2	no	—
418	C₂×C₄⋊C₄	—	3	8	no	—
419	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
423	C₂×C₂²⋊C₄	—	3	1	no	—
424	C₂×C₂²⋊C₄	—	3	1	no	—
425	C₂×C₂²⋊C₄	—	3	2	no	—
426	C₂×C₂²⋊C₄	—	3	2	no	—
427	C₂×C₂²⋊C₄	—	3	2	no	—
428	C₂×C₄²	—	3	1	no	—
429	C₂×C₃×C₅	—	2	4	no	—
430	C₂×C₃×C₅	#547	1	4	yes	complemented
431	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
432	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
433	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₅×D₃	—	2	4	no	—
435	C₅×D₃	—	4	4	no	—
436	C₂³×C₃	—	2	2	no	—
437	C₂³×C₃	—	2	2	no	—
438	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
439	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
440	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
441	C₂²×D₃	—	2	2	no	—
442	C₂²×D₃	—	2	2	no	—
443	C₂²×D₃	—	2	4	no	—
444	C₂²×D₃	—	2	4	no	—
445	C₂²×D₃	—	2	4	no	—
446	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
447	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
448	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
449	C₂×C₃×C₄	—	2	4	no	—
450	C₂×C₃×C₄	—	2	4	no	—
451	C₂×C₃×C₄	—	2	16	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	8	no	—
454	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
455	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
456	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
457	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
458	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
459	#67	—	2	16	no	—
460	#67	C₂×C₅×D₄	1	16	yes	complemented
461	C₂×Dic₃	—	2	4	no	—
462	C₂×Dic₃	—	2	2	no	—
463	C₂×Dic₃	—	2	2	no	—
464	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
465	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
466	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
467	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
468	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
469	D₁₂	—	2	16	no	—
470	D₁₂	—	2	8	no	—
471	C₄×D₃	—	2	16	no	—
472	C₄×D₃	—	2	8	no	—
473	C₄×D₃	—	2	16	no	—
474	Dic₆	—	2	16	no	—
475	C₂²×C₅	—	2	2	no	—
476	C₂²×C₅	—	2	2	no	—
477	C₂²×C₅	—	2	8	no	—
478	C₂²×C₅	—	3	4	no	—
479	C₂²×C₅	—	6	2	no	—
480	C₂²×C₅	—	6	2	no	—
481	C₂²×C₅	—	6	8	no	—
482	C₂²×C₅	—	6	4	no	—
483	C₂²×C₅	—	6	4	no	—
484	C₂²×C₅	—	6	4	no	—
485	C₂²×C₅	—	12	8	no	—
486	C₂²×C₅	C₂×#235	1	2	yes	—
487	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
488	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
489	C₂²×C₅	#1007	1	2	yes	—
490	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	2	4	no	—
493	C₄×C₅	—	2	4	no	—
494	C₄×C₅	—	3	4	no	—
495	C₄×C₅	—	6	2	no	—
496	C₄×C₅	—	6	4	no	—
497	C₄×C₅	—	6	2	no	—
498	C₄×C₅	C₂×#235	1	4	yes	complemented
499	C₂⁴	—	3	1	no	—
500	C₂⁴	—	3	2	no	—
501	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
502	#41	—	6	64	no	—
503	C₂×Q₈	—	3	8	no	—
504	C₂×Q₈	—	6	8	no	—
505	C₂×D₄	—	3	8	no	—
506	C₂×D₄	—	3	4	no	—
507	C₂×D₄	—	3	8	no	—
508	C₂×D₄	—	3	4	no	—
509	C₂×D₄	—	3	8	no	—
510	C₂×D₄	—	6	8	no	—
511	C₂×D₄	—	6	8	no	—
512	C₂×D₄	—	6	4	no	—
513	C₂²×C₄	—	2	8	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	3	1	no	—
516	C₂²×C₄	—	3	1	no	—
517	C₂²×C₄	—	3	1	no	—
518	C₂²×C₄	—	3	2	no	—
519	C₂²×C₄	—	3	4	no	—
520	C₂²×C₄	—	3	8	no	—
521	C₂²×C₄	—	3	8	no	—
522	C₂²×C₄	—	6	8	no	—
523	C₂²×C₄	—	6	8	no	—
524	C₂²×C₄	—	6	4	no	—
525	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
527	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
528	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
529	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
530	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
531	C₄⋊C₄	—	3	4	no	—
532	C₄⋊C₄	—	3	8	no	—
533	C₄⋊C₄	—	3	4	no	—
534	C₄⋊C₄	—	3	8	no	—
535	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
536	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
537	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
538	C₂²⋊C₄	—	3	4	no	—
539	C₂²⋊C₄	—	3	4	no	—
540	C₂²⋊C₄	—	3	8	no	—
541	C₂²⋊C₄	—	3	8	no	—
542	C₂²⋊C₄	—	3	8	no	—
543	C₄²	—	3	4	no	—
544	C₃×C₅	C₂×#547	1	1	yes	characteristic, complemented, Hall
545	C₂²×C₃	—	2	8	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
549	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
550	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
551	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
552	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
553	C₂×D₃	—	2	8	no	—
554	C₂×D₃	—	2	2	no	—
555	C₂×D₃	—	2	2	no	—
556	C₂×D₃	—	2	4	no	—
557	C₂×D₃	—	2	4	no	—
558	C₂×D₃	—	2	4	no	—
559	C₂×D₃	—	4	8	no	—
560	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
561	C₃×C₄	—	2	4	no	—
562	C₃×C₄	—	2	4	no	—
563	C₃×C₄	—	2	2	no	—
564	C₃×C₄	C₂×C₅×#41	1	4	yes	complemented
565	Dic₃	—	2	4	no	—
566	Dic₃	—	2	2	no	—
567	Dic₃	—	2	2	no	—
568	Dic₃	C₂²×C₅×D₄	1	4	yes	—
569	C₂×C₅	—	2	4	no	—
570	C₂×C₅	—	6	4	no	—
571	C₂×C₅	—	12	4	no	—
572	C₂×C₅	#5507	1	4	yes	direct product factor
573	C₂×C₅	C₂²×#235	1	1	yes	characteristic
574	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
575	C₂×C₅	C₂×#1007	1	1	yes	characteristic
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	3	4	no	—
579	C₂³	—	3	2	no	—
580	C₂³	—	3	4	no	—
581	C₂³	—	6	2	no	—
582	C₂³	—	6	2	no	—
583	C₂³	—	6	4	no	—
584	C₂³	—	6	4	no	—
585	C₂³	—	6	4	no	—
586	C₂³	C₅×D₃×D₄	1	4	yes	—
587	C₂³	C₂³×C₅×D₃	1	2	yes	—
588	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
589	Q₈	—	6	16	no	—
590	D₄	—	3	16	no	—
591	D₄	—	6	16	no	—
592	D₄	—	6	16	no	—
593	D₄	—	6	8	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	16	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	3	4	no	—
600	C₂×C₄	—	3	2	no	—
601	C₂×C₄	—	3	2	no	—
602	C₂×C₄	—	3	2	no	—
603	C₂×C₄	—	3	4	no	—
604	C₂×C₄	—	6	16	no	—
605	C₂×C₄	—	6	16	no	—
606	C₂×C₄	—	6	2	no	—
607	C₂×C₄	—	6	4	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	6	8	no	—
610	C₂×C₄	C₅×#235	1	4	yes	complemented
611	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
612	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
613	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
614	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
615	C₂×C₃	—	2	4	no	—
616	C₂×C₃	C₅×#547	1	4	yes	complemented
617	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
618	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
619	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
620	D₃	—	2	4	no	—
621	D₃	—	4	4	no	—
622	C₅	C₂×#5507	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	8	no	—
626	C₂²	—	3	4	no	—
627	C₂²	—	6	2	no	—
628	C₂²	—	6	2	no	—
629	C₂²	—	6	8	no	—
630	C₂²	—	6	4	no	—
631	C₂²	—	6	4	no	—
632	C₂²	—	6	4	no	—
633	C₂²	—	12	8	no	—
634	C₂²	C₂×C₅×#235	1	2	yes	—
635	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
636	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
637	C₂²	C₅×#1007	1	2	yes	—
638	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
639	C₄	—	2	2	no	—
640	C₄	—	2	4	no	—
641	C₄	—	2	4	no	—
642	C₄	—	3	4	no	—
643	C₄	—	6	2	no	—
644	C₄	—	6	4	no	—
645	C₄	—	6	2	no	—
646	C₄	C₂×C₅×#235	1	4	yes	complemented
647	C₃	C₂×C₅×#547	1	1	yes	characteristic, complemented, Sylow
648	C₂	—	2	4	no	—
649	C₂	—	6	4	no	—
650	C₂	—	12	4	no	—
651	C₂	C₅×#5507	1	4	yes	direct product factor
652	C₂	C₂²×C₅×#235	1	1	yes	characteristic
653	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
654	C₂	C₂×C₅×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#235	C₂	semidirect
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₂×C₅×#929	C₂	semidirect
5. C₂×C₄×C₅×#67	C₂	semidirect
6. C₂×C₅×#896	C₂	semidirect
7. C₅×#5507	C₂	direct (N × H)
8. C₂×C₅×#895	C₂	semidirect
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#893	C₂	semidirect
11. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
12. C₂×C₅×#888	C₂	semidirect
19. C₂×C₅×#235	C₂²	semidirect
29. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₅×#930	C₂²	semidirect
32. C₅×#929	C₂²	semidirect
33. C₄×C₅×#67	C₂²	semidirect
43. C₅×#896	C₂²	semidirect
44. C₅×#895	C₂²	semidirect
45. C₅×#894	C₂²	semidirect
46. C₅×#893	C₂²	semidirect
47. C₅×D₃×C₄⋊C₄	C₂²	semidirect
48. C₅×#888	C₂²	semidirect
49. C₂×#5507	C₅	direct (N × H)
61. C₂²×C₅×C₄⋊C₄	D₃	semidirect
74. C₂×C₅×#67	D₄	semidirect
107. C₂²×#235	C₂×C₅	semidirect
108. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
109. C₂×#930	C₂×C₅	semidirect
110. C₂×#929	C₂×C₅	semidirect
111. C₂×C₄×#67	C₂×C₅	semidirect
112. C₂×#896	C₂×C₅	semidirect
113. #5507	C₂×C₅	direct (N × H)
114. C₂×#895	C₂×C₅	semidirect
115. C₂×#894	C₂×C₅	semidirect
116. C₂×#893	C₂×C₅	semidirect
117. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
118. C₂×#888	C₂×C₅	semidirect
147. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
173. C₂×C₃×C₄×C₅	#41	semidirect
179. C₅×#67	C₂×D₄	semidirect
199. C₂×#235	C₂²×C₅	semidirect
209. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
211. #930	C₂²×C₅	semidirect
212. #929	C₂²×C₅	semidirect
213. C₄×#67	C₂²×C₅	semidirect
223. #896	C₂²×C₅	semidirect
224. #895	C₂²×C₅	semidirect
225. #894	C₂²×C₅	semidirect
226. #893	C₂²×C₅	semidirect
227. D₃×C₄⋊C₄	C₂²×C₅	semidirect
228. #888	C₂²×C₅	semidirect
285. C₂²×C₄⋊C₄	C₅×D₃	semidirect
305. C₃×C₄×C₅	C₂×#41	semidirect
322. C₂×#67	C₅×D₄	semidirect
389. C₂×C₄×C₅	#235	semidirect
422. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
430. C₂×C₃×C₅	#547	semidirect
454. C₂×C₃×C₄	C₅×#41	semidirect
460. #67	C₂×C₅×D₄	semidirect
498. C₄×C₅	C₂×#235	semidirect
544. C₃×C₅	C₂×#547	semidirect
564. C₃×C₄	C₂×C₅×#41	semidirect
572. C₂×C₅	#5507	direct (N × H)
610. C₂×C₄	C₅×#235	semidirect
616. C₂×C₃	C₅×#547	semidirect
622. C₅	C₂×#5507	direct (N × H)
646. C₄	C₂×C₅×#235	semidirect
647. C₃	C₂×C₅×#547	semidirect
651. C₂	C₅×#5507	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×C₃×C₅×C₄⋊C₄	2
C₂×C₅×#930	2
C₂×C₅×#929	2
C₂×C₄×C₅×#67	2
C₂×C₅×#896	2
C₅×#5507	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#888	2
C₂×C₅×#547	3
C₂×#5507	5

Subgroups — C2×C5×#5507 #14482679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5507 #14482679