Subgroups — C₂×C₅×#5654 #14482490

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×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5654	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#546	—	3	1	no	maximal, Hall
18	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
26	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×D₃×D₄	—	2	8	no	—
28	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
29	C₂×C₅×#235	—	2	8	no	—
30	C₂×C₅×#235	C₂²	1	8	yes	complemented
31	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
32	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#123	C₂²	1	8	yes	complemented
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
47	C₅×#939	C₂²	1	8	yes	complemented
48	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
52	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	C₅×#896	C₂²	1	8	yes	complemented
61	C₅×#895	C₂²	1	8	yes	complemented
62	C₅×#894	C₂²	1	8	yes	complemented
63	C₅×#893	C₂²	1	8	yes	complemented
64	C₅×#885	C₂²	1	8	yes	complemented
65	C₅×#884	C₂²	1	8	yes	complemented
66	C₅×#882	C₂²	1	8	yes	complemented
67	C₅×#882	C₂²	1	8	yes	complemented
68	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
69	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
70	C₂×#5654	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
71	C₂²×C₅×#41	—	3	1	no	—
72	C₂³×C₅×D₄	—	3	1	no	—
73	C₅×#546	—	3	16	no	—
74	C₂×C₅×#124	—	3	1	no	—
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×#123	D₃	1	1	yes	characteristic, complemented
77	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
78	C₂×C₅×#121	—	3	1	no	—
79	C₂×C₅×#121	—	3	1	no	—
80	C₂×C₅×#121	—	3	1	no	—
81	C₂×C₅×#120	—	3	1	no	—
82	C₂×C₅×#120	—	3	1	no	—
83	C₂×C₄×C₅×D₄	—	3	1	no	—
84	C₂×C₄×C₅×D₄	—	3	1	no	—
85	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
86	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
87	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
88	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
89	C₂³×C₅×D₃	—	2	4	no	—
90	C₂³×C₅×D₃	—	2	4	no	—
91	C₂³×C₅×D₃	—	2	4	no	—
92	C₂³×C₅×D₃	—	2	4	no	—
93	C₂³×C₅×D₃	—	4	2	no	—
94	C₂³×C₅×D₃	—	4	2	no	—
95	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
96	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
97	C₂³×C₅×D₃	C₂³	1	4	yes	—
98	C₂³×C₅×D₃	C₂³	1	4	yes	—
99	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
100	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×D₄	—	2	4	no	—
102	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
103	C₂²×C₃×C₄×C₅	—	2	4	no	—
104	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
110	C₂×C₅×#67	—	2	4	no	—
111	C₂×C₅×#67	—	2	4	no	—
112	C₂×C₅×#67	—	4	2	no	—
113	C₂×C₅×#67	D₄	1	8	yes	complemented
114	C₂×C₅×#67	C₂³	1	4	yes	—
115	C₂×C₅×#67	C₂³	1	4	yes	—
116	C₂×C₅×#67	C₂³	1	4	yes	complemented
117	C₂×C₅×#67	C₂³	1	4	yes	complemented
118	C₂²×C₅×Dic₃	—	4	2	no	—
119	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
121	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
122	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
123	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
124	C₅×D₃×D₄	—	2	32	no	—
125	C₅×#235	—	2	32	no	—
126	C₂×C₅×D₁₂	—	2	4	no	—
127	C₂×C₅×D₁₂	—	2	4	no	—
128	C₂×C₅×D₁₂	—	2	4	no	—
129	C₂×C₅×D₁₂	—	4	2	no	—
130	C₂×C₅×D₁₂	C₂³	1	4	yes	—
131	C₂×C₅×D₁₂	C₂³	1	4	yes	—
132	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
133	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
134	C₂×C₄×C₅×D₃	—	2	4	no	—
135	C₂×C₄×C₅×D₃	—	2	4	no	—
136	C₂×C₄×C₅×D₃	—	2	4	no	—
137	C₂×C₄×C₅×D₃	—	4	2	no	—
138	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
139	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
140	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
141	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
142	C₂×C₅×Dic₆	—	2	4	no	—
143	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
144	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
145	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
146	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
147	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
148	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
149	C₅×#217	C₂³	1	4	yes	complemented
150	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
151	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
154	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
155	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
156	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
157	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
158	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
159	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
160	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
161	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
165	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
166	#5654	C₂×C₅	1	16	yes	direct product factor
167	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
170	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×#885	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
173	C₂×#882	C₂×C₅	1	1	yes	characteristic, complemented
174	C₂×#882	C₂×C₅	1	1	yes	characteristic, complemented
175	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
176	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
177	C₂⁵×C₅	—	3	1	no	—
178	C₂⁵×C₅	—	3	1	no	—
179	C₂×C₅×#41	—	3	8	no	—
180	C₂×C₅×#41	—	6	8	no	—
181	C₂²×C₅×Q₈	—	3	1	no	—
182	C₂²×C₅×D₄	—	3	1	no	—
183	C₂²×C₅×D₄	—	3	1	no	—
184	C₂²×C₅×D₄	—	3	1	no	—
185	C₂²×C₅×D₄	—	3	1	no	—
186	C₂²×C₅×D₄	—	3	8	no	—
187	C₂²×C₅×D₄	—	3	1	no	—
188	C₂²×C₅×D₄	—	3	1	no	—
189	C₂²×C₅×D₄	—	3	1	no	—
190	C₂²×C₅×D₄	—	3	1	no	—
191	C₂²×C₅×D₄	—	6	8	no	—
192	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
193	C₂³×C₄×C₅	—	3	1	no	—
194	C₂³×C₄×C₅	—	3	1	no	—
195	C₂³×C₄×C₅	—	3	1	no	—
196	C₂³×C₄×C₅	—	3	1	no	—
197	C₂³×C₄×C₅	—	3	1	no	—
198	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
199	C₅×#124	—	3	8	no	—
200	C₅×#123	—	3	8	no	—
201	C₅×#123	C₂×D₃	1	8	yes	complemented
202	C₅×C₂²⋊Q₈	—	3	8	no	—
203	C₅×#121	—	3	8	no	—
204	C₅×#121	—	3	8	no	—
205	C₅×#121	—	3	8	no	—
206	C₅×#120	—	3	8	no	—
207	C₅×#120	—	3	8	no	—
208	C₄×C₅×D₄	—	3	8	no	—
209	C₄×C₅×D₄	—	3	8	no	—
210	C₂×C₅×C₄⋊C₄	—	3	1	no	—
211	C₂×C₅×C₄⋊C₄	—	3	1	no	—
212	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
213	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
214	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
215	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
216	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
217	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
218	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
219	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
220	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
221	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
222	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
223	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
224	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
225	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
226	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
227	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
228	C₂×C₄²×C₅	—	3	1	no	—
229	C₂×#546	—	3	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	C₂×D₄	1	4	yes	—
236	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
237	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
238	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
239	C₂²×C₅×D₃	—	2	2	no	—
240	C₂²×C₅×D₃	—	2	2	no	—
241	C₂²×C₅×D₃	—	2	2	no	—
242	C₂²×C₅×D₃	—	2	2	no	—
243	C₂²×C₅×D₃	—	2	2	no	—
244	C₂²×C₅×D₃	—	2	2	no	—
245	C₂²×C₅×D₃	—	2	8	no	—
246	C₂²×C₅×D₃	—	2	2	no	—
247	C₂²×C₅×D₃	—	2	2	no	—
248	C₂²×C₅×D₃	—	2	2	no	—
249	C₂²×C₅×D₃	—	2	2	no	—
250	C₂²×C₅×D₃	—	2	8	no	—
251	C₂²×C₅×D₃	—	2	8	no	—
252	C₂²×C₅×D₃	—	2	8	no	—
253	C₂²×C₅×D₃	—	4	4	no	—
254	C₂²×C₅×D₃	—	4	4	no	—
255	C₂²×C₅×D₃	—	4	16	no	—
256	C₂²×C₅×D₃	—	4	16	no	—
257	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
258	C₂²×C₅×D₃	#41	1	4	yes	complemented
259	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
260	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
261	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
262	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
263	C₃×C₅×D₄	—	2	8	no	—
264	C₂×C₃×C₄×C₅	—	2	2	no	—
265	C₂×C₃×C₄×C₅	—	2	2	no	—
266	C₂×C₃×C₄×C₅	—	2	2	no	—
267	C₂×C₃×C₄×C₅	—	2	8	no	—
268	C₂×C₃×C₄×C₅	—	2	2	no	—
269	C₂×C₃×C₄×C₅	—	2	2	no	—
270	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	C₅×#67	—	2	8	no	—
276	C₅×#67	—	2	8	no	—
277	C₅×#67	—	4	4	no	—
278	C₅×#67	C₂×D₄	1	16	yes	complemented
279	C₂×C₅×Dic₃	—	2	2	no	—
280	C₂×C₅×Dic₃	—	2	2	no	—
281	C₂×C₅×Dic₃	—	2	2	no	—
282	C₂×C₅×Dic₃	—	4	4	no	—
283	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
284	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
285	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
286	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
287	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
288	C₅×D₁₂	—	2	8	no	—
289	C₅×D₁₂	—	2	8	no	—
290	C₅×D₁₂	—	2	8	no	—
291	C₅×D₁₂	—	4	4	no	—
292	C₄×C₅×D₃	—	2	8	no	—
293	C₄×C₅×D₃	—	2	8	no	—
294	C₄×C₅×D₃	—	2	8	no	—
295	C₄×C₅×D₃	—	4	4	no	—
296	C₅×Dic₆	—	2	8	no	—
297	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
298	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
299	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
300	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
302	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
303	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂×D₃×D₄	—	2	8	no	—
307	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
308	C₂×#235	—	2	8	no	—
309	C₂×#235	C₂²×C₅	1	8	yes	complemented
310	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
311	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
312	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
314	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
315	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
316	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
317	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
318	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
319	C₃×#123	C₂²×C₅	1	8	yes	complemented
320	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
321	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
322	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
323	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
325	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
326	#939	C₂²×C₅	1	8	yes	complemented
327	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
328	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
329	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
330	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
331	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
332	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
333	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
334	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
335	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
336	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
337	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
338	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
339	#896	C₂²×C₅	1	8	yes	complemented
340	#895	C₂²×C₅	1	8	yes	complemented
341	#894	C₂²×C₅	1	8	yes	complemented
342	#893	C₂²×C₅	1	8	yes	complemented
343	#885	C₂²×C₅	1	8	yes	complemented
344	#884	C₂²×C₅	1	8	yes	complemented
345	#882	C₂²×C₅	1	8	yes	complemented
346	#882	C₂²×C₅	1	8	yes	complemented
347	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
348	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
349	C₂⁴×C₅	—	3	1	no	—
350	C₂⁴×C₅	—	3	1	no	—
351	C₂⁴×C₅	—	3	1	no	—
352	C₂⁴×C₅	—	3	1	no	—
353	C₂⁴×C₅	—	3	4	no	—
354	C₂⁴×C₅	—	3	4	no	—
355	C₂⁴×C₅	—	6	4	no	—
356	C₂⁴×C₅	—	6	4	no	—
357	C₂⁴×C₅	—	6	4	no	—
358	C₂⁴×C₅	—	6	4	no	—
359	C₂⁴×C₅	—	12	2	no	—
360	C₂⁴×C₅	—	12	2	no	—
361	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
362	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
363	C₅×#41	—	6	32	no	—
364	C₂×C₅×Q₈	—	3	4	no	—
365	C₂×C₅×Q₈	—	6	4	no	—
366	C₂×C₅×D₄	—	2	4	no	—
367	C₂×C₅×D₄	—	3	8	no	—
368	C₂×C₅×D₄	—	3	4	no	—
369	C₂×C₅×D₄	—	3	4	no	—
370	C₂×C₅×D₄	—	3	4	no	—
371	C₂×C₅×D₄	—	3	4	no	—
372	C₂×C₅×D₄	—	3	4	no	—
373	C₂×C₅×D₄	—	3	4	no	—
374	C₂×C₅×D₄	—	3	4	no	—
375	C₂×C₅×D₄	—	3	4	no	—
376	C₂×C₅×D₄	—	6	4	no	—
377	C₂×C₅×D₄	—	6	4	no	—
378	C₂×C₅×D₄	—	6	4	no	—
379	C₂×C₅×D₄	—	6	4	no	—
380	C₂×C₅×D₄	—	6	32	no	—
381	C₂×C₅×D₄	—	6	4	no	—
382	C₂×C₅×D₄	—	12	2	no	—
383	C₂×C₅×D₄	—	12	2	no	—
384	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
385	C₂²×C₄×C₅	—	2	4	no	—
386	C₂²×C₄×C₅	—	3	1	no	—
387	C₂²×C₄×C₅	—	3	1	no	—
388	C₂²×C₄×C₅	—	3	1	no	—
389	C₂²×C₄×C₅	—	3	1	no	—
390	C₂²×C₄×C₅	—	3	4	no	—
391	C₂²×C₄×C₅	—	3	4	no	—
392	C₂²×C₄×C₅	—	3	4	no	—
393	C₂²×C₄×C₅	—	3	4	no	—
394	C₂²×C₄×C₅	—	3	4	no	—
395	C₂²×C₄×C₅	—	6	4	no	—
396	C₂²×C₄×C₅	—	6	4	no	—
397	C₂²×C₄×C₅	—	6	4	no	—
398	C₂²×C₄×C₅	—	12	2	no	—
399	C₂²×C₄×C₅	—	12	2	no	—
400	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
401	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
402	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
403	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
404	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
405	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
406	C₅×C₄⋊C₄	—	3	4	no	—
407	C₅×C₄⋊C₄	—	3	4	no	—
408	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
409	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
410	C₅×C₂²⋊C₄	—	3	4	no	—
411	C₅×C₂²⋊C₄	—	3	4	no	—
412	C₅×C₂²⋊C₄	—	3	4	no	—
413	C₅×C₂²⋊C₄	—	3	4	no	—
414	C₅×C₂²⋊C₄	—	3	4	no	—
415	C₅×C₂²⋊C₄	—	3	4	no	—
416	C₅×C₂²⋊C₄	—	3	4	no	—
417	C₅×C₂²⋊C₄	—	3	4	no	—
418	C₅×C₂²⋊C₄	—	3	4	no	—
419	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
420	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
421	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
422	C₄²×C₅	—	3	4	no	—
423	C₂²×#41	—	3	1	no	—
424	C₂³×D₄	—	3	1	no	—
425	#546	—	3	16	no	—
426	C₂×#124	—	3	1	no	—
427	C₂×#123	—	3	1	no	—
428	C₂×#123	C₅×D₃	1	1	yes	characteristic, complemented
429	C₂×C₂²⋊Q₈	—	3	1	no	—
430	C₂×#121	—	3	1	no	—
431	C₂×#121	—	3	1	no	—
432	C₂×#121	—	3	1	no	—
433	C₂×#120	—	3	1	no	—
434	C₂×#120	—	3	1	no	—
435	C₂×C₄×D₄	—	3	1	no	—
436	C₂×C₄×D₄	—	3	1	no	—
437	C₂²×C₂²⋊C₄	—	3	1	no	—
438	C₂²×C₂²⋊C₄	—	3	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	—	4	4	no	—
446	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
447	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
448	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
449	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
450	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
451	C₂×C₅×D₃	—	2	8	no	—
452	C₂×C₅×D₃	—	2	8	no	—
453	C₂×C₅×D₃	—	2	2	no	—
454	C₂×C₅×D₃	—	2	2	no	—
455	C₂×C₅×D₃	—	2	2	no	—
456	C₂×C₅×D₃	—	2	2	no	—
457	C₂×C₅×D₃	—	2	2	no	—
458	C₂×C₅×D₃	—	2	2	no	—
459	C₂×C₅×D₃	—	2	2	no	—
460	C₂×C₅×D₃	—	2	2	no	—
461	C₂×C₅×D₃	—	2	2	no	—
462	C₂×C₅×D₃	—	2	2	no	—
463	C₂×C₅×D₃	—	4	16	no	—
464	C₂×C₅×D₃	—	4	16	no	—
465	C₂×C₅×D₃	—	4	4	no	—
466	C₂×C₅×D₃	—	4	4	no	—
467	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
468	C₂×C₅×D₃	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×C₄×C₅	—	2	2	no	—
474	C₅×Dic₃	—	2	2	no	—
475	C₅×Dic₃	—	2	2	no	—
476	C₅×Dic₃	—	2	2	no	—
477	C₅×Dic₃	C₂²×D₄	1	4	yes	—
478	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
479	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
480	C₂³×D₃	—	2	4	no	—
481	C₂³×D₃	—	2	4	no	—
482	C₂³×D₃	—	2	4	no	—
483	C₂³×D₃	—	2	4	no	—
484	C₂³×D₃	—	4	2	no	—
485	C₂³×D₃	—	4	2	no	—
486	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
487	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
488	C₂³×D₃	C₂³×C₅	1	4	yes	—
489	C₂³×D₃	C₂³×C₅	1	4	yes	—
490	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
491	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
492	C₂×C₃×D₄	—	2	4	no	—
493	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
494	C₂²×C₃×C₄	—	2	4	no	—
495	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
497	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
498	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
499	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
500	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
501	C₂×#67	—	2	4	no	—
502	C₂×#67	—	2	4	no	—
503	C₂×#67	—	4	2	no	—
504	C₂×#67	C₅×D₄	1	8	yes	complemented
505	C₂×#67	C₂³×C₅	1	4	yes	—
506	C₂×#67	C₂³×C₅	1	4	yes	—
507	C₂×#67	C₂³×C₅	1	4	yes	complemented
508	C₂×#67	C₂³×C₅	1	4	yes	complemented
509	C₂²×Dic₃	—	4	2	no	—
510	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
511	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
512	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
513	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
514	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
515	D₃×D₄	—	2	32	no	—
516	#235	—	2	32	no	—
517	C₂×D₁₂	—	2	4	no	—
518	C₂×D₁₂	—	2	4	no	—
519	C₂×D₁₂	—	2	4	no	—
520	C₂×D₁₂	—	4	2	no	—
521	C₂×D₁₂	C₂³×C₅	1	4	yes	—
522	C₂×D₁₂	C₂³×C₅	1	4	yes	—
523	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
524	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
525	C₂×C₄×D₃	—	2	4	no	—
526	C₂×C₄×D₃	—	2	4	no	—
527	C₂×C₄×D₃	—	2	4	no	—
528	C₂×C₄×D₃	—	4	2	no	—
529	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
530	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
531	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
532	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
533	C₂×Dic₆	—	2	4	no	—
534	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
535	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
536	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
537	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
538	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
539	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
540	#217	C₂³×C₅	1	4	yes	complemented
541	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
542	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
543	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
544	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
545	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
546	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
547	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
548	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
549	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
550	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
551	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
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	—	3	4	no	—
558	C₂³×C₅	—	3	4	no	—
559	C₂³×C₅	—	3	2	no	—
560	C₂³×C₅	—	3	2	no	—
561	C₂³×C₅	—	3	2	no	—
562	C₂³×C₅	—	3	2	no	—
563	C₂³×C₅	—	6	8	no	—
564	C₂³×C₅	—	6	8	no	—
565	C₂³×C₅	—	6	8	no	—
566	C₂³×C₅	—	6	2	no	—
567	C₂³×C₅	—	6	2	no	—
568	C₂³×C₅	—	6	2	no	—
569	C₂³×C₅	—	6	2	no	—
570	C₂³×C₅	—	6	2	no	—
571	C₂³×C₅	—	6	8	no	—
572	C₂³×C₅	—	6	2	no	—
573	C₂³×C₅	—	6	2	no	—
574	C₂³×C₅	—	6	2	no	—
575	C₂³×C₅	—	6	2	no	—
576	C₂³×C₅	—	6	2	no	—
577	C₂³×C₅	—	12	4	no	—
578	C₂³×C₅	—	12	4	no	—
579	C₂³×C₅	—	12	16	no	—
580	C₂³×C₅	—	12	16	no	—
581	C₂³×C₅	D₃×D₄	1	4	yes	—
582	C₂³×C₅	C₂³×D₃	1	2	yes	—
583	C₂³×C₅	C₂³×D₃	1	2	yes	—
584	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
585	C₅×Q₈	—	6	8	no	—
586	C₅×D₄	—	2	8	no	—
587	C₅×D₄	—	3	16	no	—
588	C₅×D₄	—	6	8	no	—
589	C₅×D₄	—	6	8	no	—
590	C₅×D₄	—	6	8	no	—
591	C₅×D₄	—	6	8	no	—
592	C₅×D₄	—	6	8	no	—
593	C₅×D₄	—	12	4	no	—
594	C₅×D₄	—	12	4	no	—
595	C₂×C₄×C₅	—	2	2	no	—
596	C₂×C₄×C₅	—	2	2	no	—
597	C₂×C₄×C₅	—	2	8	no	—
598	C₂×C₄×C₅	—	2	2	no	—
599	C₂×C₄×C₅	—	2	2	no	—
600	C₂×C₄×C₅	—	2	2	no	—
601	C₂×C₄×C₅	—	3	4	no	—
602	C₂×C₄×C₅	—	3	2	no	—
603	C₂×C₄×C₅	—	3	2	no	—
604	C₂×C₄×C₅	—	3	2	no	—
605	C₂×C₄×C₅	—	3	2	no	—
606	C₂×C₄×C₅	—	6	8	no	—
607	C₂×C₄×C₅	—	6	8	no	—
608	C₂×C₄×C₅	—	6	8	no	—
609	C₂×C₄×C₅	—	6	2	no	—
610	C₂×C₄×C₅	—	6	2	no	—
611	C₂×C₄×C₅	—	6	2	no	—
612	C₂×C₄×C₅	—	12	4	no	—
613	C₂×C₄×C₅	—	12	4	no	—
614	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
615	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
616	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
617	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
618	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
619	C₂⁵	—	3	1	no	—
620	C₂⁵	—	3	1	no	—
621	C₂×#41	—	3	8	no	—
622	C₂×#41	—	6	8	no	—
623	C₂²×Q₈	—	3	1	no	—
624	C₂²×D₄	—	3	1	no	—
625	C₂²×D₄	—	3	1	no	—
626	C₂²×D₄	—	3	1	no	—
627	C₂²×D₄	—	3	1	no	—
628	C₂²×D₄	—	3	8	no	—
629	C₂²×D₄	—	3	1	no	—
630	C₂²×D₄	—	3	1	no	—
631	C₂²×D₄	—	3	1	no	—
632	C₂²×D₄	—	3	1	no	—
633	C₂²×D₄	—	6	8	no	—
634	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
635	C₂³×C₄	—	3	1	no	—
636	C₂³×C₄	—	3	1	no	—
637	C₂³×C₄	—	3	1	no	—
638	C₂³×C₄	—	3	1	no	—
639	C₂³×C₄	—	3	1	no	—
640	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
641	#124	—	3	8	no	—
642	#123	—	3	8	no	—
643	#123	C₂×C₅×D₃	1	8	yes	complemented
644	C₂²⋊Q₈	—	3	8	no	—
645	#121	—	3	8	no	—
646	#121	—	3	8	no	—
647	#121	—	3	8	no	—
648	#120	—	3	8	no	—
649	#120	—	3	8	no	—
650	C₄×D₄	—	3	8	no	—
651	C₄×D₄	—	3	8	no	—
652	C₂×C₄⋊C₄	—	3	1	no	—
653	C₂×C₄⋊C₄	—	3	1	no	—
654	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
655	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
656	C₂×C₂²⋊C₄	—	3	1	no	—
657	C₂×C₂²⋊C₄	—	3	1	no	—
658	C₂×C₂²⋊C₄	—	3	1	no	—
659	C₂×C₂²⋊C₄	—	3	1	no	—
660	C₂×C₂²⋊C₄	—	3	1	no	—
661	C₂×C₂²⋊C₄	—	3	1	no	—
662	C₂×C₂²⋊C₄	—	3	1	no	—
663	C₂×C₂²⋊C₄	—	3	1	no	—
664	C₂×C₂²⋊C₄	—	3	1	no	—
665	C₂×C₂²⋊C₄	—	3	8	no	—
666	C₂×C₂²⋊C₄	—	3	8	no	—
667	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
668	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
669	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
670	C₂×C₄²	—	3	1	no	—
671	C₂×C₃×C₅	—	2	4	no	—
672	C₂×C₃×C₅	—	4	2	no	—
673	C₂×C₃×C₅	#546	1	4	yes	complemented
674	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
675	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
676	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
677	C₅×D₃	—	2	4	no	—
678	C₅×D₃	—	2	4	no	—
679	C₅×D₃	—	4	2	no	—
680	C₅×D₃	—	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	C₂×C₅×D₄	1	4	yes	—
687	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
688	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
689	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
690	C₂²×D₃	—	2	2	no	—
691	C₂²×D₃	—	2	2	no	—
692	C₂²×D₃	—	2	2	no	—
693	C₂²×D₃	—	2	2	no	—
694	C₂²×D₃	—	2	2	no	—
695	C₂²×D₃	—	2	2	no	—
696	C₂²×D₃	—	2	8	no	—
697	C₂²×D₃	—	2	2	no	—
698	C₂²×D₃	—	2	2	no	—
699	C₂²×D₃	—	2	2	no	—
700	C₂²×D₃	—	2	2	no	—
701	C₂²×D₃	—	2	8	no	—
702	C₂²×D₃	—	2	8	no	—
703	C₂²×D₃	—	2	8	no	—
704	C₂²×D₃	—	4	4	no	—
705	C₂²×D₃	—	4	4	no	—
706	C₂²×D₃	—	4	16	no	—
707	C₂²×D₃	—	4	16	no	—
708	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
709	C₂²×D₃	C₅×#41	1	4	yes	complemented
710	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
711	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
712	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
713	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
714	C₃×D₄	—	2	8	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	2	no	—
718	C₂×C₃×C₄	—	2	8	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	2	no	—
721	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
722	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
723	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
724	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
725	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
726	#67	—	2	8	no	—
727	#67	—	2	8	no	—
728	#67	—	4	4	no	—
729	#67	C₂×C₅×D₄	1	16	yes	complemented
730	C₂×Dic₃	—	2	2	no	—
731	C₂×Dic₃	—	2	2	no	—
732	C₂×Dic₃	—	2	2	no	—
733	C₂×Dic₃	—	4	4	no	—
734	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
735	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
736	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
737	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
738	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
739	D₁₂	—	2	8	no	—
740	D₁₂	—	2	8	no	—
741	D₁₂	—	2	8	no	—
742	D₁₂	—	4	4	no	—
743	C₄×D₃	—	2	8	no	—
744	C₄×D₃	—	2	8	no	—
745	C₄×D₃	—	2	8	no	—
746	C₄×D₃	—	4	4	no	—
747	Dic₆	—	2	8	no	—
748	C₂²×C₅	—	2	8	no	—
749	C₂²×C₅	—	2	2	no	—
750	C₂²×C₅	—	2	2	no	—
751	C₂²×C₅	—	2	2	no	—
752	C₂²×C₅	—	2	2	no	—
753	C₂²×C₅	—	2	2	no	—
754	C₂²×C₅	—	3	4	no	—
755	C₂²×C₅	—	3	4	no	—
756	C₂²×C₅	—	4	4	no	—
757	C₂²×C₅	—	6	8	no	—
758	C₂²×C₅	—	6	8	no	—
759	C₂²×C₅	—	6	2	no	—
760	C₂²×C₅	—	6	2	no	—
761	C₂²×C₅	—	6	2	no	—
762	C₂²×C₅	—	6	2	no	—
763	C₂²×C₅	—	6	2	no	—
764	C₂²×C₅	—	6	2	no	—
765	C₂²×C₅	—	6	2	no	—
766	C₂²×C₅	—	6	2	no	—
767	C₂²×C₅	—	6	2	no	—
768	C₂²×C₅	—	6	2	no	—
769	C₂²×C₅	—	12	16	no	—
770	C₂²×C₅	—	12	16	no	—
771	C₂²×C₅	—	12	4	no	—
772	C₂²×C₅	—	12	4	no	—
773	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
774	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
775	C₂²×C₅	D₃×#41	1	2	yes	—
776	C₂²×C₅	#1009	1	2	yes	—
777	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
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	C₄×C₅	—	2	2	no	—
783	C₄×C₅	—	3	4	no	—
784	C₄×C₅	—	6	2	no	—
785	C₄×C₅	—	6	2	no	—
786	C₄×C₅	—	6	2	no	—
787	C₂⁴	—	3	1	no	—
788	C₂⁴	—	3	1	no	—
789	C₂⁴	—	3	1	no	—
790	C₂⁴	—	3	1	no	—
791	C₂⁴	—	3	4	no	—
792	C₂⁴	—	3	4	no	—
793	C₂⁴	—	6	4	no	—
794	C₂⁴	—	6	4	no	—
795	C₂⁴	—	6	4	no	—
796	C₂⁴	—	6	4	no	—
797	C₂⁴	—	12	2	no	—
798	C₂⁴	—	12	2	no	—
799	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
800	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
801	#41	—	6	32	no	—
802	C₂×Q₈	—	3	4	no	—
803	C₂×Q₈	—	6	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	3	8	no	—
806	C₂×D₄	—	3	4	no	—
807	C₂×D₄	—	3	4	no	—
808	C₂×D₄	—	3	4	no	—
809	C₂×D₄	—	3	4	no	—
810	C₂×D₄	—	3	4	no	—
811	C₂×D₄	—	3	4	no	—
812	C₂×D₄	—	3	4	no	—
813	C₂×D₄	—	3	4	no	—
814	C₂×D₄	—	6	4	no	—
815	C₂×D₄	—	6	4	no	—
816	C₂×D₄	—	6	4	no	—
817	C₂×D₄	—	6	4	no	—
818	C₂×D₄	—	6	32	no	—
819	C₂×D₄	—	6	4	no	—
820	C₂×D₄	—	12	2	no	—
821	C₂×D₄	—	12	2	no	—
822	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	3	1	no	—
825	C₂²×C₄	—	3	1	no	—
826	C₂²×C₄	—	3	1	no	—
827	C₂²×C₄	—	3	1	no	—
828	C₂²×C₄	—	3	4	no	—
829	C₂²×C₄	—	3	4	no	—
830	C₂²×C₄	—	3	4	no	—
831	C₂²×C₄	—	3	4	no	—
832	C₂²×C₄	—	3	4	no	—
833	C₂²×C₄	—	6	4	no	—
834	C₂²×C₄	—	6	4	no	—
835	C₂²×C₄	—	6	4	no	—
836	C₂²×C₄	—	12	2	no	—
837	C₂²×C₄	—	12	2	no	—
838	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
839	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
840	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
841	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
842	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
843	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
844	C₄⋊C₄	—	3	4	no	—
845	C₄⋊C₄	—	3	4	no	—
846	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
847	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
848	C₂²⋊C₄	—	3	4	no	—
849	C₂²⋊C₄	—	3	4	no	—
850	C₂²⋊C₄	—	3	4	no	—
851	C₂²⋊C₄	—	3	4	no	—
852	C₂²⋊C₄	—	3	4	no	—
853	C₂²⋊C₄	—	3	4	no	—
854	C₂²⋊C₄	—	3	4	no	—
855	C₂²⋊C₄	—	3	4	no	—
856	C₂²⋊C₄	—	3	4	no	—
857	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
858	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
859	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
860	C₄²	—	3	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	—	4	4	no	—
869	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
870	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
871	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
872	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
873	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
874	C₂×D₃	—	2	8	no	—
875	C₂×D₃	—	2	8	no	—
876	C₂×D₃	—	2	2	no	—
877	C₂×D₃	—	2	2	no	—
878	C₂×D₃	—	2	2	no	—
879	C₂×D₃	—	2	2	no	—
880	C₂×D₃	—	2	2	no	—
881	C₂×D₃	—	2	2	no	—
882	C₂×D₃	—	2	2	no	—
883	C₂×D₃	—	2	2	no	—
884	C₂×D₃	—	2	2	no	—
885	C₂×D₃	—	2	2	no	—
886	C₂×D₃	—	4	16	no	—
887	C₂×D₃	—	4	16	no	—
888	C₂×D₃	—	4	4	no	—
889	C₂×D₃	—	4	4	no	—
890	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
891	C₂×D₃	C₂×C₅×#41	1	4	yes	complemented
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	—	2	2	no	—
897	Dic₃	—	2	2	no	—
898	Dic₃	—	2	2	no	—
899	Dic₃	—	2	2	no	—
900	Dic₃	C₂²×C₅×D₄	1	4	yes	—
901	C₂×C₅	—	2	4	no	—
902	C₂×C₅	—	4	2	no	—
903	C₂×C₅	—	6	4	no	—
904	C₂×C₅	—	6	4	no	—
905	C₂×C₅	—	12	2	no	—
906	C₂×C₅	—	12	2	no	—
907	C₂×C₅	#5654	1	4	yes	direct product factor
908	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
909	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
910	C₂×C₅	C₂×#1009	1	1	yes	characteristic
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	—	3	4	no	—
917	C₂³	—	3	4	no	—
918	C₂³	—	3	2	no	—
919	C₂³	—	3	2	no	—
920	C₂³	—	3	2	no	—
921	C₂³	—	3	2	no	—
922	C₂³	—	6	8	no	—
923	C₂³	—	6	8	no	—
924	C₂³	—	6	8	no	—
925	C₂³	—	6	2	no	—
926	C₂³	—	6	2	no	—
927	C₂³	—	6	2	no	—
928	C₂³	—	6	2	no	—
929	C₂³	—	6	2	no	—
930	C₂³	—	6	8	no	—
931	C₂³	—	6	2	no	—
932	C₂³	—	6	2	no	—
933	C₂³	—	6	2	no	—
934	C₂³	—	6	2	no	—
935	C₂³	—	6	2	no	—
936	C₂³	—	12	4	no	—
937	C₂³	—	12	4	no	—
938	C₂³	—	12	16	no	—
939	C₂³	—	12	16	no	—
940	C₂³	C₅×D₃×D₄	1	4	yes	—
941	C₂³	C₂³×C₅×D₃	1	2	yes	—
942	C₂³	C₂³×C₅×D₃	1	2	yes	—
943	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
944	Q₈	—	6	8	no	—
945	D₄	—	2	8	no	—
946	D₄	—	3	16	no	—
947	D₄	—	6	8	no	—
948	D₄	—	6	8	no	—
949	D₄	—	6	8	no	—
950	D₄	—	6	8	no	—
951	D₄	—	6	8	no	—
952	D₄	—	12	4	no	—
953	D₄	—	12	4	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	8	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	3	4	no	—
961	C₂×C₄	—	3	2	no	—
962	C₂×C₄	—	3	2	no	—
963	C₂×C₄	—	3	2	no	—
964	C₂×C₄	—	3	2	no	—
965	C₂×C₄	—	6	8	no	—
966	C₂×C₄	—	6	8	no	—
967	C₂×C₄	—	6	8	no	—
968	C₂×C₄	—	6	2	no	—
969	C₂×C₄	—	6	2	no	—
970	C₂×C₄	—	6	2	no	—
971	C₂×C₄	—	12	4	no	—
972	C₂×C₄	—	12	4	no	—
973	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
974	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
975	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
976	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
977	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
978	C₂×C₃	—	2	4	no	—
979	C₂×C₃	—	4	2	no	—
980	C₂×C₃	C₅×#546	1	4	yes	complemented
981	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
982	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
983	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
984	D₃	—	2	4	no	—
985	D₃	—	2	4	no	—
986	D₃	—	4	2	no	—
987	D₃	—	4	2	no	—
988	C₅	C₂×#5654	1	1	yes	characteristic, direct product factor, Sylow
989	C₂²	—	2	8	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	3	4	no	—
996	C₂²	—	3	4	no	—
997	C₂²	—	4	4	no	—
998	C₂²	—	6	8	no	—
999	C₂²	—	6	8	no	—
1000	C₂²	—	6	2	no	—
1001	C₂²	—	6	2	no	—
1002	C₂²	—	6	2	no	—
1003	C₂²	—	6	2	no	—
1004	C₂²	—	6	2	no	—
1005	C₂²	—	6	2	no	—
1006	C₂²	—	6	2	no	—
1007	C₂²	—	6	2	no	—
1008	C₂²	—	6	2	no	—
1009	C₂²	—	6	2	no	—
1010	C₂²	—	12	16	no	—
1011	C₂²	—	12	16	no	—
1012	C₂²	—	12	4	no	—
1013	C₂²	—	12	4	no	—
1014	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
1015	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
1016	C₂²	C₅×D₃×#41	1	2	yes	—
1017	C₂²	C₅×#1009	1	2	yes	—
1018	C₂²	C₂⁴×C₅×D₃	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	—	2	2	no	—
1024	C₄	—	3	4	no	—
1025	C₄	—	6	2	no	—
1026	C₄	—	6	2	no	—
1027	C₄	—	6	2	no	—
1028	C₃	C₂×C₅×#546	1	1	yes	characteristic, complemented, Sylow
1029	C₂	—	2	4	no	—
1030	C₂	—	4	2	no	—
1031	C₂	—	6	4	no	—
1032	C₂	—	6	4	no	—
1033	C₂	—	12	2	no	—
1034	C₂	—	12	2	no	—
1035	C₂	C₅×#5654	1	4	yes	direct product factor
1036	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
1037	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1038	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#123	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#123	D₃
hypocenter	C₃	C₂×C₅×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#123

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×D₄	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₂×C₃×C₅×#123	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₅×#5654	C₂	direct (N × H)
7. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#895	C₂	semidirect
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#893	C₂	semidirect
11. C₂×C₅×#885	C₂	semidirect
12. C₂×C₅×#884	C₂	semidirect
13. C₂×C₅×#882	C₂	semidirect
14. C₂×C₅×#882	C₂	semidirect
15. C₂×C₅×#67⋊C₄	C₂	semidirect
16. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
21. C₂³×C₃×C₄×C₅	C₂²	semidirect
24. C₂²×C₅×#67	C₂²	semidirect
25. C₂²×C₅×#67	C₂²	semidirect
26. C₂³×C₅×Dic₃	C₂²	semidirect
28. C₂×C₅×D₃×D₄	C₂²	semidirect
30. C₂×C₅×#235	C₂²	semidirect
33. C₂²×C₅×D₁₂	C₂²	semidirect
34. C₂²×C₅×D₁₂	C₂²	semidirect
36. C₂²×C₄×C₅×D₃	C₂²	semidirect
37. C₂²×C₄×C₅×D₃	C₂²	semidirect
38. C₂²×C₄×C₅×D₃	C₂²	semidirect
39. C₂²×C₅×Dic₆	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
42. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
43. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
44. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
45. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
46. C₂×C₅×#217	C₂²	semidirect
47. C₅×#939	C₂²	semidirect
51. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
52. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
53. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
54. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
55. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
56. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
57. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
58. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
59. C₂×C₄×C₅×Dic₃	C₂²	semidirect
60. C₅×#896	C₂²	semidirect
61. C₅×#895	C₂²	semidirect
62. C₅×#894	C₂²	semidirect
63. C₅×#893	C₂²	semidirect
64. C₅×#885	C₂²	semidirect
65. C₅×#884	C₂²	semidirect
66. C₅×#882	C₂²	semidirect
67. C₅×#882	C₂²	semidirect
68. C₅×#67⋊C₄	C₂²	semidirect
69. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
70. C₂×#5654	C₅	direct (N × H)
76. C₂×C₅×#123	D₃	semidirect
109. C₂²×C₃×C₄×C₅	C₂³	semidirect
113. C₂×C₅×#67	D₄	semidirect
116. C₂×C₅×#67	C₂³	semidirect
117. C₂×C₅×#67	C₂³	semidirect
123. C₂²×C₅×Dic₃	C₂³	semidirect
132. C₂×C₅×D₁₂	C₂³	semidirect
133. C₂×C₅×D₁₂	C₂³	semidirect
139. C₂×C₄×C₅×D₃	C₂³	semidirect
140. C₂×C₄×C₅×D₃	C₂³	semidirect
141. C₂×C₄×C₅×D₃	C₂³	semidirect
143. C₂×C₅×Dic₆	C₂³	semidirect
144. C₃×C₅×C₄⋊C₄	C₂³	semidirect
145. C₃×C₅×C₄⋊C₄	C₂³	semidirect
146. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
147. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
148. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
149. C₅×#217	C₂³	semidirect
153. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
154. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
155. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
156. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
157. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
158. C₅×Dic₃⋊C₄	C₂³	semidirect
159. C₅×Dic₃⋊C₄	C₂³	semidirect
160. C₄×C₅×Dic₃	C₂³	semidirect
161. C₂²×D₃×D₄	C₂×C₅	semidirect
162. C₂²×#235	C₂×C₅	semidirect
163. C₂×C₃×#123	C₂×C₅	semidirect
164. C₂×#939	C₂×C₅	semidirect
165. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
166. #5654	C₂×C₅	direct (N × H)
167. C₂×#896	C₂×C₅	semidirect
168. C₂×#895	C₂×C₅	semidirect
169. C₂×#894	C₂×C₅	semidirect
170. C₂×#893	C₂×C₅	semidirect
171. C₂×#885	C₂×C₅	semidirect
172. C₂×#884	C₂×C₅	semidirect
173. C₂×#882	C₂×C₅	semidirect
174. C₂×#882	C₂×C₅	semidirect
175. C₂×#67⋊C₄	C₂×C₅	semidirect
176. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
198. C₂³×C₄×C₅	C₂×D₃	semidirect
201. C₅×#123	C₂×D₃	semidirect
212. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
213. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
225. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
226. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
227. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
258. C₂²×C₅×D₃	#41	semidirect
278. C₅×#67	C₂×D₄	semidirect
300. C₂³×C₃×C₄	C₂²×C₅	semidirect
303. C₂²×#67	C₂²×C₅	semidirect
304. C₂²×#67	C₂²×C₅	semidirect
305. C₂³×Dic₃	C₂²×C₅	semidirect
307. C₂×D₃×D₄	C₂²×C₅	semidirect
309. C₂×#235	C₂²×C₅	semidirect
312. C₂²×D₁₂	C₂²×C₅	semidirect
313. C₂²×D₁₂	C₂²×C₅	semidirect
315. C₂²×C₄×D₃	C₂²×C₅	semidirect
316. C₂²×C₄×D₃	C₂²×C₅	semidirect
317. C₂²×C₄×D₃	C₂²×C₅	semidirect
318. C₂²×Dic₆	C₂²×C₅	semidirect
319. C₃×#123	C₂²×C₅	semidirect
320. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
321. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
322. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
323. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
324. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
325. C₂×#217	C₂²×C₅	semidirect
326. #939	C₂²×C₅	semidirect
330. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
331. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
332. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
333. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
334. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
335. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
336. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
337. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
338. C₂×C₄×Dic₃	C₂²×C₅	semidirect
339. #896	C₂²×C₅	semidirect
340. #895	C₂²×C₅	semidirect
341. #894	C₂²×C₅	semidirect
342. #893	C₂²×C₅	semidirect
343. #885	C₂²×C₅	semidirect
344. #884	C₂²×C₅	semidirect
345. #882	C₂²×C₅	semidirect
346. #882	C₂²×C₅	semidirect
347. #67⋊C₄	C₂²×C₅	semidirect
348. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
405. C₂²×C₄×C₅	C₂²×D₃	semidirect
408. C₅×C₄⋊C₄	C₂²×D₃	semidirect
409. C₅×C₄⋊C₄	C₂²×D₃	semidirect
419. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
420. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
421. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
428. C₂×#123	C₅×D₃	semidirect
468. C₂×C₅×D₃	C₂×#41	semidirect
500. C₂²×C₃×C₄	C₂³×C₅	semidirect
504. C₂×#67	C₅×D₄	semidirect
507. C₂×#67	C₂³×C₅	semidirect
508. C₂×#67	C₂³×C₅	semidirect
514. C₂²×Dic₃	C₂³×C₅	semidirect
523. C₂×D₁₂	C₂³×C₅	semidirect
524. C₂×D₁₂	C₂³×C₅	semidirect
530. C₂×C₄×D₃	C₂³×C₅	semidirect
531. C₂×C₄×D₃	C₂³×C₅	semidirect
532. C₂×C₄×D₃	C₂³×C₅	semidirect
534. C₂×Dic₆	C₂³×C₅	semidirect
535. C₃×C₄⋊C₄	C₂³×C₅	semidirect
536. C₃×C₄⋊C₄	C₂³×C₅	semidirect
537. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
538. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
539. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
540. #217	C₂³×C₅	semidirect
544. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
545. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
546. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
547. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
548. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
549. Dic₃⋊C₄	C₂³×C₅	semidirect
550. Dic₃⋊C₄	C₂³×C₅	semidirect
551. C₄×Dic₃	C₂³×C₅	semidirect
640. C₂³×C₄	C₂×C₅×D₃	semidirect
643. #123	C₂×C₅×D₃	semidirect
654. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
655. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
667. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
668. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
669. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
673. C₂×C₃×C₅	#546	semidirect
709. C₂²×D₃	C₅×#41	semidirect
729. #67	C₂×C₅×D₄	semidirect
843. C₂²×C₄	C₂²×C₅×D₃	semidirect
846. C₄⋊C₄	C₂²×C₅×D₃	semidirect
847. C₄⋊C₄	C₂²×C₅×D₃	semidirect
857. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
858. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
859. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
861. C₃×C₅	C₂×#546	semidirect
891. C₂×D₃	C₂×C₅×#41	semidirect
907. C₂×C₅	#5654	direct (N × H)
980. C₂×C₃	C₅×#546	semidirect
988. C₅	C₂×#5654	direct (N × H)
1028. C₃	C₂×C₅×#546	semidirect
1035. C₂	C₅×#5654	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×D₃×D₄	2
C₂²×C₅×#235	2
C₂×C₃×C₅×#123	2
C₂×C₅×#939	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₅×#5654	2
C₂×C₅×#896	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#885	2
C₂×C₅×#884	2
C₂×C₅×#882	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#546	3
C₂×#5654	5

Subgroups — C2×C5×#5654 #14482490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5654 #14482490