Subgroups — C₃×D₄×#709 #14483049

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 1024 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	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66125	C₂	1	2	yes	maximal, complemented
5	C₃×#65887	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65886	C₂	1	2	yes	maximal, complemented
7	C₃×#65885	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65884	C₂	1	2	yes	maximal, complemented
9	C₃×D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65882	C₂	1	2	yes	maximal, complemented
11	C₃×#65881	C₂	1	4	yes	maximal, complemented
12	C₃×C₄×D₄×D₅	C₂	1	2	yes	maximal, complemented
13	C₃×D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65841	C₂	1	2	yes	maximal, complemented
15	C₃×#65824	C₂	1	4	yes	maximal, complemented
16	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×#709	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
21	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	complemented
22	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
23	C₂×C₃×#709	—	2	16	no	—
24	C₂×C₃×#709	C₂²	1	1	yes	characteristic
25	C₂×C₃×#709	C₂²	1	2	yes	complemented
26	C₂×C₃×#709	C₂²	1	4	yes	complemented
27	C₂×C₃×#709	C₂²	1	2	yes	complemented
28	C₂×C₃×#709	C₂²	1	2	yes	complemented
29	C₂×C₃×#709	C₂²	1	4	yes	complemented
30	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
31	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	complemented
32	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	complemented
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
36	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
42	C₃×#4099	C₂²	1	4	yes	complemented
43	C₃×#4086	C₂²	1	2	yes	complemented
44	C₃×#4085	C₂²	1	4	yes	complemented
45	C₃×#4084	C₂²	1	2	yes	complemented
46	C₃×#4083	C₂²	1	4	yes	complemented
47	C₃×D₄×Dic₅	C₂²	1	2	yes	—
48	C₃×#4076	C₂²	1	2	yes	complemented
49	C₃×#4076	C₂²	1	2	yes	complemented
50	C₃×#4076	C₂²	1	2	yes	complemented
51	C₃×#4076	C₂²	1	2	yes	complemented
52	C₃×#4075	C₂²	1	4	yes	complemented
53	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
54	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
55	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
56	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
57	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
58	C₃×#4070	C₂²	1	2	yes	complemented
59	C₃×#4070	C₂²	1	2	yes	complemented
60	C₃×#4042	C₂²	1	4	yes	complemented
61	C₃×#4041	C₂²	1	2	yes	complemented
62	C₃×#4040	C₂²	1	4	yes	complemented
63	C₃×#4039	C₂²	1	2	yes	complemented
64	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
65	C₃×#4034	C₂²	1	2	yes	complemented
66	C₃×#4031	C₂²	1	4	yes	complemented
67	C₃×#4030	C₂²	1	4	yes	complemented
68	C₃×#4030	C₂²	1	4	yes	complemented
69	C₃×#4029	C₂²	1	4	yes	complemented
70	C₃×#4028	C₂²	1	4	yes	complemented
71	C₃×#4027	C₂²	1	4	yes	complemented
72	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
73	C₃×#4024	C₂²	1	4	yes	complemented
74	C₃×#4021	C₂²	1	2	yes	complemented
75	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
76	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
77	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
78	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
79	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
80	C₃×#4018	C₂²	1	2	yes	complemented
81	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
82	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
85	C₃×D₄×#41	—	5	1	no	maximal, Hall
86	C₂²×#709	C₂×C₃	1	2	yes	complemented
87	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
88	D₄×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
89	#66125	C₂×C₃	1	2	yes	complemented
90	#65887	C₂×C₃	1	1	yes	characteristic, complemented
91	#65886	C₂×C₃	1	2	yes	complemented
92	#65885	C₂×C₃	1	1	yes	characteristic, complemented
93	#65884	C₂×C₃	1	2	yes	complemented
94	D₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
95	#65882	C₂×C₃	1	2	yes	complemented
96	#65881	C₂×C₃	1	4	yes	complemented
97	C₄×D₄×D₅	C₂×C₃	1	2	yes	complemented
98	D₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
99	#65841	C₂×C₃	1	2	yes	complemented
100	#65824	C₂×C₃	1	4	yes	complemented
101	#65811	C₂×C₃	1	1	yes	characteristic, complemented
102	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
104	C₂³×C₃×D₅	C₂³	1	4	yes	—
105	C₂×C₃×C₅×D₄	—	2	4	no	—
106	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
107	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	—	2	8	no	—
110	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
111	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
112	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
113	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
114	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
115	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
116	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
119	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
120	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
121	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
122	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
123	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
124	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
125	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
126	C₃×D₄×D₅	—	2	8	no	—
127	C₃×#709	—	2	8	no	—
128	C₃×#709	—	2	16	no	—
129	C₃×#709	—	2	8	no	—
130	C₃×#709	—	2	16	no	—
131	C₃×#709	—	2	8	no	—
132	C₃×#709	D₄	1	8	yes	direct product factor
133	C₂×C₃×D₂₀	—	2	8	no	—
134	C₂×C₃×D₂₀	C₂³	1	2	yes	—
135	C₂×C₃×D₂₀	C₂³	1	2	yes	—
136	C₂×C₃×D₂₀	C₂³	1	4	yes	—
137	C₂×C₃×D₂₀	C₂³	1	2	yes	—
138	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄×D₅	—	2	16	no	—
140	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
141	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
142	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
143	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
144	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
145	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
146	C₂×C₃×Dic₁₀	—	2	8	no	—
147	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
148	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
149	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
150	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
158	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
160	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
162	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
163	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
164	C₃×#685	C₂³	1	2	yes	—
165	C₃×#685	C₂³	1	4	yes	—
166	C₃×#685	C₂³	1	2	yes	—
167	C₃×#685	C₂³	1	4	yes	—
168	C₃×#685	C₂³	1	4	yes	—
169	C₃×#685	C₂³	1	4	yes	—
170	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
171	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
172	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
174	C₃×#683	C₂³	1	2	yes	—
175	C₃×#683	C₂³	1	2	yes	—
176	C₃×#683	C₂³	1	4	yes	—
177	C₃×#683	C₂³	1	4	yes	—
178	C₃×C₄×Dic₅	C₂³	1	2	yes	—
179	C₃×C₄×Dic₅	C₂³	1	2	yes	—
180	C₃×C₄×Dic₅	C₂³	1	2	yes	—
181	C₂²×C₃×#41	—	5	2	no	—
182	C₃×#550	—	5	1	no	—
183	C₃×D₄×Q₈	—	5	1	no	—
184	C₃×#548	—	5	2	no	—
185	C₃×#547	—	5	1	no	—
186	C₃×#547	—	5	2	no	—
187	C₃×#546	—	5	2	no	—
188	C₃×#546	—	5	4	no	—
189	C₃×D₄²	—	5	2	no	—
190	C₃×D₄²	—	5	1	no	—
191	C₃×#532	—	5	2	no	—
192	C₃×#532	—	5	1	no	—
193	C₃×#525	—	5	2	no	—
194	C₃×#525	—	5	4	no	—
195	C₃×C₄×#41	—	5	1	no	—
196	C₂×C₃×C₄×D₄	—	5	2	no	—
197	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
198	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
199	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	complemented
200	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
201	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
202	C₂×#709	—	2	16	no	—
203	C₂×#709	C₂²×C₃	1	1	yes	characteristic
204	C₂×#709	C₂²×C₃	1	2	yes	complemented
205	C₂×#709	C₂²×C₃	1	4	yes	complemented
206	C₂×#709	C₂²×C₃	1	4	yes	complemented
207	C₂×#709	C₂²×C₃	1	2	yes	complemented
208	C₂×#709	C₂²×C₃	1	2	yes	complemented
209	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
210	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	complemented
211	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	complemented
212	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
213	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
214	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
215	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
217	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
220	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
221	#4099	C₂²×C₃	1	4	yes	complemented
222	#4086	C₂²×C₃	1	2	yes	complemented
223	#4085	C₂²×C₃	1	4	yes	complemented
224	#4084	C₂²×C₃	1	2	yes	complemented
225	#4083	C₂²×C₃	1	4	yes	complemented
226	D₄×Dic₅	C₂²×C₃	1	2	yes	—
227	#4076	C₂²×C₃	1	2	yes	complemented
228	#4076	C₂²×C₃	1	2	yes	complemented
229	#4076	C₂²×C₃	1	2	yes	complemented
230	#4076	C₂²×C₃	1	2	yes	complemented
231	#4075	C₂²×C₃	1	4	yes	complemented
232	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
233	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
234	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
235	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
236	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
237	#4070	C₂²×C₃	1	2	yes	complemented
238	#4070	C₂²×C₃	1	2	yes	complemented
239	#4042	C₂²×C₃	1	4	yes	complemented
240	#4041	C₂²×C₃	1	2	yes	complemented
241	#4040	C₂²×C₃	1	4	yes	complemented
242	#4039	C₂²×C₃	1	2	yes	complemented
243	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
244	#4034	C₂²×C₃	1	2	yes	complemented
245	#4031	C₂²×C₃	1	4	yes	complemented
246	#4030	C₂²×C₃	1	4	yes	complemented
247	#4030	C₂²×C₃	1	4	yes	complemented
248	#4029	C₂²×C₃	1	4	yes	complemented
249	#4028	C₂²×C₃	1	4	yes	complemented
250	#4027	C₂²×C₃	1	4	yes	complemented
251	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
252	#4024	C₂²×C₃	1	4	yes	complemented
253	#4021	C₂²×C₃	1	2	yes	complemented
254	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
255	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
256	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
258	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
259	#4018	C₂²×C₃	1	2	yes	complemented
260	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
261	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
262	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
263	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
264	D₄×#41	—	5	1	no	Sylow
265	C₂³×C₃×C₅	—	2	4	no	—
266	C₂³×C₃×C₅	—	2	4	no	—
267	C₂³×C₃×C₅	—	4	2	no	—
268	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
269	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
270	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
271	C₂²×C₃×D₅	—	2	8	no	—
272	C₂²×C₃×D₅	—	2	8	no	—
273	C₂²×C₃×D₅	—	4	4	no	—
274	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
275	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
276	C₃×C₅×D₄	—	2	4	no	—
277	C₃×C₅×D₄	—	2	2	no	—
278	C₃×C₅×D₄	#41	1	4	yes	complemented
279	C₂×C₃×C₄×C₅	—	2	4	no	—
280	C₂×C₃×C₄×C₅	—	2	4	no	—
281	C₂×C₃×C₄×C₅	—	2	4	no	—
282	C₂×C₃×C₄×C₅	—	2	4	no	—
283	C₂×C₃×C₄×C₅	—	2	4	no	—
284	C₂×C₃×C₄×C₅	—	2	2	no	—
285	C₂×C₃×C₄×C₅	—	4	1	no	—
286	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
287	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
291	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
293	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₃×C₂²⋊D₅	—	2	8	no	—
296	C₃×C₂²⋊D₅	—	2	8	no	—
297	C₃×C₂²⋊D₅	—	2	8	no	—
298	C₃×C₂²⋊D₅	—	2	8	no	—
299	C₃×C₂²⋊D₅	—	4	4	no	—
300	C₃×C₂²⋊D₅	C₂×D₄	1	8	yes	complemented
301	C₂×C₃×Dic₅	—	2	8	no	—
302	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
303	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
304	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
305	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
306	C₃×D₂₀	—	2	8	no	—
307	C₃×D₂₀	—	2	4	no	—
308	C₃×D₂₀	—	2	4	no	—
309	C₃×D₂₀	—	4	2	no	—
310	C₃×D₂₀	C₂×D₄	1	4	yes	complemented
311	C₃×C₄×D₅	—	2	8	no	—
312	C₃×C₄×D₅	—	2	8	no	—
313	C₃×C₄×D₅	—	2	4	no	—
314	C₃×C₄×D₅	—	2	8	no	—
315	C₃×C₄×D₅	—	4	2	no	—
316	C₃×C₄×D₅	C₂×D₄	1	8	yes	complemented
317	C₃×Dic₁₀	—	2	4	no	—
318	C₃×Dic₁₀	—	2	8	no	—
319	C₃×Dic₁₀	C₂×D₄	1	4	yes	complemented
320	C₂×C₃×#41	—	5	1	no	—
321	C₂×C₃×#41	—	5	4	no	—
322	C₂×C₃×#41	—	5	2	no	—
323	C₂×C₃×#41	—	5	2	no	—
324	C₂×C₃×#41	—	5	4	no	—
325	C₂×C₃×#41	—	5	2	no	—
326	C₂×C₃×#41	—	10	16	no	—
327	C₂²×C₃×Q₈	—	5	2	no	—
328	C₂²×C₃×D₄	—	5	4	no	—
329	C₂²×C₃×D₄	—	5	2	no	—
330	C₂²×C₃×D₄	—	5	2	no	—
331	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
332	C₂³×C₃×C₄	—	5	4	no	—
333	C₂³×C₃×C₄	C₂×D₅	1	2	yes	complemented
334	C₃×C₄⋊Q₈	—	5	2	no	—
335	C₃×C₄⋊Q₈	—	5	1	no	—
336	C₃×#127	—	5	2	no	—
337	C₃×#127	—	5	1	no	—
338	C₃×#124	—	5	4	no	—
339	C₃×#124	—	5	2	no	—
340	C₃×#123	—	5	4	no	—
341	C₃×#123	—	5	4	no	—
342	C₃×#123	—	5	4	no	—
343	C₃×C₂²⋊Q₈	—	5	2	no	—
344	C₃×C₂²⋊Q₈	—	5	2	no	—
345	C₃×C₂²⋊Q₈	—	5	4	no	—
346	C₃×C₂²⋊Q₈	—	5	4	no	—
347	C₃×#121	—	5	2	no	—
348	C₃×#121	—	5	4	no	—
349	C₃×#121	—	5	2	no	—
350	C₃×#121	—	5	2	no	—
351	C₃×#121	—	5	2	no	—
352	C₃×#121	—	5	2	no	—
353	C₃×#121	—	5	2	no	—
354	C₃×#121	—	5	4	no	—
355	C₃×#121	—	5	4	no	—
356	C₃×#120	—	5	4	no	—
357	C₃×#120	—	5	4	no	—
358	C₃×#120	—	5	4	no	—
359	C₃×C₄×Q₈	—	5	1	no	—
360	C₃×C₄×Q₈	—	5	1	no	—
361	C₃×C₄×D₄	—	5	2	no	—
362	C₃×C₄×D₄	—	5	4	no	—
363	C₃×C₄×D₄	—	5	2	no	—
364	C₃×C₄×D₄	—	5	2	no	—
365	C₃×C₄×D₄	—	5	4	no	—
366	C₃×C₄×D₄	—	5	2	no	—
367	C₃×C₄×D₄	—	5	4	no	—
368	C₃×C₄×D₄	—	5	2	no	—
369	C₃×C₄×D₄	—	5	1	no	—
370	C₃×C₄×D₄	—	5	1	no	—
371	C₃×C₄×D₄	—	5	2	no	—
372	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
373	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
374	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
375	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
376	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
377	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
378	C₃×#117	—	5	1	no	—
379	C₃×#117	—	5	2	no	—
380	C₂×C₃×C₄⋊C₄	—	5	2	no	—
381	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
382	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
383	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
384	C₂×C₃×C₄²	—	5	2	no	—
385	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
386	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
387	C₂³×D₅	C₂³×C₃	1	4	yes	—
388	C₂×C₅×D₄	—	2	4	no	—
389	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
390	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
391	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
392	C₂²×C₄×C₅	—	2	8	no	—
393	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
394	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
395	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
396	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
397	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
398	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
399	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
400	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₂²⋊D₅	—	2	16	no	—
402	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
403	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
404	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
405	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
406	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
407	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
408	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
409	D₄×D₅	—	2	8	no	—
410	#709	—	2	8	no	—
411	#709	—	2	16	no	—
412	#709	—	2	8	no	—
413	#709	—	2	16	no	—
414	#709	—	2	8	no	—
415	#709	C₃×D₄	1	8	yes	direct product factor
416	C₂×D₂₀	—	2	8	no	—
417	C₂×D₂₀	C₂³×C₃	1	2	yes	—
418	C₂×D₂₀	C₂³×C₃	1	4	yes	—
419	C₂×D₂₀	C₂³×C₃	1	2	yes	—
420	C₂×D₂₀	C₂³×C₃	1	2	yes	—
421	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄×D₅	—	2	16	no	—
423	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
424	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
425	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
426	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
427	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
428	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
429	C₂×Dic₁₀	—	2	8	no	—
430	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
431	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
432	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
433	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
434	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
435	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
436	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
441	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
442	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
443	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
444	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
445	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
446	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
447	#685	C₂³×C₃	1	2	yes	—
448	#685	C₂³×C₃	1	2	yes	—
449	#685	C₂³×C₃	1	4	yes	—
450	#685	C₂³×C₃	1	4	yes	—
451	#685	C₂³×C₃	1	4	yes	—
452	#685	C₂³×C₃	1	4	yes	—
453	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
454	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
455	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
456	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
457	#683	C₂³×C₃	1	2	yes	—
458	#683	C₂³×C₃	1	2	yes	—
459	#683	C₂³×C₃	1	4	yes	—
460	#683	C₂³×C₃	1	4	yes	—
461	C₄×Dic₅	C₂³×C₃	1	2	yes	—
462	C₄×Dic₅	C₂³×C₃	1	2	yes	—
463	C₄×Dic₅	C₂³×C₃	1	2	yes	—
464	C₂²×#41	—	5	2	no	—
465	#550	—	5	1	no	—
466	D₄×Q₈	—	5	1	no	—
467	#548	—	5	2	no	—
468	#547	—	5	1	no	—
469	#547	—	5	2	no	—
470	#546	—	5	2	no	—
471	#546	—	5	4	no	—
472	D₄²	—	5	2	no	—
473	D₄²	—	5	1	no	—
474	#532	—	5	2	no	—
475	#532	—	5	1	no	—
476	#525	—	5	2	no	—
477	#525	—	5	4	no	—
478	C₄×#41	—	5	1	no	—
479	C₂×C₄×D₄	—	5	2	no	—
480	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
481	C₂²×C₃×C₅	—	2	2	no	—
482	C₂²×C₃×C₅	—	2	1	no	—
483	C₂²×C₃×C₅	—	2	1	no	—
484	C₂²×C₃×C₅	—	2	2	no	—
485	C₂²×C₃×C₅	—	2	2	no	—
486	C₂²×C₃×C₅	—	2	2	no	—
487	C₂²×C₃×C₅	—	2	2	no	—
488	C₂²×C₃×C₅	—	4	8	no	—
489	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
490	C₂²×C₃×C₅	C₂×#41	1	4	yes	complemented
491	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
492	C₂×C₃×D₅	—	2	2	no	—
493	C₂×C₃×D₅	—	2	2	no	—
494	C₂×C₃×D₅	—	2	4	no	—
495	C₂×C₃×D₅	—	2	4	no	—
496	C₂×C₃×D₅	—	2	4	no	—
497	C₂×C₃×D₅	—	4	16	no	—
498	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
499	C₃×C₄×C₅	—	2	2	no	—
500	C₃×C₄×C₅	—	2	2	no	—
501	C₃×C₄×C₅	—	2	1	no	—
502	C₃×C₄×C₅	—	2	1	no	—
503	C₃×C₄×C₅	—	2	1	no	—
504	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
505	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
506	C₃×C₄×C₅	C₂×#41	1	2	yes	complemented
507	C₃×Dic₅	—	2	4	no	—
508	C₃×Dic₅	—	2	2	no	—
509	C₃×Dic₅	—	2	2	no	—
510	C₃×Dic₅	C₂²×D₄	1	4	yes	—
511	C₂⁴×C₃	—	5	4	no	—
512	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
513	C₃×#41	—	5	8	no	—
514	C₃×#41	—	10	16	no	—
515	C₃×#41	—	10	16	no	—
516	C₃×#41	—	10	8	no	—
517	C₃×#41	—	10	8	no	—
518	C₃×#41	—	10	8	no	—
519	C₂×C₃×Q₈	—	5	1	no	—
520	C₂×C₃×Q₈	—	5	4	no	—
521	C₂×C₃×Q₈	—	5	2	no	—
522	C₂×C₃×Q₈	—	10	8	no	—
523	C₂×C₃×D₄	—	2	4	no	—
524	C₂×C₃×D₄	—	5	2	no	—
525	C₂×C₃×D₄	—	5	4	no	—
526	C₂×C₃×D₄	—	5	4	no	—
527	C₂×C₃×D₄	—	5	4	no	—
528	C₂×C₃×D₄	—	5	4	no	—
529	C₂×C₃×D₄	—	5	4	no	—
530	C₂×C₃×D₄	—	5	1	no	—
531	C₂×C₃×D₄	—	5	2	no	—
532	C₂×C₃×D₄	—	5	4	no	—
533	C₂×C₃×D₄	—	5	2	no	—
534	C₂×C₃×D₄	—	5	2	no	—
535	C₂×C₃×D₄	—	10	8	no	—
536	C₂×C₃×D₄	—	10	16	no	—
537	C₂×C₃×D₄	—	10	8	no	—
538	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
539	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
540	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
541	C₂²×C₃×C₄	—	2	8	no	—
542	C₂²×C₃×C₄	—	5	2	no	—
543	C₂²×C₃×C₄	—	5	4	no	—
544	C₂²×C₃×C₄	—	5	2	no	—
545	C₂²×C₃×C₄	—	5	4	no	—
546	C₂²×C₃×C₄	—	5	4	no	—
547	C₂²×C₃×C₄	—	5	4	no	—
548	C₂²×C₃×C₄	—	5	2	no	—
549	C₂²×C₃×C₄	—	10	16	no	—
550	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
551	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
552	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
553	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
554	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
555	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
556	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
557	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
558	C₃×C₄⋊C₄	—	5	4	no	—
559	C₃×C₄⋊C₄	—	5	2	no	—
560	C₃×C₄⋊C₄	—	5	2	no	—
561	C₃×C₄⋊C₄	—	5	4	no	—
562	C₃×C₄⋊C₄	—	5	2	no	—
563	C₃×C₄⋊C₄	—	5	1	no	—
564	C₃×C₄⋊C₄	—	5	1	no	—
565	C₃×C₄⋊C₄	—	5	2	no	—
566	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
567	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
568	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
569	C₃×C₂²⋊C₄	—	5	4	no	—
570	C₃×C₂²⋊C₄	—	5	2	no	—
571	C₃×C₂²⋊C₄	—	5	4	no	—
572	C₃×C₂²⋊C₄	—	5	4	no	—
573	C₃×C₂²⋊C₄	—	5	4	no	—
574	C₃×C₂²⋊C₄	—	5	2	no	—
575	C₃×C₂²⋊C₄	—	5	2	no	—
576	C₃×C₂²⋊C₄	—	5	4	no	—
577	C₃×C₂²⋊C₄	—	5	4	no	—
578	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
579	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
580	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
581	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
582	C₃×C₄²	—	5	2	no	—
583	C₃×C₄²	—	5	2	no	—
584	C₃×C₄²	—	5	2	no	—
585	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
586	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
587	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
588	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
589	C₂³×C₅	—	2	4	no	—
590	C₂³×C₅	—	2	4	no	—
591	C₂³×C₅	—	4	2	no	—
592	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
593	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
594	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
595	C₂²×D₅	—	2	8	no	—
596	C₂²×D₅	—	2	8	no	—
597	C₂²×D₅	—	4	4	no	—
598	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
599	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
600	C₅×D₄	—	2	4	no	—
601	C₅×D₄	—	2	2	no	—
602	C₅×D₄	C₃×#41	1	4	yes	complemented
603	C₂×C₄×C₅	—	2	4	no	—
604	C₂×C₄×C₅	—	2	4	no	—
605	C₂×C₄×C₅	—	2	4	no	—
606	C₂×C₄×C₅	—	2	4	no	—
607	C₂×C₄×C₅	—	2	4	no	—
608	C₂×C₄×C₅	—	2	2	no	—
609	C₂×C₄×C₅	—	4	1	no	—
610	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
611	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
612	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
613	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
614	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
615	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
616	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
617	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
618	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
619	C₂²⋊D₅	—	2	8	no	—
620	C₂²⋊D₅	—	2	8	no	—
621	C₂²⋊D₅	—	2	8	no	—
622	C₂²⋊D₅	—	2	8	no	—
623	C₂²⋊D₅	—	4	4	no	—
624	C₂²⋊D₅	C₂×C₃×D₄	1	8	yes	complemented
625	C₂×Dic₅	—	2	8	no	—
626	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
627	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
628	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
629	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
630	D₂₀	—	2	8	no	—
631	D₂₀	—	2	4	no	—
632	D₂₀	—	2	4	no	—
633	D₂₀	—	4	2	no	—
634	D₂₀	C₂×C₃×D₄	1	4	yes	complemented
635	C₄×D₅	—	2	8	no	—
636	C₄×D₅	—	2	8	no	—
637	C₄×D₅	—	2	4	no	—
638	C₄×D₅	—	2	8	no	—
639	C₄×D₅	—	4	2	no	—
640	C₄×D₅	C₂×C₃×D₄	1	8	yes	complemented
641	Dic₁₀	—	2	4	no	—
642	Dic₁₀	—	2	8	no	—
643	Dic₁₀	C₂×C₃×D₄	1	4	yes	complemented
644	C₂×#41	—	5	1	no	—
645	C₂×#41	—	5	4	no	—
646	C₂×#41	—	5	2	no	—
647	C₂×#41	—	5	2	no	—
648	C₂×#41	—	5	4	no	—
649	C₂×#41	—	5	2	no	—
650	C₂×#41	—	10	16	no	—
651	C₂²×Q₈	—	5	2	no	—
652	C₂²×D₄	—	5	4	no	—
653	C₂²×D₄	—	5	2	no	—
654	C₂²×D₄	—	5	2	no	—
655	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
656	C₂³×C₄	—	5	4	no	—
657	C₂³×C₄	C₂×C₃×D₅	1	2	yes	complemented
658	C₄⋊Q₈	—	5	2	no	—
659	C₄⋊Q₈	—	5	1	no	—
660	#127	—	5	2	no	—
661	#127	—	5	1	no	—
662	#124	—	5	4	no	—
663	#124	—	5	2	no	—
664	#123	—	5	4	no	—
665	#123	—	5	4	no	—
666	#123	—	5	4	no	—
667	C₂²⋊Q₈	—	5	2	no	—
668	C₂²⋊Q₈	—	5	2	no	—
669	C₂²⋊Q₈	—	5	4	no	—
670	C₂²⋊Q₈	—	5	4	no	—
671	#121	—	5	4	no	—
672	#121	—	5	2	no	—
673	#121	—	5	2	no	—
674	#121	—	5	2	no	—
675	#121	—	5	2	no	—
676	#121	—	5	2	no	—
677	#121	—	5	2	no	—
678	#121	—	5	4	no	—
679	#121	—	5	4	no	—
680	#120	—	5	4	no	—
681	#120	—	5	4	no	—
682	#120	—	5	4	no	—
683	C₄×Q₈	—	5	1	no	—
684	C₄×Q₈	—	5	1	no	—
685	C₄×D₄	—	5	2	no	—
686	C₄×D₄	—	5	4	no	—
687	C₄×D₄	—	5	2	no	—
688	C₄×D₄	—	5	2	no	—
689	C₄×D₄	—	5	4	no	—
690	C₄×D₄	—	5	2	no	—
691	C₄×D₄	—	5	4	no	—
692	C₄×D₄	—	5	2	no	—
693	C₄×D₄	—	5	1	no	—
694	C₄×D₄	—	5	1	no	—
695	C₄×D₄	—	5	2	no	—
696	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
697	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
698	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
699	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
700	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
701	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
702	#117	—	5	1	no	—
703	#117	—	5	2	no	—
704	C₂×C₄⋊C₄	—	5	2	no	—
705	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
706	C₂×C₂²⋊C₄	—	5	4	no	—
707	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
708	C₂×C₄²	—	5	2	no	—
709	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
710	C₂×C₃×C₅	—	2	4	no	—
711	C₂×C₃×C₅	—	2	2	no	—
712	C₂×C₃×C₅	—	4	2	no	—
713	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
714	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
715	C₂×C₃×C₅	#585	1	1	yes	characteristic
716	C₃×D₅	—	2	4	no	—
717	C₃×D₅	—	4	4	no	—
718	C₂³×C₃	—	2	4	no	—
719	C₂³×C₃	—	2	4	no	—
720	C₂³×C₃	—	4	2	no	—
721	C₂³×C₃	—	5	2	no	—
722	C₂³×C₃	—	5	4	no	—
723	C₂³×C₃	—	10	8	no	—
724	C₂³×C₃	—	10	8	no	—
725	C₂³×C₃	—	20	4	no	—
726	C₂³×C₃	C₂³×D₅	1	2	yes	—
727	C₂³×C₃	C₂³×D₅	1	2	yes	—
728	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
729	C₃×Q₈	—	5	4	no	—
730	C₃×Q₈	—	10	8	no	—
731	C₃×Q₈	—	10	4	no	—
732	C₃×D₄	—	2	4	no	—
733	C₃×D₄	—	2	2	no	—
734	C₃×D₄	—	5	8	no	—
735	C₃×D₄	—	5	4	no	—
736	C₃×D₄	—	10	8	no	—
737	C₃×D₄	—	10	8	no	—
738	C₃×D₄	—	10	8	no	—
739	C₃×D₄	—	10	8	no	—
740	C₃×D₄	—	10	8	no	—
741	C₃×D₄	—	10	4	no	—
742	C₃×D₄	—	10	4	no	—
743	C₃×D₄	—	20	2	no	—
744	C₃×D₄	—	20	4	no	—
745	C₃×D₄	#709	1	4	yes	direct product factor
746	C₂×C₃×C₄	—	2	4	no	—
747	C₂×C₃×C₄	—	2	2	no	—
748	C₂×C₃×C₄	—	2	4	no	—
749	C₂×C₃×C₄	—	2	4	no	—
750	C₂×C₃×C₄	—	2	4	no	—
751	C₂×C₃×C₄	—	2	4	no	—
752	C₂×C₃×C₄	—	4	1	no	—
753	C₂×C₃×C₄	—	5	2	no	—
754	C₂×C₃×C₄	—	5	8	no	—
755	C₂×C₃×C₄	—	5	2	no	—
756	C₂×C₃×C₄	—	5	2	no	—
757	C₂×C₃×C₄	—	5	4	no	—
758	C₂×C₃×C₄	—	10	8	no	—
759	C₂×C₃×C₄	—	10	8	no	—
760	C₂×C₃×C₄	—	10	8	no	—
761	C₂×C₃×C₄	—	10	4	no	—
762	C₂×C₃×C₄	—	10	8	no	—
763	C₂×C₃×C₄	—	20	2	no	—
764	C₂×C₃×C₄	D₄×D₅	1	4	yes	complemented
765	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
766	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
767	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
768	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
769	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
770	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
771	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
772	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
773	C₂²×C₅	—	2	2	no	—
774	C₂²×C₅	—	2	1	no	—
775	C₂²×C₅	—	2	1	no	—
776	C₂²×C₅	—	2	2	no	—
777	C₂²×C₅	—	2	2	no	—
778	C₂²×C₅	—	2	2	no	—
779	C₂²×C₅	—	2	2	no	—
780	C₂²×C₅	—	4	8	no	—
781	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
782	C₂²×C₅	C₂×C₃×#41	1	4	yes	complemented
783	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
784	C₂×D₅	—	2	2	no	—
785	C₂×D₅	—	2	2	no	—
786	C₂×D₅	—	2	4	no	—
787	C₂×D₅	—	2	4	no	—
788	C₂×D₅	—	2	4	no	—
789	C₂×D₅	—	4	16	no	—
790	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
791	C₄×C₅	—	2	2	no	—
792	C₄×C₅	—	2	2	no	—
793	C₄×C₅	—	2	1	no	—
794	C₄×C₅	—	2	1	no	—
795	C₄×C₅	—	2	1	no	—
796	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
797	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
798	C₄×C₅	C₂×C₃×#41	1	2	yes	complemented
799	Dic₅	—	2	4	no	—
800	Dic₅	—	2	2	no	—
801	Dic₅	—	2	2	no	—
802	Dic₅	C₂²×C₃×D₄	1	4	yes	—
803	C₂⁴	—	5	4	no	—
804	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
805	#41	—	5	8	no	—
806	#41	—	10	16	no	—
807	#41	—	10	16	no	—
808	#41	—	10	8	no	—
809	#41	—	10	8	no	—
810	#41	—	10	8	no	—
811	C₂×Q₈	—	5	1	no	—
812	C₂×Q₈	—	5	4	no	—
813	C₂×Q₈	—	5	2	no	—
814	C₂×Q₈	—	10	8	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	5	2	no	—
817	C₂×D₄	—	5	4	no	—
818	C₂×D₄	—	5	4	no	—
819	C₂×D₄	—	5	4	no	—
820	C₂×D₄	—	5	4	no	—
821	C₂×D₄	—	5	4	no	—
822	C₂×D₄	—	5	1	no	—
823	C₂×D₄	—	5	2	no	—
824	C₂×D₄	—	5	4	no	—
825	C₂×D₄	—	5	2	no	—
826	C₂×D₄	—	5	2	no	—
827	C₂×D₄	—	10	8	no	—
828	C₂×D₄	—	10	16	no	—
829	C₂×D₄	—	10	8	no	—
830	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
831	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
832	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
833	C₂²×C₄	—	2	8	no	—
834	C₂²×C₄	—	5	2	no	—
835	C₂²×C₄	—	5	4	no	—
836	C₂²×C₄	—	5	2	no	—
837	C₂²×C₄	—	5	4	no	—
838	C₂²×C₄	—	5	4	no	—
839	C₂²×C₄	—	5	4	no	—
840	C₂²×C₄	—	5	2	no	—
841	C₂²×C₄	—	10	16	no	—
842	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
843	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
844	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
845	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
846	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
847	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
848	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
849	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
850	C₄⋊C₄	—	5	2	no	—
851	C₄⋊C₄	—	5	4	no	—
852	C₄⋊C₄	—	5	2	no	—
853	C₄⋊C₄	—	5	2	no	—
854	C₄⋊C₄	—	5	1	no	—
855	C₄⋊C₄	—	5	1	no	—
856	C₄⋊C₄	—	5	4	no	—
857	C₄⋊C₄	—	5	2	no	—
858	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
859	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
860	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
861	C₂²⋊C₄	—	5	4	no	—
862	C₂²⋊C₄	—	5	2	no	—
863	C₂²⋊C₄	—	5	4	no	—
864	C₂²⋊C₄	—	5	4	no	—
865	C₂²⋊C₄	—	5	4	no	—
866	C₂²⋊C₄	—	5	2	no	—
867	C₂²⋊C₄	—	5	2	no	—
868	C₂²⋊C₄	—	5	4	no	—
869	C₂²⋊C₄	—	5	4	no	—
870	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
871	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
872	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
873	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
874	C₄²	—	5	2	no	—
875	C₄²	—	5	2	no	—
876	C₄²	—	5	2	no	—
877	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
878	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
879	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
880	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
881	C₃×C₅	D₄×#41	1	1	yes	characteristic, complemented, Hall
882	C₂²×C₃	—	2	1	no	—
883	C₂²×C₃	—	2	2	no	—
884	C₂²×C₃	—	2	1	no	—
885	C₂²×C₃	—	2	2	no	—
886	C₂²×C₃	—	2	2	no	—
887	C₂²×C₃	—	2	2	no	—
888	C₂²×C₃	—	2	2	no	—
889	C₂²×C₃	—	4	8	no	—
890	C₂²×C₃	—	5	4	no	—
891	C₂²×C₃	—	10	2	no	—
892	C₂²×C₃	—	10	2	no	—
893	C₂²×C₃	—	10	4	no	—
894	C₂²×C₃	—	10	4	no	—
895	C₂²×C₃	—	10	4	no	—
896	C₂²×C₃	—	20	16	no	—
897	C₂²×C₃	C₂×#709	1	4	yes	complemented
898	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
899	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
900	C₃×C₄	—	2	1	no	—
901	C₃×C₄	—	2	2	no	—
902	C₃×C₄	—	2	2	no	—
903	C₃×C₄	—	2	1	no	—
904	C₃×C₄	—	2	1	no	—
905	C₃×C₄	—	5	4	no	—
906	C₃×C₄	—	10	2	no	—
907	C₃×C₄	—	10	4	no	—
908	C₃×C₄	—	10	2	no	—
909	C₃×C₄	C₂×#709	1	2	yes	complemented
910	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
911	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
912	C₂×C₅	—	2	4	no	—
913	C₂×C₅	—	2	2	no	—
914	C₂×C₅	—	4	2	no	—
915	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
916	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
917	C₂×C₅	C₃×#585	1	1	yes	characteristic
918	D₅	—	2	4	no	—
919	D₅	—	4	4	no	—
920	C₂³	—	2	4	no	—
921	C₂³	—	2	4	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	5	2	no	—
924	C₂³	—	5	4	no	—
925	C₂³	—	10	8	no	—
926	C₂³	—	10	8	no	—
927	C₂³	—	20	4	no	—
928	C₂³	C₂³×C₃×D₅	1	2	yes	—
929	C₂³	C₂³×C₃×D₅	1	2	yes	—
930	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
931	Q₈	—	5	4	no	—
932	Q₈	—	10	8	no	—
933	Q₈	—	10	4	no	—
934	D₄	—	2	4	no	—
935	D₄	—	2	2	no	—
936	D₄	—	5	8	no	—
937	D₄	—	5	4	no	—
938	D₄	—	10	8	no	—
939	D₄	—	10	8	no	—
940	D₄	—	10	8	no	—
941	D₄	—	10	8	no	—
942	D₄	—	10	8	no	—
943	D₄	—	10	4	no	—
944	D₄	—	10	4	no	—
945	D₄	—	20	2	no	—
946	D₄	—	20	4	no	—
947	D₄	C₃×#709	1	4	yes	direct product factor
948	C₂×C₄	—	2	4	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	4	no	—
951	C₂×C₄	—	2	4	no	—
952	C₂×C₄	—	2	4	no	—
953	C₂×C₄	—	2	4	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	5	2	no	—
956	C₂×C₄	—	5	8	no	—
957	C₂×C₄	—	5	2	no	—
958	C₂×C₄	—	5	2	no	—
959	C₂×C₄	—	5	4	no	—
960	C₂×C₄	—	10	8	no	—
961	C₂×C₄	—	10	8	no	—
962	C₂×C₄	—	10	8	no	—
963	C₂×C₄	—	10	4	no	—
964	C₂×C₄	—	10	8	no	—
965	C₂×C₄	—	20	2	no	—
966	C₂×C₄	C₃×D₄×D₅	1	4	yes	complemented
967	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
968	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
969	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
970	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
971	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
972	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
973	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
974	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
975	C₂×C₃	—	2	2	no	—
976	C₂×C₃	—	2	4	no	—
977	C₂×C₃	—	4	2	no	—
978	C₂×C₃	—	10	4	no	—
979	C₂×C₃	—	20	4	no	—
980	C₂×C₃	C₂²×#709	1	1	yes	characteristic
981	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
982	C₂×C₃	#66283	1	1	yes	characteristic
983	C₅	C₃×D₄×#41	1	1	yes	characteristic, complemented, Sylow
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	4	8	no	—
992	C₂²	—	5	4	no	—
993	C₂²	—	10	2	no	—
994	C₂²	—	10	2	no	—
995	C₂²	—	10	4	no	—
996	C₂²	—	10	4	no	—
997	C₂²	—	10	4	no	—
998	C₂²	—	20	16	no	—
999	C₂²	C₂×C₃×#709	1	4	yes	complemented
1000	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
1001	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1002	C₄	—	2	1	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	5	4	no	—
1008	C₄	—	10	2	no	—
1009	C₄	—	10	4	no	—
1010	C₄	—	10	2	no	—
1011	C₄	C₂×C₃×#709	1	2	yes	complemented
1012	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
1013	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
1014	C₃	D₄×#709	1	1	yes	characteristic, direct product factor, Sylow
1015	C₂	—	2	2	no	—
1016	C₂	—	2	4	no	—
1017	C₂	—	4	2	no	—
1018	C₂	—	10	4	no	—
1019	C₂	—	20	4	no	—
1020	C₂	C₂²×C₃×#709	1	1	yes	characteristic
1021	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
1022	C₂	C₃×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×D₄×#41
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#709	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×D₄×C₂²⋊D₅	C₂	semidirect
4. C₃×#66125	C₂	semidirect
5. C₃×#65887	C₂	semidirect
6. C₃×#65886	C₂	semidirect
7. C₃×#65885	C₂	semidirect
8. C₃×#65884	C₂	semidirect
9. C₃×D₄×D₂₀	C₂	semidirect
10. C₃×#65882	C₂	semidirect
11. C₃×#65881	C₂	semidirect
12. C₃×C₄×D₄×D₅	C₂	semidirect
13. C₃×D₄×Dic₁₀	C₂	semidirect
14. C₃×#65841	C₂	semidirect
15. C₃×#65824	C₂	semidirect
16. C₃×#65811	C₂	semidirect
17. C₃×C₄×#709	C₂	semidirect
18. D₄×#709	C₃	direct (N × H)
20. C₂³×C₃×C₄×C₅	C₂²	semidirect
21. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
25. C₂×C₃×#709	C₂²	semidirect
26. C₂×C₃×#709	C₂²	semidirect
27. C₂×C₃×#709	C₂²	semidirect
28. C₂×C₃×#709	C₂²	semidirect
29. C₂×C₃×#709	C₂²	semidirect
30. C₂²×C₃×D₂₀	C₂²	semidirect
31. C₂²×C₃×C₄×D₅	C₂²	semidirect
32. C₂²×C₃×Dic₁₀	C₂²	semidirect
35. C₃×C₄×C₅×D₄	C₂²	semidirect
36. C₃×C₄×C₅×D₄	C₂²	semidirect
37. C₃×C₄×C₅×D₄	C₂²	semidirect
38. C₃×C₄×C₅×D₄	C₂²	semidirect
39. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
40. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
41. C₂×C₃×C₄²×C₅	C₂²	semidirect
42. C₃×#4099	C₂²	semidirect
43. C₃×#4086	C₂²	semidirect
44. C₃×#4085	C₂²	semidirect
45. C₃×#4084	C₂²	semidirect
46. C₃×#4083	C₂²	semidirect
48. C₃×#4076	C₂²	semidirect
49. C₃×#4076	C₂²	semidirect
50. C₃×#4076	C₂²	semidirect
51. C₃×#4076	C₂²	semidirect
52. C₃×#4075	C₂²	semidirect
53. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
54. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
55. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
56. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
57. C₃×#4072	C₂²	semidirect
58. C₃×#4070	C₂²	semidirect
59. C₃×#4070	C₂²	semidirect
60. C₃×#4042	C₂²	semidirect
61. C₃×#4041	C₂²	semidirect
62. C₃×#4040	C₂²	semidirect
63. C₃×#4039	C₂²	semidirect
64. C₃×D₅×C₄⋊C₄	C₂²	semidirect
65. C₃×#4034	C₂²	semidirect
66. C₃×#4031	C₂²	semidirect
67. C₃×#4030	C₂²	semidirect
68. C₃×#4030	C₂²	semidirect
69. C₃×#4029	C₂²	semidirect
70. C₃×#4028	C₂²	semidirect
71. C₃×#4027	C₂²	semidirect
72. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
73. C₃×#4024	C₂²	semidirect
74. C₃×#4021	C₂²	semidirect
75. C₃×#4020	C₂²	semidirect
76. C₃×C₄×D₂₀	C₂²	semidirect
77. C₃×C₄×D₂₀	C₂²	semidirect
78. C₃×C₄×D₂₀	C₂²	semidirect
79. C₃×C₄×D₂₀	C₂²	semidirect
80. C₃×#4018	C₂²	semidirect
81. C₃×C₄²×D₅	C₂²	semidirect
82. C₃×#4015	C₂²	semidirect
83. C₃×C₄×Dic₁₀	C₂²	semidirect
84. C₃×C₄×Dic₁₀	C₂²	semidirect
86. C₂²×#709	C₂×C₃	semidirect
87. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
88. D₄×C₂²⋊D₅	C₂×C₃	semidirect
89. #66125	C₂×C₃	semidirect
90. #65887	C₂×C₃	semidirect
91. #65886	C₂×C₃	semidirect
92. #65885	C₂×C₃	semidirect
93. #65884	C₂×C₃	semidirect
94. D₄×D₂₀	C₂×C₃	semidirect
95. #65882	C₂×C₃	semidirect
96. #65881	C₂×C₃	semidirect
97. C₄×D₄×D₅	C₂×C₃	semidirect
98. D₄×Dic₁₀	C₂×C₃	semidirect
99. #65841	C₂×C₃	semidirect
100. #65824	C₂×C₃	semidirect
101. #65811	C₂×C₃	semidirect
102. C₄×#709	C₂×C₃	semidirect
132. C₃×#709	D₄	direct (N × H)
197. C₂×C₃×C₄×D₄	D₅	semidirect
199. C₂³×C₄×C₅	C₂²×C₃	semidirect
200. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
204. C₂×#709	C₂²×C₃	semidirect
205. C₂×#709	C₂²×C₃	semidirect
206. C₂×#709	C₂²×C₃	semidirect
207. C₂×#709	C₂²×C₃	semidirect
208. C₂×#709	C₂²×C₃	semidirect
209. C₂²×D₂₀	C₂²×C₃	semidirect
210. C₂²×C₄×D₅	C₂²×C₃	semidirect
211. C₂²×Dic₁₀	C₂²×C₃	semidirect
214. C₄×C₅×D₄	C₂²×C₃	semidirect
215. C₄×C₅×D₄	C₂²×C₃	semidirect
216. C₄×C₅×D₄	C₂²×C₃	semidirect
217. C₄×C₅×D₄	C₂²×C₃	semidirect
218. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
219. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
220. C₂×C₄²×C₅	C₂²×C₃	semidirect
221. #4099	C₂²×C₃	semidirect
222. #4086	C₂²×C₃	semidirect
223. #4085	C₂²×C₃	semidirect
224. #4084	C₂²×C₃	semidirect
225. #4083	C₂²×C₃	semidirect
227. #4076	C₂²×C₃	semidirect
228. #4076	C₂²×C₃	semidirect
229. #4076	C₂²×C₃	semidirect
230. #4076	C₂²×C₃	semidirect
231. #4075	C₂²×C₃	semidirect
232. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
233. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
234. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
235. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
236. #4072	C₂²×C₃	semidirect
237. #4070	C₂²×C₃	semidirect
238. #4070	C₂²×C₃	semidirect
239. #4042	C₂²×C₃	semidirect
240. #4041	C₂²×C₃	semidirect
241. #4040	C₂²×C₃	semidirect
242. #4039	C₂²×C₃	semidirect
243. D₅×C₄⋊C₄	C₂²×C₃	semidirect
244. #4034	C₂²×C₃	semidirect
245. #4031	C₂²×C₃	semidirect
246. #4030	C₂²×C₃	semidirect
247. #4030	C₂²×C₃	semidirect
248. #4029	C₂²×C₃	semidirect
249. #4028	C₂²×C₃	semidirect
250. #4027	C₂²×C₃	semidirect
251. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
252. #4024	C₂²×C₃	semidirect
253. #4021	C₂²×C₃	semidirect
254. #4020	C₂²×C₃	semidirect
255. C₄×D₂₀	C₂²×C₃	semidirect
256. C₄×D₂₀	C₂²×C₃	semidirect
257. C₄×D₂₀	C₂²×C₃	semidirect
258. C₄×D₂₀	C₂²×C₃	semidirect
259. #4018	C₂²×C₃	semidirect
260. C₄²×D₅	C₂²×C₃	semidirect
261. #4015	C₂²×C₃	semidirect
262. C₄×Dic₁₀	C₂²×C₃	semidirect
263. C₄×Dic₁₀	C₂²×C₃	semidirect
278. C₃×C₅×D₄	#41	semidirect
286. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
300. C₃×C₂²⋊D₅	C₂×D₄	semidirect
310. C₃×D₂₀	C₂×D₄	semidirect
316. C₃×C₄×D₅	C₂×D₄	semidirect
319. C₃×Dic₁₀	C₂×D₄	semidirect
333. C₂³×C₃×C₄	C₂×D₅	semidirect
374. C₃×C₄×D₄	C₂×D₅	semidirect
375. C₃×C₄×D₄	C₂×D₅	semidirect
376. C₃×C₄×D₄	C₂×D₅	semidirect
377. C₃×C₄×D₄	C₂×D₅	semidirect
381. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
383. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
385. C₂×C₃×C₄²	C₂×D₅	semidirect
415. #709	C₃×D₄	direct (N × H)
480. C₂×C₄×D₄	C₃×D₅	semidirect
490. C₂²×C₃×C₅	C₂×#41	semidirect
506. C₃×C₄×C₅	C₂×#41	semidirect
602. C₅×D₄	C₃×#41	semidirect
610. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
624. C₂²⋊D₅	C₂×C₃×D₄	semidirect
634. D₂₀	C₂×C₃×D₄	semidirect
640. C₄×D₅	C₂×C₃×D₄	semidirect
643. Dic₁₀	C₂×C₃×D₄	semidirect
657. C₂³×C₄	C₂×C₃×D₅	semidirect
698. C₄×D₄	C₂×C₃×D₅	semidirect
699. C₄×D₄	C₂×C₃×D₅	semidirect
700. C₄×D₄	C₂×C₃×D₅	semidirect
701. C₄×D₄	C₂×C₃×D₅	semidirect
705. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
707. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
709. C₂×C₄²	C₂×C₃×D₅	semidirect
745. C₃×D₄	#709	direct (N × H)
764. C₂×C₃×C₄	D₄×D₅	semidirect
782. C₂²×C₅	C₂×C₃×#41	semidirect
798. C₄×C₅	C₂×C₃×#41	semidirect
881. C₃×C₅	D₄×#41	semidirect
897. C₂²×C₃	C₂×#709	semidirect
909. C₃×C₄	C₂×#709	semidirect
947. D₄	C₃×#709	direct (N × H)
966. C₂×C₄	C₃×D₄×D₅	semidirect
983. C₅	C₃×D₄×#41	semidirect
999. C₂²	C₂×C₃×#709	semidirect
1011. C₄	C₂×C₃×#709	semidirect
1014. C₃	D₄×#709	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
C₂×C₃×C₄×C₅×D₄	2
C₃×D₄×C₂²⋊D₅	2
C₃×#66125	2
C₃×#65887	2
C₃×#65886	2
C₃×#65885	2
C₃×#65884	2
C₃×D₄×D₂₀	2
C₃×#65882	2
C₃×#65881	2
C₃×C₄×D₄×D₅	2
C₃×D₄×Dic₁₀	2
C₃×#65841	2
C₃×#65824	2
C₃×#65811	2
C₃×C₄×#709	2
D₄×#709	3
C₃×D₄×#41	5

Subgroups — C3×D4×#709 #14483049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#709 #14483049