Subgroups — D₃×#65400 #14414720

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₃×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65400	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748506	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748503	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#3952	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747720	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747719	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747712	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747711	C₂	1	1	yes	maximal, characteristic, complemented
14	D₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#65400	—	3	1	no	maximal, Hall
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂×D₃×C₂²⋊D₅	C₄	1	1	yes	characteristic
19	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
21	C₄×#1220	C₂²	1	1	yes	characteristic
22	C₂×#6705	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×D₃×C₈	—	2	4	no	—
25	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
31	#91556	C₄	1	1	yes	characteristic
32	D₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
33	Dic₃×C₂²⋊D₅	C₄	1	1	yes	characteristic
34	D₃×#685	C₄	1	1	yes	characteristic
35	#91446	C₄	1	1	yes	characteristic
36	C₄×#1203	C₂²	1	1	yes	characteristic
37	#91441	C₄	1	1	yes	characteristic
38	C₄×#1201	C₂²	1	1	yes	characteristic
39	D₃×#683	C₄	1	1	yes	characteristic
40	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
41	C₂×#6651	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6649	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₃×#168	C₂²	1	1	yes	characteristic
44	C₂×D₃×#168	C₂²	1	1	yes	characteristic
45	D₃×#676	—	2	4	no	—
46	#91114	C₂²	1	1	yes	characteristic, complemented
47	#91104	C₂²	1	1	yes	characteristic, complemented
48	#91099	C₂²	1	1	yes	characteristic, complemented
49	#91098	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
51	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
52	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
54	#90983	C₂²	1	1	yes	characteristic, complemented
55	#90982	C₂²	1	1	yes	characteristic, complemented
56	#90957	C₂²	1	1	yes	characteristic, complemented
57	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
58	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
59	#90955	C₂²	1	1	yes	characteristic, complemented
60	#90954	C₂²	1	1	yes	characteristic, complemented
61	#90952	C₂²	1	1	yes	characteristic, complemented
62	D₃×#435	—	5	1	no	maximal, Hall
63	C₂³×C₅×C₈	—	3	1	no	—
64	C₂×C₄×C₂²⋊D₅	—	3	1	no	—
65	C₂²×#676	—	3	1	no	—
66	C₂×C₂²⋊#168	—	3	1	no	—
67	#65400	—	3	1	no	—
68	#65400	—	3	1	no	—
69	#65400	—	3	1	no	—
70	#65400	—	3	1	no	—
71	#65400	—	3	1	no	—
72	#65400	—	3	1	no	—
73	#65400	—	3	1	no	—
74	#65400	D₃	1	1	yes	characteristic, direct product factor
75	C₂×#3952	—	3	1	no	—
76	C₂×#3947	—	3	1	no	—
77	C₂×#3946	—	3	1	no	—
78	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×#1220	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	—	2	2	no	—
85	C₂×C₄×C₅×D₃	—	2	2	no	—
86	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
92	D₃×C₂²⋊D₅	—	2	4	no	—
93	C₂×#1203	C₂×C₄	1	1	yes	characteristic
94	C₂×#1201	C₂×C₄	1	1	yes	characteristic
95	C₂×#1200	C₂×C₄	1	1	yes	characteristic
96	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₄×D₃×D₅	—	2	2	no	—
101	C₄×D₃×D₅	—	2	2	no	—
102	C₂×C₃×C₅×C₈	—	2	2	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	#6719	C₂×C₄	1	1	yes	characteristic
106	#6714	C₂×C₄	1	1	yes	characteristic
107	#6712	C₂×C₄	1	1	yes	characteristic
108	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
109	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
110	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
111	#6705	—	2	2	no	—
112	C₂×C₅×C₃⋊C₈	—	2	2	no	—
113	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
115	C₅×D₃×C₈	—	2	2	no	—
116	C₅×D₃×C₈	—	2	2	no	—
117	C₅×D₃×C₈	—	2	2	no	—
118	C₅×D₃×C₈	D₄	1	4	yes	complemented
119	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
120	C₃×#685	C₂×C₄	1	1	yes	characteristic
121	C₃×#683	C₂×C₄	1	1	yes	characteristic
122	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
123	C₂×C₃×#168	C₂³	1	1	yes	characteristic
124	C₂×C₃×#168	C₂³	1	1	yes	characteristic
125	C₃×#676	—	2	2	no	—
126	#6669	C₂×C₄	1	1	yes	characteristic
127	#6668	C₂×C₄	1	1	yes	characteristic
128	#6667	C₂×C₄	1	1	yes	characteristic
129	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
130	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
131	#6665	C₂×C₄	1	1	yes	characteristic
132	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
133	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
134	#6651	—	2	2	no	—
135	#6649	—	2	2	no	—
136	D₃×#168	—	2	2	no	—
137	D₃×#168	—	2	2	no	—
138	C₂×D₃×M₁₆	—	5	1	no	—
139	C₂²×D₃×C₈	D₅	1	1	yes	characteristic, complemented
140	C₄×D₃×D₄	—	5	1	no	—
141	C₃×#435	—	5	1	no	—
142	#5127	—	5	1	no	—
143	#5111	—	5	1	no	—
144	#5011	—	5	1	no	—
145	#4836	—	5	1	no	—
146	D₃×C₄⋊C₈	—	5	1	no	—
147	#4730	—	5	1	no	—
148	#4728	—	5	1	no	—
149	D₃×C₂²⋊C₈	—	5	1	no	—
150	D₃×C₂²⋊C₈	—	5	1	no	—
151	#4706	—	5	1	no	—
152	D₃×#97	—	5	1	no	—
153	C₂³×C₄×C₅	—	3	1	no	—
154	C₂²×C₂²⋊D₅	—	3	1	no	—
155	C₂²×C₄×D₅	—	3	1	no	—
156	C₂²×C₅×C₈	—	3	1	no	—
157	C₂²×C₅×C₈	—	3	1	no	—
158	C₂²×C₅×C₈	—	3	1	no	—
159	C₂²×C₅×C₈	—	3	1	no	—
160	C₂²×C₅×C₈	—	3	1	no	—
161	C₂²×C₅×C₈	—	6	4	no	—
162	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊Dic₅	—	3	1	no	—
164	C₄×C₂²⋊D₅	—	3	1	no	—
165	C₄×C₂²⋊D₅	—	3	1	no	—
166	C₄×C₂²⋊D₅	—	3	1	no	—
167	C₄×C₂²⋊D₅	—	3	1	no	—
168	C₄×C₂²⋊D₅	—	3	1	no	—
169	C₄×C₂²⋊D₅	—	3	1	no	—
170	C₄×C₂²⋊D₅	—	3	1	no	—
171	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
172	C₂×#685	—	3	1	no	—
173	C₂×#683	—	3	1	no	—
174	C₂×C₄×Dic₅	—	3	1	no	—
175	C₂²×#168	—	3	1	no	—
176	C₂²×#168	—	3	1	no	—
177	C₂×#676	—	3	1	no	—
178	C₂×#676	—	3	1	no	—
179	C₂×#676	—	3	1	no	—
180	C₂×#676	—	6	4	no	—
181	C₂×#676	C₂×D₃	1	1	yes	characteristic, complemented
182	C₂²⋊#168	—	3	1	no	—
183	C₂²⋊#168	—	3	1	no	—
184	C₂²⋊#168	—	3	1	no	—
185	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
186	#3952	—	3	1	no	—
187	#3952	—	3	1	no	—
188	#3952	—	3	1	no	—
189	#3952	C₂×D₃	1	1	yes	characteristic, complemented
190	#3947	—	3	1	no	—
191	#3947	—	3	1	no	—
192	#3947	—	3	1	no	—
193	#3947	C₂×D₃	1	1	yes	characteristic, complemented
194	#3946	—	3	1	no	—
195	#3946	—	3	1	no	—
196	#3946	—	3	1	no	—
197	#3946	C₂×D₃	1	1	yes	characteristic, complemented
198	C₂×#435	—	15	1	no	Sylow
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	—	2	2	no	—
202	C₂²×C₅×D₃	—	2	2	no	—
203	C₂²×C₅×D₃	M₁₆	1	4	yes	complemented
204	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
207	C₂×D₃×D₅	—	2	2	no	—
208	C₂×D₃×D₅	—	2	2	no	—
209	C₂×D₃×D₅	—	2	2	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	#1220	—	2	2	no	—
215	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
216	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
217	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
218	C₄×D₁₅	—	2	1	no	—
219	C₄×D₁₅	—	2	1	no	—
220	C₂×C₅×Dic₃	—	2	2	no	—
221	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
223	C₄×C₅×D₃	—	2	2	no	—
224	C₄×C₅×D₃	—	2	1	no	—
225	C₄×C₅×D₃	—	2	1	no	—
226	C₄×C₅×D₃	—	2	2	no	—
227	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
228	C₄×C₅×D₃	#41	1	2	yes	—
229	C₃×C₂²⋊D₅	—	2	2	no	—
230	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
233	C₃×C₄×D₅	—	2	1	no	—
234	C₃×C₄×D₅	—	2	1	no	—
235	#1203	—	2	2	no	—
236	#1201	—	2	2	no	—
237	#1200	—	2	2	no	—
238	D₃×Dic₅	—	2	2	no	—
239	D₃×Dic₅	—	2	2	no	—
240	D₃×Dic₅	—	2	2	no	—
241	D₅×Dic₃	—	2	2	no	—
242	C₃×C₅×C₈	—	2	1	no	—
243	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
244	C₃⋊#168	—	2	1	no	—
245	C₃⋊#168	—	2	1	no	—
246	C₃×#168	—	2	1	no	—
247	C₃×#168	—	2	1	no	—
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
250	C₂×D₃×D₄	—	5	1	no	—
251	C₂²×C₄×D₃	—	5	1	no	—
252	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
255	C₃×C₄×D₄	—	5	1	no	—
256	D₄×Dic₃	—	5	1	no	—
257	C₄×#67	—	5	1	no	—
258	C₄×#67	—	5	1	no	—
259	C₂×#208	—	5	1	no	—
260	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
261	D₃×M₁₆	—	10	4	no	—
262	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
263	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
264	C₂×D₃×C₈	—	2	4	no	—
265	C₂×D₃×C₈	—	5	1	no	—
266	C₂×D₃×C₈	—	5	1	no	—
267	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
268	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
269	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
270	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
271	#893	—	5	1	no	—
272	D₃×C₄⋊C₄	—	5	1	no	—
273	#67⋊C₄	—	5	1	no	—
274	#67⋊C₄	—	5	1	no	—
275	D₃×C₂²⋊C₄	—	5	1	no	—
276	D₃×C₂²⋊C₄	—	5	1	no	—
277	C₄×D₁₂	—	5	1	no	—
278	C₄²×D₃	—	5	1	no	—
279	C₃×C₄⋊C₈	—	5	1	no	—
280	C₃×C₂²⋊C₈	—	5	1	no	—
281	C₃×C₂²⋊C₈	—	5	1	no	—
282	C₃×#97	—	5	1	no	—
283	#830	—	5	1	no	—
284	#830	—	5	1	no	—
285	(C₂×D₃)⋊C₈	—	5	1	no	—
286	(C₂×D₃)⋊C₈	—	5	1	no	—
287	(C₂×D₃)⋊C₈	—	5	1	no	—
288	(C₂×D₃)⋊C₈	—	5	1	no	—
289	#815	—	5	1	no	—
290	#815	—	5	1	no	—
291	Dic₃⋊C₈	—	5	1	no	—
292	Dic₃⋊C₈	—	5	1	no	—
293	C₄⋊(C₃⋊C₈)	—	5	1	no	—
294	#803	—	5	1	no	—
295	C₂⁴×C₅	—	3	1	no	—
296	C₂³×D₅	—	3	1	no	—
297	C₂²×C₄×C₅	—	3	1	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	1	no	—
302	C₂²×C₄×C₅	—	6	2	no	—
303	C₂²×C₄×C₅	—	6	2	no	—
304	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₂²⋊D₅	—	3	1	no	—
306	C₂×C₂²⋊D₅	—	3	1	no	—
307	C₂×C₂²⋊D₅	—	3	1	no	—
308	C₂×C₂²⋊D₅	—	6	4	no	—
309	C₂×C₂²⋊D₅	C₄×D₃	1	1	yes	characteristic
310	C₂²×Dic₅	—	3	1	no	—
311	C₂²×Dic₅	—	3	1	no	—
312	C₂²×Dic₅	—	3	1	no	—
313	C₂×C₄×D₅	—	3	1	no	—
314	C₂×C₄×D₅	—	3	1	no	—
315	C₂×C₄×D₅	—	3	1	no	—
316	C₂×C₄×D₅	—	6	2	no	—
317	C₂×C₄×D₅	—	6	2	no	—
318	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₅×C₈	—	2	2	no	—
320	C₂×C₅×C₈	—	3	1	no	—
321	C₂×C₅×C₈	—	3	4	no	—
322	C₂×C₅×C₈	—	3	1	no	—
323	C₂×C₅×C₈	—	6	2	no	—
324	C₂×C₅×C₈	—	6	2	no	—
325	C₂×C₅×C₈	—	6	2	no	—
326	C₂×C₅×C₈	—	6	2	no	—
327	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
328	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
329	C₂²⋊Dic₅	—	3	1	no	—
330	C₂²⋊Dic₅	—	3	1	no	—
331	C₂²⋊Dic₅	—	3	1	no	—
332	C₂²⋊Dic₅	C₄×D₃	1	1	yes	characteristic
333	#685	—	3	1	no	—
334	#685	—	3	1	no	—
335	#685	—	3	1	no	—
336	#685	C₄×D₃	1	1	yes	characteristic
337	#683	—	3	1	no	—
338	#683	—	3	1	no	—
339	#683	—	3	1	no	—
340	#683	C₄×D₃	1	1	yes	characteristic
341	C₄×Dic₅	—	3	1	no	—
342	C₄×Dic₅	—	3	1	no	—
343	C₄×Dic₅	—	3	1	no	—
344	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
345	C₂×#168	—	3	1	no	—
346	C₂×#168	—	3	1	no	—
347	C₂×#168	—	6	2	no	—
348	C₂×#168	—	6	2	no	—
349	C₂×#168	C₂²×D₃	1	1	yes	characteristic
350	C₂×#168	C₂²×D₃	1	1	yes	characteristic
351	#676	—	2	2	no	—
352	#676	—	6	2	no	—
353	#676	—	6	2	no	—
354	#676	—	6	2	no	—
355	C₂²×M₁₆	—	15	1	no	—
356	C₂³×C₈	—	3	1	no	—
357	C₂×C₄×D₄	—	15	1	no	—
358	#435	—	5	1	no	—
359	#435	—	15	1	no	—
360	#435	—	15	1	no	—
361	#435	—	15	1	no	—
362	#435	—	15	1	no	—
363	#435	—	15	1	no	—
364	#435	—	15	1	no	—
365	#435	—	15	1	no	—
366	C₂×C₄⋊C₈	—	15	1	no	—
367	C₂×C₂²⋊C₈	—	15	1	no	—
368	C₂×C₂²⋊C₈	—	15	1	no	—
369	C₂×#97	—	15	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
373	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
374	C₂×D₁₅	—	2	1	no	—
375	C₂×D₁₅	—	2	1	no	—
376	C₂×D₁₅	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	—	2	8	no	—
380	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
381	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
382	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	complemented
383	C₂×C₅×D₃	#131	1	2	yes	—
384	C₂×C₃×D₅	—	2	1	no	—
385	C₂×C₃×D₅	—	2	1	no	—
386	C₂×C₃×D₅	—	2	1	no	—
387	D₃×D₅	—	4	4	no	—
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
391	Dic₁₅	—	2	1	no	—
392	Dic₁₅	—	2	1	no	—
393	Dic₁₅	—	2	1	no	—
394	C₃×Dic₅	—	2	1	no	—
395	C₃×Dic₅	—	2	1	no	—
396	C₃×Dic₅	—	2	1	no	—
397	C₅×Dic₃	—	2	1	no	—
398	C₅×Dic₃	C₄×D₄	1	2	yes	—
399	C₂³×D₃	—	5	1	no	—
400	C₂³×D₃	C₄×D₅	1	1	yes	characteristic
401	C₂×C₃×D₄	—	5	1	no	—
402	C₂²×C₃×C₄	—	5	1	no	—
403	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
404	C₂×#67	—	5	1	no	—
405	C₂×#67	—	5	1	no	—
406	C₂²×Dic₃	—	5	1	no	—
407	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
408	D₃×D₄	—	10	4	no	—
409	C₂×D₁₂	—	5	1	no	—
410	C₂×C₄×D₃	—	2	2	no	—
411	C₂×C₄×D₃	—	2	2	no	—
412	C₂×C₄×D₃	—	5	1	no	—
413	C₂×C₄×D₃	—	5	1	no	—
414	C₂×C₄×D₃	—	5	1	no	—
415	C₂×C₄×D₃	—	5	1	no	—
416	C₂×C₄×D₃	—	5	1	no	—
417	C₂×C₄×D₃	—	10	2	no	—
418	C₂×C₄×D₃	—	10	2	no	—
419	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
420	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
421	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
422	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
423	C₃×M₁₆	—	10	2	no	—
424	C₂×C₃×C₈	—	2	2	no	—
425	C₂×C₃×C₈	—	5	1	no	—
426	C₂×C₃×C₈	—	5	1	no	—
427	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
428	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
429	C₃×C₄⋊C₄	—	5	1	no	—
430	C₃×C₂²⋊C₄	—	5	1	no	—
431	C₃×C₂²⋊C₄	—	5	1	no	—
432	C₃×C₄²	—	5	1	no	—
433	#217	—	5	1	no	—
434	#217	—	5	1	no	—
435	(C₂×D₃)⋊C₄	—	5	1	no	—
436	(C₂×D₃)⋊C₄	—	5	1	no	—
437	(C₂×D₃)⋊C₄	—	5	1	no	—
438	(C₂×D₃)⋊C₄	—	5	1	no	—
439	C₄⋊Dic₃	—	5	1	no	—
440	Dic₃⋊C₄	—	5	1	no	—
441	Dic₃⋊C₄	—	5	1	no	—
442	C₄×Dic₃	—	5	1	no	—
443	C₄×Dic₃	—	5	1	no	—
444	C₄×Dic₃	—	5	1	no	—
445	#208	—	10	2	no	—
446	C₂×C₃⋊C₈	—	2	2	no	—
447	C₂×C₃⋊C₈	—	5	1	no	—
448	C₂×C₃⋊C₈	—	5	1	no	—
449	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
450	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
451	ΓL(1,𝔽₂₅)	—	10	2	no	—
452	ΓL(1,𝔽₂₅)	—	10	2	no	—
453	D₃×C₈	—	2	2	no	—
454	D₃×C₈	—	2	2	no	—
455	D₃×C₈	—	2	2	no	—
456	D₃×C₈	—	10	2	no	—
457	D₃×C₈	—	10	2	no	—
458	D₃×C₈	C₂²⋊D₅	1	4	yes	complemented
459	C₂³×C₅	—	3	1	no	—
460	C₂³×C₅	—	3	4	no	—
461	C₂³×C₅	—	3	1	no	—
462	C₂³×C₅	—	6	2	no	—
463	C₂³×C₅	—	6	2	no	—
464	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
465	C₂²×D₅	—	3	1	no	—
466	C₂²×D₅	—	6	2	no	—
467	C₂²×D₅	—	6	2	no	—
468	C₂²×D₅	—	6	2	no	—
469	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	3	1	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	3	2	no	—
475	C₂×C₄×C₅	—	3	1	no	—
476	C₂×C₄×C₅	—	6	2	no	—
477	C₂×C₄×C₅	—	6	2	no	—
478	C₂×C₄×C₅	—	6	2	no	—
479	C₂×C₄×C₅	—	6	1	no	—
480	C₂×C₄×C₅	—	6	1	no	—
481	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
482	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
483	C₂²⋊D₅	—	2	2	no	—
484	C₂²⋊D₅	—	6	2	no	—
485	C₂²⋊D₅	—	6	2	no	—
486	C₂²⋊D₅	—	6	2	no	—
487	C₂×Dic₅	—	3	1	no	—
488	C₂×Dic₅	—	3	1	no	—
489	C₂×Dic₅	—	3	1	no	—
490	C₂×Dic₅	—	6	2	no	—
491	C₂×Dic₅	—	6	2	no	—
492	C₂×Dic₅	—	6	2	no	—
493	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
494	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
495	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
496	C₄×D₅	—	2	1	no	—
497	C₄×D₅	—	2	1	no	—
498	C₄×D₅	—	6	2	no	—
499	C₄×D₅	—	6	2	no	—
500	C₄×D₅	—	6	1	no	—
501	C₄×D₅	—	6	1	no	—
502	C₅×C₈	—	2	1	no	—
503	C₅×C₈	—	3	2	no	—
504	C₅×C₈	—	6	1	no	—
505	C₅×C₈	D₃×D₄	1	2	yes	complemented
506	#168	—	2	1	no	—
507	#168	—	2	1	no	—
508	#168	—	6	1	no	—
509	#168	—	6	1	no	—
510	C₂²×D₄	—	15	1	no	—
511	C₂³×C₄	—	3	1	no	—
512	C₂³×C₄	—	15	1	no	—
513	C₂×M₁₆	—	5	1	no	—
514	C₂×M₁₆	—	15	1	no	—
515	C₂×M₁₆	—	15	1	no	—
516	C₂×M₁₆	—	15	1	no	—
517	C₂×M₁₆	—	30	4	no	—
518	C₂²×C₈	—	3	1	no	—
519	C₂²×C₈	—	3	1	no	—
520	C₂²×C₈	—	3	1	no	—
521	C₂²×C₈	—	3	1	no	—
522	C₂²×C₈	—	3	1	no	—
523	C₂²×C₈	—	6	4	no	—
524	C₂²×C₈	—	15	1	no	—
525	C₂²×C₈	—	15	1	no	—
526	C₂²×C₈	D₃×D₅	1	1	yes	characteristic, complemented
527	C₄×D₄	—	5	1	no	—
528	C₄×D₄	—	15	1	no	—
529	C₄×D₄	—	15	1	no	—
530	C₄×D₄	—	15	1	no	—
531	C₄×D₄	—	15	1	no	—
532	C₄×D₄	—	15	1	no	—
533	C₄×D₄	—	15	1	no	—
534	C₄×D₄	—	15	1	no	—
535	C₂×C₄⋊C₄	—	15	1	no	—
536	C₂×C₂²⋊C₄	—	15	1	no	—
537	C₂×C₂²⋊C₄	—	15	1	no	—
538	C₂×C₄²	—	15	1	no	—
539	C₄⋊C₈	—	5	1	no	—
540	C₄⋊C₈	—	15	1	no	—
541	C₄⋊C₈	—	15	1	no	—
542	C₄⋊C₈	—	15	1	no	—
543	C₂²⋊C₈	—	5	1	no	—
544	C₂²⋊C₈	—	5	1	no	—
545	C₂²⋊C₈	—	15	1	no	—
546	C₂²⋊C₈	—	15	1	no	—
547	C₂²⋊C₈	—	15	1	no	—
548	C₂²⋊C₈	—	15	1	no	—
549	C₂²⋊C₈	—	15	1	no	—
550	C₂²⋊C₈	—	15	1	no	—
551	#97	—	5	1	no	—
552	#97	—	15	1	no	—
553	#97	—	15	1	no	—
554	#97	—	15	1	no	—
555	C₂×C₃×C₅	—	2	2	no	—
556	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
557	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
558	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
559	D₁₅	—	4	1	no	—
560	C₃×D₅	—	4	1	no	—
561	C₅×D₃	—	2	2	no	—
562	C₅×D₃	#435	1	4	yes	complemented
563	C₂³×C₃	—	5	1	no	—
564	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
565	C₂²×D₃	—	2	2	no	—
566	C₂²×D₃	—	2	2	no	—
567	C₂²×D₃	—	5	1	no	—
568	C₂²×D₃	—	10	2	no	—
569	C₂²×D₃	—	10	2	no	—
570	C₂²×D₃	—	10	2	no	—
571	C₂²×D₃	#676	1	4	yes	complemented
572	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
573	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
574	C₃×D₄	—	10	2	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	5	1	no	—
578	C₂×C₃×C₄	—	5	1	no	—
579	C₂×C₃×C₄	—	5	1	no	—
580	C₂×C₃×C₄	—	10	1	no	—
581	C₂×C₃×C₄	—	10	1	no	—
582	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
584	#67	—	10	2	no	—
585	#67	—	10	2	no	—
586	C₂×Dic₃	—	2	2	no	—
587	C₂×Dic₃	—	5	1	no	—
588	C₂×Dic₃	—	5	1	no	—
589	C₂×Dic₃	—	5	1	no	—
590	C₂×Dic₃	—	10	2	no	—
591	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
592	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
593	D₁₂	—	10	2	no	—
594	C₄×D₃	—	2	2	no	—
595	C₄×D₃	—	2	1	no	—
596	C₄×D₃	—	2	1	no	—
597	C₄×D₃	—	2	2	no	—
598	C₄×D₃	—	10	2	no	—
599	C₄×D₃	—	10	2	no	—
600	C₄×D₃	—	10	2	no	—
601	C₄×D₃	—	10	1	no	—
602	C₄×D₃	—	10	1	no	—
603	C₄×D₃	—	10	2	no	—
604	C₄×D₃	#709	1	2	yes	—
605	C₄×D₃	C₂×C₂²⋊D₅	1	2	yes	—
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	10	1	no	—
608	C₃×C₈	—	10	1	no	—
609	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	complemented
610	C₃⋊C₈	—	2	1	no	—
611	C₃⋊C₈	—	10	1	no	—
612	C₃⋊C₈	—	10	1	no	—
613	C₃⋊C₈	C₂×C₂²⋊D₅	1	2	yes	complemented
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	3	2	no	—
617	C₂²×C₅	—	3	2	no	—
618	C₂²×C₅	—	3	2	no	—
619	C₂²×C₅	—	3	2	no	—
620	C₂²×C₅	—	6	8	no	—
621	C₂²×C₅	—	6	1	no	—
622	C₂²×C₅	—	6	1	no	—
623	C₂²×C₅	D₃×M₁₆	1	2	yes	complemented
624	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
625	C₂×D₅	—	2	1	no	—
626	C₂×D₅	—	2	1	no	—
627	C₂×D₅	—	2	1	no	—
628	C₂×D₅	—	6	1	no	—
629	C₂×D₅	—	6	1	no	—
630	C₂×D₅	—	6	1	no	—
631	C₂×D₅	—	12	4	no	—
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	3	2	no	—
634	C₄×C₅	—	6	1	no	—
635	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
636	C₄×C₅	D₃×#41	1	1	yes	characteristic
637	Dic₅	—	2	1	no	—
638	Dic₅	—	2	1	no	—
639	Dic₅	—	2	1	no	—
640	Dic₅	—	6	1	no	—
641	Dic₅	—	6	1	no	—
642	Dic₅	—	6	1	no	—
643	C₂⁴	—	3	1	no	—
644	C₂⁴	—	15	1	no	—
645	C₂×D₄	—	5	1	no	—
646	C₂×D₄	—	15	1	no	—
647	C₂×D₄	—	15	1	no	—
648	C₂×D₄	—	15	1	no	—
649	C₂×D₄	—	30	4	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	—	5	1	no	—
656	C₂²×C₄	—	6	2	no	—
657	C₂²×C₄	—	6	2	no	—
658	C₂²×C₄	—	15	1	no	—
659	C₂²×C₄	—	15	1	no	—
660	C₂²×C₄	—	15	1	no	—
661	C₂²×C₄	—	15	1	no	—
662	C₂²×C₄	—	15	1	no	—
663	C₂²×C₄	—	15	1	no	—
664	C₂²×C₄	—	30	2	no	—
665	C₂²×C₄	—	30	2	no	—
666	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
667	M₁₆	—	10	2	no	—
668	M₁₆	—	30	2	no	—
669	M₁₆	—	30	2	no	—
670	M₁₆	—	30	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	3	1	no	—
673	C₂×C₈	—	3	4	no	—
674	C₂×C₈	—	3	1	no	—
675	C₂×C₈	—	5	1	no	—
676	C₂×C₈	—	5	1	no	—
677	C₂×C₈	—	6	2	no	—
678	C₂×C₈	—	6	2	no	—
679	C₂×C₈	—	6	2	no	—
680	C₂×C₈	—	6	2	no	—
681	C₂×C₈	—	15	1	no	—
682	C₂×C₈	—	15	1	no	—
683	C₂×C₈	—	30	2	no	—
684	C₂×C₈	—	30	2	no	—
685	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
686	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
687	C₄⋊C₄	—	5	1	no	—
688	C₄⋊C₄	—	15	1	no	—
689	C₄⋊C₄	—	15	1	no	—
690	C₄⋊C₄	—	15	1	no	—
691	C₂²⋊C₄	—	5	1	no	—
692	C₂²⋊C₄	—	5	1	no	—
693	C₂²⋊C₄	—	15	1	no	—
694	C₂²⋊C₄	—	15	1	no	—
695	C₂²⋊C₄	—	15	1	no	—
696	C₂²⋊C₄	—	15	1	no	—
697	C₂²⋊C₄	—	15	1	no	—
698	C₂²⋊C₄	—	15	1	no	—
699	C₄²	—	5	1	no	—
700	C₄²	—	15	1	no	—
701	C₄²	—	15	1	no	—
702	C₄²	—	15	1	no	—
703	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	10	1	no	—
707	C₂²×C₃	—	10	1	no	—
708	C₂²×C₃	—	10	1	no	—
709	C₂²×C₃	C₂×#676	1	2	yes	complemented
710	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
711	C₂×D₃	—	2	1	no	—
712	C₂×D₃	—	2	1	no	—
713	C₂×D₃	—	2	8	no	—
714	C₂×D₃	—	10	1	no	—
715	C₂×D₃	—	10	1	no	—
716	C₂×D₃	—	10	1	no	—
717	C₂×D₃	—	20	4	no	—
718	C₂×D₃	C₂×#676	1	2	yes	—
719	C₂×D₃	C₂×#676	1	2	yes	complemented
720	C₂×D₃	#4047	1	2	yes	—
721	C₂×D₃	C₄×C₂²⋊D₅	1	2	yes	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	10	1	no	—
724	C₃×C₄	—	10	1	no	—
725	C₃×C₄	—	10	1	no	—
726	C₃×C₄	C₂×#709	1	1	yes	characteristic
727	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
728	Dic₃	—	2	1	no	—
729	Dic₃	—	10	1	no	—
730	Dic₃	—	10	1	no	—
731	Dic₃	—	10	1	no	—
732	Dic₃	C₄×C₂²⋊D₅	1	2	yes	—
733	C₂×C₅	—	2	2	no	—
734	C₂×C₅	—	3	4	no	—
735	C₂×C₅	—	6	2	no	—
736	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
737	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
738	C₂×C₅	D₃×#131	1	1	yes	characteristic
739	D₅	—	4	1	no	—
740	D₅	—	12	1	no	—
741	C₂³	—	3	1	no	—
742	C₂³	—	3	1	no	—
743	C₂³	—	3	4	no	—
744	C₂³	—	5	1	no	—
745	C₂³	—	6	2	no	—
746	C₂³	—	6	2	no	—
747	C₂³	—	15	1	no	—
748	C₂³	—	30	2	no	—
749	C₂³	—	30	2	no	—
750	C₂³	—	30	2	no	—
751	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
752	D₄	—	10	2	no	—
753	D₄	—	30	2	no	—
754	D₄	—	30	2	no	—
755	D₄	—	30	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	3	1	no	—
759	C₂×C₄	—	3	2	no	—
760	C₂×C₄	—	3	2	no	—
761	C₂×C₄	—	3	1	no	—
762	C₂×C₄	—	5	1	no	—
763	C₂×C₄	—	5	1	no	—
764	C₂×C₄	—	5	1	no	—
765	C₂×C₄	—	6	2	no	—
766	C₂×C₄	—	6	2	no	—
767	C₂×C₄	—	6	2	no	—
768	C₂×C₄	—	6	1	no	—
769	C₂×C₄	—	6	1	no	—
770	C₂×C₄	—	10	1	no	—
771	C₂×C₄	—	10	1	no	—
772	C₂×C₄	—	15	1	no	—
773	C₂×C₄	—	15	1	no	—
774	C₂×C₄	—	15	1	no	—
775	C₂×C₄	—	30	2	no	—
776	C₂×C₄	—	30	2	no	—
777	C₂×C₄	—	30	2	no	—
778	C₂×C₄	—	30	2	no	—
779	C₂×C₄	—	30	2	no	—
780	C₂×C₄	—	30	1	no	—
781	C₂×C₄	—	30	1	no	—
782	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
784	C₈	—	2	1	no	—
785	C₈	—	3	2	no	—
786	C₈	—	6	1	no	—
787	C₈	—	10	1	no	—
788	C₈	—	10	1	no	—
789	C₈	—	30	1	no	—
790	C₈	—	30	1	no	—
791	C₈	D₃×C₂²⋊D₅	1	2	yes	complemented
792	C₂×C₃	—	2	2	no	—
793	C₂×C₃	—	20	1	no	—
794	C₂×C₃	C₂²×#676	1	1	yes	characteristic
795	C₂×C₃	C₂×#4047	1	1	yes	characteristic
796	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
797	D₃	—	2	2	no	—
798	D₃	—	20	1	no	—
799	D₃	#65400	1	4	yes	direct product factor
800	C₅	D₃×#435	1	1	yes	characteristic, complemented, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	3	2	no	—
804	C₂²	—	3	2	no	—
805	C₂²	—	3	2	no	—
806	C₂²	—	3	2	no	—
807	C₂²	—	6	8	no	—
808	C₂²	—	6	1	no	—
809	C₂²	—	6	1	no	—
810	C₂²	—	10	1	no	—
811	C₂²	—	10	1	no	—
812	C₂²	—	10	1	no	—
813	C₂²	—	30	1	no	—
814	C₂²	—	30	1	no	—
815	C₂²	—	30	1	no	—
816	C₂²	—	60	4	no	—
817	C₂²	D₃×#676	1	2	yes	complemented
818	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	3	2	no	—
821	C₄	—	6	1	no	—
822	C₄	—	10	1	no	—
823	C₄	—	10	1	no	—
824	C₄	—	10	1	no	—
825	C₄	—	30	1	no	—
826	C₄	—	30	1	no	—
827	C₄	—	30	1	no	—
828	C₄	D₃×#709	1	1	yes	characteristic
829	C₄	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
830	C₃	C₂×#65400	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	2	2	no	—
832	C₂	—	3	4	no	—
833	C₂	—	6	2	no	—
834	C₂	—	20	1	no	—
835	C₂	—	60	1	no	—
836	C₂	C₂×D₃×#676	1	1	yes	characteristic
837	C₂	D₃×#4047	1	1	yes	characteristic
838	C₂	C₄×D₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	C₂×D₃×C₂²⋊D₅	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#435
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×C₈	C₂	semidirect
3. C₂×D₃×#676	C₂	semidirect
4. #11751212	C₂	semidirect
5. C₃×#65400	C₂	semidirect
6. #11748506	C₂	semidirect
7. #11748503	C₂	semidirect
8. D₃×C₂²⋊#168	C₂	semidirect
9. D₃×#3952	C₂	semidirect
10. #11747720	C₂	semidirect
11. #11747719	C₂	semidirect
12. #11747712	C₂	semidirect
13. #11747711	C₂	semidirect
14. D₃×#3947	C₂	semidirect
15. D₃×#3946	C₂	semidirect
20. C₂²×C₃×C₅×C₈	C₂²	semidirect
22. C₂×#6705	C₂²	semidirect
23. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
27. C₂×C₅×D₃×C₈	C₂²	semidirect
28. C₂×C₅×D₃×C₈	C₂²	semidirect
30. C₂×C₃×#676	C₂²	semidirect
41. C₂×#6651	C₂²	semidirect
42. C₂×#6649	C₂²	semidirect
46. #91114	C₂²	semidirect
47. #91104	C₂²	semidirect
48. #91099	C₂²	semidirect
49. #91098	C₂²	semidirect
50. C₃×C₂²⋊#168	C₂²	semidirect
51. C₃×#3952	C₂²	semidirect
52. C₃×#3947	C₂²	semidirect
53. C₃×#3946	C₂²	semidirect
54. #90983	C₂²	semidirect
55. #90982	C₂²	semidirect
56. #90957	C₂²	semidirect
57. (C₂×D₃)⋊#168	C₂²	semidirect
58. (C₂×D₃)⋊#168	C₂²	semidirect
59. #90955	C₂²	semidirect
60. #90954	C₂²	semidirect
61. #90952	C₂²	semidirect
74. #65400	D₃	direct (N × H)
118. C₅×D₃×C₈	D₄	semidirect
139. C₂²×D₃×C₈	D₅	semidirect
162. C₂²×C₅×C₈	C₂×D₃	semidirect
181. C₂×#676	C₂×D₃	semidirect
185. C₂²⋊#168	C₂×D₃	semidirect
189. #3952	C₂×D₃	semidirect
193. #3947	C₂×D₃	semidirect
197. #3946	C₂×D₃	semidirect
203. C₂²×C₅×D₃	M₁₆	semidirect
243. C₃×C₅×C₈	C₂×D₄	semidirect
249. C₅×C₃⋊C₈	C₂×D₄	semidirect
254. C₂²×C₃×C₈	C₂×D₅	semidirect
260. C₂²×C₃⋊C₈	C₂×D₅	semidirect
269. C₂×D₃×C₈	C₂×D₅	semidirect
270. C₂×D₃×C₈	C₂×D₅	semidirect
372. C₂²×C₃×C₅	C₂×M₁₆	semidirect
382. C₂×C₅×D₃	C₂×M₁₆	semidirect
458. D₃×C₈	C₂²⋊D₅	semidirect
505. C₅×C₈	D₃×D₄	semidirect
526. C₂²×C₈	D₃×D₅	semidirect
562. C₅×D₃	#435	semidirect
571. C₂²×D₃	#676	semidirect
609. C₃×C₈	C₂×C₂²⋊D₅	semidirect
613. C₃⋊C₈	C₂×C₂²⋊D₅	semidirect
623. C₂²×C₅	D₃×M₁₆	semidirect
703. C₃×C₅	C₂×#435	semidirect
709. C₂²×C₃	C₂×#676	semidirect
719. C₂×D₃	C₂×#676	semidirect
791. C₈	D₃×C₂²⋊D₅	semidirect
799. D₃	#65400	direct (N × H)
800. C₅	D₃×#435	semidirect
817. C₂²	D₃×#676	semidirect
830. C₃	C₂×#65400	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×C₈	2
C₄×D₃×C₂²⋊D₅	2
C₂×D₃×#676	2
#11751212	2
C₃×#65400	2
#11748506	2
#11748503	2
D₃×C₂²⋊#168	2
D₃×#3952	2
#11747720	2
#11747719	2
#11747712	2
#11747711	2
D₃×#3947	2
D₃×#3946	2
C₂×#65400	3
D₃×#435	5

Subgroups — D3×#65400 #14414720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65400 #14414720