Subgroups — C₂×C₅×D₃×#104 #14412788

Order 1920.

1712 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	C₂×C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#825	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₃×#104	C₂	1	8	yes	maximal, direct product factor
9	C₂²×C₅×#104	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₅×D₃×#41	—	2	2	no	—
12	C₅×D₃×#41	—	2	2	no	—
13	C₅×D₃×#41	C₄	1	4	yes	complemented
14	C₅×D₃×#41	C₂²	1	4	yes	—
15	C₂×C₅×#239	C₄	1	1	yes	characteristic, complemented
16	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₅×#237	—	2	1	no	—
18	C₂×C₅×#237	C₄	1	1	yes	characteristic, complemented
19	C₂×C₅×D₃×D₄	—	2	1	no	—
20	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic, complemented
21	C₂×C₅×#235	—	2	1	no	—
22	C₂×C₅×#235	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	—	2	1	no	—
24	C₂²×C₄×C₅×D₃	—	2	1	no	—
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×C₅×Dic₃	—	2	1	no	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
31	C₅×D₃×M₁₆	—	2	2	no	—
32	C₅×D₃×M₁₆	C₂²	1	4	yes	complemented
33	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
34	C₂×C₅×D₃×C₈	—	2	1	no	—
35	C₄²×C₅×D₃	—	2	2	no	—
36	C₄²×C₅×D₃	C₂²	1	4	yes	complemented
37	C₃×C₅×#104	C₂²	1	4	yes	complemented
38	C₅×#837	C₂²	1	4	yes	complemented
39	C₅×#825	C₂²	1	4	yes	complemented
40	C₅×#805	C₂²	1	4	yes	complemented
41	C₂×D₃×#104	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×#41	—	3	1	no	—
43	C₂²×C₅×M₁₆	—	3	1	no	—
44	C₂²×C₄²×C₅	—	3	1	no	—
45	C₂×C₅×#104	—	3	8	no	—
46	C₂×C₅×#104	—	3	1	no	—
47	C₂×C₅×#104	—	3	1	no	—
48	C₂×C₅×#104	—	3	1	no	—
49	C₂×C₅×#104	D₃	1	1	yes	characteristic, direct product factor
50	C₂³×C₅×D₃	—	2	1	no	—
51	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
52	C₃×C₅×#41	—	2	1	no	—
53	C₃×C₅×#41	—	2	1	no	—
54	C₃×C₅×#41	C₂×C₄	1	2	yes	complemented
55	C₃×C₅×#41	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₅×#67	—	2	1	no	—
63	C₂×C₅×#67	—	2	1	no	—
64	C₂×C₅×#67	—	2	1	no	—
65	C₂²×C₅×Dic₃	—	2	1	no	—
66	C₂²×C₅×Dic₃	—	2	1	no	—
67	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
68	C₅×#239	—	2	2	no	—
69	C₅×#239	C₂×C₄	1	4	yes	complemented
70	C₅×D₃×Q₈	—	2	2	no	—
71	C₅×D₃×Q₈	C₂×C₄	1	4	yes	complemented
72	C₅×#237	—	2	4	no	—
73	C₅×#237	—	2	4	no	—
74	C₅×#237	—	2	2	no	—
75	C₅×#237	C₂×C₄	1	4	yes	complemented
76	C₅×D₃×D₄	—	2	4	no	—
77	C₅×D₃×D₄	—	2	4	no	—
78	C₅×D₃×D₄	—	2	2	no	—
79	C₅×D₃×D₄	C₂×C₄	1	4	yes	complemented
80	C₅×#235	—	2	1	no	—
81	C₅×#235	—	2	1	no	—
82	C₅×#235	—	2	4	no	—
83	C₅×#235	—	2	4	no	—
84	C₅×#235	C₂×C₄	1	2	yes	complemented
85	C₅×#235	C₂³	1	2	yes	—
86	C₂×C₅×D₁₂	—	2	1	no	—
87	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
88	C₂×C₄×C₅×D₃	—	2	8	no	—
89	C₂×C₄×C₅×D₃	—	2	1	no	—
90	C₂×C₄×C₅×D₃	—	2	4	no	—
91	C₂×C₄×C₅×D₃	—	2	1	no	—
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₄×C₅×D₃	—	2	4	no	—
94	C₂×C₄×C₅×D₃	—	2	4	no	—
95	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
98	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
99	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
102	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
103	C₂×C₅×Dic₆	—	2	1	no	—
104	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
105	C₃×C₅×M₁₆	—	2	1	no	—
106	C₃×C₅×M₁₆	C₂³	1	2	yes	complemented
107	C₂×C₃×C₅×C₈	—	2	1	no	—
108	C₃×C₄²×C₅	—	2	1	no	—
109	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
110	C₄×C₅×Dic₃	—	2	1	no	—
111	C₄×C₅×Dic₃	—	2	4	no	—
112	C₄×C₅×Dic₃	C₂³	1	2	yes	complemented
113	C₅×#208	—	2	1	no	—
114	C₅×#208	C₂³	1	2	yes	complemented
115	C₂×C₅×C₃⋊C₈	—	2	1	no	—
116	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
117	C₅×D₃×C₈	—	2	4	no	—
118	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic
119	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂×#837	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂×#825	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×#805	C₂×C₅	1	1	yes	characteristic, complemented
125	D₃×#104	C₂×C₅	1	8	yes	direct product factor
126	C₂×C₅×#41	—	3	4	no	—
127	C₂×C₅×#41	—	3	4	no	—
128	C₂×C₅×#41	—	3	1	no	—
129	C₂×C₅×#41	—	3	1	no	—
130	C₂×C₅×#41	—	3	1	no	—
131	C₂×C₅×#41	—	6	1	no	—
132	C₂×C₅×#41	—	6	1	no	—
133	C₂×C₅×#41	—	6	2	no	—
134	C₂×C₅×#41	—	6	2	no	—
135	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
136	C₂²×C₅×Q₈	—	3	1	no	—
137	C₂²×C₅×D₄	—	3	1	no	—
138	C₂²×C₅×D₄	—	6	1	no	—
139	C₂³×C₄×C₅	—	3	1	no	—
140	C₂³×C₄×C₅	—	6	1	no	—
141	C₂³×C₄×C₅	—	6	1	no	—
142	C₂×C₅×M₁₆	—	3	1	no	—
143	C₂×C₅×M₁₆	—	3	4	no	—
144	C₂×C₅×M₁₆	—	6	1	no	—
145	C₂×C₅×M₁₆	—	6	2	no	—
146	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
147	C₂²×C₅×C₈	—	6	1	no	—
148	C₂×C₄²×C₅	—	3	1	no	—
149	C₂×C₄²×C₅	—	3	4	no	—
150	C₂×C₄²×C₅	—	6	2	no	—
151	C₂×C₄²×C₅	—	6	1	no	—
152	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
153	C₅×#104	—	3	4	no	—
154	C₅×#104	—	3	4	no	—
155	C₅×#104	—	3	4	no	—
156	C₅×#104	C₂×D₃	1	4	yes	direct product factor
157	C₂²×#104	—	3	1	no	Sylow
158	C₂³×C₃×C₅	—	2	1	no	—
159	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₅×D₃	—	2	4	no	—
161	C₂²×C₅×D₃	—	2	1	no	—
162	C₂²×C₅×D₃	—	2	4	no	—
163	C₂²×C₅×D₃	—	4	4	no	—
164	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
166	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
168	C₃×C₅×Q₈	—	2	1	no	—
169	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
170	C₃×C₅×D₄	—	2	2	no	—
171	C₃×C₅×D₄	—	2	2	no	—
172	C₃×C₅×D₄	—	2	1	no	—
173	C₃×C₅×D₄	C₂²×C₄	1	2	yes	complemented
174	C₂×C₃×C₄×C₅	—	2	4	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	2	no	—
178	C₂×C₃×C₄×C₅	—	2	2	no	—
179	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₅×#67	—	2	2	no	—
186	C₅×#67	—	2	2	no	—
187	C₅×#67	—	2	4	no	—
188	C₅×#67	—	2	4	no	—
189	C₂×C₅×Dic₃	—	2	4	no	—
190	C₂×C₅×Dic₃	—	2	1	no	—
191	C₂×C₅×Dic₃	—	2	2	no	—
192	C₂×C₅×Dic₃	—	2	4	no	—
193	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
196	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
197	C₅×D₁₂	—	2	4	no	—
198	C₅×D₁₂	—	2	1	no	—
199	C₅×D₁₂	C₂²×C₄	1	2	yes	complemented
200	C₄×C₅×D₃	—	2	16	no	—
201	C₄×C₅×D₃	—	2	4	no	—
202	C₄×C₅×D₃	—	2	2	no	—
203	C₄×C₅×D₃	—	2	2	no	—
204	C₄×C₅×D₃	—	2	4	no	—
205	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
206	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
207	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
208	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
209	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
210	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
211	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
212	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
213	C₅×Dic₆	—	2	1	no	—
214	C₅×Dic₆	—	2	4	no	—
215	C₅×Dic₆	C₂²×C₄	1	2	yes	complemented
216	C₃×C₅×C₈	—	2	2	no	—
217	C₅×C₃⋊C₈	—	2	2	no	—
218	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
219	D₃×#41	—	2	2	no	—
220	D₃×#41	—	2	2	no	—
221	D₃×#41	C₄×C₅	1	4	yes	complemented
222	D₃×#41	C₂²×C₅	1	4	yes	—
223	C₂×#239	C₄×C₅	1	1	yes	characteristic, complemented
224	C₂×D₃×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
225	C₂×#237	—	2	1	no	—
226	C₂×#237	C₄×C₅	1	1	yes	characteristic, complemented
227	C₂×D₃×D₄	—	2	1	no	—
228	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic, complemented
229	C₂×#235	—	2	1	no	—
230	C₂×#235	C₂²×C₅	1	1	yes	characteristic
231	C₂²×C₄×D₃	—	2	1	no	—
232	C₂²×C₄×D₃	—	2	1	no	—
233	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
236	C₂×C₄×Dic₃	—	2	1	no	—
237	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
239	D₃×M₁₆	—	2	2	no	—
240	D₃×M₁₆	C₂²×C₅	1	4	yes	complemented
241	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
242	C₂×D₃×C₈	—	2	1	no	—
243	C₄²×D₃	—	2	2	no	—
244	C₄²×D₃	C₂²×C₅	1	4	yes	complemented
245	C₃×#104	C₂²×C₅	1	4	yes	complemented
246	#837	C₂²×C₅	1	4	yes	complemented
247	#825	C₂²×C₅	1	4	yes	complemented
248	#805	C₂²×C₅	1	4	yes	complemented
249	C₂⁴×C₅	—	3	1	no	—
250	C₂⁴×C₅	—	6	1	no	—
251	C₅×#41	—	2	1	no	—
252	C₅×#41	—	2	1	no	—
253	C₅×#41	—	3	4	no	—
254	C₅×#41	—	3	4	no	—
255	C₅×#41	—	3	2	no	—
256	C₅×#41	—	3	2	no	—
257	C₅×#41	—	6	4	no	—
258	C₅×#41	—	6	4	no	—
259	C₅×#41	—	6	4	no	—
260	C₅×#41	—	6	4	no	—
261	C₅×#41	—	6	2	no	—
262	C₅×#41	—	6	2	no	—
263	C₅×#41	—	6	1	no	—
264	C₅×#41	—	6	1	no	—
265	C₅×#41	C₄×D₃	1	2	yes	complemented
266	C₅×#41	C₂²×D₃	1	2	yes	—
267	C₂×C₅×Q₈	—	3	4	no	—
268	C₂×C₅×Q₈	—	3	1	no	—
269	C₂×C₅×Q₈	—	6	1	no	—
270	C₂×C₅×Q₈	—	6	2	no	—
271	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic, complemented
272	C₂×C₅×D₄	—	2	1	no	—
273	C₂×C₅×D₄	—	3	4	no	—
274	C₂×C₅×D₄	—	3	1	no	—
275	C₂×C₅×D₄	—	6	1	no	—
276	C₂×C₅×D₄	—	6	2	no	—
277	C₂×C₅×D₄	—	6	1	no	—
278	C₂×C₅×D₄	—	6	4	no	—
279	C₂×C₅×D₄	—	6	4	no	—
280	C₂×C₅×D₄	—	6	1	no	—
281	C₂×C₅×D₄	—	6	1	no	—
282	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic, complemented
283	C₂²×C₄×C₅	—	2	1	no	—
284	C₂²×C₄×C₅	—	2	1	no	—
285	C₂²×C₄×C₅	—	3	1	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	1	no	—
288	C₂²×C₄×C₅	—	3	2	no	—
289	C₂²×C₄×C₅	—	3	2	no	—
290	C₂²×C₄×C₅	—	3	2	no	—
291	C₂²×C₄×C₅	—	3	1	no	—
292	C₂²×C₄×C₅	—	3	1	no	—
293	C₂²×C₄×C₅	—	3	2	no	—
294	C₂²×C₄×C₅	—	6	1	no	—
295	C₂²×C₄×C₅	—	6	4	no	—
296	C₂²×C₄×C₅	—	6	4	no	—
297	C₂²×C₄×C₅	—	6	4	no	—
298	C₂²×C₄×C₅	—	6	1	no	—
299	C₂²×C₄×C₅	—	6	8	no	—
300	C₂²×C₄×C₅	—	6	1	no	—
301	C₂²×C₄×C₅	—	6	1	no	—
302	C₂²×C₄×C₅	—	6	1	no	—
303	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
304	C₅×M₁₆	—	2	1	no	—
305	C₅×M₁₆	—	3	2	no	—
306	C₅×M₁₆	—	6	4	no	—
307	C₅×M₁₆	—	6	1	no	—
308	C₅×M₁₆	C₂²×D₃	1	2	yes	complemented
309	C₂×C₅×C₈	—	2	1	no	—
310	C₂×C₅×C₈	—	6	4	no	—
311	C₂×C₅×C₈	—	6	1	no	—
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	3	2	no	—
314	C₄²×C₅	—	6	4	no	—
315	C₄²×C₅	—	6	1	no	—
316	C₄²×C₅	C₂²×D₃	1	2	yes	complemented
317	C₂²×#41	—	3	1	no	—
318	C₂²×M₁₆	—	3	1	no	—
319	C₂²×C₄²	—	3	1	no	—
320	C₂×#104	—	3	1	no	—
321	C₂×#104	—	3	1	no	—
322	C₂×#104	—	3	1	no	—
323	C₂×#104	—	3	8	no	—
324	C₂×#104	C₅×D₃	1	1	yes	characteristic, direct product factor
325	C₂²×C₃×C₅	—	2	2	no	—
326	C₂²×C₃×C₅	—	2	2	no	—
327	C₂²×C₃×C₅	—	4	2	no	—
328	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₅×D₃	—	2	2	no	—
332	C₂×C₅×D₃	—	2	4	no	—
333	C₂×C₅×D₃	—	2	4	no	—
334	C₂×C₅×D₃	—	2	2	no	—
335	C₂×C₅×D₃	—	4	2	no	—
336	C₂×C₅×D₃	—	4	8	no	—
337	C₂×C₅×D₃	#104	1	4	yes	direct product factor
338	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
339	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
340	C₃×C₄×C₅	—	2	4	no	—
341	C₃×C₄×C₅	—	2	2	no	—
342	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
345	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
346	C₅×Dic₃	—	2	4	no	—
347	C₅×Dic₃	—	2	2	no	—
348	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
349	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂³×D₃	—	2	1	no	—
351	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
352	C₃×#41	—	2	1	no	—
353	C₃×#41	—	2	1	no	—
354	C₃×#41	C₂×C₄×C₅	1	2	yes	complemented
355	C₃×#41	C₂³×C₅	1	2	yes	—
356	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
357	C₂×C₃×D₄	—	2	1	no	—
358	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
359	C₂²×C₃×C₄	—	2	1	no	—
360	C₂²×C₃×C₄	—	2	1	no	—
361	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×#67	—	2	1	no	—
363	C₂×#67	—	2	1	no	—
364	C₂×#67	—	2	1	no	—
365	C₂²×Dic₃	—	2	1	no	—
366	C₂²×Dic₃	—	2	1	no	—
367	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
368	#239	—	2	2	no	—
369	#239	C₂×C₄×C₅	1	4	yes	complemented
370	D₃×Q₈	—	2	2	no	—
371	D₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
372	#237	—	2	4	no	—
373	#237	—	2	4	no	—
374	#237	—	2	2	no	—
375	#237	C₂×C₄×C₅	1	4	yes	complemented
376	D₃×D₄	—	2	4	no	—
377	D₃×D₄	—	2	4	no	—
378	D₃×D₄	—	2	2	no	—
379	D₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
380	#235	—	2	1	no	—
381	#235	—	2	1	no	—
382	#235	—	2	4	no	—
383	#235	—	2	4	no	—
384	#235	C₂×C₄×C₅	1	2	yes	complemented
385	#235	C₂³×C₅	1	2	yes	—
386	C₂×D₁₂	—	2	1	no	—
387	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic, complemented
388	C₂×C₄×D₃	—	2	8	no	—
389	C₂×C₄×D₃	—	2	1	no	—
390	C₂×C₄×D₃	—	2	4	no	—
391	C₂×C₄×D₃	—	2	1	no	—
392	C₂×C₄×D₃	—	2	1	no	—
393	C₂×C₄×D₃	—	2	4	no	—
394	C₂×C₄×D₃	—	2	4	no	—
395	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
396	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
397	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
398	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
399	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
400	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
401	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
402	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
403	C₂×Dic₆	—	2	1	no	—
404	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
405	C₃×M₁₆	—	2	1	no	—
406	C₃×M₁₆	C₂³×C₅	1	2	yes	complemented
407	C₂×C₃×C₈	—	2	1	no	—
408	C₃×C₄²	—	2	1	no	—
409	C₃×C₄²	C₂³×C₅	1	2	yes	complemented
410	C₄×Dic₃	—	2	1	no	—
411	C₄×Dic₃	—	2	4	no	—
412	C₄×Dic₃	C₂³×C₅	1	2	yes	complemented
413	#208	—	2	1	no	—
414	#208	C₂³×C₅	1	2	yes	complemented
415	C₂×C₃⋊C₈	—	2	1	no	—
416	ΓL(1,𝔽₂₅)	—	2	4	no	—
417	D₃×C₈	—	2	4	no	—
418	C₂³×C₅	—	2	1	no	—
419	C₂³×C₅	—	3	1	no	—
420	C₂³×C₅	—	3	2	no	—
421	C₂³×C₅	—	3	1	no	—
422	C₂³×C₅	—	3	2	no	—
423	C₂³×C₅	—	6	4	no	—
424	C₂³×C₅	—	6	4	no	—
425	C₂³×C₅	—	6	1	no	—
426	C₂³×C₅	—	12	4	no	—
427	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
428	C₅×Q₈	—	2	1	no	—
429	C₅×Q₈	—	3	2	no	—
430	C₅×Q₈	—	6	4	no	—
431	C₅×Q₈	—	6	1	no	—
432	C₅×Q₈	C₂×C₄×D₃	1	2	yes	complemented
433	C₅×D₄	—	2	2	no	—
434	C₅×D₄	—	2	2	no	—
435	C₅×D₄	—	2	1	no	—
436	C₅×D₄	—	3	2	no	—
437	C₅×D₄	—	6	4	no	—
438	C₅×D₄	—	6	4	no	—
439	C₅×D₄	—	6	4	no	—
440	C₅×D₄	—	6	2	no	—
441	C₅×D₄	—	6	2	no	—
442	C₅×D₄	—	6	1	no	—
443	C₅×D₄	C₂×C₄×D₃	1	2	yes	complemented
444	C₂×C₄×C₅	—	2	4	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	2	no	—
447	C₂×C₄×C₅	—	2	2	no	—
448	C₂×C₄×C₅	—	2	2	no	—
449	C₂×C₄×C₅	—	3	1	no	—
450	C₂×C₄×C₅	—	3	1	no	—
451	C₂×C₄×C₅	—	3	2	no	—
452	C₂×C₄×C₅	—	3	2	no	—
453	C₂×C₄×C₅	—	3	2	no	—
454	C₂×C₄×C₅	—	3	2	no	—
455	C₂×C₄×C₅	—	3	2	no	—
456	C₂×C₄×C₅	—	3	2	no	—
457	C₂×C₄×C₅	—	3	2	no	—
458	C₂×C₄×C₅	—	3	2	no	—
459	C₂×C₄×C₅	—	3	2	no	—
460	C₂×C₄×C₅	—	3	2	no	—
461	C₂×C₄×C₅	—	6	4	no	—
462	C₂×C₄×C₅	—	6	4	no	—
463	C₂×C₄×C₅	—	6	16	no	—
464	C₂×C₄×C₅	—	6	4	no	—
465	C₂×C₄×C₅	—	6	4	no	—
466	C₂×C₄×C₅	—	6	1	no	—
467	C₂×C₄×C₅	—	6	2	no	—
468	C₂×C₄×C₅	—	6	2	no	—
469	C₂×C₄×C₅	—	6	2	no	—
470	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
471	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
472	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
473	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
474	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
475	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
476	C₅×C₈	—	2	2	no	—
477	C₅×C₈	—	6	2	no	—
478	C₂×#41	—	3	4	no	—
479	C₂×#41	—	3	4	no	—
480	C₂×#41	—	3	1	no	—
481	C₂×#41	—	3	1	no	—
482	C₂×#41	—	3	1	no	—
483	C₂×#41	—	6	1	no	—
484	C₂×#41	—	6	1	no	—
485	C₂×#41	—	6	2	no	—
486	C₂×#41	—	6	2	no	—
487	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
488	C₂²×Q₈	—	3	1	no	—
489	C₂²×D₄	—	3	1	no	—
490	C₂²×D₄	—	6	1	no	—
491	C₂³×C₄	—	3	1	no	—
492	C₂³×C₄	—	6	1	no	—
493	C₂³×C₄	—	6	1	no	—
494	C₂×M₁₆	—	3	1	no	—
495	C₂×M₁₆	—	3	4	no	—
496	C₂×M₁₆	—	6	1	no	—
497	C₂×M₁₆	—	6	2	no	—
498	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
499	C₂²×C₈	—	6	1	no	—
500	C₂×C₄²	—	3	1	no	—
501	C₂×C₄²	—	3	4	no	—
502	C₂×C₄²	—	6	2	no	—
503	C₂×C₄²	—	6	1	no	—
504	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	#104	—	3	4	no	—
506	#104	—	3	4	no	—
507	#104	—	3	4	no	—
508	#104	C₂×C₅×D₃	1	4	yes	direct product factor
509	C₂×C₃×C₅	—	2	1	no	—
510	C₂×C₃×C₅	—	2	1	no	—
511	C₂×C₃×C₅	—	4	2	no	—
512	C₂×C₃×C₅	C₂×#104	1	2	yes	complemented
513	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
514	C₅×D₃	—	2	2	no	—
515	C₅×D₃	—	4	2	no	—
516	C₅×D₃	C₂×#104	1	4	yes	direct product factor
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂²×D₃	—	2	4	no	—
520	C₂²×D₃	—	2	1	no	—
521	C₂²×D₃	—	2	4	no	—
522	C₂²×D₃	—	4	4	no	—
523	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
524	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
525	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
526	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
527	C₃×Q₈	—	2	1	no	—
528	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	complemented
529	C₃×D₄	—	2	2	no	—
530	C₃×D₄	—	2	2	no	—
531	C₃×D₄	—	2	1	no	—
532	C₃×D₄	C₂²×C₄×C₅	1	2	yes	complemented
533	C₂×C₃×C₄	—	2	4	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
544	#67	—	2	2	no	—
545	#67	—	2	2	no	—
546	#67	—	2	4	no	—
547	#67	—	2	4	no	—
548	C₂×Dic₃	—	2	4	no	—
549	C₂×Dic₃	—	2	1	no	—
550	C₂×Dic₃	—	2	2	no	—
551	C₂×Dic₃	—	2	4	no	—
552	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
553	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
554	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
555	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
556	D₁₂	—	2	4	no	—
557	D₁₂	—	2	1	no	—
558	D₁₂	C₂²×C₄×C₅	1	2	yes	complemented
559	C₄×D₃	—	2	16	no	—
560	C₄×D₃	—	2	4	no	—
561	C₄×D₃	—	2	2	no	—
562	C₄×D₃	—	2	2	no	—
563	C₄×D₃	—	2	4	no	—
564	C₄×D₃	C₅×C₂²⋊C₄	1	2	yes	—
565	C₄×D₃	C₅×C₂²⋊C₄	1	2	yes	—
566	C₄×D₃	C₅×C₂²⋊C₄	1	2	yes	—
567	C₄×D₃	C₅×C₂²⋊C₄	1	2	yes	—
568	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
569	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
570	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
571	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
572	Dic₆	—	2	1	no	—
573	Dic₆	—	2	4	no	—
574	Dic₆	C₂²×C₄×C₅	1	2	yes	complemented
575	C₃×C₈	—	2	2	no	—
576	C₃⋊C₈	—	2	2	no	—
577	C₂²×C₅	—	2	2	no	—
578	C₂²×C₅	—	2	2	no	—
579	C₂²×C₅	—	3	2	no	—
580	C₂²×C₅	—	3	4	no	—
581	C₂²×C₅	—	3	2	no	—
582	C₂²×C₅	—	4	2	no	—
583	C₂²×C₅	—	6	4	no	—
584	C₂²×C₅	—	6	4	no	—
585	C₂²×C₅	—	6	2	no	—
586	C₂²×C₅	—	6	2	no	—
587	C₂²×C₅	—	12	8	no	—
588	C₂²×C₅	—	12	2	no	—
589	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
590	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
591	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
592	C₄×C₅	—	2	4	no	—
593	C₄×C₅	—	2	2	no	—
594	C₄×C₅	—	3	2	no	—
595	C₄×C₅	—	3	2	no	—
596	C₄×C₅	—	6	4	no	—
597	C₄×C₅	—	6	2	no	—
598	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
599	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
600	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
601	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
602	C₂⁴	—	3	1	no	—
603	C₂⁴	—	6	1	no	—
604	#41	—	2	1	no	—
605	#41	—	2	1	no	—
606	#41	—	3	4	no	—
607	#41	—	3	4	no	—
608	#41	—	3	2	no	—
609	#41	—	3	2	no	—
610	#41	—	6	4	no	—
611	#41	—	6	4	no	—
612	#41	—	6	4	no	—
613	#41	—	6	4	no	—
614	#41	—	6	2	no	—
615	#41	—	6	2	no	—
616	#41	—	6	1	no	—
617	#41	—	6	1	no	—
618	#41	C₄×C₅×D₃	1	2	yes	complemented
619	#41	C₂²×C₅×D₃	1	2	yes	—
620	C₂×Q₈	—	3	4	no	—
621	C₂×Q₈	—	3	1	no	—
622	C₂×Q₈	—	6	1	no	—
623	C₂×Q₈	—	6	2	no	—
624	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic, complemented
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	3	4	no	—
627	C₂×D₄	—	3	1	no	—
628	C₂×D₄	—	6	1	no	—
629	C₂×D₄	—	6	2	no	—
630	C₂×D₄	—	6	1	no	—
631	C₂×D₄	—	6	4	no	—
632	C₂×D₄	—	6	4	no	—
633	C₂×D₄	—	6	1	no	—
634	C₂×D₄	—	6	1	no	—
635	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic, complemented
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	3	1	no	—
639	C₂²×C₄	—	3	1	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	2	no	—
642	C₂²×C₄	—	3	2	no	—
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	3	1	no	—
645	C₂²×C₄	—	3	2	no	—
646	C₂²×C₄	—	3	2	no	—
647	C₂²×C₄	—	6	1	no	—
648	C₂²×C₄	—	6	4	no	—
649	C₂²×C₄	—	6	4	no	—
650	C₂²×C₄	—	6	4	no	—
651	C₂²×C₄	—	6	1	no	—
652	C₂²×C₄	—	6	8	no	—
653	C₂²×C₄	—	6	1	no	—
654	C₂²×C₄	—	6	1	no	—
655	C₂²×C₄	—	6	1	no	—
656	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
657	M₁₆	—	2	1	no	—
658	M₁₆	—	3	2	no	—
659	M₁₆	—	6	4	no	—
660	M₁₆	—	6	1	no	—
661	M₁₆	C₂²×C₅×D₃	1	2	yes	complemented
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	6	4	no	—
664	C₂×C₈	—	6	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	3	2	no	—
667	C₄²	—	6	4	no	—
668	C₄²	—	6	1	no	—
669	C₄²	C₂²×C₅×D₃	1	2	yes	complemented
670	C₃×C₅	C₂²×#104	1	1	yes	characteristic, complemented, Hall
671	C₂²×C₃	—	2	2	no	—
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	4	2	no	—
674	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
675	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
676	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
677	C₂×D₃	—	2	2	no	—
678	C₂×D₃	—	2	4	no	—
679	C₂×D₃	—	2	4	no	—
680	C₂×D₃	—	2	2	no	—
681	C₂×D₃	—	4	2	no	—
682	C₂×D₃	—	4	8	no	—
683	C₂×D₃	C₅×#104	1	4	yes	direct product factor
684	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
685	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
686	C₃×C₄	—	2	4	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
689	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
690	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
691	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
692	Dic₃	—	2	4	no	—
693	Dic₃	—	2	2	no	—
694	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
695	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
696	C₂×C₅	—	2	1	no	—
697	C₂×C₅	—	2	1	no	—
698	C₂×C₅	—	3	4	no	—
699	C₂×C₅	—	4	2	no	—
700	C₂×C₅	—	6	2	no	—
701	C₂×C₅	—	12	2	no	—
702	C₂×C₅	D₃×#104	1	2	yes	direct product factor
703	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
704	C₂³	—	2	1	no	—
705	C₂³	—	3	1	no	—
706	C₂³	—	3	2	no	—
707	C₂³	—	3	1	no	—
708	C₂³	—	3	2	no	—
709	C₂³	—	6	4	no	—
710	C₂³	—	6	4	no	—
711	C₂³	—	6	1	no	—
712	C₂³	—	12	4	no	—
713	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
714	Q₈	—	2	1	no	—
715	Q₈	—	3	2	no	—
716	Q₈	—	6	4	no	—
717	Q₈	—	6	1	no	—
718	Q₈	C₂×C₄×C₅×D₃	1	2	yes	complemented
719	D₄	—	2	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	1	no	—
722	D₄	—	3	2	no	—
723	D₄	—	6	4	no	—
724	D₄	—	6	4	no	—
725	D₄	—	6	4	no	—
726	D₄	—	6	2	no	—
727	D₄	—	6	2	no	—
728	D₄	—	6	1	no	—
729	D₄	C₂×C₄×C₅×D₃	1	2	yes	complemented
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	3	1	no	—
736	C₂×C₄	—	3	1	no	—
737	C₂×C₄	—	3	2	no	—
738	C₂×C₄	—	3	2	no	—
739	C₂×C₄	—	3	2	no	—
740	C₂×C₄	—	3	2	no	—
741	C₂×C₄	—	3	2	no	—
742	C₂×C₄	—	3	2	no	—
743	C₂×C₄	—	3	2	no	—
744	C₂×C₄	—	3	2	no	—
745	C₂×C₄	—	3	2	no	—
746	C₂×C₄	—	3	2	no	—
747	C₂×C₄	—	6	4	no	—
748	C₂×C₄	—	6	4	no	—
749	C₂×C₄	—	6	16	no	—
750	C₂×C₄	—	6	4	no	—
751	C₂×C₄	—	6	4	no	—
752	C₂×C₄	—	6	1	no	—
753	C₂×C₄	—	6	2	no	—
754	C₂×C₄	—	6	2	no	—
755	C₂×C₄	—	6	2	no	—
756	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
757	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
758	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
759	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
760	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
762	C₈	—	2	2	no	—
763	C₈	—	6	2	no	—
764	C₂×C₃	—	2	1	no	—
765	C₂×C₃	—	2	1	no	—
766	C₂×C₃	—	4	2	no	—
767	C₂×C₃	C₂×C₅×#104	1	2	yes	complemented
768	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
769	D₃	—	2	2	no	—
770	D₃	—	4	2	no	—
771	D₃	C₂×C₅×#104	1	4	yes	direct product factor
772	C₅	C₂×D₃×#104	1	1	yes	characteristic, direct product factor, Sylow
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	3	2	no	—
776	C₂²	—	3	4	no	—
777	C₂²	—	3	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	6	4	no	—
780	C₂²	—	6	4	no	—
781	C₂²	—	6	2	no	—
782	C₂²	—	6	2	no	—
783	C₂²	—	12	8	no	—
784	C₂²	—	12	2	no	—
785	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
786	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
787	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
788	C₄	—	2	4	no	—
789	C₄	—	2	2	no	—
790	C₄	—	3	2	no	—
791	C₄	—	3	2	no	—
792	C₄	—	6	4	no	—
793	C₄	—	6	2	no	—
794	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
795	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
796	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
797	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
798	C₃	C₂²×C₅×#104	1	1	yes	characteristic, complemented, Sylow
799	C₂	—	2	1	no	—
800	C₂	—	2	1	no	—
801	C₂	—	3	4	no	—
802	C₂	—	4	2	no	—
803	C₂	—	6	2	no	—
804	C₂	—	12	2	no	—
805	C₂	C₅×D₃×#104	1	2	yes	direct product factor
806	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×D₃×#41	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₂²×C₅×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₂×C₄²×C₅×D₃	C₂	semidirect
4. C₂×C₃×C₅×#104	C₂	semidirect
5. C₂×C₅×#837	C₂	semidirect
6. C₂×C₅×#825	C₂	semidirect
7. C₂×C₅×#805	C₂	semidirect
8. C₅×D₃×#104	C₂	direct (N × H)
13. C₅×D₃×#41	C₄	semidirect
15. C₂×C₅×#239	C₄	semidirect
16. C₂×C₅×D₃×Q₈	C₄	semidirect
18. C₂×C₅×#237	C₄	semidirect
20. C₂×C₅×D₃×D₄	C₄	semidirect
26. C₂×C₃×C₅×M₁₆	C₂²	semidirect
27. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₂×C₄×C₅×Dic₃	C₂²	semidirect
30. C₂×C₅×#208	C₂²	semidirect
32. C₅×D₃×M₁₆	C₂²	semidirect
36. C₄²×C₅×D₃	C₂²	semidirect
37. C₃×C₅×#104	C₂²	semidirect
38. C₅×#837	C₂²	semidirect
39. C₅×#825	C₂²	semidirect
40. C₅×#805	C₂²	semidirect
41. C₂×D₃×#104	C₅	direct (N × H)
49. C₂×C₅×#104	D₃	direct (N × H)
54. C₃×C₅×#41	C₂×C₄	semidirect
56. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
58. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
69. C₅×#239	C₂×C₄	semidirect
71. C₅×D₃×Q₈	C₂×C₄	semidirect
75. C₅×#237	C₂×C₄	semidirect
79. C₅×D₃×D₄	C₂×C₄	semidirect
84. C₅×#235	C₂×C₄	semidirect
87. C₂×C₅×D₁₂	C₂×C₄	semidirect
104. C₂×C₅×Dic₆	C₂×C₄	semidirect
106. C₃×C₅×M₁₆	C₂³	semidirect
109. C₃×C₄²×C₅	C₂³	semidirect
112. C₄×C₅×Dic₃	C₂³	semidirect
114. C₅×#208	C₂³	semidirect
119. C₂×D₃×M₁₆	C₂×C₅	semidirect
120. C₂×C₄²×D₃	C₂×C₅	semidirect
121. C₂×C₃×#104	C₂×C₅	semidirect
122. C₂×#837	C₂×C₅	semidirect
123. C₂×#825	C₂×C₅	semidirect
124. C₂×#805	C₂×C₅	semidirect
125. D₃×#104	C₂×C₅	direct (N × H)
146. C₂×C₅×M₁₆	C₂×D₃	semidirect
152. C₂×C₄²×C₅	C₂×D₃	semidirect
156. C₅×#104	C₂×D₃	direct (N × H)
169. C₃×C₅×Q₈	C₂²×C₄	semidirect
173. C₃×C₅×D₄	C₂²×C₄	semidirect
199. C₅×D₁₂	C₂²×C₄	semidirect
215. C₅×Dic₆	C₂²×C₄	semidirect
221. D₃×#41	C₄×C₅	semidirect
223. C₂×#239	C₄×C₅	semidirect
224. C₂×D₃×Q₈	C₄×C₅	semidirect
226. C₂×#237	C₄×C₅	semidirect
228. C₂×D₃×D₄	C₄×C₅	semidirect
234. C₂×C₃×M₁₆	C₂²×C₅	semidirect
235. C₂×C₃×C₄²	C₂²×C₅	semidirect
237. C₂×C₄×Dic₃	C₂²×C₅	semidirect
238. C₂×#208	C₂²×C₅	semidirect
240. D₃×M₁₆	C₂²×C₅	semidirect
244. C₄²×D₃	C₂²×C₅	semidirect
245. C₃×#104	C₂²×C₅	semidirect
246. #837	C₂²×C₅	semidirect
247. #825	C₂²×C₅	semidirect
248. #805	C₂²×C₅	semidirect
265. C₅×#41	C₄×D₃	semidirect
271. C₂×C₅×Q₈	C₄×D₃	semidirect
282. C₂×C₅×D₄	C₄×D₃	semidirect
308. C₅×M₁₆	C₂²×D₃	semidirect
316. C₄²×C₅	C₂²×D₃	semidirect
324. C₂×#104	C₅×D₃	direct (N × H)
337. C₂×C₅×D₃	#104	direct (N × H)
354. C₃×#41	C₂×C₄×C₅	semidirect
356. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
358. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
369. #239	C₂×C₄×C₅	semidirect
371. D₃×Q₈	C₂×C₄×C₅	semidirect
375. #237	C₂×C₄×C₅	semidirect
379. D₃×D₄	C₂×C₄×C₅	semidirect
384. #235	C₂×C₄×C₅	semidirect
387. C₂×D₁₂	C₂×C₄×C₅	semidirect
404. C₂×Dic₆	C₂×C₄×C₅	semidirect
406. C₃×M₁₆	C₂³×C₅	semidirect
409. C₃×C₄²	C₂³×C₅	semidirect
412. C₄×Dic₃	C₂³×C₅	semidirect
414. #208	C₂³×C₅	semidirect
432. C₅×Q₈	C₂×C₄×D₃	semidirect
443. C₅×D₄	C₂×C₄×D₃	semidirect
498. C₂×M₁₆	C₂×C₅×D₃	semidirect
504. C₂×C₄²	C₂×C₅×D₃	semidirect
508. #104	C₂×C₅×D₃	direct (N × H)
512. C₂×C₃×C₅	C₂×#104	semidirect
516. C₅×D₃	C₂×#104	direct (N × H)
528. C₃×Q₈	C₂²×C₄×C₅	semidirect
532. C₃×D₄	C₂²×C₄×C₅	semidirect
558. D₁₂	C₂²×C₄×C₅	semidirect
574. Dic₆	C₂²×C₄×C₅	semidirect
618. #41	C₄×C₅×D₃	semidirect
624. C₂×Q₈	C₄×C₅×D₃	semidirect
635. C₂×D₄	C₄×C₅×D₃	semidirect
661. M₁₆	C₂²×C₅×D₃	semidirect
669. C₄²	C₂²×C₅×D₃	semidirect
670. C₃×C₅	C₂²×#104	semidirect
683. C₂×D₃	C₅×#104	direct (N × H)
702. C₂×C₅	D₃×#104	direct (N × H)
718. Q₈	C₂×C₄×C₅×D₃	semidirect
729. D₄	C₂×C₄×C₅×D₃	semidirect
767. C₂×C₃	C₂×C₅×#104	semidirect
771. D₃	C₂×C₅×#104	direct (N × H)
772. C₅	C₂×D₃×#104	direct (N × H)
798. C₃	C₂²×C₅×#104	semidirect
805. C₂	C₅×D₃×#104	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₂×C₅×D₃×M₁₆	2
C₂×C₄²×C₅×D₃	2
C₂×C₃×C₅×#104	2
C₂×C₅×#837	2
C₂×C₅×#825	2
C₂×C₅×#805	2
C₅×D₃×#104	2
C₂²×C₅×#104	3
C₂×D₃×#104	5

Subgroups — C2×C5×D3×#104 #14412788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×#104 #14412788