Subgroups — C₂×C₅×#5609 #14482409

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 808 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×D₃×D₄	C₂	1	2	yes	maximal, complemented
3	C₂³×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5609	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#882	C₂	1	2	yes	maximal, complemented
13	C₂×C₅×D₄²	—	3	1	no	maximal, Hall
14	C₂⁴×C₅×D₃	C₂²	1	2	yes	complemented
15	C₂⁴×C₅×D₃	C₂²	1	2	yes	complemented
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	C₂²	1	2	yes	complemented
21	C₂²×C₅×#67	C₂²	1	2	yes	complemented
22	C₂²×C₅×#67	C₂²	1	2	yes	complemented
23	C₂×C₅×D₃×D₄	—	2	16	no	—
24	C₂×C₅×D₃×D₄	—	2	8	no	—
25	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
26	C₂×C₅×D₃×D₄	C₂²	1	16	yes	complemented
27	C₂²×C₅×D₁₂	—	2	8	no	—
28	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₂²×C₅×D₁₂	C₂²	1	8	yes	complemented
30	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
31	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
33	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
34	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#121	C₂²	1	8	yes	complemented
36	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
38	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
39	C₅×#940	C₂²	1	8	yes	complemented
40	C₅×#937	C₂²	1	16	yes	complemented
41	C₄×C₅×#67	C₂²	1	8	yes	complemented
42	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₅×#895	C₂²	1	8	yes	complemented
48	C₅×#893	C₂²	1	8	yes	complemented
49	C₅×#884	C₂²	1	16	yes	complemented
50	C₅×#882	C₂²	1	16	yes	complemented
51	C₂×#5609	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₂³×C₅×D₄	—	3	2	no	—
53	C₂³×C₅×D₄	—	3	1	no	—
54	C₂³×C₅×D₄	—	3	1	no	—
55	C₅×D₄²	—	3	16	no	—
56	C₂×C₅×#127	—	3	1	no	—
57	C₂×C₅×#121	—	3	1	no	—
58	C₂×C₅×#121	—	3	2	no	—
59	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
60	C₂×C₅×#120	—	3	2	no	—
61	C₂×C₅×#120	—	3	2	no	—
62	C₂×C₄×C₅×D₄	—	3	1	no	—
63	C₂×C₄×C₅×D₄	—	3	1	no	—
64	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
65	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
66	C₂³×C₅×D₃	—	2	8	no	—
67	C₂³×C₅×D₃	—	2	8	no	—
68	C₂³×C₅×D₃	—	2	8	no	—
69	C₂³×C₅×D₃	—	2	8	no	—
70	C₂³×C₅×D₃	—	4	4	no	—
71	C₂³×C₅×D₃	—	4	4	no	—
72	C₂³×C₅×D₃	C₂³	1	2	yes	—
73	C₂³×C₅×D₃	C₂³	1	2	yes	—
74	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₂³×C₅×D₃	C₂³	1	8	yes	complemented
76	C₂³×C₅×D₃	C₂³	1	8	yes	complemented
77	C₂×C₃×C₅×D₄	—	2	8	no	—
78	C₂×C₃×C₅×D₄	—	2	4	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
80	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
81	C₂²×C₃×C₄×C₅	—	2	4	no	—
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
86	C₂×C₅×#67	—	2	8	no	—
87	C₂×C₅×#67	—	2	8	no	—
88	C₂×C₅×#67	—	4	4	no	—
89	C₂×C₅×#67	D₄	1	8	yes	complemented
90	C₂×C₅×#67	C₂³	1	4	yes	—
91	C₂×C₅×#67	C₂³	1	8	yes	complemented
92	C₂×C₅×#67	C₂³	1	8	yes	complemented
93	C₂×C₅×#67	C₂³	1	8	yes	complemented
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₅×D₃×D₄	—	2	64	no	—
98	C₅×D₃×D₄	—	2	32	no	—
99	C₂×C₅×D₁₂	—	2	8	no	—
100	C₂×C₅×D₁₂	—	2	8	no	—
101	C₂×C₅×D₁₂	—	2	4	no	—
102	C₂×C₅×D₁₂	—	2	32	no	—
103	C₂×C₅×D₁₂	D₄	1	8	yes	complemented
104	C₂×C₅×D₁₂	C₂³	1	4	yes	—
105	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
106	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
107	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
108	C₂×C₄×C₅×D₃	—	2	4	no	—
109	C₂×C₄×C₅×D₃	—	2	8	no	—
110	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
111	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
112	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
113	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
114	C₅×#217	C₂³	1	4	yes	complemented
115	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
116	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
117	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
118	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
119	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
120	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂²×D₃×D₄	C₂×C₅	1	2	yes	complemented
122	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂×#937	C₂×C₅	1	2	yes	complemented
126	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
127	#5609	C₂×C₅	1	16	yes	direct product factor
128	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂×#884	C₂×C₅	1	2	yes	complemented
131	C₂×#882	C₂×C₅	1	2	yes	complemented
132	C₂⁵×C₅	—	3	2	no	—
133	C₂⁵×C₅	—	3	2	no	—
134	C₂²×C₅×D₄	—	3	1	no	—
135	C₂²×C₅×D₄	—	3	2	no	—
136	C₂²×C₅×D₄	—	3	2	no	—
137	C₂²×C₅×D₄	—	3	2	no	—
138	C₂²×C₅×D₄	—	3	16	no	—
139	C₂²×C₅×D₄	—	3	8	no	—
140	C₂²×C₅×D₄	—	3	1	no	—
141	C₂²×C₅×D₄	—	3	2	no	—
142	C₂²×C₅×D₄	—	3	2	no	—
143	C₂²×C₅×D₄	—	3	1	no	—
144	C₂²×C₅×D₄	—	3	8	no	—
145	C₂²×C₅×D₄	—	6	8	no	—
146	C₂²×C₅×D₄	—	6	16	no	—
147	C₂²×C₅×D₄	—	6	8	no	—
148	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
149	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
150	C₂³×C₄×C₅	—	3	2	no	—
151	C₂³×C₄×C₅	—	3	1	no	—
152	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
153	C₅×#127	—	3	8	no	—
154	C₅×#121	—	3	8	no	—
155	C₅×#121	—	3	16	no	—
156	C₅×#121	C₂×D₃	1	8	yes	complemented
157	C₅×#120	—	3	16	no	—
158	C₅×#120	—	3	16	no	—
159	C₄×C₅×D₄	—	3	8	no	—
160	C₄×C₅×D₄	—	3	8	no	—
161	C₂×C₅×C₄⋊C₄	—	3	1	no	—
162	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
163	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
166	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
167	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
168	C₂×C₄²×C₅	—	3	1	no	—
169	C₂×D₄²	—	3	1	no	Sylow
170	C₂³×C₃×C₅	—	2	2	no	—
171	C₂³×C₃×C₅	—	2	2	no	—
172	C₂³×C₃×C₅	—	2	4	no	—
173	C₂³×C₃×C₅	—	2	4	no	—
174	C₂³×C₃×C₅	—	2	4	no	—
175	C₂³×C₃×C₅	C₂×D₄	1	4	yes	complemented
176	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
177	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
178	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₅×D₃	—	2	2	no	—
180	C₂²×C₅×D₃	—	2	4	no	—
181	C₂²×C₅×D₃	—	2	4	no	—
182	C₂²×C₅×D₃	—	2	2	no	—
183	C₂²×C₅×D₃	—	2	4	no	—
184	C₂²×C₅×D₃	—	2	4	no	—
185	C₂²×C₅×D₃	—	2	16	no	—
186	C₂²×C₅×D₃	—	2	4	no	—
187	C₂²×C₅×D₃	—	2	16	no	—
188	C₂²×C₅×D₃	—	2	16	no	—
189	C₂²×C₅×D₃	—	2	16	no	—
190	C₂²×C₅×D₃	—	4	8	no	—
191	C₂²×C₅×D₃	—	4	8	no	—
192	C₂²×C₅×D₃	—	4	32	no	—
193	C₂²×C₅×D₃	—	4	32	no	—
194	C₂²×C₅×D₃	C₂×D₄	1	4	yes	complemented
195	C₂²×C₅×D₃	C₂×D₄	1	8	yes	complemented
196	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
197	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
198	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
199	C₃×C₅×D₄	—	2	16	no	—
200	C₃×C₅×D₄	—	2	8	no	—
201	C₂×C₃×C₄×C₅	—	2	4	no	—
202	C₂×C₃×C₄×C₅	—	2	2	no	—
203	C₂×C₃×C₄×C₅	—	2	8	no	—
204	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
205	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
206	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
207	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
208	C₅×#67	—	2	16	no	—
209	C₅×#67	—	2	16	no	—
210	C₅×#67	—	4	8	no	—
211	C₅×#67	C₂×D₄	1	16	yes	complemented
212	C₂×C₅×Dic₃	—	2	2	no	—
213	C₂×C₅×Dic₃	—	2	2	no	—
214	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	complemented
215	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
216	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
217	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
218	C₅×D₁₂	—	2	16	no	—
219	C₅×D₁₂	—	2	16	no	—
220	C₅×D₁₂	—	2	8	no	—
221	C₅×D₁₂	C₂×D₄	1	16	yes	complemented
222	C₄×C₅×D₃	—	2	8	no	—
223	C₄×C₅×D₃	—	2	16	no	—
224	C₂⁴×D₃	C₂²×C₅	1	2	yes	complemented
225	C₂⁴×D₃	C₂²×C₅	1	2	yes	complemented
226	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
227	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
229	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
230	C₂²×#67	C₂²×C₅	1	2	yes	complemented
231	C₂²×#67	C₂²×C₅	1	2	yes	complemented
232	C₂²×#67	C₂²×C₅	1	2	yes	complemented
233	C₂×D₃×D₄	—	2	16	no	—
234	C₂×D₃×D₄	—	2	8	no	—
235	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
236	C₂×D₃×D₄	C₂²×C₅	1	16	yes	complemented
237	C₂²×D₁₂	—	2	8	no	—
238	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
239	C₂²×D₁₂	C₂²×C₅	1	8	yes	complemented
240	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
241	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
243	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
244	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₃×#121	C₂²×C₅	1	8	yes	complemented
246	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
248	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
249	#940	C₂²×C₅	1	8	yes	complemented
250	#937	C₂²×C₅	1	16	yes	complemented
251	C₄×#67	C₂²×C₅	1	8	yes	complemented
252	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
254	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
255	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
257	#895	C₂²×C₅	1	8	yes	complemented
258	#893	C₂²×C₅	1	8	yes	complemented
259	#884	C₂²×C₅	1	16	yes	complemented
260	#882	C₂²×C₅	1	16	yes	complemented
261	C₂⁴×C₅	—	3	1	no	—
262	C₂⁴×C₅	—	3	2	no	—
263	C₂⁴×C₅	—	3	2	no	—
264	C₂⁴×C₅	—	3	8	no	—
265	C₂⁴×C₅	—	3	8	no	—
266	C₂⁴×C₅	—	6	8	no	—
267	C₂⁴×C₅	—	6	8	no	—
268	C₂⁴×C₅	—	6	8	no	—
269	C₂⁴×C₅	—	6	8	no	—
270	C₂⁴×C₅	—	12	4	no	—
271	C₂⁴×C₅	—	12	4	no	—
272	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
273	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
274	C₂×C₅×D₄	—	2	8	no	—
275	C₂×C₅×D₄	—	2	4	no	—
276	C₂×C₅×D₄	—	3	8	no	—
277	C₂×C₅×D₄	—	3	4	no	—
278	C₂×C₅×D₄	—	3	8	no	—
279	C₂×C₅×D₄	—	3	8	no	—
280	C₂×C₅×D₄	—	3	8	no	—
281	C₂×C₅×D₄	—	3	8	no	—
282	C₂×C₅×D₄	—	3	4	no	—
283	C₂×C₅×D₄	—	3	8	no	—
284	C₂×C₅×D₄	—	3	8	no	—
285	C₂×C₅×D₄	—	3	4	no	—
286	C₂×C₅×D₄	—	6	32	no	—
287	C₂×C₅×D₄	—	6	8	no	—
288	C₂×C₅×D₄	—	6	8	no	—
289	C₂×C₅×D₄	—	6	8	no	—
290	C₂×C₅×D₄	—	6	64	no	—
291	C₂×C₅×D₄	—	6	32	no	—
292	C₂×C₅×D₄	—	6	8	no	—
293	C₂×C₅×D₄	—	6	4	no	—
294	C₂×C₅×D₄	—	12	4	no	—
295	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
296	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
297	C₂²×C₄×C₅	—	2	4	no	—
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	3	1	no	—
300	C₂²×C₄×C₅	—	3	1	no	—
301	C₂²×C₄×C₅	—	3	8	no	—
302	C₂²×C₄×C₅	—	3	4	no	—
303	C₂²×C₄×C₅	—	6	8	no	—
304	C₂²×C₄×C₅	—	6	4	no	—
305	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
306	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
309	C₅×C₄⋊C₄	—	3	4	no	—
310	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
311	C₅×C₂²⋊C₄	—	3	4	no	—
312	C₅×C₂²⋊C₄	—	3	8	no	—
313	C₅×C₂²⋊C₄	—	3	4	no	—
314	C₅×C₂²⋊C₄	—	3	8	no	—
315	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
316	C₄²×C₅	—	3	4	no	—
317	C₂³×D₄	—	3	2	no	—
318	C₂³×D₄	—	3	1	no	—
319	C₂³×D₄	—	3	1	no	—
320	D₄²	—	3	16	no	—
321	C₂×#127	—	3	1	no	—
322	C₂×#121	—	3	1	no	—
323	C₂×#121	—	3	2	no	—
324	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
325	C₂×#120	—	3	2	no	—
326	C₂×#120	—	3	2	no	—
327	C₂×C₄×D₄	—	3	1	no	—
328	C₂×C₄×D₄	—	3	1	no	—
329	C₂²×C₃×C₅	—	2	8	no	—
330	C₂²×C₃×C₅	—	2	2	no	—
331	C₂²×C₃×C₅	—	2	2	no	—
332	C₂²×C₃×C₅	—	2	4	no	—
333	C₂²×C₃×C₅	—	2	4	no	—
334	C₂²×C₃×C₅	—	2	4	no	—
335	C₂²×C₃×C₅	—	4	8	no	—
336	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
337	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
338	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	complemented
339	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
340	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
341	C₂×C₅×D₃	—	2	8	no	—
342	C₂×C₅×D₃	—	2	16	no	—
343	C₂×C₅×D₃	—	2	2	no	—
344	C₂×C₅×D₃	—	2	4	no	—
345	C₂×C₅×D₃	—	2	4	no	—
346	C₂×C₅×D₃	—	2	2	no	—
347	C₂×C₅×D₃	—	2	4	no	—
348	C₂×C₅×D₃	—	2	4	no	—
349	C₂×C₅×D₃	—	2	4	no	—
350	C₂×C₅×D₃	—	4	32	no	—
351	C₂×C₅×D₃	—	4	32	no	—
352	C₂×C₅×D₃	—	4	8	no	—
353	C₂×C₅×D₃	C₂²×D₄	1	4	yes	complemented
354	C₂×C₅×D₃	C₂²×D₄	1	8	yes	complemented
355	C₃×C₄×C₅	—	2	4	no	—
356	C₃×C₄×C₅	—	2	2	no	—
357	C₃×C₄×C₅	C₂²×D₄	1	4	yes	complemented
358	C₅×Dic₃	—	2	2	no	—
359	C₅×Dic₃	—	2	2	no	—
360	C₅×Dic₃	C₂²×D₄	1	4	yes	complemented
361	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
362	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
363	C₂³×D₃	—	2	8	no	—
364	C₂³×D₃	—	2	8	no	—
365	C₂³×D₃	—	2	8	no	—
366	C₂³×D₃	—	2	8	no	—
367	C₂³×D₃	—	4	4	no	—
368	C₂³×D₃	—	4	4	no	—
369	C₂³×D₃	C₂³×C₅	1	2	yes	—
370	C₂³×D₃	C₂³×C₅	1	2	yes	—
371	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
372	C₂³×D₃	C₂³×C₅	1	8	yes	complemented
373	C₂³×D₃	C₂³×C₅	1	8	yes	complemented
374	C₂×C₃×D₄	—	2	8	no	—
375	C₂×C₃×D₄	—	2	4	no	—
376	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
377	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
378	C₂²×C₃×C₄	—	2	4	no	—
379	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
381	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
383	C₂×#67	—	2	8	no	—
384	C₂×#67	—	2	8	no	—
385	C₂×#67	—	4	4	no	—
386	C₂×#67	C₅×D₄	1	8	yes	complemented
387	C₂×#67	C₂³×C₅	1	4	yes	—
388	C₂×#67	C₂³×C₅	1	8	yes	complemented
389	C₂×#67	C₂³×C₅	1	8	yes	complemented
390	C₂×#67	C₂³×C₅	1	8	yes	complemented
391	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
392	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
393	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
394	D₃×D₄	—	2	64	no	—
395	D₃×D₄	—	2	32	no	—
396	C₂×D₁₂	—	2	8	no	—
397	C₂×D₁₂	—	2	8	no	—
398	C₂×D₁₂	—	2	4	no	—
399	C₂×D₁₂	—	2	32	no	—
400	C₂×D₁₂	C₅×D₄	1	8	yes	complemented
401	C₂×D₁₂	C₂³×C₅	1	4	yes	—
402	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
403	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
404	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
405	C₂×C₄×D₃	—	2	4	no	—
406	C₂×C₄×D₃	—	2	8	no	—
407	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
408	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
409	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
410	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
411	#217	C₂³×C₅	1	4	yes	complemented
412	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
413	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
414	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
415	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
416	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
417	C₂³×C₅	—	2	2	no	—
418	C₂³×C₅	—	2	2	no	—
419	C₂³×C₅	—	2	4	no	—
420	C₂³×C₅	—	2	4	no	—
421	C₂³×C₅	—	2	4	no	—
422	C₂³×C₅	—	3	4	no	—
423	C₂³×C₅	—	3	8	no	—
424	C₂³×C₅	—	3	2	no	—
425	C₂³×C₅	—	3	4	no	—
426	C₂³×C₅	—	3	4	no	—
427	C₂³×C₅	—	6	16	no	—
428	C₂³×C₅	—	6	16	no	—
429	C₂³×C₅	—	6	16	no	—
430	C₂³×C₅	—	6	4	no	—
431	C₂³×C₅	—	6	2	no	—
432	C₂³×C₅	—	6	4	no	—
433	C₂³×C₅	—	6	2	no	—
434	C₂³×C₅	—	6	4	no	—
435	C₂³×C₅	—	6	4	no	—
436	C₂³×C₅	—	6	16	no	—
437	C₂³×C₅	—	6	4	no	—
438	C₂³×C₅	—	12	8	no	—
439	C₂³×C₅	—	12	8	no	—
440	C₂³×C₅	—	12	32	no	—
441	C₂³×C₅	—	12	32	no	—
442	C₂³×C₅	D₃×D₄	1	4	yes	complemented
443	C₂³×C₅	C₂³×D₃	1	4	yes	—
444	C₂³×C₅	C₂³×D₃	1	2	yes	—
445	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
446	C₅×D₄	—	2	16	no	—
447	C₅×D₄	—	2	8	no	—
448	C₅×D₄	—	3	16	no	—
449	C₅×D₄	—	3	16	no	—
450	C₅×D₄	—	6	16	no	—
451	C₅×D₄	—	6	16	no	—
452	C₅×D₄	—	6	16	no	—
453	C₅×D₄	—	6	16	no	—
454	C₅×D₄	—	6	8	no	—
455	C₅×D₄	—	12	8	no	—
456	C₂×C₄×C₅	—	2	2	no	—
457	C₂×C₄×C₅	—	2	4	no	—
458	C₂×C₄×C₅	—	2	8	no	—
459	C₂×C₄×C₅	—	3	4	no	—
460	C₂×C₄×C₅	—	3	2	no	—
461	C₂×C₄×C₅	—	3	2	no	—
462	C₂×C₄×C₅	—	3	2	no	—
463	C₂×C₄×C₅	—	6	16	no	—
464	C₂×C₄×C₅	—	6	2	no	—
465	C₂×C₄×C₅	—	6	2	no	—
466	C₂×C₄×C₅	—	6	8	no	—
467	C₂×C₄×C₅	D₃×D₄	1	4	yes	complemented
468	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
469	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
470	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
471	C₂⁵	—	3	2	no	—
472	C₂⁵	—	3	2	no	—
473	C₂²×D₄	—	3	1	no	—
474	C₂²×D₄	—	3	2	no	—
475	C₂²×D₄	—	3	2	no	—
476	C₂²×D₄	—	3	2	no	—
477	C₂²×D₄	—	3	16	no	—
478	C₂²×D₄	—	3	8	no	—
479	C₂²×D₄	—	3	1	no	—
480	C₂²×D₄	—	3	2	no	—
481	C₂²×D₄	—	3	2	no	—
482	C₂²×D₄	—	3	1	no	—
483	C₂²×D₄	—	3	8	no	—
484	C₂²×D₄	—	6	8	no	—
485	C₂²×D₄	—	6	16	no	—
486	C₂²×D₄	—	6	8	no	—
487	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
488	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
489	C₂³×C₄	—	3	2	no	—
490	C₂³×C₄	—	3	1	no	—
491	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
492	#127	—	3	8	no	—
493	#121	—	3	8	no	—
494	#121	—	3	16	no	—
495	#121	C₂×C₅×D₃	1	8	yes	complemented
496	#120	—	3	16	no	—
497	#120	—	3	16	no	—
498	C₄×D₄	—	3	8	no	—
499	C₄×D₄	—	3	8	no	—
500	C₂×C₄⋊C₄	—	3	1	no	—
501	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
502	C₂×C₂²⋊C₄	—	3	1	no	—
503	C₂×C₂²⋊C₄	—	3	2	no	—
504	C₂×C₂²⋊C₄	—	3	1	no	—
505	C₂×C₂²⋊C₄	—	3	2	no	—
506	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
507	C₂×C₄²	—	3	1	no	—
508	C₂×C₃×C₅	—	2	4	no	—
509	C₂×C₃×C₅	—	4	4	no	—
510	C₂×C₃×C₅	D₄²	1	4	yes	complemented
511	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
512	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
513	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₅×D₃	—	2	4	no	—
515	C₅×D₃	—	2	8	no	—
516	C₅×D₃	—	4	4	no	—
517	C₂³×C₃	—	2	2	no	—
518	C₂³×C₃	—	2	2	no	—
519	C₂³×C₃	—	2	4	no	—
520	C₂³×C₃	—	2	4	no	—
521	C₂³×C₃	—	2	4	no	—
522	C₂³×C₃	C₂×C₅×D₄	1	4	yes	complemented
523	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
524	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
525	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
526	C₂²×D₃	—	2	2	no	—
527	C₂²×D₃	—	2	4	no	—
528	C₂²×D₃	—	2	4	no	—
529	C₂²×D₃	—	2	2	no	—
530	C₂²×D₃	—	2	4	no	—
531	C₂²×D₃	—	2	4	no	—
532	C₂²×D₃	—	2	16	no	—
533	C₂²×D₃	—	2	4	no	—
534	C₂²×D₃	—	2	16	no	—
535	C₂²×D₃	—	2	16	no	—
536	C₂²×D₃	—	2	16	no	—
537	C₂²×D₃	—	4	8	no	—
538	C₂²×D₃	—	4	8	no	—
539	C₂²×D₃	—	4	32	no	—
540	C₂²×D₃	—	4	32	no	—
541	C₂²×D₃	C₂×C₅×D₄	1	4	yes	complemented
542	C₂²×D₃	C₂×C₅×D₄	1	8	yes	complemented
543	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
544	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
545	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
546	C₃×D₄	—	2	16	no	—
547	C₃×D₄	—	2	8	no	—
548	C₂×C₃×C₄	—	2	4	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	8	no	—
551	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
552	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
553	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
554	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
555	#67	—	2	16	no	—
556	#67	—	2	16	no	—
557	#67	—	4	8	no	—
558	#67	C₂×C₅×D₄	1	16	yes	complemented
559	C₂×Dic₃	—	2	2	no	—
560	C₂×Dic₃	—	2	2	no	—
561	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	complemented
562	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
563	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
564	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
565	D₁₂	—	2	16	no	—
566	D₁₂	—	2	16	no	—
567	D₁₂	—	2	8	no	—
568	D₁₂	C₂×C₅×D₄	1	16	yes	complemented
569	C₄×D₃	—	2	8	no	—
570	C₄×D₃	—	2	16	no	—
571	C₂²×C₅	—	2	2	no	—
572	C₂²×C₅	—	2	2	no	—
573	C₂²×C₅	—	2	8	no	—
574	C₂²×C₅	—	2	4	no	—
575	C₂²×C₅	—	2	4	no	—
576	C₂²×C₅	—	2	4	no	—
577	C₂²×C₅	—	3	4	no	—
578	C₂²×C₅	—	3	8	no	—
579	C₂²×C₅	—	4	8	no	—
580	C₂²×C₅	—	6	4	no	—
581	C₂²×C₅	—	6	2	no	—
582	C₂²×C₅	—	6	4	no	—
583	C₂²×C₅	—	6	2	no	—
584	C₂²×C₅	—	6	16	no	—
585	C₂²×C₅	—	6	8	no	—
586	C₂²×C₅	—	6	4	no	—
587	C₂²×C₅	—	6	4	no	—
588	C₂²×C₅	—	6	4	no	—
589	C₂²×C₅	—	12	32	no	—
590	C₂²×C₅	—	12	32	no	—
591	C₂²×C₅	—	12	8	no	—
592	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
593	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
594	C₂²×C₅	C₂×D₃×D₄	1	4	yes	complemented
595	C₂²×C₅	#1009	1	2	yes	—
596	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
597	C₄×C₅	—	2	2	no	—
598	C₄×C₅	—	2	4	no	—
599	C₄×C₅	—	3	4	no	—
600	C₄×C₅	—	6	2	no	—
601	C₄×C₅	—	6	2	no	—
602	C₄×C₅	C₂×D₃×D₄	1	4	yes	complemented
603	C₂⁴	—	3	1	no	—
604	C₂⁴	—	3	2	no	—
605	C₂⁴	—	3	2	no	—
606	C₂⁴	—	3	8	no	—
607	C₂⁴	—	3	8	no	—
608	C₂⁴	—	6	8	no	—
609	C₂⁴	—	6	8	no	—
610	C₂⁴	—	6	8	no	—
611	C₂⁴	—	6	8	no	—
612	C₂⁴	—	12	4	no	—
613	C₂⁴	—	12	4	no	—
614	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
615	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	3	8	no	—
619	C₂×D₄	—	3	4	no	—
620	C₂×D₄	—	3	8	no	—
621	C₂×D₄	—	3	8	no	—
622	C₂×D₄	—	3	8	no	—
623	C₂×D₄	—	3	8	no	—
624	C₂×D₄	—	3	4	no	—
625	C₂×D₄	—	3	8	no	—
626	C₂×D₄	—	3	8	no	—
627	C₂×D₄	—	3	4	no	—
628	C₂×D₄	—	6	32	no	—
629	C₂×D₄	—	6	8	no	—
630	C₂×D₄	—	6	8	no	—
631	C₂×D₄	—	6	8	no	—
632	C₂×D₄	—	6	64	no	—
633	C₂×D₄	—	6	32	no	—
634	C₂×D₄	—	6	8	no	—
635	C₂×D₄	—	6	4	no	—
636	C₂×D₄	—	12	4	no	—
637	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
638	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	3	8	no	—
644	C₂²×C₄	—	3	4	no	—
645	C₂²×C₄	—	6	8	no	—
646	C₂²×C₄	—	6	4	no	—
647	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
648	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
650	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
651	C₄⋊C₄	—	3	4	no	—
652	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
653	C₂²⋊C₄	—	3	4	no	—
654	C₂²⋊C₄	—	3	8	no	—
655	C₂²⋊C₄	—	3	4	no	—
656	C₂²⋊C₄	—	3	8	no	—
657	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
658	C₄²	—	3	4	no	—
659	C₃×C₅	C₂×D₄²	1	1	yes	characteristic, complemented, Hall
660	C₂²×C₃	—	2	8	no	—
661	C₂²×C₃	—	2	2	no	—
662	C₂²×C₃	—	2	2	no	—
663	C₂²×C₃	—	2	4	no	—
664	C₂²×C₃	—	2	4	no	—
665	C₂²×C₃	—	2	4	no	—
666	C₂²×C₃	—	4	8	no	—
667	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
668	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
669	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	complemented
670	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
671	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
672	C₂×D₃	—	2	8	no	—
673	C₂×D₃	—	2	16	no	—
674	C₂×D₃	—	2	2	no	—
675	C₂×D₃	—	2	4	no	—
676	C₂×D₃	—	2	4	no	—
677	C₂×D₃	—	2	2	no	—
678	C₂×D₃	—	2	4	no	—
679	C₂×D₃	—	2	4	no	—
680	C₂×D₃	—	2	4	no	—
681	C₂×D₃	—	4	32	no	—
682	C₂×D₃	—	4	32	no	—
683	C₂×D₃	—	4	8	no	—
684	C₂×D₃	C₂²×C₅×D₄	1	4	yes	complemented
685	C₂×D₃	C₂²×C₅×D₄	1	8	yes	complemented
686	C₃×C₄	—	2	4	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	C₂²×C₅×D₄	1	4	yes	complemented
689	Dic₃	—	2	2	no	—
690	Dic₃	—	2	2	no	—
691	Dic₃	C₂²×C₅×D₄	1	4	yes	complemented
692	C₂×C₅	—	2	4	no	—
693	C₂×C₅	—	4	4	no	—
694	C₂×C₅	—	6	8	no	—
695	C₂×C₅	—	6	4	no	—
696	C₂×C₅	—	12	4	no	—
697	C₂×C₅	#5609	1	4	yes	direct product factor
698	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
699	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
700	C₂×C₅	C₂×#1009	1	1	yes	characteristic
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	3	4	no	—
707	C₂³	—	3	8	no	—
708	C₂³	—	3	2	no	—
709	C₂³	—	3	4	no	—
710	C₂³	—	3	4	no	—
711	C₂³	—	6	16	no	—
712	C₂³	—	6	16	no	—
713	C₂³	—	6	16	no	—
714	C₂³	—	6	4	no	—
715	C₂³	—	6	2	no	—
716	C₂³	—	6	4	no	—
717	C₂³	—	6	2	no	—
718	C₂³	—	6	4	no	—
719	C₂³	—	6	4	no	—
720	C₂³	—	6	16	no	—
721	C₂³	—	6	4	no	—
722	C₂³	—	12	8	no	—
723	C₂³	—	12	8	no	—
724	C₂³	—	12	32	no	—
725	C₂³	—	12	32	no	—
726	C₂³	C₅×D₃×D₄	1	4	yes	complemented
727	C₂³	C₂³×C₅×D₃	1	4	yes	—
728	C₂³	C₂³×C₅×D₃	1	2	yes	—
729	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
730	D₄	—	2	16	no	—
731	D₄	—	2	8	no	—
732	D₄	—	3	16	no	—
733	D₄	—	3	16	no	—
734	D₄	—	6	16	no	—
735	D₄	—	6	16	no	—
736	D₄	—	6	16	no	—
737	D₄	—	6	16	no	—
738	D₄	—	6	8	no	—
739	D₄	—	12	8	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	3	4	no	—
744	C₂×C₄	—	3	2	no	—
745	C₂×C₄	—	3	2	no	—
746	C₂×C₄	—	3	2	no	—
747	C₂×C₄	—	6	16	no	—
748	C₂×C₄	—	6	2	no	—
749	C₂×C₄	—	6	2	no	—
750	C₂×C₄	—	6	8	no	—
751	C₂×C₄	C₅×D₃×D₄	1	4	yes	complemented
752	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
753	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
754	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
755	C₂×C₃	—	2	4	no	—
756	C₂×C₃	—	4	4	no	—
757	C₂×C₃	C₅×D₄²	1	4	yes	complemented
758	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
759	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
760	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
761	D₃	—	2	4	no	—
762	D₃	—	2	8	no	—
763	D₃	—	4	4	no	—
764	C₅	C₂×#5609	1	1	yes	characteristic, direct product factor, Sylow
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	8	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	3	4	no	—
772	C₂²	—	3	8	no	—
773	C₂²	—	4	8	no	—
774	C₂²	—	6	4	no	—
775	C₂²	—	6	2	no	—
776	C₂²	—	6	4	no	—
777	C₂²	—	6	2	no	—
778	C₂²	—	6	16	no	—
779	C₂²	—	6	8	no	—
780	C₂²	—	6	4	no	—
781	C₂²	—	6	4	no	—
782	C₂²	—	6	4	no	—
783	C₂²	—	12	32	no	—
784	C₂²	—	12	32	no	—
785	C₂²	—	12	8	no	—
786	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
787	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
788	C₂²	C₂×C₅×D₃×D₄	1	4	yes	complemented
789	C₂²	C₅×#1009	1	2	yes	—
790	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
791	C₄	—	2	2	no	—
792	C₄	—	2	4	no	—
793	C₄	—	3	4	no	—
794	C₄	—	6	2	no	—
795	C₄	—	6	2	no	—
796	C₄	C₂×C₅×D₃×D₄	1	4	yes	complemented
797	C₃	C₂×C₅×D₄²	1	1	yes	characteristic, complemented, Sylow
798	C₂	—	2	4	no	—
799	C₂	—	4	4	no	—
800	C₂	—	6	8	no	—
801	C₂	—	6	4	no	—
802	C₂	—	12	4	no	—
803	C₂	C₅×#5609	1	4	yes	direct product factor
804	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
805	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
806	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×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#121

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×D₃×D₄	C₂	semidirect
3. C₂³×C₅×D₁₂	C₂	semidirect
4. C₂×C₃×C₅×#121	C₂	semidirect
5. C₂×C₅×#940	C₂	semidirect
6. C₂×C₅×#937	C₂	semidirect
7. C₂×C₄×C₅×#67	C₂	semidirect
8. C₅×#5609	C₂	direct (N × H)
9. C₂×C₅×#895	C₂	semidirect
10. C₂×C₅×#893	C₂	semidirect
11. C₂×C₅×#884	C₂	semidirect
12. C₂×C₅×#882	C₂	semidirect
14. C₂⁴×C₅×D₃	C₂²	semidirect
15. C₂⁴×C₅×D₃	C₂²	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂³×C₃×C₄×C₅	C₂²	semidirect
20. C₂²×C₅×#67	C₂²	semidirect
21. C₂²×C₅×#67	C₂²	semidirect
22. C₂²×C₅×#67	C₂²	semidirect
25. C₂×C₅×D₃×D₄	C₂²	semidirect
26. C₂×C₅×D₃×D₄	C₂²	semidirect
29. C₂²×C₅×D₁₂	C₂²	semidirect
30. C₂²×C₅×D₁₂	C₂²	semidirect
31. C₂²×C₅×D₁₂	C₂²	semidirect
32. C₂²×C₅×D₁₂	C₂²	semidirect
33. C₂²×C₄×C₅×D₃	C₂²	semidirect
34. C₂²×C₄×C₅×D₃	C₂²	semidirect
35. C₃×C₅×#121	C₂²	semidirect
36. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
37. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₅×#217	C₂²	semidirect
39. C₅×#940	C₂²	semidirect
40. C₅×#937	C₂²	semidirect
41. C₄×C₅×#67	C₂²	semidirect
42. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
43. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
46. C₂×C₄×C₅×Dic₃	C₂²	semidirect
47. C₅×#895	C₂²	semidirect
48. C₅×#893	C₂²	semidirect
49. C₅×#884	C₂²	semidirect
50. C₅×#882	C₂²	semidirect
51. C₂×#5609	C₅	direct (N × H)
59. C₂×C₅×#121	D₃	semidirect
75. C₂³×C₅×D₃	C₂³	semidirect
76. C₂³×C₅×D₃	C₂³	semidirect
79. C₂×C₃×C₅×D₄	C₂³	semidirect
80. C₂×C₃×C₅×D₄	C₂³	semidirect
85. C₂²×C₃×C₄×C₅	C₂³	semidirect
89. C₂×C₅×#67	D₄	semidirect
91. C₂×C₅×#67	C₂³	semidirect
92. C₂×C₅×#67	C₂³	semidirect
93. C₂×C₅×#67	C₂³	semidirect
103. C₂×C₅×D₁₂	D₄	semidirect
105. C₂×C₅×D₁₂	C₂³	semidirect
106. C₂×C₅×D₁₂	C₂³	semidirect
107. C₂×C₅×D₁₂	C₂³	semidirect
110. C₂×C₄×C₅×D₃	C₂³	semidirect
111. C₂×C₄×C₅×D₃	C₂³	semidirect
112. C₃×C₅×C₄⋊C₄	C₂³	semidirect
113. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
114. C₅×#217	C₂³	semidirect
115. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
116. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
117. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
118. C₅×Dic₃⋊C₄	C₂³	semidirect
119. C₄×C₅×Dic₃	C₂³	semidirect
120. C₂²×D₃×D₄	C₂×C₅	semidirect
121. C₂²×D₃×D₄	C₂×C₅	semidirect
122. C₂³×D₁₂	C₂×C₅	semidirect
123. C₂×C₃×#121	C₂×C₅	semidirect
124. C₂×#940	C₂×C₅	semidirect
125. C₂×#937	C₂×C₅	semidirect
126. C₂×C₄×#67	C₂×C₅	semidirect
127. #5609	C₂×C₅	direct (N × H)
128. C₂×#895	C₂×C₅	semidirect
129. C₂×#893	C₂×C₅	semidirect
130. C₂×#884	C₂×C₅	semidirect
131. C₂×#882	C₂×C₅	semidirect
148. C₂²×C₅×D₄	C₂×D₃	semidirect
149. C₂²×C₅×D₄	C₂×D₃	semidirect
152. C₂³×C₄×C₅	C₂×D₃	semidirect
156. C₅×#121	C₂×D₃	semidirect
162. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
167. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
175. C₂³×C₃×C₅	C₂×D₄	semidirect
194. C₂²×C₅×D₃	C₂×D₄	semidirect
195. C₂²×C₅×D₃	C₂×D₄	semidirect
204. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
211. C₅×#67	C₂×D₄	semidirect
214. C₂×C₅×Dic₃	C₂×D₄	semidirect
221. C₅×D₁₂	C₂×D₄	semidirect
224. C₂⁴×D₃	C₂²×C₅	semidirect
225. C₂⁴×D₃	C₂²×C₅	semidirect
226. C₂²×C₃×D₄	C₂²×C₅	semidirect
227. C₂²×C₃×D₄	C₂²×C₅	semidirect
228. C₂³×C₃×C₄	C₂²×C₅	semidirect
230. C₂²×#67	C₂²×C₅	semidirect
231. C₂²×#67	C₂²×C₅	semidirect
232. C₂²×#67	C₂²×C₅	semidirect
235. C₂×D₃×D₄	C₂²×C₅	semidirect
236. C₂×D₃×D₄	C₂²×C₅	semidirect
239. C₂²×D₁₂	C₂²×C₅	semidirect
240. C₂²×D₁₂	C₂²×C₅	semidirect
241. C₂²×D₁₂	C₂²×C₅	semidirect
242. C₂²×D₁₂	C₂²×C₅	semidirect
243. C₂²×C₄×D₃	C₂²×C₅	semidirect
244. C₂²×C₄×D₃	C₂²×C₅	semidirect
245. C₃×#121	C₂²×C₅	semidirect
246. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
247. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
248. C₂×#217	C₂²×C₅	semidirect
249. #940	C₂²×C₅	semidirect
250. #937	C₂²×C₅	semidirect
251. C₄×#67	C₂²×C₅	semidirect
252. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
253. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
254. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
255. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
256. C₂×C₄×Dic₃	C₂²×C₅	semidirect
257. #895	C₂²×C₅	semidirect
258. #893	C₂²×C₅	semidirect
259. #884	C₂²×C₅	semidirect
260. #882	C₂²×C₅	semidirect
295. C₂×C₅×D₄	C₂²×D₃	semidirect
296. C₂×C₅×D₄	C₂²×D₃	semidirect
308. C₂²×C₄×C₅	C₂²×D₃	semidirect
310. C₅×C₄⋊C₄	C₂²×D₃	semidirect
315. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
324. C₂×#121	C₅×D₃	semidirect
338. C₂²×C₃×C₅	C₂²×D₄	semidirect
353. C₂×C₅×D₃	C₂²×D₄	semidirect
354. C₂×C₅×D₃	C₂²×D₄	semidirect
357. C₃×C₄×C₅	C₂²×D₄	semidirect
360. C₅×Dic₃	C₂²×D₄	semidirect
372. C₂³×D₃	C₂³×C₅	semidirect
373. C₂³×D₃	C₂³×C₅	semidirect
376. C₂×C₃×D₄	C₂³×C₅	semidirect
377. C₂×C₃×D₄	C₂³×C₅	semidirect
382. C₂²×C₃×C₄	C₂³×C₅	semidirect
386. C₂×#67	C₅×D₄	semidirect
388. C₂×#67	C₂³×C₅	semidirect
389. C₂×#67	C₂³×C₅	semidirect
390. C₂×#67	C₂³×C₅	semidirect
400. C₂×D₁₂	C₅×D₄	semidirect
402. C₂×D₁₂	C₂³×C₅	semidirect
403. C₂×D₁₂	C₂³×C₅	semidirect
404. C₂×D₁₂	C₂³×C₅	semidirect
407. C₂×C₄×D₃	C₂³×C₅	semidirect
408. C₂×C₄×D₃	C₂³×C₅	semidirect
409. C₃×C₄⋊C₄	C₂³×C₅	semidirect
410. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
411. #217	C₂³×C₅	semidirect
412. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
413. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
414. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
415. Dic₃⋊C₄	C₂³×C₅	semidirect
416. C₄×Dic₃	C₂³×C₅	semidirect
442. C₂³×C₅	D₃×D₄	semidirect
467. C₂×C₄×C₅	D₃×D₄	semidirect
487. C₂²×D₄	C₂×C₅×D₃	semidirect
488. C₂²×D₄	C₂×C₅×D₃	semidirect
491. C₂³×C₄	C₂×C₅×D₃	semidirect
495. #121	C₂×C₅×D₃	semidirect
501. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
506. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
510. C₂×C₃×C₅	D₄²	semidirect
522. C₂³×C₃	C₂×C₅×D₄	semidirect
541. C₂²×D₃	C₂×C₅×D₄	semidirect
542. C₂²×D₃	C₂×C₅×D₄	semidirect
551. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
558. #67	C₂×C₅×D₄	semidirect
561. C₂×Dic₃	C₂×C₅×D₄	semidirect
568. D₁₂	C₂×C₅×D₄	semidirect
594. C₂²×C₅	C₂×D₃×D₄	semidirect
602. C₄×C₅	C₂×D₃×D₄	semidirect
637. C₂×D₄	C₂²×C₅×D₃	semidirect
638. C₂×D₄	C₂²×C₅×D₃	semidirect
650. C₂²×C₄	C₂²×C₅×D₃	semidirect
652. C₄⋊C₄	C₂²×C₅×D₃	semidirect
657. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
659. C₃×C₅	C₂×D₄²	semidirect
669. C₂²×C₃	C₂²×C₅×D₄	semidirect
684. C₂×D₃	C₂²×C₅×D₄	semidirect
685. C₂×D₃	C₂²×C₅×D₄	semidirect
688. C₃×C₄	C₂²×C₅×D₄	semidirect
691. Dic₃	C₂²×C₅×D₄	semidirect
697. C₂×C₅	#5609	direct (N × H)
726. C₂³	C₅×D₃×D₄	semidirect
751. C₂×C₄	C₅×D₃×D₄	semidirect
757. C₂×C₃	C₅×D₄²	semidirect
764. C₅	C₂×#5609	direct (N × H)
788. C₂²	C₂×C₅×D₃×D₄	semidirect
796. C₄	C₂×C₅×D₃×D₄	semidirect
797. C₃	C₂×C₅×D₄²	semidirect
803. C₂	C₅×#5609	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
C₂³×C₅×D₁₂	2
C₂×C₃×C₅×#121	2
C₂×C₅×#940	2
C₂×C₅×#937	2
C₂×C₄×C₅×#67	2
C₅×#5609	2
C₂×C₅×#895	2
C₂×C₅×#893	2
C₂×C₅×#884	2
C₂×C₅×#882	2
C₂×C₅×D₄²	3
C₂×#5609	5

Subgroups — C2×C5×#5609 #14482409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5609 #14482409