Subgroups — C₃×D₅×#535 #14480360

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66164	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66139	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66049	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×#127	C₂	1	2	yes	maximal, complemented
8	C₃×#66008	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#124	C₂	1	2	yes	maximal, complemented
10	C₃×#65941	C₂	1	4	yes	maximal, complemented
11	C₃×D₅×#121	C₂	1	4	yes	maximal, complemented
12	C₃×#65926	C₂	1	4	yes	maximal, complemented
13	C₃×D₅×#120	C₂	1	4	yes	maximal, complemented
14	C₃×#65859	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×#535	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₃×D₅×#41	—	2	8	no	—
22	C₂×C₃×#713	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#711	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#711	C₂²	1	2	yes	complemented
26	C₂×C₃×D₄×D₅	—	2	8	no	—
27	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
28	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
29	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
30	C₂×C₃×D₄×D₅	C₂²	1	2	yes	complemented
31	C₂×C₃×D₄×D₅	C₂²	1	2	yes	complemented
32	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
34	C₂×C₃×#709	C₂²	1	2	yes	complemented
35	C₂×C₃×#709	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
38	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
39	C₃×C₅×#127	C₂²	1	2	yes	complemented
40	C₃×C₅×#124	C₂²	1	2	yes	complemented
41	C₃×C₅×#121	C₂²	1	4	yes	complemented
42	C₃×C₅×#120	C₂²	1	4	yes	complemented
43	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	C₃×#4099	C₂²	1	4	yes	complemented
45	C₃×#4093	C₂²	1	2	yes	complemented
46	C₃×#4086	C₂²	1	2	yes	complemented
47	C₃×#4086	C₂²	1	8	yes	complemented
48	C₃×#4086	C₂²	1	2	yes	complemented
49	C₃×#4085	C₂²	1	8	yes	complemented
50	C₃×#4084	C₂²	1	4	yes	complemented
51	C₃×#4083	C₂²	1	8	yes	complemented
52	C₃×#4083	C₂²	1	4	yes	complemented
53	C₃×#4082	C₂²	1	2	yes	complemented
54	C₃×#4076	C₂²	1	4	yes	complemented
55	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
56	C₃×#4041	C₂²	1	4	yes	complemented
57	C₃×#4038	C₂²	1	2	yes	complemented
58	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₃×#4031	C₂²	1	8	yes	complemented
60	C₃×#4030	C₂²	1	8	yes	complemented
61	C₃×#4028	C₂²	1	8	yes	complemented
62	C₃×#4028	C₂²	1	4	yes	complemented
63	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
65	C₃×#4023	C₂²	1	2	yes	complemented
66	C₃×#4021	C₂²	1	2	yes	complemented
67	C₃×#4020	C₂²	1	2	yes	complemented
68	C₃×#4018	C₂²	1	2	yes	complemented
69	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
70	C₂×C₃×#535	—	5	1	no	maximal, Hall
71	C₂×D₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
74	#66164	C₂×C₃	1	1	yes	characteristic, complemented
75	#66139	C₂×C₃	1	1	yes	characteristic, complemented
76	#66049	C₂×C₃	1	2	yes	complemented
77	D₅×#127	C₂×C₃	1	2	yes	complemented
78	#66008	C₂×C₃	1	2	yes	complemented
79	D₅×#124	C₂×C₃	1	2	yes	complemented
80	#65941	C₂×C₃	1	4	yes	complemented
81	D₅×#121	C₂×C₃	1	4	yes	complemented
82	#65926	C₂×C₃	1	4	yes	complemented
83	D₅×#120	C₂×C₃	1	4	yes	complemented
84	#65859	C₂×C₃	1	1	yes	characteristic, complemented
85	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
87	C₂³×C₃×D₅	—	2	8	no	—
88	C₂³×C₃×D₅	—	4	8	no	—
89	C₂³×C₃×D₅	C₂³	1	2	yes	—
90	C₂³×C₃×D₅	C₂³	1	4	yes	—
91	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
92	C₂³×C₃×D₅	C₂³	1	2	yes	—
93	C₂³×C₃×D₅	C₂³	1	4	yes	—
94	C₃×C₅×#41	—	2	4	no	—
95	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
96	C₂×C₃×C₅×D₄	—	2	4	no	—
97	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
98	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
99	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
100	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
101	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
104	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
105	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
106	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
107	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
108	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
109	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	complemented
110	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
111	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
112	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
113	C₂²×C₃×Dic₅	C₂³	1	2	yes	complemented
114	C₃×#713	—	2	4	no	—
115	C₃×Q₈×D₅	—	2	4	no	—
116	C₃×#711	—	2	8	no	—
117	C₃×#711	—	2	4	no	—
118	C₃×D₄×D₅	—	2	8	no	—
119	C₃×D₄×D₅	—	2	8	no	—
120	C₃×D₄×D₅	—	2	8	no	—
121	C₃×D₄×D₅	—	2	4	no	—
122	C₃×D₄×D₅	—	2	8	no	—
123	C₃×D₄×D₅	—	2	8	no	—
124	C₃×D₄×D₅	—	4	16	no	—
125	C₃×#709	—	2	4	no	—
126	C₃×#709	—	2	8	no	—
127	C₂×C₃×D₂₀	—	2	4	no	—
128	C₂×C₃×D₂₀	C₂³	1	2	yes	—
129	C₂×C₃×D₂₀	C₂³	1	2	yes	—
130	C₂×C₃×D₂₀	C₂³	1	2	yes	—
131	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic, complemented
132	C₂×C₃×D₂₀	C₂³	1	8	yes	complemented
133	C₂×C₃×C₄×D₅	—	2	8	no	—
134	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
135	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
136	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
137	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₄×D₅	C₂³	1	2	yes	complemented
142	C₂×C₃×C₄×D₅	C₂³	1	2	yes	complemented
143	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
144	C₂×C₃×Dic₁₀	C₂³	1	2	yes	complemented
145	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
146	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
148	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
149	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
150	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
151	C₃×#685	C₂³	1	4	yes	—
152	C₃×#685	C₂³	1	8	yes	complemented
153	C₃×#685	C₂³	1	8	yes	complemented
154	C₃×C₄⋊Dic₅	C₂³	1	2	yes	complemented
155	C₃×#683	C₂³	1	4	yes	complemented
156	C₃×C₄×Dic₅	C₂³	1	2	yes	complemented
157	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
158	C₂²×C₃×#41	—	5	1	no	—
159	C₂³×C₃×D₄	—	5	1	no	—
160	C₃×#535	—	5	1	no	—
161	C₃×#535	—	5	1	no	—
162	C₃×#535	—	5	2	no	—
163	C₃×#535	—	5	2	no	—
164	C₃×#535	—	5	4	no	—
165	C₃×#535	—	5	4	no	—
166	C₃×#535	—	5	1	no	—
167	C₃×#535	D₅	1	1	yes	characteristic, direct product factor
168	C₂×C₃×#127	—	5	2	no	—
169	C₂×C₃×#124	—	5	2	no	—
170	C₂×C₃×#121	—	5	4	no	—
171	C₂×C₃×#120	—	5	4	no	—
172	C₂×C₃×#117	—	5	1	no	—
173	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
174	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
177	D₅×#41	—	2	8	no	—
178	C₂×#713	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₂×#711	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂×#711	C₂²×C₃	1	2	yes	complemented
182	C₂×D₄×D₅	—	2	8	no	—
183	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
184	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
185	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
186	C₂×D₄×D₅	C₂²×C₃	1	2	yes	complemented
187	C₂×D₄×D₅	C₂²×C₃	1	2	yes	complemented
188	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
190	C₂×#709	C₂²×C₃	1	2	yes	complemented
191	C₂×#709	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
194	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
195	C₅×#127	C₂²×C₃	1	2	yes	complemented
196	C₅×#124	C₂²×C₃	1	2	yes	complemented
197	C₅×#121	C₂²×C₃	1	4	yes	complemented
198	C₅×#120	C₂²×C₃	1	4	yes	complemented
199	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
200	#4099	C₂²×C₃	1	4	yes	complemented
201	#4093	C₂²×C₃	1	2	yes	complemented
202	#4086	C₂²×C₃	1	2	yes	complemented
203	#4086	C₂²×C₃	1	8	yes	complemented
204	#4086	C₂²×C₃	1	2	yes	complemented
205	#4085	C₂²×C₃	1	8	yes	complemented
206	#4084	C₂²×C₃	1	4	yes	complemented
207	#4083	C₂²×C₃	1	8	yes	complemented
208	#4083	C₂²×C₃	1	4	yes	complemented
209	#4082	C₂²×C₃	1	2	yes	complemented
210	#4076	C₂²×C₃	1	4	yes	complemented
211	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
212	#4041	C₂²×C₃	1	4	yes	complemented
213	#4038	C₂²×C₃	1	2	yes	complemented
214	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
215	#4031	C₂²×C₃	1	8	yes	complemented
216	#4030	C₂²×C₃	1	8	yes	complemented
217	#4028	C₂²×C₃	1	8	yes	complemented
218	#4028	C₂²×C₃	1	4	yes	complemented
219	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
220	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
221	#4023	C₂²×C₃	1	2	yes	complemented
222	#4021	C₂²×C₃	1	2	yes	complemented
223	#4020	C₂²×C₃	1	2	yes	complemented
224	#4018	C₂²×C₃	1	2	yes	complemented
225	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
226	C₂×#535	—	5	1	no	Sylow
227	C₂³×C₃×C₅	—	2	4	no	—
228	C₂³×C₃×C₅	—	4	4	no	—
229	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
231	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
232	C₂²×C₃×D₅	—	2	4	no	—
233	C₂²×C₃×D₅	—	2	4	no	—
234	C₂²×C₃×D₅	—	2	4	no	—
235	C₂²×C₃×D₅	—	2	8	no	—
236	C₂²×C₃×D₅	—	2	8	no	—
237	C₂²×C₃×D₅	—	2	8	no	—
238	C₂²×C₃×D₅	—	2	16	no	—
239	C₂²×C₃×D₅	—	4	8	no	—
240	C₂²×C₃×D₅	—	4	4	no	—
241	C₂²×C₃×D₅	—	4	32	no	—
242	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
243	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
244	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
245	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
246	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
247	C₃×C₅×Q₈	—	2	2	no	—
248	C₃×C₅×D₄	—	2	4	no	—
249	C₃×C₅×D₄	—	2	4	no	—
250	C₃×C₅×D₄	—	2	4	no	—
251	C₃×C₅×D₄	—	2	2	no	—
252	C₃×C₅×D₄	—	4	8	no	—
253	C₂×C₃×C₄×C₅	—	2	4	no	—
254	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
255	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
256	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
257	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
259	C₃×C₂²⋊D₅	—	2	4	no	—
260	C₃×C₂²⋊D₅	—	2	4	no	—
261	C₃×C₂²⋊D₅	—	2	4	no	—
262	C₃×C₂²⋊D₅	—	2	8	no	—
263	C₃×C₂²⋊D₅	—	2	8	no	—
264	C₃×C₂²⋊D₅	—	4	8	no	—
265	C₃×C₂²⋊D₅	—	4	8	no	—
266	C₂×C₃×Dic₅	—	2	4	no	—
267	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	complemented
268	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
269	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
270	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
272	C₃×D₂₀	—	2	4	no	—
273	C₃×D₂₀	—	2	4	no	—
274	C₃×D₂₀	—	2	4	no	—
275	C₃×D₂₀	—	2	2	no	—
276	C₃×D₂₀	—	4	8	no	—
277	C₃×C₄×D₅	—	2	4	no	—
278	C₃×C₄×D₅	—	2	8	no	—
279	C₃×C₄×D₅	—	2	4	no	—
280	C₃×C₄×D₅	—	2	4	no	—
281	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
282	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
283	C₃×C₄×D₅	C₂×D₄	1	4	yes	complemented
284	C₃×C₄×D₅	C₂×D₄	1	4	yes	complemented
285	C₃×Dic₁₀	—	2	2	no	—
286	C₃×Dic₁₀	—	2	4	no	—
287	C₂⁵×C₃	—	5	2	no	—
288	C₂×C₃×#41	—	5	1	no	—
289	C₂×C₃×#41	—	5	2	no	—
290	C₂×C₃×#41	—	5	1	no	—
291	C₂×C₃×#41	—	5	1	no	—
292	C₂×C₃×#41	—	5	2	no	—
293	C₂×C₃×#41	—	10	8	no	—
294	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic, complemented
295	C₂²×C₃×Q₈	—	5	1	no	—
296	C₂²×C₃×D₄	—	5	2	no	—
297	C₂²×C₃×D₄	—	5	2	no	—
298	C₂²×C₃×D₄	—	5	2	no	—
299	C₂²×C₃×D₄	—	5	2	no	—
300	C₂²×C₃×D₄	—	5	2	no	—
301	C₂²×C₃×D₄	—	5	2	no	—
302	C₂²×C₃×D₄	—	5	1	no	—
303	C₂²×C₃×D₄	—	5	8	no	—
304	C₂²×C₃×D₄	—	5	1	no	—
305	C₂²×C₃×D₄	—	10	8	no	—
306	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
307	C₂³×C₃×C₄	—	5	1	no	—
308	C₂³×C₃×C₄	—	5	2	no	—
309	C₃×#127	—	5	2	no	—
310	C₃×#127	—	5	8	no	—
311	C₃×#127	—	5	2	no	—
312	C₃×#127	—	5	2	no	—
313	C₃×#127	C₂×D₅	1	2	yes	complemented
314	C₃×#124	—	5	2	no	—
315	C₃×#124	—	5	2	no	—
316	C₃×#124	—	5	8	no	—
317	C₃×#124	—	5	2	no	—
318	C₃×#124	C₂×D₅	1	2	yes	complemented
319	C₃×#121	—	5	4	no	—
320	C₃×#121	—	5	8	no	—
321	C₃×#121	—	5	4	no	—
322	C₃×#121	—	5	4	no	—
323	C₃×#121	—	5	8	no	—
324	C₃×#121	C₂×D₅	1	4	yes	complemented
325	C₃×#120	—	5	4	no	—
326	C₃×#120	—	5	4	no	—
327	C₃×#120	—	5	8	no	—
328	C₃×#120	—	5	4	no	—
329	C₃×#120	—	5	8	no	—
330	C₃×#120	C₂×D₅	1	4	yes	complemented
331	C₃×#117	—	5	1	no	—
332	C₃×#117	—	5	2	no	—
333	C₃×#117	—	5	2	no	—
334	C₃×#117	—	5	2	no	—
335	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
336	C₂×C₃×C₄⋊C₄	—	5	2	no	—
337	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
338	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
339	C₂×C₃×C₄²	—	5	2	no	—
340	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
341	C₂³×D₅	—	2	8	no	—
342	C₂³×D₅	—	4	8	no	—
343	C₂³×D₅	C₂³×C₃	1	2	yes	—
344	C₂³×D₅	C₂³×C₃	1	4	yes	—
345	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
346	C₂³×D₅	C₂³×C₃	1	2	yes	—
347	C₂³×D₅	C₂³×C₃	1	4	yes	—
348	C₅×#41	—	2	4	no	—
349	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
350	C₂×C₅×D₄	—	2	4	no	—
351	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
352	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
353	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
354	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
355	C₂×C₅×D₄	C₂³×C₃	1	8	yes	complemented
356	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	complemented
358	C₂×C₂²⋊D₅	—	2	8	no	—
359	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
360	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
361	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
362	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
363	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	complemented
364	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
365	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
366	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
367	C₂²×Dic₅	C₂³×C₃	1	2	yes	complemented
368	#713	—	2	4	no	—
369	Q₈×D₅	—	2	4	no	—
370	#711	—	2	8	no	—
371	#711	—	2	4	no	—
372	D₄×D₅	—	2	8	no	—
373	D₄×D₅	—	2	8	no	—
374	D₄×D₅	—	2	8	no	—
375	D₄×D₅	—	2	4	no	—
376	D₄×D₅	—	2	8	no	—
377	D₄×D₅	—	2	8	no	—
378	D₄×D₅	—	4	16	no	—
379	#709	—	2	4	no	—
380	#709	—	2	8	no	—
381	C₂×D₂₀	—	2	4	no	—
382	C₂×D₂₀	C₂³×C₃	1	2	yes	—
383	C₂×D₂₀	C₂³×C₃	1	2	yes	—
384	C₂×D₂₀	C₂³×C₃	1	2	yes	—
385	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic, complemented
386	C₂×D₂₀	C₂³×C₃	1	8	yes	complemented
387	C₂×C₄×D₅	—	2	8	no	—
388	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
389	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
390	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
391	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
392	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
393	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
394	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₄×D₅	C₂³×C₃	1	2	yes	complemented
396	C₂×C₄×D₅	C₂³×C₃	1	2	yes	complemented
397	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic, complemented
398	C₂×Dic₁₀	C₂³×C₃	1	2	yes	complemented
399	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
400	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
401	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
402	C₄²×C₅	C₂³×C₃	1	2	yes	complemented
403	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
404	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
405	#685	C₂³×C₃	1	4	yes	—
406	#685	C₂³×C₃	1	8	yes	complemented
407	#685	C₂³×C₃	1	8	yes	complemented
408	C₄⋊Dic₅	C₂³×C₃	1	2	yes	complemented
409	#683	C₂³×C₃	1	4	yes	complemented
410	C₄×Dic₅	C₂³×C₃	1	2	yes	complemented
411	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
412	C₂²×#41	—	5	1	no	—
413	C₂³×D₄	—	5	1	no	—
414	#535	—	5	1	no	—
415	#535	—	5	1	no	—
416	#535	—	5	2	no	—
417	#535	—	5	2	no	—
418	#535	—	5	4	no	—
419	#535	—	5	4	no	—
420	#535	—	5	1	no	—
421	#535	C₃×D₅	1	1	yes	characteristic, direct product factor
422	C₂×#127	—	5	2	no	—
423	C₂×#124	—	5	2	no	—
424	C₂×#121	—	5	4	no	—
425	C₂×#120	—	5	4	no	—
426	C₂×#117	—	5	1	no	—
427	C₂²×C₃×C₅	—	2	2	no	—
428	C₂²×C₃×C₅	—	2	2	no	—
429	C₂²×C₃×C₅	—	2	4	no	—
430	C₂²×C₃×C₅	—	2	4	no	—
431	C₂²×C₃×C₅	—	2	8	no	—
432	C₂²×C₃×C₅	—	4	8	no	—
433	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
434	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
435	C₂×C₃×D₅	—	2	2	no	—
436	C₂×C₃×D₅	—	2	8	no	—
437	C₂×C₃×D₅	—	2	2	no	—
438	C₂×C₃×D₅	—	2	4	no	—
439	C₂×C₃×D₅	—	2	4	no	—
440	C₂×C₃×D₅	—	2	8	no	—
441	C₂×C₃×D₅	—	4	16	no	—
442	C₂×C₃×D₅	—	4	8	no	—
443	C₂×C₃×D₅	—	4	8	no	—
444	C₂×C₃×D₅	—	4	16	no	—
445	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
446	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
447	C₂×C₃×D₅	H(5,𝔽₂)	1	4	yes	—
448	C₃×C₄×C₅	—	2	2	no	—
449	C₃×C₄×C₅	—	2	4	no	—
450	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
451	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
452	C₃×Dic₅	—	2	2	no	—
453	C₃×Dic₅	—	2	4	no	—
454	C₃×Dic₅	C₂²×D₄	1	2	yes	—
455	C₃×Dic₅	C₂²×D₄	1	2	yes	—
456	C₂⁴×C₃	—	5	1	no	—
457	C₂⁴×C₃	—	5	4	no	—
458	C₂⁴×C₃	—	5	2	no	—
459	C₂⁴×C₃	—	5	4	no	—
460	C₂⁴×C₃	—	5	2	no	—
461	C₂⁴×C₃	—	10	8	no	—
462	C₂⁴×C₃	—	20	8	no	—
463	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
464	C₃×#41	—	2	4	no	—
465	C₃×#41	—	10	8	no	—
466	C₃×#41	—	10	8	no	—
467	C₃×#41	—	10	4	no	—
468	C₃×#41	—	10	4	no	—
469	C₃×#41	—	10	4	no	—
470	C₂×C₃×Q₈	—	5	2	no	—
471	C₂×C₃×Q₈	—	5	1	no	—
472	C₂×C₃×Q₈	—	10	4	no	—
473	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
474	C₂×C₃×D₄	—	2	4	no	—
475	C₂×C₃×D₄	—	5	2	no	—
476	C₂×C₃×D₄	—	5	2	no	—
477	C₂×C₃×D₄	—	5	4	no	—
478	C₂×C₃×D₄	—	5	4	no	—
479	C₂×C₃×D₄	—	5	2	no	—
480	C₂×C₃×D₄	—	5	8	no	—
481	C₂×C₃×D₄	—	5	8	no	—
482	C₂×C₃×D₄	—	5	2	no	—
483	C₂×C₃×D₄	—	5	2	no	—
484	C₂×C₃×D₄	—	5	2	no	—
485	C₂×C₃×D₄	—	5	1	no	—
486	C₂×C₃×D₄	—	5	8	no	—
487	C₂×C₃×D₄	—	10	8	no	—
488	C₂×C₃×D₄	—	10	8	no	—
489	C₂×C₃×D₄	—	10	8	no	—
490	C₂×C₃×D₄	—	10	8	no	—
491	C₂×C₃×D₄	—	10	4	no	—
492	C₂×C₃×D₄	—	10	8	no	—
493	C₂×C₃×D₄	—	10	8	no	—
494	C₂×C₃×D₄	—	10	4	no	—
495	C₂×C₃×D₄	—	20	16	no	—
496	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
497	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
498	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
499	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
500	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
501	C₂²×C₃×C₄	—	5	1	no	—
502	C₂²×C₃×C₄	—	5	8	no	—
503	C₂²×C₃×C₄	—	5	1	no	—
504	C₂²×C₃×C₄	—	5	1	no	—
505	C₂²×C₃×C₄	—	5	1	no	—
506	C₂²×C₃×C₄	—	5	1	no	—
507	C₂²×C₃×C₄	—	5	2	no	—
508	C₂²×C₃×C₄	—	5	4	no	—
509	C₂²×C₃×C₄	—	5	2	no	—
510	C₂²×C₃×C₄	—	5	2	no	—
511	C₂²×C₃×C₄	—	5	2	no	—
512	C₂²×C₃×C₄	—	10	8	no	—
513	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
514	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	complemented
515	C₃×C₄⋊C₄	—	5	4	no	—
516	C₃×C₄⋊C₄	—	5	2	no	—
517	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
518	C₃×C₂²⋊C₄	—	5	2	no	—
519	C₃×C₂²⋊C₄	—	5	8	no	—
520	C₃×C₂²⋊C₄	—	5	4	no	—
521	C₃×C₂²⋊C₄	—	5	8	no	—
522	C₃×C₂²⋊C₄	—	5	8	no	—
523	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
524	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	complemented
525	C₃×C₄²	—	5	4	no	—
526	C₃×C₄²	—	5	2	no	—
527	C₃×C₄²	C₂²×D₅	1	2	yes	complemented
528	C₂³×C₅	—	2	4	no	—
529	C₂³×C₅	—	4	4	no	—
530	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
531	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
532	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
533	C₂²×D₅	—	2	4	no	—
534	C₂²×D₅	—	2	4	no	—
535	C₂²×D₅	—	2	4	no	—
536	C₂²×D₅	—	2	8	no	—
537	C₂²×D₅	—	2	8	no	—
538	C₂²×D₅	—	2	8	no	—
539	C₂²×D₅	—	2	16	no	—
540	C₂²×D₅	—	4	8	no	—
541	C₂²×D₅	—	4	4	no	—
542	C₂²×D₅	—	4	32	no	—
543	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
544	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
545	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
546	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
547	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
548	C₅×Q₈	—	2	2	no	—
549	C₅×D₄	—	2	4	no	—
550	C₅×D₄	—	2	4	no	—
551	C₅×D₄	—	2	4	no	—
552	C₅×D₄	—	2	2	no	—
553	C₅×D₄	—	4	8	no	—
554	C₂×C₄×C₅	—	2	4	no	—
555	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
556	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
557	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
558	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
559	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
560	C₂²⋊D₅	—	2	4	no	—
561	C₂²⋊D₅	—	2	4	no	—
562	C₂²⋊D₅	—	2	4	no	—
563	C₂²⋊D₅	—	2	8	no	—
564	C₂²⋊D₅	—	2	8	no	—
565	C₂²⋊D₅	—	4	8	no	—
566	C₂²⋊D₅	—	4	8	no	—
567	C₂×Dic₅	—	2	4	no	—
568	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	complemented
569	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
570	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
571	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
572	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
573	D₂₀	—	2	4	no	—
574	D₂₀	—	2	4	no	—
575	D₂₀	—	2	4	no	—
576	D₂₀	—	2	2	no	—
577	D₂₀	—	4	8	no	—
578	C₄×D₅	—	2	4	no	—
579	C₄×D₅	—	2	8	no	—
580	C₄×D₅	—	2	4	no	—
581	C₄×D₅	—	2	4	no	—
582	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
583	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
584	C₄×D₅	C₂×C₃×D₄	1	4	yes	complemented
585	C₄×D₅	C₂×C₃×D₄	1	4	yes	complemented
586	Dic₁₀	—	2	2	no	—
587	Dic₁₀	—	2	4	no	—
588	C₂⁵	—	5	2	no	—
589	C₂×#41	—	5	1	no	—
590	C₂×#41	—	5	2	no	—
591	C₂×#41	—	5	1	no	—
592	C₂×#41	—	5	1	no	—
593	C₂×#41	—	5	2	no	—
594	C₂×#41	—	10	8	no	—
595	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic, complemented
596	C₂²×Q₈	—	5	1	no	—
597	C₂²×D₄	—	5	2	no	—
598	C₂²×D₄	—	5	2	no	—
599	C₂²×D₄	—	5	2	no	—
600	C₂²×D₄	—	5	2	no	—
601	C₂²×D₄	—	5	2	no	—
602	C₂²×D₄	—	5	2	no	—
603	C₂²×D₄	—	5	1	no	—
604	C₂²×D₄	—	5	8	no	—
605	C₂²×D₄	—	5	1	no	—
606	C₂²×D₄	—	10	8	no	—
607	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
608	C₂³×C₄	—	5	1	no	—
609	C₂³×C₄	—	5	2	no	—
610	#127	—	5	2	no	—
611	#127	—	5	8	no	—
612	#127	—	5	2	no	—
613	#127	—	5	2	no	—
614	#127	C₂×C₃×D₅	1	2	yes	complemented
615	#124	—	5	2	no	—
616	#124	—	5	2	no	—
617	#124	—	5	8	no	—
618	#124	—	5	2	no	—
619	#124	C₂×C₃×D₅	1	2	yes	complemented
620	#121	—	5	4	no	—
621	#121	—	5	8	no	—
622	#121	—	5	4	no	—
623	#121	—	5	4	no	—
624	#121	—	5	8	no	—
625	#121	C₂×C₃×D₅	1	4	yes	complemented
626	#120	—	5	4	no	—
627	#120	—	5	4	no	—
628	#120	—	5	8	no	—
629	#120	—	5	4	no	—
630	#120	—	5	8	no	—
631	#120	C₂×C₃×D₅	1	4	yes	complemented
632	#117	—	5	1	no	—
633	#117	—	5	2	no	—
634	#117	—	5	2	no	—
635	#117	—	5	2	no	—
636	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
637	C₂×C₄⋊C₄	—	5	2	no	—
638	C₂×C₂²⋊C₄	—	5	2	no	—
639	C₂×C₂²⋊C₄	—	5	8	no	—
640	C₂×C₄²	—	5	2	no	—
641	C₂×C₃×C₅	—	2	2	no	—
642	C₂×C₃×C₅	—	4	4	no	—
643	C₂×C₃×C₅	—	4	2	no	—
644	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
645	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
646	C₃×D₅	—	2	2	no	—
647	C₃×D₅	—	4	2	no	—
648	C₃×D₅	—	4	4	no	—
649	C₃×D₅	#535	1	4	yes	direct product factor
650	C₂³×C₃	—	2	4	no	—
651	C₂³×C₃	—	4	4	no	—
652	C₂³×C₃	—	5	1	no	—
653	C₂³×C₃	—	5	4	no	—
654	C₂³×C₃	—	5	1	no	—
655	C₂³×C₃	—	5	4	no	—
656	C₂³×C₃	—	5	2	no	—
657	C₂³×C₃	—	10	4	no	—
658	C₂³×C₃	—	10	4	no	—
659	C₂³×C₃	—	10	8	no	—
660	C₂³×C₃	—	10	8	no	—
661	C₂³×C₃	—	10	8	no	—
662	C₂³×C₃	—	10	16	no	—
663	C₂³×C₃	—	10	4	no	—
664	C₂³×C₃	—	20	4	no	—
665	C₂³×C₃	—	20	8	no	—
666	C₂³×C₃	—	20	32	no	—
667	C₂³×C₃	C₂³×D₅	1	4	yes	—
668	C₂³×C₃	C₂³×D₅	1	2	yes	—
669	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
670	C₃×Q₈	—	2	2	no	—
671	C₃×Q₈	—	10	4	no	—
672	C₃×Q₈	—	10	2	no	—
673	C₃×D₄	—	2	4	no	—
674	C₃×D₄	—	2	4	no	—
675	C₃×D₄	—	2	4	no	—
676	C₃×D₄	—	2	2	no	—
677	C₃×D₄	—	4	8	no	—
678	C₃×D₄	—	10	4	no	—
679	C₃×D₄	—	10	8	no	—
680	C₃×D₄	—	10	8	no	—
681	C₃×D₄	—	10	4	no	—
682	C₃×D₄	—	10	4	no	—
683	C₃×D₄	—	10	4	no	—
684	C₃×D₄	—	10	4	no	—
685	C₃×D₄	—	10	4	no	—
686	C₃×D₄	—	10	2	no	—
687	C₃×D₄	—	20	8	no	—
688	C₃×D₄	—	20	8	no	—
689	C₃×D₄	—	20	8	no	—
690	C₂×C₃×C₄	—	2	4	no	—
691	C₂×C₃×C₄	—	5	4	no	—
692	C₂×C₃×C₄	—	5	1	no	—
693	C₂×C₃×C₄	—	5	1	no	—
694	C₂×C₃×C₄	—	5	4	no	—
695	C₂×C₃×C₄	—	5	4	no	—
696	C₂×C₃×C₄	—	5	4	no	—
697	C₂×C₃×C₄	—	5	4	no	—
698	C₂×C₃×C₄	—	5	4	no	—
699	C₂×C₃×C₄	—	5	2	no	—
700	C₂×C₃×C₄	—	10	4	no	—
701	C₂×C₃×C₄	—	10	4	no	—
702	C₂×C₃×C₄	—	10	8	no	—
703	C₂×C₃×C₄	—	10	4	no	—
704	C₂×C₃×C₄	—	10	4	no	—
705	C₂×C₃×C₄	D₄×D₅	1	4	yes	complemented
706	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
707	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
708	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
709	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	2	2	no	—
712	C₂²×C₅	—	2	4	no	—
713	C₂²×C₅	—	2	4	no	—
714	C₂²×C₅	—	2	8	no	—
715	C₂²×C₅	—	4	8	no	—
716	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
717	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
718	C₂×D₅	—	2	2	no	—
719	C₂×D₅	—	2	8	no	—
720	C₂×D₅	—	2	2	no	—
721	C₂×D₅	—	2	4	no	—
722	C₂×D₅	—	2	4	no	—
723	C₂×D₅	—	2	8	no	—
724	C₂×D₅	—	4	16	no	—
725	C₂×D₅	—	4	8	no	—
726	C₂×D₅	—	4	8	no	—
727	C₂×D₅	—	4	16	no	—
728	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
729	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
730	C₂×D₅	C₃×H(5,𝔽₂)	1	4	yes	—
731	C₄×C₅	—	2	2	no	—
732	C₄×C₅	—	2	4	no	—
733	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
734	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
735	Dic₅	—	2	2	no	—
736	Dic₅	—	2	4	no	—
737	Dic₅	C₂²×C₃×D₄	1	2	yes	—
738	Dic₅	C₂²×C₃×D₄	1	2	yes	—
739	C₂⁴	—	5	1	no	—
740	C₂⁴	—	5	4	no	—
741	C₂⁴	—	5	2	no	—
742	C₂⁴	—	5	4	no	—
743	C₂⁴	—	5	2	no	—
744	C₂⁴	—	10	8	no	—
745	C₂⁴	—	20	8	no	—
746	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
747	#41	—	2	4	no	—
748	#41	—	10	8	no	—
749	#41	—	10	8	no	—
750	#41	—	10	4	no	—
751	#41	—	10	4	no	—
752	#41	—	10	4	no	—
753	C₂×Q₈	—	5	2	no	—
754	C₂×Q₈	—	5	1	no	—
755	C₂×Q₈	—	10	4	no	—
756	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	5	2	no	—
759	C₂×D₄	—	5	2	no	—
760	C₂×D₄	—	5	4	no	—
761	C₂×D₄	—	5	4	no	—
762	C₂×D₄	—	5	2	no	—
763	C₂×D₄	—	5	8	no	—
764	C₂×D₄	—	5	8	no	—
765	C₂×D₄	—	5	2	no	—
766	C₂×D₄	—	5	2	no	—
767	C₂×D₄	—	5	2	no	—
768	C₂×D₄	—	5	1	no	—
769	C₂×D₄	—	5	8	no	—
770	C₂×D₄	—	10	8	no	—
771	C₂×D₄	—	10	8	no	—
772	C₂×D₄	—	10	8	no	—
773	C₂×D₄	—	10	8	no	—
774	C₂×D₄	—	10	4	no	—
775	C₂×D₄	—	10	8	no	—
776	C₂×D₄	—	10	8	no	—
777	C₂×D₄	—	10	4	no	—
778	C₂×D₄	—	20	16	no	—
779	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
780	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
781	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
782	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
783	C₂×D₄	C₂²×C₃×D₅	1	8	yes	complemented
784	C₂²×C₄	—	5	1	no	—
785	C₂²×C₄	—	5	8	no	—
786	C₂²×C₄	—	5	1	no	—
787	C₂²×C₄	—	5	1	no	—
788	C₂²×C₄	—	5	1	no	—
789	C₂²×C₄	—	5	1	no	—
790	C₂²×C₄	—	5	2	no	—
791	C₂²×C₄	—	5	4	no	—
792	C₂²×C₄	—	5	2	no	—
793	C₂²×C₄	—	5	2	no	—
794	C₂²×C₄	—	5	2	no	—
795	C₂²×C₄	—	10	8	no	—
796	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
797	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	complemented
798	C₄⋊C₄	—	5	4	no	—
799	C₄⋊C₄	—	5	2	no	—
800	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	complemented
801	C₂²⋊C₄	—	5	2	no	—
802	C₂²⋊C₄	—	5	8	no	—
803	C₂²⋊C₄	—	5	4	no	—
804	C₂²⋊C₄	—	5	8	no	—
805	C₂²⋊C₄	—	5	8	no	—
806	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
807	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
808	C₄²	—	5	4	no	—
809	C₄²	—	5	2	no	—
810	C₄²	C₂²×C₃×D₅	1	2	yes	complemented
811	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	4	no	—
815	C₂²×C₃	—	2	4	no	—
816	C₂²×C₃	—	2	8	no	—
817	C₂²×C₃	—	4	8	no	—
818	C₂²×C₃	—	5	2	no	—
819	C₂²×C₃	—	5	4	no	—
820	C₂²×C₃	—	5	2	no	—
821	C₂²×C₃	—	10	8	no	—
822	C₂²×C₃	—	10	2	no	—
823	C₂²×C₃	—	10	2	no	—
824	C₂²×C₃	—	10	4	no	—
825	C₂²×C₃	—	10	4	no	—
826	C₂²×C₃	—	10	8	no	—
827	C₂²×C₃	—	20	8	no	—
828	C₂²×C₃	—	20	8	no	—
829	C₂²×C₃	—	20	16	no	—
830	C₂²×C₃	—	20	16	no	—
831	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
832	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
833	C₃×C₄	—	2	2	no	—
834	C₃×C₄	—	2	4	no	—
835	C₃×C₄	—	5	2	no	—
836	C₃×C₄	—	5	2	no	—
837	C₃×C₄	—	10	2	no	—
838	C₃×C₄	—	10	4	no	—
839	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
840	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
841	C₂×C₅	—	2	2	no	—
842	C₂×C₅	—	4	4	no	—
843	C₂×C₅	—	4	2	no	—
844	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
845	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
846	D₅	—	2	2	no	—
847	D₅	—	4	4	no	—
848	D₅	—	4	2	no	—
849	D₅	C₃×#535	1	4	yes	direct product factor
850	C₂³	—	2	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	5	1	no	—
853	C₂³	—	5	4	no	—
854	C₂³	—	5	1	no	—
855	C₂³	—	5	4	no	—
856	C₂³	—	5	2	no	—
857	C₂³	—	10	4	no	—
858	C₂³	—	10	4	no	—
859	C₂³	—	10	8	no	—
860	C₂³	—	10	8	no	—
861	C₂³	—	10	8	no	—
862	C₂³	—	10	16	no	—
863	C₂³	—	10	4	no	—
864	C₂³	—	20	4	no	—
865	C₂³	—	20	8	no	—
866	C₂³	—	20	32	no	—
867	C₂³	C₂³×C₃×D₅	1	4	yes	—
868	C₂³	C₂³×C₃×D₅	1	2	yes	—
869	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
870	Q₈	—	2	2	no	—
871	Q₈	—	10	4	no	—
872	Q₈	—	10	2	no	—
873	D₄	—	2	4	no	—
874	D₄	—	2	4	no	—
875	D₄	—	2	4	no	—
876	D₄	—	2	2	no	—
877	D₄	—	4	8	no	—
878	D₄	—	10	4	no	—
879	D₄	—	10	8	no	—
880	D₄	—	10	8	no	—
881	D₄	—	10	4	no	—
882	D₄	—	10	4	no	—
883	D₄	—	10	4	no	—
884	D₄	—	10	4	no	—
885	D₄	—	10	4	no	—
886	D₄	—	10	2	no	—
887	D₄	—	20	8	no	—
888	D₄	—	20	8	no	—
889	D₄	—	20	8	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	5	4	no	—
892	C₂×C₄	—	5	1	no	—
893	C₂×C₄	—	5	1	no	—
894	C₂×C₄	—	5	4	no	—
895	C₂×C₄	—	5	4	no	—
896	C₂×C₄	—	5	4	no	—
897	C₂×C₄	—	5	4	no	—
898	C₂×C₄	—	5	4	no	—
899	C₂×C₄	—	5	2	no	—
900	C₂×C₄	—	10	4	no	—
901	C₂×C₄	—	10	4	no	—
902	C₂×C₄	—	10	8	no	—
903	C₂×C₄	—	10	4	no	—
904	C₂×C₄	—	10	4	no	—
905	C₂×C₄	C₃×D₄×D₅	1	4	yes	complemented
906	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
907	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
908	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
909	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
910	C₂×C₃	—	2	2	no	—
911	C₂×C₃	—	4	4	no	—
912	C₂×C₃	—	4	2	no	—
913	C₂×C₃	—	5	4	no	—
914	C₂×C₃	—	10	2	no	—
915	C₂×C₃	—	20	4	no	—
916	C₂×C₃	—	20	2	no	—
917	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
918	C₂×C₃	D₅×H(5,𝔽₂)	1	2	yes	—
919	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	4	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	4	8	no	—
926	C₂²	—	5	2	no	—
927	C₂²	—	5	4	no	—
928	C₂²	—	5	2	no	—
929	C₂²	—	10	8	no	—
930	C₂²	—	10	2	no	—
931	C₂²	—	10	2	no	—
932	C₂²	—	10	4	no	—
933	C₂²	—	10	4	no	—
934	C₂²	—	10	8	no	—
935	C₂²	—	20	8	no	—
936	C₂²	—	20	16	no	—
937	C₂²	—	20	8	no	—
938	C₂²	—	20	16	no	—
939	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
940	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
941	C₄	—	2	2	no	—
942	C₄	—	2	4	no	—
943	C₄	—	5	2	no	—
944	C₄	—	5	2	no	—
945	C₄	—	10	2	no	—
946	C₄	—	10	4	no	—
947	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
948	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
949	C₃	D₅×#535	1	1	yes	characteristic, direct product factor, Sylow
950	C₂	—	2	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	5	4	no	—
954	C₂	—	10	2	no	—
955	C₂	—	20	4	no	—
956	C₂	—	20	2	no	—
957	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
958	C₂	C₃×D₅×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#535	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#535	D₅
hypocenter	C₅	C₂×C₃×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#535

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×#41	C₂	semidirect
2. C₂²×C₃×D₄×D₅	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₃×#66164	C₂	semidirect
5. C₃×#66139	C₂	semidirect
6. C₃×#66049	C₂	semidirect
7. C₃×D₅×#127	C₂	semidirect
8. C₃×#66008	C₂	semidirect
9. C₃×D₅×#124	C₂	semidirect
10. C₃×#65941	C₂	semidirect
11. C₃×D₅×#121	C₂	semidirect
12. C₃×#65926	C₂	semidirect
13. C₃×D₅×#120	C₂	semidirect
14. C₃×#65859	C₂	semidirect
15. C₃×D₅×#117	C₂	semidirect
16. D₅×#535	C₃	direct (N × H)
18. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
22. C₂×C₃×#713	C₂²	semidirect
23. C₂×C₃×Q₈×D₅	C₂²	semidirect
24. C₂×C₃×#711	C₂²	semidirect
25. C₂×C₃×#711	C₂²	semidirect
30. C₂×C₃×D₄×D₅	C₂²	semidirect
31. C₂×C₃×D₄×D₅	C₂²	semidirect
32. C₂×C₃×D₄×D₅	C₂²	semidirect
33. C₂×C₃×D₄×D₅	C₂²	semidirect
34. C₂×C₃×#709	C₂²	semidirect
35. C₂×C₃×#709	C₂²	semidirect
36. C₂²×C₃×D₂₀	C₂²	semidirect
38. C₂²×C₃×C₄×D₅	C₂²	semidirect
39. C₃×C₅×#127	C₂²	semidirect
40. C₃×C₅×#124	C₂²	semidirect
41. C₃×C₅×#121	C₂²	semidirect
42. C₃×C₅×#120	C₂²	semidirect
43. C₃×C₅×#117	C₂²	semidirect
44. C₃×#4099	C₂²	semidirect
45. C₃×#4093	C₂²	semidirect
46. C₃×#4086	C₂²	semidirect
47. C₃×#4086	C₂²	semidirect
48. C₃×#4086	C₂²	semidirect
49. C₃×#4085	C₂²	semidirect
50. C₃×#4084	C₂²	semidirect
51. C₃×#4083	C₂²	semidirect
52. C₃×#4083	C₂²	semidirect
53. C₃×#4082	C₂²	semidirect
54. C₃×#4076	C₂²	semidirect
55. C₃×#4072	C₂²	semidirect
56. C₃×#4041	C₂²	semidirect
57. C₃×#4038	C₂²	semidirect
58. C₃×D₅×C₄⋊C₄	C₂²	semidirect
59. C₃×#4031	C₂²	semidirect
60. C₃×#4030	C₂²	semidirect
61. C₃×#4028	C₂²	semidirect
62. C₃×#4028	C₂²	semidirect
64. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
65. C₃×#4023	C₂²	semidirect
66. C₃×#4021	C₂²	semidirect
67. C₃×#4020	C₂²	semidirect
68. C₃×#4018	C₂²	semidirect
69. C₃×C₄²×D₅	C₂²	semidirect
71. C₂×D₅×#41	C₂×C₃	semidirect
72. C₂²×D₄×D₅	C₂×C₃	semidirect
73. C₅×#535	C₂×C₃	semidirect
74. #66164	C₂×C₃	semidirect
75. #66139	C₂×C₃	semidirect
76. #66049	C₂×C₃	semidirect
77. D₅×#127	C₂×C₃	semidirect
78. #66008	C₂×C₃	semidirect
79. D₅×#124	C₂×C₃	semidirect
80. #65941	C₂×C₃	semidirect
81. D₅×#121	C₂×C₃	semidirect
82. #65926	C₂×C₃	semidirect
83. D₅×#120	C₂×C₃	semidirect
84. #65859	C₂×C₃	semidirect
85. D₅×#117	C₂×C₃	semidirect
95. C₂×C₃×C₅×Q₈	C₂³	semidirect
100. C₂×C₃×C₅×D₄	C₂³	semidirect
101. C₂×C₃×C₅×D₄	C₂³	semidirect
103. C₂²×C₃×C₄×C₅	C₂³	semidirect
109. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
110. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
111. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
113. C₂²×C₃×Dic₅	C₂³	semidirect
131. C₂×C₃×D₂₀	C₂³	semidirect
132. C₂×C₃×D₂₀	C₂³	semidirect
134. C₂×C₃×C₄×D₅	D₄	semidirect
141. C₂×C₃×C₄×D₅	C₂³	semidirect
142. C₂×C₃×C₄×D₅	C₂³	semidirect
143. C₂×C₃×Dic₁₀	C₂³	semidirect
144. C₂×C₃×Dic₁₀	C₂³	semidirect
145. C₃×C₅×C₄⋊C₄	C₂³	semidirect
147. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
148. C₃×C₄²×C₅	C₂³	semidirect
150. C₃×C₂²⋊Dic₅	C₂³	semidirect
152. C₃×#685	C₂³	semidirect
153. C₃×#685	C₂³	semidirect
154. C₃×C₄⋊Dic₅	C₂³	semidirect
155. C₃×#683	C₂³	semidirect
156. C₃×C₄×Dic₅	C₂³	semidirect
157. C₃×C₄×Dic₅	C₂³	semidirect
167. C₃×#535	D₅	direct (N × H)
174. C₂×C₅×#41	C₂²×C₃	semidirect
175. C₂²×C₅×D₄	C₂²×C₃	semidirect
176. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
178. C₂×#713	C₂²×C₃	semidirect
179. C₂×Q₈×D₅	C₂²×C₃	semidirect
180. C₂×#711	C₂²×C₃	semidirect
181. C₂×#711	C₂²×C₃	semidirect
186. C₂×D₄×D₅	C₂²×C₃	semidirect
187. C₂×D₄×D₅	C₂²×C₃	semidirect
188. C₂×D₄×D₅	C₂²×C₃	semidirect
189. C₂×D₄×D₅	C₂²×C₃	semidirect
190. C₂×#709	C₂²×C₃	semidirect
191. C₂×#709	C₂²×C₃	semidirect
192. C₂²×D₂₀	C₂²×C₃	semidirect
194. C₂²×C₄×D₅	C₂²×C₃	semidirect
195. C₅×#127	C₂²×C₃	semidirect
196. C₅×#124	C₂²×C₃	semidirect
197. C₅×#121	C₂²×C₃	semidirect
198. C₅×#120	C₂²×C₃	semidirect
199. C₅×#117	C₂²×C₃	semidirect
200. #4099	C₂²×C₃	semidirect
201. #4093	C₂²×C₃	semidirect
202. #4086	C₂²×C₃	semidirect
203. #4086	C₂²×C₃	semidirect
204. #4086	C₂²×C₃	semidirect
205. #4085	C₂²×C₃	semidirect
206. #4084	C₂²×C₃	semidirect
207. #4083	C₂²×C₃	semidirect
208. #4083	C₂²×C₃	semidirect
209. #4082	C₂²×C₃	semidirect
210. #4076	C₂²×C₃	semidirect
211. #4072	C₂²×C₃	semidirect
212. #4041	C₂²×C₃	semidirect
213. #4038	C₂²×C₃	semidirect
214. D₅×C₄⋊C₄	C₂²×C₃	semidirect
215. #4031	C₂²×C₃	semidirect
216. #4030	C₂²×C₃	semidirect
217. #4028	C₂²×C₃	semidirect
218. #4028	C₂²×C₃	semidirect
220. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
221. #4023	C₂²×C₃	semidirect
222. #4021	C₂²×C₃	semidirect
223. #4020	C₂²×C₃	semidirect
224. #4018	C₂²×C₃	semidirect
225. C₄²×D₅	C₂²×C₃	semidirect
254. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
267. C₂×C₃×Dic₅	C₂×D₄	semidirect
283. C₃×C₄×D₅	C₂×D₄	semidirect
284. C₃×C₄×D₅	C₂×D₄	semidirect
294. C₂×C₃×#41	C₂×D₅	semidirect
306. C₂²×C₃×D₄	C₂×D₅	semidirect
313. C₃×#127	C₂×D₅	semidirect
318. C₃×#124	C₂×D₅	semidirect
324. C₃×#121	C₂×D₅	semidirect
330. C₃×#120	C₂×D₅	semidirect
335. C₃×#117	C₂×D₅	semidirect
349. C₂×C₅×Q₈	C₂³×C₃	semidirect
354. C₂×C₅×D₄	C₂³×C₃	semidirect
355. C₂×C₅×D₄	C₂³×C₃	semidirect
357. C₂²×C₄×C₅	C₂³×C₃	semidirect
363. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
364. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
365. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
367. C₂²×Dic₅	C₂³×C₃	semidirect
385. C₂×D₂₀	C₂³×C₃	semidirect
386. C₂×D₂₀	C₂³×C₃	semidirect
388. C₂×C₄×D₅	C₃×D₄	semidirect
395. C₂×C₄×D₅	C₂³×C₃	semidirect
396. C₂×C₄×D₅	C₂³×C₃	semidirect
397. C₂×Dic₁₀	C₂³×C₃	semidirect
398. C₂×Dic₁₀	C₂³×C₃	semidirect
399. C₅×C₄⋊C₄	C₂³×C₃	semidirect
401. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
402. C₄²×C₅	C₂³×C₃	semidirect
404. C₂²⋊Dic₅	C₂³×C₃	semidirect
406. #685	C₂³×C₃	semidirect
407. #685	C₂³×C₃	semidirect
408. C₄⋊Dic₅	C₂³×C₃	semidirect
409. #683	C₂³×C₃	semidirect
410. C₄×Dic₅	C₂³×C₃	semidirect
411. C₄×Dic₅	C₂³×C₃	semidirect
421. #535	C₃×D₅	direct (N × H)
473. C₂×C₃×Q₈	C₂²×D₅	semidirect
499. C₂×C₃×D₄	C₂²×D₅	semidirect
500. C₂×C₃×D₄	C₂²×D₅	semidirect
514. C₂²×C₃×C₄	C₂²×D₅	semidirect
517. C₃×C₄⋊C₄	C₂²×D₅	semidirect
524. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
527. C₃×C₄²	C₂²×D₅	semidirect
555. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
568. C₂×Dic₅	C₂×C₃×D₄	semidirect
584. C₄×D₅	C₂×C₃×D₄	semidirect
585. C₄×D₅	C₂×C₃×D₄	semidirect
595. C₂×#41	C₂×C₃×D₅	semidirect
607. C₂²×D₄	C₂×C₃×D₅	semidirect
614. #127	C₂×C₃×D₅	semidirect
619. #124	C₂×C₃×D₅	semidirect
625. #121	C₂×C₃×D₅	semidirect
631. #120	C₂×C₃×D₅	semidirect
636. #117	C₂×C₃×D₅	semidirect
649. C₃×D₅	#535	direct (N × H)
705. C₂×C₃×C₄	D₄×D₅	semidirect
756. C₂×Q₈	C₂²×C₃×D₅	semidirect
782. C₂×D₄	C₂²×C₃×D₅	semidirect
783. C₂×D₄	C₂²×C₃×D₅	semidirect
797. C₂²×C₄	C₂²×C₃×D₅	semidirect
800. C₄⋊C₄	C₂²×C₃×D₅	semidirect
807. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
810. C₄²	C₂²×C₃×D₅	semidirect
811. C₃×C₅	C₂×#535	semidirect
849. D₅	C₃×#535	direct (N × H)
905. C₂×C₄	C₃×D₄×D₅	semidirect
919. C₅	C₂×C₃×#535	semidirect
949. C₃	D₅×#535	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×D₅×#41	2
C₂²×C₃×D₄×D₅	2
C₃×C₅×#535	2
C₃×#66164	2
C₃×#66139	2
C₃×#66049	2
C₃×D₅×#127	2
C₃×#66008	2
C₃×D₅×#124	2
C₃×#65941	2
C₃×D₅×#121	2
C₃×#65926	2
C₃×D₅×#120	2
C₃×#65859	2
C₃×D₅×#117	2
D₅×#535	3
C₂×C₃×#535	5

Subgroups — C3×D5×#535 #14480360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#535 #14480360