Subgroups — C₅×D₄×(C₂×D₃)⋊C₄ #14325895

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 792 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
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₅×#5213	C₂	1	2	yes	maximal, complemented
6	C₅×#4988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4958	C₂	1	2	yes	maximal, complemented
9	C₅×#4955	C₂	1	2	yes	maximal, complemented
10	C₅×#4939	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₄×C₂²⋊C₄	—	3	1	no	maximal, Hall
13	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₅×D₃×D₄	—	2	4	no	—
19	C₂×C₅×D₃×D₄	—	2	4	no	—
20	C₂×C₅×D₃×D₄	C₄	1	8	yes	complemented
21	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×D₄	—	2	4	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#217	C₂²	1	2	yes	complemented
28	C₅×D₄×Dic₃	—	2	4	no	—
29	C₂×C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
40	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
41	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
42	D₄×(C₂×D₃)⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂³×C₅×D₄	—	3	1	no	—
44	C₂×C₄×C₅×D₄	—	3	1	no	—
45	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
46	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
47	C₅×#390	—	3	1	no	—
48	C₅×#390	—	3	1	no	—
49	C₅×#386	—	3	2	no	—
50	C₅×#386	—	3	2	no	—
51	C₅×#380	—	3	1	no	—
52	C₅×#379	—	3	2	no	—
53	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
54	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
55	C₂³×C₅×D₃	—	2	4	no	—
56	C₂³×C₅×D₃	—	2	4	no	—
57	C₂³×C₅×D₃	—	2	4	no	—
58	C₂³×C₅×D₃	—	2	4	no	—
59	C₂³×C₅×D₃	—	4	2	no	—
60	C₂³×C₅×D₃	—	4	2	no	—
61	C₂³×C₅×D₃	C₂×C₄	1	8	yes	complemented
62	C₂³×C₅×D₃	C₂³	1	2	yes	—
63	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
65	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
66	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
67	C₂²×C₃×C₄×C₅	—	2	4	no	—
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	—	4	2	no	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₅×#67	—	2	4	no	—
75	C₂×C₅×#67	—	2	4	no	—
76	C₂×C₅×#67	C₂×C₄	1	8	yes	complemented
77	C₂²×C₅×Dic₃	—	2	4	no	—
78	C₂²×C₅×Dic₃	—	2	4	no	—
79	C₂²×C₅×Dic₃	—	4	2	no	—
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
82	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₅×D₃×D₄	—	2	32	no	—
85	C₂×C₅×D₁₂	—	2	2	no	—
86	C₂×C₅×D₁₂	—	2	2	no	—
87	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
88	C₂×C₄×C₅×D₃	—	2	2	no	—
89	C₂×C₄×C₅×D₃	—	2	2	no	—
90	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
91	C₃×C₅×C₄⋊C₄	—	2	2	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
93	C₃×C₄²×C₅	—	2	2	no	—
94	C₅×#217	—	2	4	no	—
95	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
96	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
97	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
98	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
99	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
100	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
101	C₅×(C₂×D₃)⋊C₄	D₄	1	4	yes	direct product factor
102	C₅×C₄⋊Dic₃	—	2	2	no	—
103	C₄×C₅×Dic₃	—	2	2	no	—
104	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
108	#5213	C₂×C₅	1	2	yes	complemented
109	#4988	C₂×C₅	1	1	yes	characteristic, complemented
110	#4987	C₂×C₅	1	1	yes	characteristic, complemented
111	#4958	C₂×C₅	1	2	yes	complemented
112	#4955	C₂×C₅	1	2	yes	complemented
113	#4939	C₂×C₅	1	1	yes	characteristic, complemented
114	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂⁵×C₅	—	3	2	no	—
116	C₂²×C₅×D₄	—	3	2	no	—
117	C₂²×C₅×D₄	—	3	8	no	—
118	C₂²×C₅×D₄	—	3	1	no	—
119	C₂²×C₅×D₄	—	6	4	no	—
120	C₂²×C₅×D₄	—	6	4	no	—
121	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
122	C₂³×C₄×C₅	—	3	1	no	—
123	C₂³×C₄×C₅	—	3	2	no	—
124	C₂³×C₄×C₅	C₂×D₃	1	2	yes	complemented
125	C₄×C₅×D₄	—	2	4	no	—
126	C₄×C₅×D₄	—	6	4	no	—
127	C₂×C₅×C₄⋊C₄	—	3	1	no	—
128	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
129	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
130	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
131	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
132	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
133	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
134	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
135	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
136	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
137	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
138	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
139	C₂×C₄²×C₅	—	3	1	no	—
140	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
141	C₅×#95	—	3	1	no	—
142	C₅×#95	—	3	1	no	—
143	C₅×#95	—	3	2	no	—
144	D₄×C₂²⋊C₄	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	2	2	no	—
149	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
150	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
151	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
152	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
153	C₂²×C₅×D₃	—	2	1	no	—
154	C₂²×C₅×D₃	—	2	1	no	—
155	C₂²×C₅×D₃	—	2	1	no	—
156	C₂²×C₅×D₃	—	2	1	no	—
157	C₂²×C₅×D₃	—	2	16	no	—
158	C₂²×C₅×D₃	—	2	2	no	—
159	C₂²×C₅×D₃	—	2	2	no	—
160	C₂²×C₅×D₃	—	2	2	no	—
161	C₂²×C₅×D₃	—	2	2	no	—
162	C₂²×C₅×D₃	—	2	2	no	—
163	C₂²×C₅×D₃	—	2	2	no	—
164	C₂²×C₅×D₃	—	2	16	no	—
165	C₂²×C₅×D₃	—	4	8	no	—
166	C₂²×C₅×D₃	—	4	8	no	—
167	C₂²×C₅×D₃	—	4	8	no	—
168	C₂²×C₅×D₃	—	4	8	no	—
169	C₂²×C₅×D₃	—	4	8	no	—
170	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
171	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
172	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
173	C₂²×C₅×D₃	#41	1	2	yes	—
174	C₃×C₅×D₄	C₂²⋊C₄	1	16	yes	complemented
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	2	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	2	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	2	no	—
183	C₂×C₃×C₄×C₅	—	4	8	no	—
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
185	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
186	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
187	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	complemented
188	C₅×#67	—	2	16	no	—
189	C₂×C₅×Dic₃	—	2	1	no	—
190	C₂×C₅×Dic₃	—	2	1	no	—
191	C₂×C₅×Dic₃	—	2	1	no	—
192	C₂×C₅×Dic₃	—	2	1	no	—
193	C₂×C₅×Dic₃	—	2	1	no	—
194	C₂×C₅×Dic₃	—	2	2	no	—
195	C₂×C₅×Dic₃	—	2	2	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	—	2	1	no	—
198	C₂×C₅×Dic₃	—	2	2	no	—
199	C₂×C₅×Dic₃	—	4	8	no	—
200	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
201	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	complemented
202	C₅×D₁₂	—	2	8	no	—
203	C₄×C₅×D₃	—	2	8	no	—
204	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
205	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
206	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
207	C₂²×#67	C₂²×C₅	1	2	yes	—
208	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
209	C₂×D₃×D₄	—	2	4	no	—
210	C₂×D₃×D₄	—	2	4	no	—
211	C₂×D₃×D₄	C₄×C₅	1	8	yes	complemented
212	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
213	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
214	C₃×C₄×D₄	—	2	4	no	—
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
217	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
218	C₂×#217	C₂²×C₅	1	2	yes	complemented
219	D₄×Dic₃	—	2	4	no	—
220	C₂×(C₂×D₃)⋊C₄	—	2	8	no	—
221	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
223	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
225	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
226	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
227	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
228	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
229	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
230	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
231	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
232	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
233	C₂⁴×C₅	—	3	1	no	—
234	C₂⁴×C₅	—	3	2	no	—
235	C₂⁴×C₅	—	3	8	no	—
236	C₂⁴×C₅	—	6	4	no	—
237	C₂⁴×C₅	—	6	4	no	—
238	C₂⁴×C₅	—	6	4	no	—
239	C₂⁴×C₅	—	6	4	no	—
240	C₂⁴×C₅	—	12	2	no	—
241	C₂⁴×C₅	—	12	2	no	—
242	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
243	C₂×C₅×D₄	—	3	8	no	—
244	C₂×C₅×D₄	—	3	4	no	—
245	C₂×C₅×D₄	—	6	4	no	—
246	C₂×C₅×D₄	—	6	4	no	—
247	C₂×C₅×D₄	—	6	32	no	—
248	C₂×C₅×D₄	—	6	2	no	—
249	C₂×C₅×D₄	—	6	2	no	—
250	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
251	C₂×C₅×D₄	D₁₂	1	4	yes	—
252	C₂×C₅×D₄	#67	1	4	yes	—
253	C₂²×C₄×C₅	—	2	4	no	—
254	C₂²×C₄×C₅	—	2	4	no	—
255	C₂²×C₄×C₅	—	3	1	no	—
256	C₂²×C₄×C₅	—	3	1	no	—
257	C₂²×C₄×C₅	—	3	4	no	—
258	C₂²×C₄×C₅	—	3	1	no	—
259	C₂²×C₄×C₅	—	3	2	no	—
260	C₂²×C₄×C₅	—	4	2	no	—
261	C₂²×C₄×C₅	—	6	4	no	—
262	C₂²×C₄×C₅	—	6	2	no	—
263	C₂²×C₄×C₅	—	6	2	no	—
264	C₂²×C₄×C₅	—	6	4	no	—
265	C₂²×C₄×C₅	—	12	2	no	—
266	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
267	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
268	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₅×C₄⋊C₄	—	2	2	no	—
271	C₅×C₄⋊C₄	—	6	2	no	—
272	C₅×C₂²⋊C₄	—	2	4	no	—
273	C₅×C₂²⋊C₄	—	3	4	no	—
274	C₅×C₂²⋊C₄	—	6	4	no	—
275	C₅×C₂²⋊C₄	—	6	4	no	—
276	C₅×C₂²⋊C₄	—	6	2	no	—
277	C₅×C₂²⋊C₄	—	6	4	no	—
278	C₅×C₂²⋊C₄	—	6	4	no	—
279	C₅×C₂²⋊C₄	—	12	2	no	—
280	C₅×C₂²⋊C₄	—	12	2	no	—
281	C₄²×C₅	—	2	2	no	—
282	C₄²×C₅	—	6	2	no	—
283	C₂³×D₄	—	3	1	no	—
284	C₂×C₄×D₄	—	3	1	no	—
285	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
286	C₂²×C₂²⋊C₄	—	3	2	no	—
287	#390	—	3	1	no	—
288	#390	—	3	1	no	—
289	#386	—	3	2	no	—
290	#386	—	3	2	no	—
291	#380	—	3	1	no	—
292	#379	—	3	2	no	—
293	C₄×C₂²⋊C₄	—	3	1	no	—
294	C₂²×C₃×C₅	—	2	4	no	—
295	C₂²×C₃×C₅	—	2	4	no	—
296	C₂²×C₃×C₅	—	2	4	no	—
297	C₂²×C₃×C₅	—	2	4	no	—
298	C₂²×C₃×C₅	—	2	4	no	—
299	C₂²×C₃×C₅	—	2	4	no	—
300	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
301	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
302	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
303	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
304	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
306	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₅×D₃	—	2	2	no	—
309	C₂×C₅×D₃	—	2	2	no	—
310	C₂×C₅×D₃	—	2	2	no	—
311	C₂×C₅×D₃	—	2	2	no	—
312	C₂×C₅×D₃	—	2	2	no	—
313	C₂×C₅×D₃	—	2	2	no	—
314	C₂×C₅×D₃	—	2	4	no	—
315	C₂×C₅×D₃	—	2	4	no	—
316	C₂×C₅×D₃	—	2	4	no	—
317	C₂×C₅×D₃	—	4	32	no	—
318	C₂×C₅×D₃	—	4	2	no	—
319	C₂×C₅×D₃	—	4	2	no	—
320	C₂×C₅×D₃	—	4	2	no	—
321	C₂×C₅×D₃	—	4	2	no	—
322	C₂×C₅×D₃	C₄×D₄	1	4	yes	complemented
323	C₃×C₄×C₅	—	2	2	no	—
324	C₃×C₄×C₅	—	4	2	no	—
325	C₃×C₄×C₅	—	4	1	no	—
326	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	complemented
327	C₅×Dic₃	—	2	2	no	—
328	C₅×Dic₃	—	2	2	no	—
329	C₅×Dic₃	—	4	2	no	—
330	C₅×Dic₃	—	4	1	no	—
331	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
332	C₂³×D₃	—	2	4	no	—
333	C₂³×D₃	—	2	4	no	—
334	C₂³×D₃	—	2	4	no	—
335	C₂³×D₃	—	2	4	no	—
336	C₂³×D₃	—	4	2	no	—
337	C₂³×D₃	—	4	2	no	—
338	C₂³×D₃	C₂×C₄×C₅	1	8	yes	complemented
339	C₂³×D₃	C₂³×C₅	1	2	yes	—
340	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
342	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
343	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
344	C₂²×C₃×C₄	—	2	4	no	—
345	C₂²×C₃×C₄	—	2	4	no	—
346	C₂²×C₃×C₄	—	4	2	no	—
347	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
349	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂×#67	—	2	4	no	—
352	C₂×#67	—	2	4	no	—
353	C₂×#67	C₂×C₄×C₅	1	8	yes	complemented
354	C₂²×Dic₃	—	2	4	no	—
355	C₂²×Dic₃	—	2	4	no	—
356	C₂²×Dic₃	—	4	2	no	—
357	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
358	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
359	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
360	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
361	D₃×D₄	—	2	32	no	—
362	C₂×D₁₂	—	2	2	no	—
363	C₂×D₁₂	—	2	2	no	—
364	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
365	C₂×C₄×D₃	—	2	2	no	—
366	C₂×C₄×D₃	—	2	2	no	—
367	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
368	C₃×C₄⋊C₄	—	2	2	no	—
369	C₃×C₂²⋊C₄	—	2	4	no	—
370	C₃×C₄²	—	2	2	no	—
371	#217	—	2	4	no	—
372	(C₂×D₃)⋊C₄	—	2	4	no	—
373	(C₂×D₃)⋊C₄	—	2	2	no	—
374	(C₂×D₃)⋊C₄	—	2	4	no	—
375	(C₂×D₃)⋊C₄	—	2	4	no	—
376	(C₂×D₃)⋊C₄	—	4	2	no	—
377	(C₂×D₃)⋊C₄	—	4	2	no	—
378	(C₂×D₃)⋊C₄	C₅×D₄	1	4	yes	direct product factor
379	C₄⋊Dic₃	—	2	2	no	—
380	C₄×Dic₃	—	2	2	no	—
381	C₂³×C₅	—	2	2	no	—
382	C₂³×C₅	—	2	2	no	—
383	C₂³×C₅	—	2	2	no	—
384	C₂³×C₅	—	2	2	no	—
385	C₂³×C₅	—	3	2	no	—
386	C₂³×C₅	—	3	2	no	—
387	C₂³×C₅	—	3	2	no	—
388	C₂³×C₅	—	3	4	no	—
389	C₂³×C₅	—	6	16	no	—
390	C₂³×C₅	—	6	1	no	—
391	C₂³×C₅	—	6	1	no	—
392	C₂³×C₅	—	6	1	no	—
393	C₂³×C₅	—	6	1	no	—
394	C₂³×C₅	—	6	16	no	—
395	C₂³×C₅	—	6	2	no	—
396	C₂³×C₅	—	6	2	no	—
397	C₂³×C₅	—	6	2	no	—
398	C₂³×C₅	—	6	2	no	—
399	C₂³×C₅	—	6	2	no	—
400	C₂³×C₅	—	6	2	no	—
401	C₂³×C₅	—	12	8	no	—
402	C₂³×C₅	—	12	8	no	—
403	C₂³×C₅	—	12	8	no	—
404	C₂³×C₅	—	12	8	no	—
405	C₂³×C₅	—	12	8	no	—
406	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
407	C₂³×C₅	C₂×D₁₂	1	4	yes	—
408	C₂³×C₅	C₂×#67	1	4	yes	—
409	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
410	C₅×D₄	—	6	16	no	—
411	C₅×D₄	—	6	8	no	—
412	C₅×D₄	(C₂×D₃)⋊C₄	1	16	yes	direct product factor
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	2	no	—
416	C₂×C₄×C₅	—	2	2	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	2	no	—
421	C₂×C₄×C₅	—	3	2	no	—
422	C₂×C₄×C₅	—	3	2	no	—
423	C₂×C₄×C₅	—	4	8	no	—
424	C₂×C₄×C₅	—	6	1	no	—
425	C₂×C₄×C₅	—	6	1	no	—
426	C₂×C₄×C₅	—	6	1	no	—
427	C₂×C₄×C₅	—	6	1	no	—
428	C₂×C₄×C₅	—	6	8	no	—
429	C₂×C₄×C₅	—	6	1	no	—
430	C₂×C₄×C₅	—	6	2	no	—
431	C₂×C₄×C₅	—	6	2	no	—
432	C₂×C₄×C₅	—	6	1	no	—
433	C₂×C₄×C₅	—	6	1	no	—
434	C₂×C₄×C₅	—	6	2	no	—
435	C₂×C₄×C₅	—	12	8	no	—
436	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
437	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
438	C₂×C₄×C₅	D₃×D₄	1	2	yes	complemented
439	C₂×C₄×C₅	C₂×#67	1	2	yes	—
440	C₂⁵	—	3	2	no	—
441	C₂²×D₄	—	3	2	no	—
442	C₂²×D₄	—	3	8	no	—
443	C₂²×D₄	—	3	1	no	—
444	C₂²×D₄	—	6	4	no	—
445	C₂²×D₄	—	6	4	no	—
446	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
447	C₂³×C₄	—	3	1	no	—
448	C₂³×C₄	—	3	2	no	—
449	C₂³×C₄	C₂×C₅×D₃	1	2	yes	complemented
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	6	4	no	—
452	C₂×C₄⋊C₄	—	3	1	no	—
453	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
454	C₂×C₂²⋊C₄	—	3	1	no	—
455	C₂×C₂²⋊C₄	—	3	2	no	—
456	C₂×C₂²⋊C₄	—	3	2	no	—
457	C₂×C₂²⋊C₄	—	3	2	no	—
458	C₂×C₂²⋊C₄	—	3	2	no	—
459	C₂×C₂²⋊C₄	—	3	1	no	—
460	C₂×C₂²⋊C₄	—	3	2	no	—
461	C₂×C₂²⋊C₄	—	3	2	no	—
462	C₂×C₂²⋊C₄	—	6	8	no	—
463	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
464	C₂×C₄²	—	3	1	no	—
465	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
466	#95	—	3	1	no	—
467	#95	—	3	1	no	—
468	#95	—	3	2	no	—
469	C₂×C₃×C₅	—	2	8	no	—
470	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
471	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
472	C₂×C₃×C₅	#518	1	1	yes	characteristic
473	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
474	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
475	C₂×C₃×C₅	#546	1	1	yes	characteristic
476	C₂×C₃×C₅	#546	1	1	yes	characteristic
477	C₅×D₃	—	2	4	no	—
478	C₅×D₃	—	4	4	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	—	2	2	no	—
483	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
484	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
485	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
486	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
487	C₂²×D₃	—	2	1	no	—
488	C₂²×D₃	—	2	1	no	—
489	C₂²×D₃	—	2	1	no	—
490	C₂²×D₃	—	2	1	no	—
491	C₂²×D₃	—	2	16	no	—
492	C₂²×D₃	—	2	2	no	—
493	C₂²×D₃	—	2	2	no	—
494	C₂²×D₃	—	2	2	no	—
495	C₂²×D₃	—	2	2	no	—
496	C₂²×D₃	—	2	2	no	—
497	C₂²×D₃	—	2	2	no	—
498	C₂²×D₃	—	2	16	no	—
499	C₂²×D₃	—	4	8	no	—
500	C₂²×D₃	—	4	8	no	—
501	C₂²×D₃	—	4	8	no	—
502	C₂²×D₃	—	4	8	no	—
503	C₂²×D₃	—	4	8	no	—
504	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
505	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
506	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
507	C₂²×D₃	C₅×#41	1	2	yes	—
508	C₃×D₄	C₅×C₂²⋊C₄	1	16	yes	complemented
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	4	8	no	—
518	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
519	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
520	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
521	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	complemented
522	#67	—	2	16	no	—
523	C₂×Dic₃	—	2	1	no	—
524	C₂×Dic₃	—	2	1	no	—
525	C₂×Dic₃	—	2	1	no	—
526	C₂×Dic₃	—	2	1	no	—
527	C₂×Dic₃	—	2	1	no	—
528	C₂×Dic₃	—	2	2	no	—
529	C₂×Dic₃	—	2	2	no	—
530	C₂×Dic₃	—	2	1	no	—
531	C₂×Dic₃	—	2	1	no	—
532	C₂×Dic₃	—	2	2	no	—
533	C₂×Dic₃	—	4	8	no	—
534	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
535	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	complemented
536	D₁₂	—	2	8	no	—
537	C₄×D₃	—	2	8	no	—
538	C₂²×C₅	—	2	4	no	—
539	C₂²×C₅	—	2	4	no	—
540	C₂²×C₅	—	2	4	no	—
541	C₂²×C₅	—	2	4	no	—
542	C₂²×C₅	—	2	4	no	—
543	C₂²×C₅	—	2	4	no	—
544	C₂²×C₅	—	3	4	no	—
545	C₂²×C₅	—	6	2	no	—
546	C₂²×C₅	—	6	2	no	—
547	C₂²×C₅	—	6	2	no	—
548	C₂²×C₅	—	6	2	no	—
549	C₂²×C₅	—	6	2	no	—
550	C₂²×C₅	—	6	2	no	—
551	C₂²×C₅	—	6	4	no	—
552	C₂²×C₅	—	6	4	no	—
553	C₂²×C₅	—	6	4	no	—
554	C₂²×C₅	—	12	32	no	—
555	C₂²×C₅	—	12	2	no	—
556	C₂²×C₅	—	12	2	no	—
557	C₂²×C₅	—	12	2	no	—
558	C₂²×C₅	—	12	2	no	—
559	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	8	yes	complemented
560	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
561	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
562	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
563	C₂²×C₅	#1004	1	1	yes	characteristic
564	C₂²×C₅	D₃×#41	1	1	yes	characteristic
565	C₂²×C₅	#1009	1	1	yes	characteristic
566	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
567	C₄×C₅	—	2	2	no	—
568	C₄×C₅	—	4	2	no	—
569	C₄×C₅	—	4	1	no	—
570	C₄×C₅	—	6	2	no	—
571	C₄×C₅	—	6	2	no	—
572	C₄×C₅	—	12	2	no	—
573	C₄×C₅	—	12	1	no	—
574	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	complemented
575	C₂⁴	—	3	1	no	—
576	C₂⁴	—	3	2	no	—
577	C₂⁴	—	3	8	no	—
578	C₂⁴	—	6	4	no	—
579	C₂⁴	—	6	4	no	—
580	C₂⁴	—	6	4	no	—
581	C₂⁴	—	6	4	no	—
582	C₂⁴	—	12	2	no	—
583	C₂⁴	—	12	2	no	—
584	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
585	C₂×D₄	—	3	8	no	—
586	C₂×D₄	—	3	4	no	—
587	C₂×D₄	—	6	4	no	—
588	C₂×D₄	—	6	4	no	—
589	C₂×D₄	—	6	32	no	—
590	C₂×D₄	—	6	2	no	—
591	C₂×D₄	—	6	2	no	—
592	C₂×D₄	C₄×C₅×D₃	1	4	yes	—
593	C₂×D₄	C₅×D₁₂	1	4	yes	—
594	C₂×D₄	C₅×#67	1	4	yes	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	3	1	no	—
598	C₂²×C₄	—	3	1	no	—
599	C₂²×C₄	—	3	4	no	—
600	C₂²×C₄	—	3	1	no	—
601	C₂²×C₄	—	3	2	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	6	4	no	—
604	C₂²×C₄	—	6	2	no	—
605	C₂²×C₄	—	6	2	no	—
606	C₂²×C₄	—	6	4	no	—
607	C₂²×C₄	—	12	2	no	—
608	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
609	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
610	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
611	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	6	2	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	3	4	no	—
616	C₂²⋊C₄	—	6	4	no	—
617	C₂²⋊C₄	—	6	4	no	—
618	C₂²⋊C₄	—	6	2	no	—
619	C₂²⋊C₄	—	6	4	no	—
620	C₂²⋊C₄	—	6	4	no	—
621	C₂²⋊C₄	—	12	2	no	—
622	C₂²⋊C₄	—	12	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	6	2	no	—
625	C₃×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
626	C₂²×C₃	—	2	4	no	—
627	C₂²×C₃	—	2	4	no	—
628	C₂²×C₃	—	2	4	no	—
629	C₂²×C₃	—	2	4	no	—
630	C₂²×C₃	—	2	4	no	—
631	C₂²×C₃	—	2	4	no	—
632	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
633	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
634	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
635	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
636	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
637	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
638	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×D₃	—	2	2	no	—
641	C₂×D₃	—	2	2	no	—
642	C₂×D₃	—	2	2	no	—
643	C₂×D₃	—	2	2	no	—
644	C₂×D₃	—	2	2	no	—
645	C₂×D₃	—	2	2	no	—
646	C₂×D₃	—	2	4	no	—
647	C₂×D₃	—	2	4	no	—
648	C₂×D₃	—	2	4	no	—
649	C₂×D₃	—	4	32	no	—
650	C₂×D₃	—	4	2	no	—
651	C₂×D₃	—	4	2	no	—
652	C₂×D₃	—	4	2	no	—
653	C₂×D₃	—	4	2	no	—
654	C₂×D₃	C₄×C₅×D₄	1	4	yes	complemented
655	C₃×C₄	—	2	2	no	—
656	C₃×C₄	—	4	2	no	—
657	C₃×C₄	—	4	1	no	—
658	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
659	Dic₃	—	2	2	no	—
660	Dic₃	—	2	2	no	—
661	Dic₃	—	4	2	no	—
662	Dic₃	—	4	1	no	—
663	C₂×C₅	—	2	8	no	—
664	C₂×C₅	—	6	4	no	—
665	C₂×C₅	—	12	4	no	—
666	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
667	C₂×C₅	#5545	1	1	yes	characteristic
668	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
669	C₂×C₅	#5554	1	1	yes	characteristic
670	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
671	C₂×C₅	D₄×#67	1	1	yes	characteristic
672	C₂×C₅	#5829	1	1	yes	characteristic
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	3	2	no	—
678	C₂³	—	3	2	no	—
679	C₂³	—	3	2	no	—
680	C₂³	—	3	4	no	—
681	C₂³	—	6	16	no	—
682	C₂³	—	6	1	no	—
683	C₂³	—	6	1	no	—
684	C₂³	—	6	1	no	—
685	C₂³	—	6	1	no	—
686	C₂³	—	6	16	no	—
687	C₂³	—	6	2	no	—
688	C₂³	—	6	2	no	—
689	C₂³	—	6	2	no	—
690	C₂³	—	6	2	no	—
691	C₂³	—	6	2	no	—
692	C₂³	—	6	2	no	—
693	C₂³	—	12	8	no	—
694	C₂³	—	12	8	no	—
695	C₂³	—	12	8	no	—
696	C₂³	—	12	8	no	—
697	C₂³	—	12	8	no	—
698	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
699	C₂³	C₂×C₅×D₁₂	1	4	yes	—
700	C₂³	C₂×C₅×#67	1	4	yes	—
701	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
702	D₄	—	6	16	no	—
703	D₄	—	6	8	no	—
704	D₄	C₅×(C₂×D₃)⋊C₄	1	16	yes	direct product factor
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	3	2	no	—
714	C₂×C₄	—	3	2	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	6	1	no	—
717	C₂×C₄	—	6	1	no	—
718	C₂×C₄	—	6	1	no	—
719	C₂×C₄	—	6	1	no	—
720	C₂×C₄	—	6	8	no	—
721	C₂×C₄	—	6	1	no	—
722	C₂×C₄	—	6	2	no	—
723	C₂×C₄	—	6	2	no	—
724	C₂×C₄	—	6	1	no	—
725	C₂×C₄	—	6	1	no	—
726	C₂×C₄	—	6	2	no	—
727	C₂×C₄	—	12	8	no	—
728	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
729	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
730	C₂×C₄	C₅×D₃×D₄	1	2	yes	complemented
731	C₂×C₄	C₂×C₅×#67	1	2	yes	—
732	C₂×C₃	—	2	8	no	—
733	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
734	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
735	C₂×C₃	C₅×#518	1	1	yes	characteristic
736	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
737	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
738	C₂×C₃	C₅×#546	1	1	yes	characteristic
739	C₂×C₃	C₅×#546	1	1	yes	characteristic
740	D₃	—	2	4	no	—
741	D₃	—	4	4	no	—
742	C₅	D₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
743	C₂²	—	2	4	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	3	4	no	—
750	C₂²	—	6	2	no	—
751	C₂²	—	6	2	no	—
752	C₂²	—	6	2	no	—
753	C₂²	—	6	2	no	—
754	C₂²	—	6	2	no	—
755	C₂²	—	6	2	no	—
756	C₂²	—	6	4	no	—
757	C₂²	—	6	4	no	—
758	C₂²	—	6	4	no	—
759	C₂²	—	12	32	no	—
760	C₂²	—	12	2	no	—
761	C₂²	—	12	2	no	—
762	C₂²	—	12	2	no	—
763	C₂²	—	12	2	no	—
764	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	8	yes	complemented
765	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
766	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
767	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
768	C₂²	C₅×#1004	1	1	yes	characteristic
769	C₂²	C₅×D₃×#41	1	1	yes	characteristic
770	C₂²	C₅×#1009	1	1	yes	characteristic
771	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
772	C₄	—	2	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	6	2	no	—
776	C₄	—	6	2	no	—
777	C₄	—	12	2	no	—
778	C₄	—	12	1	no	—
779	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	complemented
780	C₃	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
781	C₂	—	2	8	no	—
782	C₂	—	6	4	no	—
783	C₂	—	12	4	no	—
784	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
785	C₂	C₅×#5545	1	1	yes	characteristic
786	C₂	C₅×D₄×D₁₂	1	1	yes	characteristic
787	C₂	C₅×#5554	1	1	yes	characteristic
788	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
789	C₂	C₅×D₄×#67	1	1	yes	characteristic
790	C₂	C₅×#5829	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₃×D₄	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×D₄×C₂²⋊C₄
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₅×D₄×Dic₃	C₂	semidirect
4. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₅×#5213	C₂	semidirect
6. C₅×#4988	C₂	semidirect
7. C₅×#4987	C₂	semidirect
8. C₅×#4958	C₂	semidirect
9. C₅×#4955	C₂	semidirect
10. C₅×#4939	C₂	semidirect
11. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
15. C₂³×C₃×C₄×C₅	C₂²	semidirect
17. C₂³×C₅×Dic₃	C₂²	semidirect
20. C₂×C₅×D₃×D₄	C₄	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
25. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
27. C₂×C₅×#217	C₂²	semidirect
33. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
38. C₂×C₄×C₅×Dic₃	C₂²	semidirect
39. C₅×C₃⋊#95	C₂²	semidirect
40. C₅×C₃⋊#95	C₂²	semidirect
41. C₅×C₃⋊#95	C₂²	semidirect
42. D₄×(C₂×D₃)⋊C₄	C₅	direct (N × H)
45. C₂×C₄×C₅×D₄	D₃	semidirect
61. C₂³×C₅×D₃	C₂×C₄	semidirect
76. C₂×C₅×#67	C₂×C₄	semidirect
87. C₂×C₅×D₁₂	C₂×C₄	semidirect
90. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
101. C₅×(C₂×D₃)⋊C₄	D₄	direct (N × H)
105. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
106. C₂×D₄×Dic₃	C₂×C₅	semidirect
107. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
108. #5213	C₂×C₅	semidirect
109. #4988	C₂×C₅	semidirect
110. #4987	C₂×C₅	semidirect
111. #4958	C₂×C₅	semidirect
112. #4955	C₂×C₅	semidirect
113. #4939	C₂×C₅	semidirect
114. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
124. C₂³×C₄×C₅	C₂×D₃	semidirect
128. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
138. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
140. C₂×C₄²×C₅	C₂×D₃	semidirect
174. C₃×C₅×D₄	C₂²⋊C₄	semidirect
187. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
201. C₂×C₅×Dic₃	C₂×D₄	semidirect
206. C₂³×C₃×C₄	C₂²×C₅	semidirect
208. C₂³×Dic₃	C₂²×C₅	semidirect
211. C₂×D₃×D₄	C₄×C₅	semidirect
215. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
216. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
217. C₂×C₃×C₄²	C₂²×C₅	semidirect
218. C₂×#217	C₂²×C₅	semidirect
224. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
225. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
226. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
227. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
228. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
229. C₂×C₄×Dic₃	C₂²×C₅	semidirect
230. C₃⋊#95	C₂²×C₅	semidirect
231. C₃⋊#95	C₂²×C₅	semidirect
232. C₃⋊#95	C₂²×C₅	semidirect
285. C₂×C₄×D₄	C₅×D₃	semidirect
300. C₂²×C₃×C₅	C₂×C₂²⋊C₄	semidirect
322. C₂×C₅×D₃	C₄×D₄	semidirect
326. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
338. C₂³×D₃	C₂×C₄×C₅	semidirect
353. C₂×#67	C₂×C₄×C₅	semidirect
364. C₂×D₁₂	C₂×C₄×C₅	semidirect
367. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
378. (C₂×D₃)⋊C₄	C₅×D₄	direct (N × H)
412. C₅×D₄	(C₂×D₃)⋊C₄	direct (N × H)
438. C₂×C₄×C₅	D₃×D₄	semidirect
449. C₂³×C₄	C₂×C₅×D₃	semidirect
453. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
463. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
465. C₂×C₄²	C₂×C₅×D₃	semidirect
508. C₃×D₄	C₅×C₂²⋊C₄	semidirect
521. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
535. C₂×Dic₃	C₂×C₅×D₄	semidirect
559. C₂²×C₅	C₂×(C₂×D₃)⋊C₄	semidirect
574. C₄×C₅	C₂×(C₂×D₃)⋊C₄	semidirect
625. C₃×C₅	D₄×C₂²⋊C₄	semidirect
632. C₂²×C₃	C₂×C₅×C₂²⋊C₄	semidirect
654. C₂×D₃	C₄×C₅×D₄	semidirect
658. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
704. D₄	C₅×(C₂×D₃)⋊C₄	direct (N × H)
730. C₂×C₄	C₅×D₃×D₄	semidirect
742. C₅	D₄×(C₂×D₃)⋊C₄	direct (N × H)
764. C₂²	C₂×C₅×(C₂×D₃)⋊C₄	semidirect
779. C₄	C₂×C₅×(C₂×D₃)⋊C₄	semidirect
780. C₃	C₅×D₄×C₂²⋊C₄	semidirect

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
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×D₄×Dic₃	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₅×#5213	2
C₅×#4988	2
C₅×#4987	2
C₅×#4958	2
C₅×#4955	2
C₅×#4939	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×D₄×C₂²⋊C₄	3
D₄×(C₂×D₃)⋊C₄	5

Subgroups — C5×D4×(C2×D3)⋊C4 #14325895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×(C₂×D₃)⋊C₄ #14325895