Subgroups — C₂×C₃×#65944 #14482482

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#711	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4085	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4081	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65944	C₂	1	16	yes	maximal, direct product factor
11	C₂×C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#4031	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#4030	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#65944	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
19	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#711	—	2	8	no	—
32	C₂×C₃×#711	C₂²	1	8	yes	complemented
33	C₂×C₃×D₄×D₅	—	2	8	no	—
34	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
35	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
37	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#121	C₂²	1	8	yes	complemented
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
47	C₃×#4085	C₂²	1	8	yes	complemented
48	C₃×#4083	C₂²	1	8	yes	complemented
49	C₃×#4083	C₂²	1	8	yes	complemented
50	C₃×#4081	C₂²	1	8	yes	complemented
51	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	complemented
52	C₂×C₃×#685	C₂²	1	1	yes	characteristic
53	C₂×C₃×#685	C₂²	1	1	yes	characteristic
54	C₂×C₃×#685	C₂²	1	1	yes	characteristic
55	C₂×C₃×#685	C₂²	1	8	yes	complemented
56	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
64	C₃×#4042	C₂²	1	8	yes	complemented
65	C₃×#4040	C₂²	1	8	yes	complemented
66	C₃×#4031	C₂²	1	8	yes	complemented
67	C₃×#4030	C₂²	1	8	yes	complemented
68	C₃×#4027	C₂²	1	8	yes	complemented
69	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
70	C₂×C₃×#546	—	5	1	no	maximal, Hall
71	C₂²×#711	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×#4085	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#4083	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#4083	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#4081	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂²×#685	C₂×C₃	1	1	yes	characteristic, complemented
80	#65944	C₂×C₃	1	16	yes	direct product factor
81	C₂×#4042	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#4040	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#4031	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#4030	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#4027	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
88	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
89	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
90	C₂³×C₃×D₅	—	2	4	no	—
91	C₂³×C₃×D₅	—	2	4	no	—
92	C₂³×C₃×D₅	—	2	4	no	—
93	C₂³×C₃×D₅	—	2	4	no	—
94	C₂³×C₃×D₅	—	4	2	no	—
95	C₂³×C₃×D₅	—	4	2	no	—
96	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
97	C₂³×C₃×D₅	C₂³	1	4	yes	—
98	C₂³×C₃×D₅	C₂³	1	4	yes	—
99	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
100	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×D₄	—	2	4	no	—
102	C₂×C₃×C₅×D₄	—	2	4	no	—
103	C₂×C₃×C₅×D₄	—	4	2	no	—
104	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
106	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
107	C₂²×C₃×C₄×C₅	—	4	2	no	—
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
113	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
114	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
115	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
116	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
117	C₂×C₃×C₂²⋊D₅	D₄	1	8	yes	complemented
118	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
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	complemented
122	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
123	C₂²×C₃×Dic₅	—	2	4	no	—
124	C₂²×C₃×Dic₅	—	2	4	no	—
125	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
126	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
127	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
130	C₂²×C₃×Dic₅	C₂³	1	4	yes	complemented
131	C₂²×C₃×Dic₅	C₂³	1	4	yes	complemented
132	C₃×#711	—	2	32	no	—
133	C₃×D₄×D₅	—	2	32	no	—
134	C₂×C₃×D₂₀	—	2	4	no	—
135	C₂×C₃×D₂₀	C₂³	1	4	yes	—
136	C₂×C₃×C₄×D₅	—	2	4	no	—
137	C₂×C₃×C₄×D₅	—	2	4	no	—
138	C₂×C₃×C₄×D₅	—	4	2	no	—
139	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
140	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
141	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
142	C₂×C₃×Dic₁₀	—	2	4	no	—
143	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
144	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
145	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
146	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
147	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
148	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
149	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
150	C₃×#685	C₂³	1	4	yes	—
151	C₃×#685	C₂³	1	4	yes	—
152	C₃×#685	C₂³	1	4	yes	—
153	C₃×#685	C₂³	1	4	yes	complemented
154	C₃×#685	C₂³	1	4	yes	complemented
155	C₃×#685	C₂³	1	4	yes	complemented
156	C₃×#685	C₂³	1	4	yes	complemented
157	C₃×#683	C₂³	1	4	yes	complemented
158	C₃×#683	C₂³	1	4	yes	complemented
159	C₃×#683	C₂³	1	4	yes	complemented
160	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
161	C₂²×C₃×#41	—	5	1	no	—
162	C₂³×C₃×D₄	—	5	1	no	—
163	C₃×#546	—	5	16	no	—
164	C₂×C₃×#124	—	5	1	no	—
165	C₂×C₃×#123	—	5	1	no	—
166	C₂×C₃×#123	—	5	1	no	—
167	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
168	C₂×C₃×#121	—	5	1	no	—
169	C₂×C₃×#121	—	5	1	no	—
170	C₂×C₃×#121	D₅	1	1	yes	characteristic, complemented
171	C₂×C₃×#120	—	5	1	no	—
172	C₂×C₃×#120	—	5	1	no	—
173	C₂×C₃×C₄×D₄	—	5	1	no	—
174	C₂×C₃×C₄×D₄	—	5	1	no	—
175	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
176	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
177	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
178	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
179	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
180	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
184	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
185	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
186	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂×#711	—	2	8	no	—
191	C₂×#711	C₂²×C₃	1	8	yes	complemented
192	C₂×D₄×D₅	—	2	8	no	—
193	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
194	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
195	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
196	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₅×#121	C₂²×C₃	1	8	yes	complemented
200	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
202	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
203	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
206	#4085	C₂²×C₃	1	8	yes	complemented
207	#4083	C₂²×C₃	1	8	yes	complemented
208	#4083	C₂²×C₃	1	8	yes	complemented
209	#4081	C₂²×C₃	1	8	yes	complemented
210	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
211	C₂×#685	C₂²×C₃	1	1	yes	characteristic
212	C₂×#685	C₂²×C₃	1	1	yes	characteristic
213	C₂×#685	C₂²×C₃	1	1	yes	characteristic
214	C₂×#685	C₂²×C₃	1	8	yes	complemented
215	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
217	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
220	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
222	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
223	#4042	C₂²×C₃	1	8	yes	complemented
224	#4040	C₂²×C₃	1	8	yes	complemented
225	#4031	C₂²×C₃	1	8	yes	complemented
226	#4030	C₂²×C₃	1	8	yes	complemented
227	#4027	C₂²×C₃	1	8	yes	complemented
228	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
229	C₂×#546	—	5	1	no	Sylow
230	C₂³×C₃×C₅	—	2	2	no	—
231	C₂³×C₃×C₅	—	2	2	no	—
232	C₂³×C₃×C₅	—	2	2	no	—
233	C₂³×C₃×C₅	—	2	2	no	—
234	C₂³×C₃×C₅	—	2	2	no	—
235	C₂³×C₃×C₅	—	2	2	no	—
236	C₂³×C₃×C₅	—	2	2	no	—
237	C₂³×C₃×C₅	—	2	2	no	—
238	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
239	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
240	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
241	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
242	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
243	C₂²×C₃×D₅	—	2	2	no	—
244	C₂²×C₃×D₅	—	2	2	no	—
245	C₂²×C₃×D₅	—	2	2	no	—
246	C₂²×C₃×D₅	—	2	2	no	—
247	C₂²×C₃×D₅	—	2	2	no	—
248	C₂²×C₃×D₅	—	2	8	no	—
249	C₂²×C₃×D₅	—	2	2	no	—
250	C₂²×C₃×D₅	—	2	2	no	—
251	C₂²×C₃×D₅	—	2	8	no	—
252	C₂²×C₃×D₅	—	2	8	no	—
253	C₂²×C₃×D₅	—	2	8	no	—
254	C₂²×C₃×D₅	—	4	4	no	—
255	C₂²×C₃×D₅	—	4	4	no	—
256	C₂²×C₃×D₅	—	4	16	no	—
257	C₂²×C₃×D₅	—	4	16	no	—
258	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
259	C₂²×C₃×D₅	#41	1	4	yes	complemented
260	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
261	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
262	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
263	C₃×C₅×D₄	—	2	8	no	—
264	C₃×C₅×D₄	—	2	8	no	—
265	C₃×C₅×D₄	—	4	4	no	—
266	C₂×C₃×C₄×C₅	—	2	2	no	—
267	C₂×C₃×C₄×C₅	—	2	2	no	—
268	C₂×C₃×C₄×C₅	—	2	2	no	—
269	C₂×C₃×C₄×C₅	—	2	2	no	—
270	C₂×C₃×C₄×C₅	—	4	4	no	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
274	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
275	C₃×C₂²⋊D₅	—	2	8	no	—
276	C₃×C₂²⋊D₅	—	2	8	no	—
277	C₃×C₂²⋊D₅	—	2	8	no	—
278	C₃×C₂²⋊D₅	—	4	4	no	—
279	C₃×C₂²⋊D₅	C₂×D₄	1	16	yes	complemented
280	C₂×C₃×Dic₅	—	2	2	no	—
281	C₂×C₃×Dic₅	—	2	2	no	—
282	C₂×C₃×Dic₅	—	2	8	no	—
283	C₂×C₃×Dic₅	—	2	2	no	—
284	C₂×C₃×Dic₅	—	2	2	no	—
285	C₂×C₃×Dic₅	—	2	8	no	—
286	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
287	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
288	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
289	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
290	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
291	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
292	C₃×D₂₀	—	2	8	no	—
293	C₃×C₄×D₅	—	2	8	no	—
294	C₃×C₄×D₅	—	2	8	no	—
295	C₃×C₄×D₅	—	4	4	no	—
296	C₃×Dic₁₀	—	2	8	no	—
297	C₂⁵×C₃	—	5	1	no	—
298	C₂⁵×C₃	—	5	1	no	—
299	C₂×C₃×#41	—	5	8	no	—
300	C₂×C₃×#41	—	10	8	no	—
301	C₂²×C₃×Q₈	—	5	1	no	—
302	C₂²×C₃×D₄	—	5	1	no	—
303	C₂²×C₃×D₄	—	5	1	no	—
304	C₂²×C₃×D₄	—	5	1	no	—
305	C₂²×C₃×D₄	—	5	1	no	—
306	C₂²×C₃×D₄	—	5	1	no	—
307	C₂²×C₃×D₄	—	5	8	no	—
308	C₂²×C₃×D₄	—	5	1	no	—
309	C₂²×C₃×D₄	—	10	8	no	—
310	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
311	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
312	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
313	C₂³×C₃×C₄	—	5	1	no	—
314	C₂³×C₃×C₄	—	5	1	no	—
315	C₂³×C₃×C₄	—	5	1	no	—
316	C₂³×C₃×C₄	—	5	1	no	—
317	C₂³×C₃×C₄	—	5	1	no	—
318	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
319	C₃×#124	—	5	8	no	—
320	C₃×#123	—	5	8	no	—
321	C₃×#123	—	5	8	no	—
322	C₃×C₂²⋊Q₈	—	5	8	no	—
323	C₃×#121	—	5	8	no	—
324	C₃×#121	—	5	8	no	—
325	C₃×#121	C₂×D₅	1	8	yes	complemented
326	C₃×#120	—	5	8	no	—
327	C₃×#120	—	5	8	no	—
328	C₃×C₄×D₄	—	5	8	no	—
329	C₃×C₄×D₄	—	5	8	no	—
330	C₂×C₃×C₄⋊C₄	—	5	1	no	—
331	C₂×C₃×C₄⋊C₄	—	5	1	no	—
332	C₂×C₃×C₄⋊C₄	—	5	1	no	—
333	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
334	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
335	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
336	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
337	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
338	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
339	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
340	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
341	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
342	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
343	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
344	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
345	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
346	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
347	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
348	C₂×C₃×C₄²	—	5	1	no	—
349	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
350	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
351	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
352	C₂³×D₅	—	2	4	no	—
353	C₂³×D₅	—	2	4	no	—
354	C₂³×D₅	—	2	4	no	—
355	C₂³×D₅	—	2	4	no	—
356	C₂³×D₅	—	4	2	no	—
357	C₂³×D₅	—	4	2	no	—
358	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
359	C₂³×D₅	C₂³×C₃	1	4	yes	—
360	C₂³×D₅	C₂³×C₃	1	4	yes	—
361	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
362	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₅×D₄	—	2	4	no	—
364	C₂×C₅×D₄	—	2	4	no	—
365	C₂×C₅×D₄	—	4	2	no	—
366	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
367	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
368	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
369	C₂²×C₄×C₅	—	4	2	no	—
370	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
371	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
372	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
373	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
374	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
375	C₂×C₂²⋊D₅	—	2	4	no	—
376	C₂×C₂²⋊D₅	—	2	4	no	—
377	C₂×C₂²⋊D₅	—	2	4	no	—
378	C₂×C₂²⋊D₅	—	4	2	no	—
379	C₂×C₂²⋊D₅	C₃×D₄	1	8	yes	complemented
380	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
381	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
382	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
383	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
384	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
385	C₂²×Dic₅	—	2	4	no	—
386	C₂²×Dic₅	—	2	4	no	—
387	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
388	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
389	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
390	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
391	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
392	C₂²×Dic₅	C₂³×C₃	1	4	yes	complemented
393	C₂²×Dic₅	C₂³×C₃	1	4	yes	complemented
394	#711	—	2	32	no	—
395	D₄×D₅	—	2	32	no	—
396	C₂×D₂₀	—	2	4	no	—
397	C₂×D₂₀	C₂³×C₃	1	4	yes	—
398	C₂×C₄×D₅	—	2	4	no	—
399	C₂×C₄×D₅	—	2	4	no	—
400	C₂×C₄×D₅	—	4	2	no	—
401	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
402	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
403	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
404	C₂×Dic₁₀	—	2	4	no	—
405	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
406	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
407	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
408	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
409	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
410	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
411	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
412	#685	C₂³×C₃	1	4	yes	—
413	#685	C₂³×C₃	1	4	yes	—
414	#685	C₂³×C₃	1	4	yes	—
415	#685	C₂³×C₃	1	4	yes	complemented
416	#685	C₂³×C₃	1	4	yes	complemented
417	#685	C₂³×C₃	1	4	yes	complemented
418	#685	C₂³×C₃	1	4	yes	complemented
419	#683	C₂³×C₃	1	4	yes	complemented
420	#683	C₂³×C₃	1	4	yes	complemented
421	#683	C₂³×C₃	1	4	yes	complemented
422	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
423	C₂²×#41	—	5	1	no	—
424	C₂³×D₄	—	5	1	no	—
425	#546	—	5	16	no	—
426	C₂×#124	—	5	1	no	—
427	C₂×#123	—	5	1	no	—
428	C₂×#123	—	5	1	no	—
429	C₂×C₂²⋊Q₈	—	5	1	no	—
430	C₂×#121	—	5	1	no	—
431	C₂×#121	—	5	1	no	—
432	C₂×#121	C₃×D₅	1	1	yes	characteristic, complemented
433	C₂×#120	—	5	1	no	—
434	C₂×#120	—	5	1	no	—
435	C₂×C₄×D₄	—	5	1	no	—
436	C₂×C₄×D₄	—	5	1	no	—
437	C₂²×C₂²⋊C₄	—	5	1	no	—
438	C₂²×C₂²⋊C₄	—	5	1	no	—
439	C₂²×C₃×C₅	—	2	8	no	—
440	C₂²×C₃×C₅	—	2	2	no	—
441	C₂²×C₃×C₅	—	2	2	no	—
442	C₂²×C₃×C₅	—	2	2	no	—
443	C₂²×C₃×C₅	—	2	2	no	—
444	C₂²×C₃×C₅	—	2	2	no	—
445	C₂²×C₃×C₅	—	2	2	no	—
446	C₂²×C₃×C₅	—	2	2	no	—
447	C₂²×C₃×C₅	—	2	2	no	—
448	C₂²×C₃×C₅	—	4	4	no	—
449	C₂²×C₃×C₅	—	4	4	no	—
450	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
451	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
452	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
453	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
454	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
455	C₂×C₃×D₅	—	2	8	no	—
456	C₂×C₃×D₅	—	2	8	no	—
457	C₂×C₃×D₅	—	2	2	no	—
458	C₂×C₃×D₅	—	2	2	no	—
459	C₂×C₃×D₅	—	2	2	no	—
460	C₂×C₃×D₅	—	2	2	no	—
461	C₂×C₃×D₅	—	2	2	no	—
462	C₂×C₃×D₅	—	2	2	no	—
463	C₂×C₃×D₅	—	2	2	no	—
464	C₂×C₃×D₅	—	4	16	no	—
465	C₂×C₃×D₅	—	4	16	no	—
466	C₂×C₃×D₅	—	4	4	no	—
467	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
468	C₂×C₃×D₅	C₂×#41	1	4	yes	complemented
469	C₃×C₄×C₅	—	2	2	no	—
470	C₃×C₄×C₅	—	2	2	no	—
471	C₃×C₄×C₅	—	2	2	no	—
472	C₃×C₄×C₅	—	2	2	no	—
473	C₃×Dic₅	—	2	2	no	—
474	C₃×Dic₅	—	2	2	no	—
475	C₃×Dic₅	—	2	2	no	—
476	C₃×Dic₅	—	2	2	no	—
477	C₃×Dic₅	C₂²×D₄	1	4	yes	—
478	C₂⁴×C₃	—	5	1	no	—
479	C₂⁴×C₃	—	5	1	no	—
480	C₂⁴×C₃	—	5	1	no	—
481	C₂⁴×C₃	—	5	4	no	—
482	C₂⁴×C₃	—	5	4	no	—
483	C₂⁴×C₃	—	10	4	no	—
484	C₂⁴×C₃	—	10	4	no	—
485	C₂⁴×C₃	—	10	4	no	—
486	C₂⁴×C₃	—	10	4	no	—
487	C₂⁴×C₃	—	20	2	no	—
488	C₂⁴×C₃	—	20	2	no	—
489	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
490	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
491	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
492	C₃×#41	—	10	32	no	—
493	C₂×C₃×Q₈	—	5	4	no	—
494	C₂×C₃×Q₈	—	10	4	no	—
495	C₂×C₃×D₄	—	2	4	no	—
496	C₂×C₃×D₄	—	2	4	no	—
497	C₂×C₃×D₄	—	4	2	no	—
498	C₂×C₃×D₄	—	5	8	no	—
499	C₂×C₃×D₄	—	5	4	no	—
500	C₂×C₃×D₄	—	5	4	no	—
501	C₂×C₃×D₄	—	5	4	no	—
502	C₂×C₃×D₄	—	5	4	no	—
503	C₂×C₃×D₄	—	5	4	no	—
504	C₂×C₃×D₄	—	5	4	no	—
505	C₂×C₃×D₄	—	10	4	no	—
506	C₂×C₃×D₄	—	10	4	no	—
507	C₂×C₃×D₄	—	10	32	no	—
508	C₂×C₃×D₄	—	10	4	no	—
509	C₂×C₃×D₄	—	10	4	no	—
510	C₂×C₃×D₄	—	20	2	no	—
511	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
512	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
513	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
514	C₂²×C₃×C₄	—	4	2	no	—
515	C₂²×C₃×C₄	—	5	1	no	—
516	C₂²×C₃×C₄	—	5	4	no	—
517	C₂²×C₃×C₄	—	5	4	no	—
518	C₂²×C₃×C₄	—	5	1	no	—
519	C₂²×C₃×C₄	—	5	1	no	—
520	C₂²×C₃×C₄	—	5	1	no	—
521	C₂²×C₃×C₄	—	5	1	no	—
522	C₂²×C₃×C₄	—	5	4	no	—
523	C₂²×C₃×C₄	—	5	4	no	—
524	C₂²×C₃×C₄	—	5	4	no	—
525	C₂²×C₃×C₄	—	10	4	no	—
526	C₂²×C₃×C₄	—	10	4	no	—
527	C₂²×C₃×C₄	—	10	4	no	—
528	C₂²×C₃×C₄	—	10	4	no	—
529	C₂²×C₃×C₄	—	20	2	no	—
530	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
531	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
532	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
533	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
534	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
535	C₃×C₄⋊C₄	—	5	4	no	—
536	C₃×C₄⋊C₄	—	5	4	no	—
537	C₃×C₄⋊C₄	—	5	4	no	—
538	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
539	C₃×C₂²⋊C₄	—	5	4	no	—
540	C₃×C₂²⋊C₄	—	5	4	no	—
541	C₃×C₂²⋊C₄	—	5	4	no	—
542	C₃×C₂²⋊C₄	—	5	4	no	—
543	C₃×C₂²⋊C₄	—	5	4	no	—
544	C₃×C₂²⋊C₄	—	5	4	no	—
545	C₃×C₂²⋊C₄	—	5	4	no	—
546	C₃×C₂²⋊C₄	—	5	4	no	—
547	C₃×C₂²⋊C₄	—	5	4	no	—
548	C₃×C₂²⋊C₄	—	5	4	no	—
549	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
550	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
551	C₃×C₄²	—	5	4	no	—
552	C₂³×C₅	—	2	2	no	—
553	C₂³×C₅	—	2	2	no	—
554	C₂³×C₅	—	2	2	no	—
555	C₂³×C₅	—	2	2	no	—
556	C₂³×C₅	—	2	2	no	—
557	C₂³×C₅	—	2	2	no	—
558	C₂³×C₅	—	2	2	no	—
559	C₂³×C₅	—	2	2	no	—
560	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
561	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
562	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
563	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
564	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
565	C₂²×D₅	—	2	2	no	—
566	C₂²×D₅	—	2	2	no	—
567	C₂²×D₅	—	2	2	no	—
568	C₂²×D₅	—	2	2	no	—
569	C₂²×D₅	—	2	2	no	—
570	C₂²×D₅	—	2	8	no	—
571	C₂²×D₅	—	2	2	no	—
572	C₂²×D₅	—	2	2	no	—
573	C₂²×D₅	—	2	8	no	—
574	C₂²×D₅	—	2	8	no	—
575	C₂²×D₅	—	2	8	no	—
576	C₂²×D₅	—	4	4	no	—
577	C₂²×D₅	—	4	4	no	—
578	C₂²×D₅	—	4	16	no	—
579	C₂²×D₅	—	4	16	no	—
580	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
581	C₂²×D₅	C₃×#41	1	4	yes	complemented
582	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
583	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
584	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
585	C₅×D₄	—	2	8	no	—
586	C₅×D₄	—	2	8	no	—
587	C₅×D₄	—	4	4	no	—
588	C₂×C₄×C₅	—	2	2	no	—
589	C₂×C₄×C₅	—	2	2	no	—
590	C₂×C₄×C₅	—	2	2	no	—
591	C₂×C₄×C₅	—	2	2	no	—
592	C₂×C₄×C₅	—	4	4	no	—
593	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
594	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
595	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
596	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
597	C₂²⋊D₅	—	2	8	no	—
598	C₂²⋊D₅	—	2	8	no	—
599	C₂²⋊D₅	—	2	8	no	—
600	C₂²⋊D₅	—	4	4	no	—
601	C₂²⋊D₅	C₂×C₃×D₄	1	16	yes	complemented
602	C₂×Dic₅	—	2	2	no	—
603	C₂×Dic₅	—	2	2	no	—
604	C₂×Dic₅	—	2	8	no	—
605	C₂×Dic₅	—	2	2	no	—
606	C₂×Dic₅	—	2	2	no	—
607	C₂×Dic₅	—	2	8	no	—
608	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
609	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
610	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
611	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
612	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
613	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
614	D₂₀	—	2	8	no	—
615	C₄×D₅	—	2	8	no	—
616	C₄×D₅	—	2	8	no	—
617	C₄×D₅	—	4	4	no	—
618	Dic₁₀	—	2	8	no	—
619	C₂⁵	—	5	1	no	—
620	C₂⁵	—	5	1	no	—
621	C₂×#41	—	5	8	no	—
622	C₂×#41	—	10	8	no	—
623	C₂²×Q₈	—	5	1	no	—
624	C₂²×D₄	—	5	1	no	—
625	C₂²×D₄	—	5	1	no	—
626	C₂²×D₄	—	5	1	no	—
627	C₂²×D₄	—	5	1	no	—
628	C₂²×D₄	—	5	1	no	—
629	C₂²×D₄	—	5	8	no	—
630	C₂²×D₄	—	5	1	no	—
631	C₂²×D₄	—	10	8	no	—
632	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
633	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
634	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
635	C₂³×C₄	—	5	1	no	—
636	C₂³×C₄	—	5	1	no	—
637	C₂³×C₄	—	5	1	no	—
638	C₂³×C₄	—	5	1	no	—
639	C₂³×C₄	—	5	1	no	—
640	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
641	#124	—	5	8	no	—
642	#123	—	5	8	no	—
643	#123	—	5	8	no	—
644	C₂²⋊Q₈	—	5	8	no	—
645	#121	—	5	8	no	—
646	#121	—	5	8	no	—
647	#121	C₂×C₃×D₅	1	8	yes	complemented
648	#120	—	5	8	no	—
649	#120	—	5	8	no	—
650	C₄×D₄	—	5	8	no	—
651	C₄×D₄	—	5	8	no	—
652	C₂×C₄⋊C₄	—	5	1	no	—
653	C₂×C₄⋊C₄	—	5	1	no	—
654	C₂×C₄⋊C₄	—	5	1	no	—
655	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
656	C₂×C₂²⋊C₄	—	5	1	no	—
657	C₂×C₂²⋊C₄	—	5	1	no	—
658	C₂×C₂²⋊C₄	—	5	1	no	—
659	C₂×C₂²⋊C₄	—	5	1	no	—
660	C₂×C₂²⋊C₄	—	5	1	no	—
661	C₂×C₂²⋊C₄	—	5	1	no	—
662	C₂×C₂²⋊C₄	—	5	1	no	—
663	C₂×C₂²⋊C₄	—	5	1	no	—
664	C₂×C₂²⋊C₄	—	5	1	no	—
665	C₂×C₂²⋊C₄	—	5	1	no	—
666	C₂×C₂²⋊C₄	—	5	8	no	—
667	C₂×C₂²⋊C₄	—	5	8	no	—
668	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
669	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
670	C₂×C₄²	—	5	1	no	—
671	C₂×C₃×C₅	—	2	4	no	—
672	C₂×C₃×C₅	—	4	2	no	—
673	C₂×C₃×C₅	—	4	2	no	—
674	C₂×C₃×C₅	#546	1	4	yes	complemented
675	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
676	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
677	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
678	C₃×D₅	—	2	4	no	—
679	C₃×D₅	—	2	4	no	—
680	C₃×D₅	—	4	2	no	—
681	C₂³×C₃	—	2	2	no	—
682	C₂³×C₃	—	2	2	no	—
683	C₂³×C₃	—	2	2	no	—
684	C₂³×C₃	—	2	2	no	—
685	C₂³×C₃	—	2	2	no	—
686	C₂³×C₃	—	2	2	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	5	4	no	—
690	C₂³×C₃	—	5	4	no	—
691	C₂³×C₃	—	5	2	no	—
692	C₂³×C₃	—	5	2	no	—
693	C₂³×C₃	—	5	2	no	—
694	C₂³×C₃	—	10	8	no	—
695	C₂³×C₃	—	10	8	no	—
696	C₂³×C₃	—	10	8	no	—
697	C₂³×C₃	—	10	2	no	—
698	C₂³×C₃	—	10	2	no	—
699	C₂³×C₃	—	10	2	no	—
700	C₂³×C₃	—	10	2	no	—
701	C₂³×C₃	—	10	8	no	—
702	C₂³×C₃	—	10	2	no	—
703	C₂³×C₃	—	10	2	no	—
704	C₂³×C₃	—	10	2	no	—
705	C₂³×C₃	—	20	4	no	—
706	C₂³×C₃	—	20	4	no	—
707	C₂³×C₃	—	20	16	no	—
708	C₂³×C₃	—	20	16	no	—
709	C₂³×C₃	D₄×D₅	1	4	yes	—
710	C₂³×C₃	C₂³×D₅	1	2	yes	—
711	C₂³×C₃	C₂³×D₅	1	2	yes	—
712	C₂³×C₃	C₂³×D₅	1	2	yes	—
713	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
714	C₃×Q₈	—	10	8	no	—
715	C₃×D₄	—	2	8	no	—
716	C₃×D₄	—	2	8	no	—
717	C₃×D₄	—	4	4	no	—
718	C₃×D₄	—	5	16	no	—
719	C₃×D₄	—	10	8	no	—
720	C₃×D₄	—	10	8	no	—
721	C₃×D₄	—	10	8	no	—
722	C₃×D₄	—	10	8	no	—
723	C₃×D₄	—	20	4	no	—
724	C₂×C₃×C₄	—	2	2	no	—
725	C₂×C₃×C₄	—	2	2	no	—
726	C₂×C₃×C₄	—	2	2	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	4	4	no	—
729	C₂×C₃×C₄	—	5	4	no	—
730	C₂×C₃×C₄	—	5	2	no	—
731	C₂×C₃×C₄	—	5	2	no	—
732	C₂×C₃×C₄	—	5	2	no	—
733	C₂×C₃×C₄	—	5	2	no	—
734	C₂×C₃×C₄	—	5	2	no	—
735	C₂×C₃×C₄	—	10	8	no	—
736	C₂×C₃×C₄	—	10	8	no	—
737	C₂×C₃×C₄	—	10	8	no	—
738	C₂×C₃×C₄	—	10	2	no	—
739	C₂×C₃×C₄	—	10	2	no	—
740	C₂×C₃×C₄	—	10	8	no	—
741	C₂×C₃×C₄	—	10	2	no	—
742	C₂×C₃×C₄	—	10	2	no	—
743	C₂×C₃×C₄	—	20	4	no	—
744	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
745	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
746	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
747	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
748	C₂²×C₅	—	2	2	no	—
749	C₂²×C₅	—	2	2	no	—
750	C₂²×C₅	—	2	8	no	—
751	C₂²×C₅	—	2	2	no	—
752	C₂²×C₅	—	2	2	no	—
753	C₂²×C₅	—	2	2	no	—
754	C₂²×C₅	—	2	2	no	—
755	C₂²×C₅	—	2	2	no	—
756	C₂²×C₅	—	2	2	no	—
757	C₂²×C₅	—	4	4	no	—
758	C₂²×C₅	—	4	4	no	—
759	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
760	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
761	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
762	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
763	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
764	C₂×D₅	—	2	2	no	—
765	C₂×D₅	—	2	2	no	—
766	C₂×D₅	—	2	2	no	—
767	C₂×D₅	—	2	2	no	—
768	C₂×D₅	—	2	8	no	—
769	C₂×D₅	—	2	8	no	—
770	C₂×D₅	—	2	2	no	—
771	C₂×D₅	—	2	2	no	—
772	C₂×D₅	—	2	2	no	—
773	C₂×D₅	—	4	16	no	—
774	C₂×D₅	—	4	16	no	—
775	C₂×D₅	—	4	4	no	—
776	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
777	C₂×D₅	C₂×C₃×#41	1	4	yes	complemented
778	C₄×C₅	—	2	2	no	—
779	C₄×C₅	—	2	2	no	—
780	C₄×C₅	—	2	2	no	—
781	C₄×C₅	—	2	2	no	—
782	Dic₅	—	2	2	no	—
783	Dic₅	—	2	2	no	—
784	Dic₅	—	2	2	no	—
785	Dic₅	—	2	2	no	—
786	Dic₅	C₂²×C₃×D₄	1	4	yes	—
787	C₂⁴	—	5	1	no	—
788	C₂⁴	—	5	1	no	—
789	C₂⁴	—	5	1	no	—
790	C₂⁴	—	5	4	no	—
791	C₂⁴	—	5	4	no	—
792	C₂⁴	—	10	4	no	—
793	C₂⁴	—	10	4	no	—
794	C₂⁴	—	10	4	no	—
795	C₂⁴	—	10	4	no	—
796	C₂⁴	—	20	2	no	—
797	C₂⁴	—	20	2	no	—
798	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
799	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
800	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
801	#41	—	10	32	no	—
802	C₂×Q₈	—	5	4	no	—
803	C₂×Q₈	—	10	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	5	8	no	—
808	C₂×D₄	—	5	4	no	—
809	C₂×D₄	—	5	4	no	—
810	C₂×D₄	—	5	4	no	—
811	C₂×D₄	—	5	4	no	—
812	C₂×D₄	—	5	4	no	—
813	C₂×D₄	—	5	4	no	—
814	C₂×D₄	—	10	4	no	—
815	C₂×D₄	—	10	4	no	—
816	C₂×D₄	—	10	32	no	—
817	C₂×D₄	—	10	4	no	—
818	C₂×D₄	—	10	4	no	—
819	C₂×D₄	—	20	2	no	—
820	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
821	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
822	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	5	1	no	—
825	C₂²×C₄	—	5	1	no	—
826	C₂²×C₄	—	5	1	no	—
827	C₂²×C₄	—	5	1	no	—
828	C₂²×C₄	—	5	1	no	—
829	C₂²×C₄	—	5	4	no	—
830	C₂²×C₄	—	5	4	no	—
831	C₂²×C₄	—	5	4	no	—
832	C₂²×C₄	—	5	4	no	—
833	C₂²×C₄	—	5	4	no	—
834	C₂²×C₄	—	10	4	no	—
835	C₂²×C₄	—	10	4	no	—
836	C₂²×C₄	—	10	4	no	—
837	C₂²×C₄	—	10	4	no	—
838	C₂²×C₄	—	20	2	no	—
839	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
840	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
841	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
842	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
843	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
844	C₄⋊C₄	—	5	4	no	—
845	C₄⋊C₄	—	5	4	no	—
846	C₄⋊C₄	—	5	4	no	—
847	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
848	C₂²⋊C₄	—	5	4	no	—
849	C₂²⋊C₄	—	5	4	no	—
850	C₂²⋊C₄	—	5	4	no	—
851	C₂²⋊C₄	—	5	4	no	—
852	C₂²⋊C₄	—	5	4	no	—
853	C₂²⋊C₄	—	5	4	no	—
854	C₂²⋊C₄	—	5	4	no	—
855	C₂²⋊C₄	—	5	4	no	—
856	C₂²⋊C₄	—	5	4	no	—
857	C₂²⋊C₄	—	5	4	no	—
858	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
859	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
860	C₄²	—	5	4	no	—
861	C₃×C₅	C₂×#546	1	1	yes	characteristic, complemented, Hall
862	C₂²×C₃	—	2	8	no	—
863	C₂²×C₃	—	2	2	no	—
864	C₂²×C₃	—	2	2	no	—
865	C₂²×C₃	—	2	2	no	—
866	C₂²×C₃	—	2	2	no	—
867	C₂²×C₃	—	2	2	no	—
868	C₂²×C₃	—	2	2	no	—
869	C₂²×C₃	—	2	2	no	—
870	C₂²×C₃	—	2	2	no	—
871	C₂²×C₃	—	4	4	no	—
872	C₂²×C₃	—	4	4	no	—
873	C₂²×C₃	—	5	4	no	—
874	C₂²×C₃	—	5	4	no	—
875	C₂²×C₃	—	10	8	no	—
876	C₂²×C₃	—	10	8	no	—
877	C₂²×C₃	—	10	2	no	—
878	C₂²×C₃	—	10	2	no	—
879	C₂²×C₃	—	10	2	no	—
880	C₂²×C₃	—	10	2	no	—
881	C₂²×C₃	—	10	2	no	—
882	C₂²×C₃	—	10	2	no	—
883	C₂²×C₃	—	10	2	no	—
884	C₂²×C₃	—	20	16	no	—
885	C₂²×C₃	—	20	16	no	—
886	C₂²×C₃	—	20	4	no	—
887	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
888	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
889	C₂²×C₃	#4144	1	2	yes	—
890	C₂²×C₃	D₅×#41	1	2	yes	—
891	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
892	C₃×C₄	—	2	2	no	—
893	C₃×C₄	—	2	2	no	—
894	C₃×C₄	—	2	2	no	—
895	C₃×C₄	—	2	2	no	—
896	C₃×C₄	—	5	4	no	—
897	C₃×C₄	—	10	2	no	—
898	C₃×C₄	—	10	2	no	—
899	C₃×C₄	—	10	2	no	—
900	C₃×C₄	—	10	2	no	—
901	C₂×C₅	—	2	4	no	—
902	C₂×C₅	—	4	2	no	—
903	C₂×C₅	—	4	2	no	—
904	C₂×C₅	C₃×#546	1	4	yes	complemented
905	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
906	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
907	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
908	D₅	—	2	4	no	—
909	D₅	—	2	4	no	—
910	D₅	—	4	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	5	4	no	—
920	C₂³	—	5	4	no	—
921	C₂³	—	5	2	no	—
922	C₂³	—	5	2	no	—
923	C₂³	—	5	2	no	—
924	C₂³	—	10	8	no	—
925	C₂³	—	10	8	no	—
926	C₂³	—	10	8	no	—
927	C₂³	—	10	2	no	—
928	C₂³	—	10	2	no	—
929	C₂³	—	10	2	no	—
930	C₂³	—	10	2	no	—
931	C₂³	—	10	8	no	—
932	C₂³	—	10	2	no	—
933	C₂³	—	10	2	no	—
934	C₂³	—	10	2	no	—
935	C₂³	—	20	4	no	—
936	C₂³	—	20	4	no	—
937	C₂³	—	20	16	no	—
938	C₂³	—	20	16	no	—
939	C₂³	C₃×D₄×D₅	1	4	yes	—
940	C₂³	C₂³×C₃×D₅	1	2	yes	—
941	C₂³	C₂³×C₃×D₅	1	2	yes	—
942	C₂³	C₂³×C₃×D₅	1	2	yes	—
943	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
944	Q₈	—	10	8	no	—
945	D₄	—	2	8	no	—
946	D₄	—	2	8	no	—
947	D₄	—	4	4	no	—
948	D₄	—	5	16	no	—
949	D₄	—	10	8	no	—
950	D₄	—	10	8	no	—
951	D₄	—	10	8	no	—
952	D₄	—	10	8	no	—
953	D₄	—	20	4	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	5	4	no	—
960	C₂×C₄	—	5	2	no	—
961	C₂×C₄	—	5	2	no	—
962	C₂×C₄	—	5	2	no	—
963	C₂×C₄	—	5	2	no	—
964	C₂×C₄	—	5	2	no	—
965	C₂×C₄	—	10	8	no	—
966	C₂×C₄	—	10	8	no	—
967	C₂×C₄	—	10	8	no	—
968	C₂×C₄	—	10	2	no	—
969	C₂×C₄	—	10	2	no	—
970	C₂×C₄	—	10	8	no	—
971	C₂×C₄	—	10	2	no	—
972	C₂×C₄	—	10	2	no	—
973	C₂×C₄	—	20	4	no	—
974	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
975	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
976	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
977	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
978	C₂×C₃	—	2	4	no	—
979	C₂×C₃	—	4	2	no	—
980	C₂×C₃	—	4	2	no	—
981	C₂×C₃	—	10	4	no	—
982	C₂×C₃	—	10	4	no	—
983	C₂×C₃	—	20	2	no	—
984	C₂×C₃	#65944	1	4	yes	direct product factor
985	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
986	C₂×C₃	C₂×#4144	1	1	yes	characteristic
987	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
988	C₅	C₂×C₃×#546	1	1	yes	characteristic, complemented, Sylow
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	8	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	4	4	no	—
999	C₂²	—	4	4	no	—
1000	C₂²	—	5	4	no	—
1001	C₂²	—	5	4	no	—
1002	C₂²	—	10	2	no	—
1003	C₂²	—	10	2	no	—
1004	C₂²	—	10	2	no	—
1005	C₂²	—	10	2	no	—
1006	C₂²	—	10	8	no	—
1007	C₂²	—	10	8	no	—
1008	C₂²	—	10	2	no	—
1009	C₂²	—	10	2	no	—
1010	C₂²	—	10	2	no	—
1011	C₂²	—	20	16	no	—
1012	C₂²	—	20	16	no	—
1013	C₂²	—	20	4	no	—
1014	C₂²	C₂×C₃×D₄×D₅	1	4	yes	—
1015	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
1016	C₂²	C₃×#4144	1	2	yes	—
1017	C₂²	C₃×D₅×#41	1	2	yes	—
1018	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	5	4	no	—
1024	C₄	—	10	2	no	—
1025	C₄	—	10	2	no	—
1026	C₄	—	10	2	no	—
1027	C₄	—	10	2	no	—
1028	C₃	C₂×#65944	1	1	yes	characteristic, direct product factor, Sylow
1029	C₂	—	2	4	no	—
1030	C₂	—	4	2	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	10	4	no	—
1033	C₂	—	10	4	no	—
1034	C₂	—	20	2	no	—
1035	C₂	C₃×#65944	1	4	yes	direct product factor
1036	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
1037	C₂	C₂×C₃×#4144	1	1	yes	characteristic
1038	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#121	D₅
hypocenter	C₅	C₂×C₃×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#711	C₂	semidirect
2. C₂²×C₃×D₄×D₅	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×#4085	C₂	semidirect
5. C₂×C₃×#4083	C₂	semidirect
6. C₂×C₃×#4083	C₂	semidirect
7. C₂×C₃×#4081	C₂	semidirect
8. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
9. C₂²×C₃×#685	C₂	semidirect
10. C₃×#65944	C₂	direct (N × H)
11. C₂×C₃×#4042	C₂	semidirect
12. C₂×C₃×#4040	C₂	semidirect
13. C₂×C₃×#4031	C₂	semidirect
14. C₂×C₃×#4030	C₂	semidirect
15. C₂×C₃×#4027	C₂	semidirect
16. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
17. C₂×#65944	C₃	direct (N × H)
21. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂²×C₃×C₅×D₄	C₂²	semidirect
23. C₂³×C₃×C₄×C₅	C₂²	semidirect
27. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
28. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
29. C₂³×C₃×Dic₅	C₂²	semidirect
30. C₂³×C₃×Dic₅	C₂²	semidirect
32. C₂×C₃×#711	C₂²	semidirect
34. C₂×C₃×D₄×D₅	C₂²	semidirect
37. C₂²×C₃×C₄×D₅	C₂²	semidirect
38. C₂²×C₃×C₄×D₅	C₂²	semidirect
39. C₂²×C₃×Dic₁₀	C₂²	semidirect
40. C₃×C₅×#121	C₂²	semidirect
41. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
42. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
43. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
44. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
45. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
46. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
47. C₃×#4085	C₂²	semidirect
48. C₃×#4083	C₂²	semidirect
49. C₃×#4083	C₂²	semidirect
50. C₃×#4081	C₂²	semidirect
51. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
55. C₂×C₃×#685	C₂²	semidirect
56. C₂×C₃×#685	C₂²	semidirect
57. C₂×C₃×#685	C₂²	semidirect
58. C₂×C₃×#685	C₂²	semidirect
59. C₂×C₃×#685	C₂²	semidirect
60. C₂×C₃×#683	C₂²	semidirect
61. C₂×C₃×#683	C₂²	semidirect
62. C₂×C₃×#683	C₂²	semidirect
63. C₂×C₃×C₄×Dic₅	C₂²	semidirect
64. C₃×#4042	C₂²	semidirect
65. C₃×#4040	C₂²	semidirect
66. C₃×#4031	C₂²	semidirect
67. C₃×#4030	C₂²	semidirect
68. C₃×#4027	C₂²	semidirect
69. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
71. C₂²×#711	C₂×C₃	semidirect
72. C₂²×D₄×D₅	C₂×C₃	semidirect
73. C₂×C₅×#121	C₂×C₃	semidirect
74. C₂×#4085	C₂×C₃	semidirect
75. C₂×#4083	C₂×C₃	semidirect
76. C₂×#4083	C₂×C₃	semidirect
77. C₂×#4081	C₂×C₃	semidirect
78. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
79. C₂²×#685	C₂×C₃	semidirect
80. #65944	C₂×C₃	direct (N × H)
81. C₂×#4042	C₂×C₃	semidirect
82. C₂×#4040	C₂×C₃	semidirect
83. C₂×#4031	C₂×C₃	semidirect
84. C₂×#4030	C₂×C₃	semidirect
85. C₂×#4027	C₂×C₃	semidirect
86. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
105. C₂×C₃×C₅×D₄	C₂³	semidirect
106. C₂×C₃×C₅×D₄	C₂³	semidirect
112. C₂²×C₃×C₄×C₅	C₂³	semidirect
117. C₂×C₃×C₂²⋊D₅	D₄	semidirect
121. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
122. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
130. C₂²×C₃×Dic₅	C₂³	semidirect
131. C₂²×C₃×Dic₅	C₂³	semidirect
140. C₂×C₃×C₄×D₅	C₂³	semidirect
141. C₂×C₃×C₄×D₅	C₂³	semidirect
143. C₂×C₃×Dic₁₀	C₂³	semidirect
144. C₃×C₅×C₄⋊C₄	C₂³	semidirect
145. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
146. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
147. C₃×C₂²⋊Dic₅	C₂³	semidirect
148. C₃×C₂²⋊Dic₅	C₂³	semidirect
149. C₃×C₂²⋊Dic₅	C₂³	semidirect
153. C₃×#685	C₂³	semidirect
154. C₃×#685	C₂³	semidirect
155. C₃×#685	C₂³	semidirect
156. C₃×#685	C₂³	semidirect
157. C₃×#683	C₂³	semidirect
158. C₃×#683	C₂³	semidirect
159. C₃×#683	C₂³	semidirect
160. C₃×C₄×Dic₅	C₂³	semidirect
170. C₂×C₃×#121	D₅	semidirect
180. C₂²×C₅×D₄	C₂²×C₃	semidirect
181. C₂²×C₅×D₄	C₂²×C₃	semidirect
182. C₂³×C₄×C₅	C₂²×C₃	semidirect
186. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
187. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
188. C₂³×Dic₅	C₂²×C₃	semidirect
189. C₂³×Dic₅	C₂²×C₃	semidirect
191. C₂×#711	C₂²×C₃	semidirect
193. C₂×D₄×D₅	C₂²×C₃	semidirect
196. C₂²×C₄×D₅	C₂²×C₃	semidirect
197. C₂²×C₄×D₅	C₂²×C₃	semidirect
198. C₂²×Dic₁₀	C₂²×C₃	semidirect
199. C₅×#121	C₂²×C₃	semidirect
200. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
201. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
202. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
203. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
204. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
205. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
206. #4085	C₂²×C₃	semidirect
207. #4083	C₂²×C₃	semidirect
208. #4083	C₂²×C₃	semidirect
209. #4081	C₂²×C₃	semidirect
210. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
214. C₂×#685	C₂²×C₃	semidirect
215. C₂×#685	C₂²×C₃	semidirect
216. C₂×#685	C₂²×C₃	semidirect
217. C₂×#685	C₂²×C₃	semidirect
218. C₂×#685	C₂²×C₃	semidirect
219. C₂×#683	C₂²×C₃	semidirect
220. C₂×#683	C₂²×C₃	semidirect
221. C₂×#683	C₂²×C₃	semidirect
222. C₂×C₄×Dic₅	C₂²×C₃	semidirect
223. #4042	C₂²×C₃	semidirect
224. #4040	C₂²×C₃	semidirect
225. #4031	C₂²×C₃	semidirect
226. #4030	C₂²×C₃	semidirect
227. #4027	C₂²×C₃	semidirect
228. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
259. C₂²×C₃×D₅	#41	semidirect
279. C₃×C₂²⋊D₅	C₂×D₄	semidirect
311. C₂²×C₃×D₄	C₂×D₅	semidirect
312. C₂²×C₃×D₄	C₂×D₅	semidirect
318. C₂³×C₃×C₄	C₂×D₅	semidirect
325. C₃×#121	C₂×D₅	semidirect
333. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
346. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
347. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
367. C₂×C₅×D₄	C₂³×C₃	semidirect
368. C₂×C₅×D₄	C₂³×C₃	semidirect
374. C₂²×C₄×C₅	C₂³×C₃	semidirect
379. C₂×C₂²⋊D₅	C₃×D₄	semidirect
383. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
384. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
392. C₂²×Dic₅	C₂³×C₃	semidirect
393. C₂²×Dic₅	C₂³×C₃	semidirect
402. C₂×C₄×D₅	C₂³×C₃	semidirect
403. C₂×C₄×D₅	C₂³×C₃	semidirect
405. C₂×Dic₁₀	C₂³×C₃	semidirect
406. C₅×C₄⋊C₄	C₂³×C₃	semidirect
407. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
408. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
409. C₂²⋊Dic₅	C₂³×C₃	semidirect
410. C₂²⋊Dic₅	C₂³×C₃	semidirect
411. C₂²⋊Dic₅	C₂³×C₃	semidirect
415. #685	C₂³×C₃	semidirect
416. #685	C₂³×C₃	semidirect
417. #685	C₂³×C₃	semidirect
418. #685	C₂³×C₃	semidirect
419. #683	C₂³×C₃	semidirect
420. #683	C₂³×C₃	semidirect
421. #683	C₂³×C₃	semidirect
422. C₄×Dic₅	C₂³×C₃	semidirect
432. C₂×#121	C₃×D₅	semidirect
468. C₂×C₃×D₅	C₂×#41	semidirect
512. C₂×C₃×D₄	C₂²×D₅	semidirect
513. C₂×C₃×D₄	C₂²×D₅	semidirect
534. C₂²×C₃×C₄	C₂²×D₅	semidirect
538. C₃×C₄⋊C₄	C₂²×D₅	semidirect
549. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
550. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
581. C₂²×D₅	C₃×#41	semidirect
601. C₂²⋊D₅	C₂×C₃×D₄	semidirect
633. C₂²×D₄	C₂×C₃×D₅	semidirect
634. C₂²×D₄	C₂×C₃×D₅	semidirect
640. C₂³×C₄	C₂×C₃×D₅	semidirect
647. #121	C₂×C₃×D₅	semidirect
655. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
668. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
669. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
674. C₂×C₃×C₅	#546	semidirect
777. C₂×D₅	C₂×C₃×#41	semidirect
821. C₂×D₄	C₂²×C₃×D₅	semidirect
822. C₂×D₄	C₂²×C₃×D₅	semidirect
843. C₂²×C₄	C₂²×C₃×D₅	semidirect
847. C₄⋊C₄	C₂²×C₃×D₅	semidirect
858. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
859. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
861. C₃×C₅	C₂×#546	semidirect
904. C₂×C₅	C₃×#546	semidirect
984. C₂×C₃	#65944	direct (N × H)
988. C₅	C₂×C₃×#546	semidirect
1028. C₃	C₂×#65944	direct (N × H)
1035. C₂	C₃×#65944	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×#711	2
C₂²×C₃×D₄×D₅	2
C₂×C₃×C₅×#121	2
C₂×C₃×#4085	2
C₂×C₃×#4083	2
C₂×C₃×#4081	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₂²×C₃×#685	2
C₃×#65944	2
C₂×C₃×#4042	2
C₂×C₃×#4040	2
C₂×C₃×#4031	2
C₂×C₃×#4030	2
C₂×C₃×#4027	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₂×#65944	3
C₂×C₃×#546	5

Subgroups — C2×C3×#65944 #14482482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65944 #14482482