Subgroups — C₂×C₃×#5589 #11900937

Order 1152.

4299 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#938	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#937	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5589	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₃×#886	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#884	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#883	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#534	—	3	1	no	maximal
14	C₂×#5589	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂⁵×C₃²	C₂²	1	1	yes	characteristic, complemented
16	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
20	C₂²×C₃×#67	—	2	8	no	—
21	C₂²×C₃×#67	C₂²	1	2	yes	—
22	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#67	C₂²	1	2	yes	complemented
24	C₂²×C₃×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×#67	C₂²	1	2	yes	complemented
26	C₂²×C₃×#67	C₂²	1	8	yes	complemented
27	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×D₃×D₄	—	2	8	no	—
29	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
30	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
33	C₃²×#120	C₂²	1	8	yes	complemented
34	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃×#953	C₂²	1	8	yes	complemented
37	C₂×C₃×#217	C₂²	1	2	yes	complemented
38	C₂×C₃×#217	C₂²	1	2	yes	complemented
39	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
40	C₃×#938	C₂²	1	16	yes	complemented
41	C₃×#937	C₂²	1	16	yes	complemented
42	C₃×#935	C₂²	1	8	yes	complemented
43	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
46	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
47	C₃×#886	C₂²	1	8	yes	complemented
48	C₃×#884	C₂²	1	16	yes	complemented
49	C₃×#883	C₂²	1	16	yes	complemented
50	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
51	C₂³×C₃×D₄	—	3	1	no	—
52	C₂³×C₃×D₄	—	3	1	no	—
53	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#534	—	3	16	no	—
56	C₂×C₃×#123	—	3	1	no	—
57	C₂×C₃×#123	—	3	2	no	—
58	C₂×C₃×#123	—	3	1	no	—
59	C₂×C₃×#121	—	3	2	no	—
60	C₂×C₃×#121	—	3	2	no	—
61	C₂×C₃×#120	—	2	1	no	—
62	C₂×C₃×#120	—	3	2	no	—
63	C₂×C₃×#120	—	3	1	no	—
64	C₂×C₃×#120	D₃	1	1	yes	characteristic, complemented
65	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
67	C₂×#953	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#938	C₂×C₃	1	2	yes	complemented
69	C₂×#937	C₂×C₃	1	2	yes	complemented
70	C₂×#935	C₂×C₃	1	1	yes	characteristic, complemented
71	#5589	C₂×C₃	1	16	yes	direct product factor
72	C₂×#886	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×#884	C₂×C₃	1	2	yes	complemented
74	C₂×#883	C₂×C₃	1	2	yes	complemented
75	C₂×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃²	—	2	4	no	—
77	C₂⁴×C₃²	—	4	4	no	—
78	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
79	C₂⁴×C₃²	C₂³	1	2	yes	—
80	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
81	C₂⁴×C₃²	C₂³	1	4	yes	complemented
82	C₂³×C₃×D₃	—	2	4	no	—
83	C₂³×C₃×D₃	—	4	4	no	—
84	C₂³×C₃×D₃	—	4	4	no	—
85	C₂³×C₃×D₃	D₄	1	8	yes	complemented
86	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
87	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
88	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
89	C₂³×C₃×D₃	C₂³	1	4	yes	—
90	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
91	C₂×C₃²×D₄	—	2	4	no	—
92	C₂×C₃²×D₄	—	4	4	no	—
93	C₂×C₃²×D₄	C₂³	1	4	yes	—
94	C₂×C₃²×D₄	C₂³	1	8	yes	complemented
95	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃²×C₄	C₂³	1	2	yes	—
97	C₂×C₃×#67	—	2	4	no	—
98	C₂×C₃×#67	—	2	4	no	—
99	C₂×C₃×#67	—	2	8	no	—
100	C₂×C₃×#67	—	2	8	no	—
101	C₂×C₃×#67	—	2	32	no	—
102	C₂×C₃×#67	—	4	4	no	—
103	C₂×C₃×#67	C₂³	1	8	yes	—
104	C₂×C₃×#67	C₂³	1	4	yes	—
105	C₂×C₃×#67	C₂³	1	8	yes	complemented
106	C₂×C₃×#67	C₂³	1	4	yes	complemented
107	C₂×C₃×#67	C₂³	1	8	yes	complemented
108	C₂²×C₃×Dic₃	—	2	4	no	—
109	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
110	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
111	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
112	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
113	C₃×D₃×D₄	—	2	32	no	—
114	C₂×C₃×D₁₂	—	2	4	no	—
115	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
116	C₂×C₃×C₄×D₃	—	2	4	no	—
117	C₂×C₃×C₄×D₃	—	4	4	no	—
118	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
119	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
120	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
121	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
122	C₃×#217	C₂³	1	4	yes	complemented
123	C₃×#217	C₂³	1	8	yes	complemented
124	C₃×#217	C₂³	1	8	yes	complemented
125	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
126	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
127	C₃×C₄⋊Dic₃	C₂³	1	8	yes	complemented
128	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
129	C₂×#534	—	3	1	no	Sylow
130	C₂⁵×C₃	—	2	1	no	—
131	C₂⁵×C₃	—	3	1	no	—
132	C₂⁵×C₃	—	3	1	no	—
133	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic, complemented
134	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
136	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂²×C₃×D₄	—	2	1	no	—
138	C₂²×C₃×D₄	—	2	2	no	—
139	C₂²×C₃×D₄	—	3	2	no	—
140	C₂²×C₃×D₄	—	3	1	no	—
141	C₂²×C₃×D₄	—	3	1	no	—
142	C₂²×C₃×D₄	—	3	2	no	—
143	C₂²×C₃×D₄	—	3	8	no	—
144	C₂²×C₃×D₄	—	3	2	no	—
145	C₂²×C₃×D₄	—	3	8	no	—
146	C₂²×C₃×D₄	—	3	1	no	—
147	C₂²×C₃×D₄	—	6	8	no	—
148	C₂²×C₃×D₄	—	6	8	no	—
149	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
150	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
151	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
153	C₂³×C₃×C₄	—	3	1	no	—
154	C₂³×C₃×C₄	—	3	1	no	—
155	C₂³×C₃×C₄	—	3	2	no	—
156	C₂²×#67	—	2	8	no	—
157	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
158	C₂²×#67	C₂²×C₃	1	2	yes	—
159	C₂²×#67	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₂²×#67	C₂²×C₃	1	2	yes	complemented
161	C₂²×#67	C₂²×C₃	1	2	yes	complemented
162	C₂²×#67	C₂²×C₃	1	8	yes	complemented
163	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₂×D₃×D₄	—	2	8	no	—
165	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
166	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
169	C₃×#123	—	3	8	no	—
170	C₃×#123	—	3	16	no	—
171	C₃×#123	—	3	8	no	—
172	C₃×#121	—	3	16	no	—
173	C₃×#121	—	3	16	no	—
174	C₃×#120	—	2	8	no	—
175	C₃×#120	—	3	8	no	—
176	C₃×#120	—	3	16	no	—
177	C₃×#120	C₂×D₃	1	8	yes	complemented
178	C₃×#120	C₂²×C₃	1	8	yes	complemented
179	C₂×C₃×C₄⋊C₄	—	3	2	no	—
180	C₂×C₃×C₄⋊C₄	—	3	2	no	—
181	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
183	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
184	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
185	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
186	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
187	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
188	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
189	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
190	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
191	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
193	#953	C₂²×C₃	1	8	yes	complemented
194	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂×#217	C₂²×C₃	1	2	yes	complemented
196	C₂×#217	C₂²×C₃	1	2	yes	complemented
197	#938	C₂²×C₃	1	16	yes	complemented
198	#937	C₂²×C₃	1	16	yes	complemented
199	#935	C₂²×C₃	1	8	yes	complemented
200	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
201	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
202	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
203	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
204	#886	C₂²×C₃	1	8	yes	complemented
205	#884	C₂²×C₃	1	16	yes	complemented
206	#883	C₂²×C₃	1	16	yes	complemented
207	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
208	C₂³×C₃²	—	2	4	no	—
209	C₂³×C₃²	—	2	4	no	—
210	C₂³×C₃²	—	2	2	no	—
211	C₂³×C₃²	—	2	4	no	—
212	C₂³×C₃²	—	2	8	no	—
213	C₂³×C₃²	—	2	4	no	—
214	C₂³×C₃²	—	2	4	no	—
215	C₂³×C₃²	—	4	8	no	—
216	C₂³×C₃²	—	4	16	no	—
217	C₂³×C₃²	C₂×D₄	1	4	yes	—
218	C₂³×C₃²	C₂⁴	1	2	yes	—
219	C₂³×C₃²	C₂⁴	1	4	yes	—
220	C₂³×C₃²	C₂⁴	1	2	yes	—
221	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
222	C₂²×C₃×D₃	—	2	4	no	—
223	C₂²×C₃×D₃	—	2	4	no	—
224	C₂²×C₃×D₃	—	2	2	no	—
225	C₂²×C₃×D₃	—	2	4	no	—
226	C₂²×C₃×D₃	—	2	8	no	—
227	C₂²×C₃×D₃	—	4	16	no	—
228	C₂²×C₃×D₃	—	4	8	no	—
229	C₂²×C₃×D₃	—	4	8	no	—
230	C₂²×C₃×D₃	—	4	16	no	—
231	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
232	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
233	C₂²×C₃×D₃	C₂×D₄	1	16	yes	complemented
234	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
235	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
236	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
237	C₃²×D₄	—	2	8	no	—
238	C₃²×D₄	—	4	8	no	—
239	C₂×C₃²×C₄	—	2	2	no	—
240	C₂×C₃²×C₄	—	2	4	no	—
241	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
242	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
243	C₃×#67	—	2	8	no	—
244	C₃×#67	—	2	8	no	—
245	C₃×#67	—	2	16	no	—
246	C₃×#67	—	2	16	no	—
247	C₃×#67	—	4	8	no	—
248	C₂×C₃×Dic₃	—	2	2	no	—
249	C₂×C₃×Dic₃	—	2	4	no	—
250	C₂×C₃×Dic₃	—	2	8	no	—
251	C₂×C₃×Dic₃	—	2	4	no	—
252	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
253	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
254	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
255	C₃×D₁₂	—	2	8	no	—
256	C₃×C₄×D₃	—	2	8	no	—
257	C₃×C₄×D₃	—	4	8	no	—
258	C₂³×D₄	—	3	1	no	—
259	C₂³×D₄	—	3	1	no	—
260	#534	—	3	16	no	—
261	C₂×#123	—	3	1	no	—
262	C₂×#123	—	3	2	no	—
263	C₂×#123	—	3	1	no	—
264	C₂×#121	—	3	2	no	—
265	C₂×#121	—	3	2	no	—
266	C₂×#120	—	3	1	no	—
267	C₂×#120	—	3	2	no	—
268	C₂×#120	C₃×D₃	1	1	yes	characteristic, complemented
269	C₂²×C₂²⋊C₄	—	3	1	no	—
270	C₂⁴×C₃	—	2	4	no	—
271	C₂⁴×C₃	—	2	4	no	—
272	C₂⁴×C₃	—	2	2	no	—
273	C₂⁴×C₃	—	2	1	no	—
274	C₂⁴×C₃	—	2	1	no	—
275	C₂⁴×C₃	—	2	4	no	—
276	C₂⁴×C₃	—	3	1	no	—
277	C₂⁴×C₃	—	3	1	no	—
278	C₂⁴×C₃	—	3	8	no	—
279	C₂⁴×C₃	—	3	4	no	—
280	C₂⁴×C₃	—	3	1	no	—
281	C₂⁴×C₃	—	3	4	no	—
282	C₂⁴×C₃	—	4	4	no	—
283	C₂⁴×C₃	—	4	4	no	—
284	C₂⁴×C₃	—	4	4	no	—
285	C₂⁴×C₃	—	4	8	no	—
286	C₂⁴×C₃	—	6	4	no	—
287	C₂⁴×C₃	—	12	4	no	—
288	C₂⁴×C₃	—	12	4	no	—
289	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
290	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
291	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
292	C₂⁴×C₃	C₂²×D₃	1	4	yes	complemented
293	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
294	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
295	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
296	C₂⁴×C₃	C₂³×C₃	1	4	yes	complemented
297	C₂³×D₃	—	2	4	no	—
298	C₂³×D₃	—	4	4	no	—
299	C₂³×D₃	—	4	4	no	—
300	C₂³×D₃	C₃×D₄	1	8	yes	complemented
301	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
302	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
303	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
304	C₂³×D₃	C₂³×C₃	1	4	yes	—
305	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
306	C₂×C₃×D₄	—	2	4	no	—
307	C₂×C₃×D₄	—	2	4	no	—
308	C₂×C₃×D₄	—	2	4	no	—
309	C₂×C₃×D₄	—	2	8	no	—
310	C₂×C₃×D₄	—	3	8	no	—
311	C₂×C₃×D₄	—	3	4	no	—
312	C₂×C₃×D₄	—	3	4	no	—
313	C₂×C₃×D₄	—	3	8	no	—
314	C₂×C₃×D₄	—	3	8	no	—
315	C₂×C₃×D₄	—	3	4	no	—
316	C₂×C₃×D₄	—	4	4	no	—
317	C₂×C₃×D₄	—	4	4	no	—
318	C₂×C₃×D₄	—	4	4	no	—
319	C₂×C₃×D₄	—	4	8	no	—
320	C₂×C₃×D₄	—	6	4	no	—
321	C₂×C₃×D₄	—	6	32	no	—
322	C₂×C₃×D₄	—	6	4	no	—
323	C₂×C₃×D₄	—	6	8	no	—
324	C₂×C₃×D₄	—	6	8	no	—
325	C₂×C₃×D₄	—	6	32	no	—
326	C₂×C₃×D₄	—	6	4	no	—
327	C₂×C₃×D₄	—	12	4	no	—
328	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
329	C₂×C₃×D₄	C₂²×D₃	1	8	yes	complemented
330	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
331	C₂×C₃×D₄	C₂³×C₃	1	8	yes	complemented
332	C₂²×C₃×C₄	—	2	2	no	—
333	C₂²×C₃×C₄	—	2	1	no	—
334	C₂²×C₃×C₄	—	3	4	no	—
335	C₂²×C₃×C₄	—	3	2	no	—
336	C₂²×C₃×C₄	—	3	1	no	—
337	C₂²×C₃×C₄	—	3	2	no	—
338	C₂²×C₃×C₄	—	3	4	no	—
339	C₂²×C₃×C₄	—	3	8	no	—
340	C₂²×C₃×C₄	—	6	4	no	—
341	C₂²×C₃×C₄	—	6	4	no	—
342	C₂²×C₃×C₄	—	12	4	no	—
343	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
344	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
347	C₂×#67	—	2	4	no	—
348	C₂×#67	—	2	4	no	—
349	C₂×#67	—	2	8	no	—
350	C₂×#67	—	2	8	no	—
351	C₂×#67	—	2	32	no	—
352	C₂×#67	—	4	4	no	—
353	C₂×#67	C₂³×C₃	1	8	yes	—
354	C₂×#67	C₂³×C₃	1	4	yes	—
355	C₂×#67	C₂³×C₃	1	8	yes	complemented
356	C₂×#67	C₂³×C₃	1	4	yes	complemented
357	C₂×#67	C₂³×C₃	1	8	yes	complemented
358	C₂²×Dic₃	—	2	4	no	—
359	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
360	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
361	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
362	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
363	D₃×D₄	—	2	32	no	—
364	C₂×D₁₂	—	2	4	no	—
365	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
366	C₂×C₄×D₃	—	2	4	no	—
367	C₂×C₄×D₃	—	4	4	no	—
368	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
369	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
370	C₃×C₄⋊C₄	—	3	8	no	—
371	C₃×C₄⋊C₄	—	3	8	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	8	no	—
374	C₃×C₂²⋊C₄	—	3	4	no	—
375	C₃×C₂²⋊C₄	—	3	8	no	—
376	C₃×C₂²⋊C₄	—	3	8	no	—
377	C₃×C₂²⋊C₄	—	3	8	no	—
378	C₃×C₂²⋊C₄	—	3	8	no	—
379	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
380	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
381	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
382	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
383	#217	C₂³×C₃	1	4	yes	complemented
384	#217	C₂³×C₃	1	8	yes	complemented
385	#217	C₂³×C₃	1	8	yes	complemented
386	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
387	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
388	C₄⋊Dic₃	C₂³×C₃	1	8	yes	complemented
389	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
390	C₂²×C₃²	—	2	4	no	—
391	C₂²×C₃²	—	2	8	no	—
392	C₂²×C₃²	—	2	4	no	—
393	C₂²×C₃²	—	2	4	no	—
394	C₂²×C₃²	—	2	2	no	—
395	C₂²×C₃²	—	2	4	no	—
396	C₂²×C₃²	—	2	4	no	—
397	C₂²×C₃²	—	4	16	no	—
398	C₂²×C₃²	—	4	8	no	—
399	C₂²×C₃²	—	4	4	no	—
400	C₂²×C₃²	C₂²×D₄	1	4	yes	—
401	C₂²×C₃²	C₂²×D₄	1	2	yes	—
402	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
403	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
404	C₂×C₃×D₃	—	2	8	no	—
405	C₂×C₃×D₃	—	2	8	no	—
406	C₂×C₃×D₃	—	2	4	no	—
407	C₂×C₃×D₃	—	2	4	no	—
408	C₂×C₃×D₃	—	2	2	no	—
409	C₂×C₃×D₃	—	2	4	no	—
410	C₂×C₃×D₃	—	4	16	no	—
411	C₂×C₃×D₃	—	4	16	no	—
412	C₂×C₃×D₃	—	4	4	no	—
413	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
414	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
415	C₃²×C₄	—	2	2	no	—
416	C₃²×C₄	—	2	4	no	—
417	C₃×Dic₃	—	2	2	no	—
418	C₃×Dic₃	—	2	4	no	—
419	C₃×Dic₃	—	2	4	no	—
420	C₂⁵	—	3	1	no	—
421	C₂⁵	—	3	1	no	—
422	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic, complemented
423	C₂²×D₄	—	3	2	no	—
424	C₂²×D₄	—	3	1	no	—
425	C₂²×D₄	—	3	1	no	—
426	C₂²×D₄	—	3	2	no	—
427	C₂²×D₄	—	3	8	no	—
428	C₂²×D₄	—	3	2	no	—
429	C₂²×D₄	—	3	8	no	—
430	C₂²×D₄	—	3	1	no	—
431	C₂²×D₄	—	6	8	no	—
432	C₂²×D₄	—	6	8	no	—
433	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
434	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
435	C₂³×C₄	—	3	1	no	—
436	C₂³×C₄	—	3	1	no	—
437	C₂³×C₄	—	3	2	no	—
438	#123	—	3	8	no	—
439	#123	—	3	16	no	—
440	#123	—	3	8	no	—
441	#121	—	3	16	no	—
442	#121	—	3	16	no	—
443	#120	—	3	8	no	—
444	#120	—	3	16	no	—
445	#120	C₂×C₃×D₃	1	8	yes	complemented
446	C₂×C₄⋊C₄	—	3	2	no	—
447	C₂×C₄⋊C₄	—	3	2	no	—
448	C₂×C₂²⋊C₄	—	3	1	no	—
449	C₂×C₂²⋊C₄	—	3	2	no	—
450	C₂×C₂²⋊C₄	—	3	2	no	—
451	C₂×C₂²⋊C₄	—	3	2	no	—
452	C₂×C₂²⋊C₄	—	3	2	no	—
453	C₂×C₂²⋊C₄	—	3	8	no	—
454	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
455	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
456	C₂³×C₃	—	2	4	no	—
457	C₂³×C₃	—	2	4	no	—
458	C₂³×C₃	—	2	8	no	—
459	C₂³×C₃	—	2	2	no	—
460	C₂³×C₃	—	2	4	no	—
461	C₂³×C₃	—	2	8	no	—
462	C₂³×C₃	—	2	4	no	—
463	C₂³×C₃	—	2	4	no	—
464	C₂³×C₃	—	2	4	no	—
465	C₂³×C₃	—	2	4	no	—
466	C₂³×C₃	—	2	8	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	4	no	—
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	2	4	no	—
471	C₂³×C₃	—	2	1	no	—
472	C₂³×C₃	—	2	4	no	—
473	C₂³×C₃	—	2	2	no	—
474	C₂³×C₃	—	2	2	no	—
475	C₂³×C₃	—	2	4	no	—
476	C₂³×C₃	—	3	4	no	—
477	C₂³×C₃	—	3	4	no	—
478	C₂³×C₃	—	3	2	no	—
479	C₂³×C₃	—	3	2	no	—
480	C₂³×C₃	—	3	16	no	—
481	C₂³×C₃	—	3	2	no	—
482	C₂³×C₃	—	4	4	no	—
483	C₂³×C₃	—	4	4	no	—
484	C₂³×C₃	—	4	8	no	—
485	C₂³×C₃	—	4	4	no	—
486	C₂³×C₃	—	4	2	no	—
487	C₂³×C₃	—	4	4	no	—
488	C₂³×C₃	—	4	8	no	—
489	C₂³×C₃	—	4	8	no	—
490	C₂³×C₃	—	4	16	no	—
491	C₂³×C₃	—	4	16	no	—
492	C₂³×C₃	—	4	16	no	—
493	C₂³×C₃	—	4	32	no	—
494	C₂³×C₃	—	6	8	no	—
495	C₂³×C₃	—	6	4	no	—
496	C₂³×C₃	—	6	4	no	—
497	C₂³×C₃	—	6	2	no	—
498	C₂³×C₃	—	6	4	no	—
499	C₂³×C₃	—	12	8	no	—
500	C₂³×C₃	—	12	16	no	—
501	C₂³×C₃	—	12	8	no	—
502	C₂³×C₃	—	12	16	no	—
503	C₂³×C₃	D₃×D₄	1	4	yes	—
504	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
505	C₂³×C₃	C₂³×D₃	1	2	yes	—
506	C₂³×C₃	C₂³×D₃	1	4	yes	—
507	C₂³×C₃	C₂³×D₃	1	2	yes	—
508	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
509	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
510	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
511	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
512	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
513	C₂²×D₃	—	2	4	no	—
514	C₂²×D₃	—	2	4	no	—
515	C₂²×D₃	—	2	2	no	—
516	C₂²×D₃	—	2	4	no	—
517	C₂²×D₃	—	2	8	no	—
518	C₂²×D₃	—	4	16	no	—
519	C₂²×D₃	—	4	8	no	—
520	C₂²×D₃	—	4	8	no	—
521	C₂²×D₃	—	4	16	no	—
522	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
523	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
524	C₂²×D₃	C₂×C₃×D₄	1	16	yes	complemented
525	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
526	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
527	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
528	C₃×D₄	—	2	8	no	—
529	C₃×D₄	—	2	8	no	—
530	C₃×D₄	—	4	8	no	—
531	C₃×D₄	—	4	8	no	—
532	C₃×D₄	—	4	8	no	—
533	C₃×D₄	—	4	16	no	—
534	C₃×D₄	—	6	8	no	—
535	C₃×D₄	—	6	8	no	—
536	C₃×D₄	—	6	16	no	—
537	C₃×D₄	—	6	16	no	—
538	C₃×D₄	—	6	8	no	—
539	C₃×D₄	—	12	8	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	4	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	4	no	—
544	C₂×C₃×C₄	—	2	4	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	3	4	no	—
547	C₂×C₃×C₄	—	3	4	no	—
548	C₂×C₃×C₄	—	3	2	no	—
549	C₂×C₃×C₄	—	4	2	no	—
550	C₂×C₃×C₄	—	4	4	no	—
551	C₂×C₃×C₄	—	6	8	no	—
552	C₂×C₃×C₄	—	6	8	no	—
553	C₂×C₃×C₄	—	6	2	no	—
554	C₂×C₃×C₄	—	6	4	no	—
555	C₂×C₃×C₄	—	6	4	no	—
556	C₂×C₃×C₄	—	12	8	no	—
557	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
558	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
559	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
560	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
561	#67	—	2	8	no	—
562	#67	—	2	8	no	—
563	#67	—	2	16	no	—
564	#67	—	2	16	no	—
565	#67	—	4	8	no	—
566	C₂×Dic₃	—	2	2	no	—
567	C₂×Dic₃	—	2	4	no	—
568	C₂×Dic₃	—	2	8	no	—
569	C₂×Dic₃	—	2	4	no	—
570	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
571	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
572	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
573	D₁₂	—	2	8	no	—
574	C₄×D₃	—	2	8	no	—
575	C₄×D₃	—	4	8	no	—
576	C₂×C₃²	—	2	4	no	—
577	C₂×C₃²	—	4	4	no	—
578	C₂×C₃²	—	4	2	no	—
579	C₂×C₃²	#534	1	4	yes	complemented
580	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
581	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
582	C₃×D₃	—	2	4	no	—
583	C₃×D₃	—	2	4	no	—
584	C₃×D₃	—	4	2	no	—
585	C₂⁴	—	2	4	no	—
586	C₂⁴	—	3	1	no	—
587	C₂⁴	—	3	1	no	—
588	C₂⁴	—	3	4	no	—
589	C₂⁴	—	3	8	no	—
590	C₂⁴	—	3	1	no	—
591	C₂⁴	—	3	4	no	—
592	C₂⁴	—	4	4	no	—
593	C₂⁴	—	6	4	no	—
594	C₂⁴	—	12	4	no	—
595	C₂⁴	—	12	4	no	—
596	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
597	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
598	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
599	C₂⁴	C₂²×C₃×D₃	1	4	yes	complemented
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	3	8	no	—
602	C₂×D₄	—	3	4	no	—
603	C₂×D₄	—	3	4	no	—
604	C₂×D₄	—	3	8	no	—
605	C₂×D₄	—	3	8	no	—
606	C₂×D₄	—	3	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	6	4	no	—
609	C₂×D₄	—	6	32	no	—
610	C₂×D₄	—	6	4	no	—
611	C₂×D₄	—	6	8	no	—
612	C₂×D₄	—	6	8	no	—
613	C₂×D₄	—	6	32	no	—
614	C₂×D₄	—	6	4	no	—
615	C₂×D₄	—	12	4	no	—
616	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
617	C₂×D₄	C₂²×C₃×D₃	1	8	yes	complemented
618	C₂²×C₄	—	3	2	no	—
619	C₂²×C₄	—	3	1	no	—
620	C₂²×C₄	—	3	2	no	—
621	C₂²×C₄	—	3	4	no	—
622	C₂²×C₄	—	3	4	no	—
623	C₂²×C₄	—	3	8	no	—
624	C₂²×C₄	—	6	4	no	—
625	C₂²×C₄	—	6	4	no	—
626	C₂²×C₄	—	12	4	no	—
627	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
628	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
629	C₄⋊C₄	—	3	8	no	—
630	C₄⋊C₄	—	3	8	no	—
631	C₂²⋊C₄	—	3	4	no	—
632	C₂²⋊C₄	—	3	8	no	—
633	C₂²⋊C₄	—	3	8	no	—
634	C₂²⋊C₄	—	3	8	no	—
635	C₂²⋊C₄	—	3	8	no	—
636	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
637	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
638	C₂²×C₃	—	2	4	no	—
639	C₂²×C₃	—	2	4	no	—
640	C₂²×C₃	—	2	8	no	—
641	C₂²×C₃	—	2	8	no	—
642	C₂²×C₃	—	2	8	no	—
643	C₂²×C₃	—	2	2	no	—
644	C₂²×C₃	—	2	4	no	—
645	C₂²×C₃	—	2	4	no	—
646	C₂²×C₃	—	2	4	no	—
647	C₂²×C₃	—	2	4	no	—
648	C₂²×C₃	—	2	4	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	2	4	no	—
651	C₂²×C₃	—	2	4	no	—
652	C₂²×C₃	—	2	4	no	—
653	C₂²×C₃	—	2	2	no	—
654	C₂²×C₃	—	2	4	no	—
655	C₂²×C₃	—	2	4	no	—
656	C₂²×C₃	—	2	1	no	—
657	C₂²×C₃	—	3	4	no	—
658	C₂²×C₃	—	3	4	no	—
659	C₂²×C₃	—	4	8	no	—
660	C₂²×C₃	—	4	4	no	—
661	C₂²×C₃	—	4	4	no	—
662	C₂²×C₃	—	4	4	no	—
663	C₂²×C₃	—	4	2	no	—
664	C₂²×C₃	—	4	4	no	—
665	C₂²×C₃	—	4	16	no	—
666	C₂²×C₃	—	4	16	no	—
667	C₂²×C₃	—	4	16	no	—
668	C₂²×C₃	—	4	32	no	—
669	C₂²×C₃	—	4	8	no	—
670	C₂²×C₃	—	4	4	no	—
671	C₂²×C₃	—	4	4	no	—
672	C₂²×C₃	—	4	8	no	—
673	C₂²×C₃	—	6	4	no	—
674	C₂²×C₃	—	6	4	no	—
675	C₂²×C₃	—	6	8	no	—
676	C₂²×C₃	—	6	8	no	—
677	C₂²×C₃	—	6	2	no	—
678	C₂²×C₃	—	6	4	no	—
679	C₂²×C₃	—	8	4	no	—
680	C₂²×C₃	—	12	16	no	—
681	C₂²×C₃	—	12	16	no	—
682	C₂²×C₃	—	12	4	no	—
683	C₂²×C₃	C₂×D₃×D₄	1	4	yes	—
684	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
685	C₂²×C₃	#1004	1	4	yes	—
686	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
687	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
688	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
689	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
690	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
691	C₂×D₃	—	2	4	no	—
692	C₂×D₃	—	2	4	no	—
693	C₂×D₃	—	2	8	no	—
694	C₂×D₃	—	2	8	no	—
695	C₂×D₃	—	2	2	no	—
696	C₂×D₃	—	2	4	no	—
697	C₂×D₃	—	4	16	no	—
698	C₂×D₃	—	4	16	no	—
699	C₂×D₃	—	4	4	no	—
700	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
701	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
702	C₃×C₄	—	2	2	no	—
703	C₃×C₄	—	2	4	no	—
704	C₃×C₄	—	2	2	no	—
705	C₃×C₄	—	2	4	no	—
706	C₃×C₄	—	4	2	no	—
707	C₃×C₄	—	4	4	no	—
708	C₃×C₄	—	6	2	no	—
709	C₃×C₄	—	6	4	no	—
710	C₃×C₄	—	6	4	no	—
711	Dic₃	—	2	2	no	—
712	Dic₃	—	2	4	no	—
713	Dic₃	—	2	4	no	—
714	C₃²	C₂×#534	1	1	yes	characteristic, complemented, Sylow
715	C₂³	—	2	4	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	8	no	—
719	C₂³	—	2	4	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	3	4	no	—
723	C₂³	—	3	4	no	—
724	C₂³	—	3	2	no	—
725	C₂³	—	3	2	no	—
726	C₂³	—	3	16	no	—
727	C₂³	—	3	2	no	—
728	C₂³	—	4	8	no	—
729	C₂³	—	4	16	no	—
730	C₂³	—	6	8	no	—
731	C₂³	—	6	4	no	—
732	C₂³	—	6	4	no	—
733	C₂³	—	6	2	no	—
734	C₂³	—	6	4	no	—
735	C₂³	—	12	16	no	—
736	C₂³	—	12	8	no	—
737	C₂³	—	12	8	no	—
738	C₂³	—	12	16	no	—
739	C₂³	C₃×D₃×D₄	1	4	yes	—
740	C₂³	C₂³×C₃×D₃	1	2	yes	—
741	C₂³	C₂³×C₃×D₃	1	4	yes	—
742	C₂³	C₂³×C₃×D₃	1	2	yes	—
743	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
744	D₄	—	2	8	no	—
745	D₄	—	4	8	no	—
746	D₄	—	6	8	no	—
747	D₄	—	6	8	no	—
748	D₄	—	6	16	no	—
749	D₄	—	6	16	no	—
750	D₄	—	6	8	no	—
751	D₄	—	12	8	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	3	4	no	—
755	C₂×C₄	—	3	2	no	—
756	C₂×C₄	—	3	4	no	—
757	C₂×C₄	—	6	8	no	—
758	C₂×C₄	—	6	8	no	—
759	C₂×C₄	—	6	2	no	—
760	C₂×C₄	—	6	4	no	—
761	C₂×C₄	—	6	4	no	—
762	C₂×C₄	—	12	8	no	—
763	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
764	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
765	C₂×C₃	—	2	4	no	—
766	C₂×C₃	—	2	4	no	—
767	C₂×C₃	—	2	4	no	—
768	C₂×C₃	—	2	1	no	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	4	4	no	—
771	C₂×C₃	—	4	8	no	—
772	C₂×C₃	—	4	2	no	—
773	C₂×C₃	—	4	4	no	—
774	C₂×C₃	—	4	4	no	—
775	C₂×C₃	—	4	2	no	—
776	C₂×C₃	—	6	4	no	—
777	C₂×C₃	—	6	4	no	—
778	C₂×C₃	—	8	2	no	—
779	C₂×C₃	—	12	2	no	—
780	C₂×C₃	#5589	1	4	yes	direct product factor
781	C₂×C₃	C₃×#534	1	4	yes	complemented
782	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
783	C₂×C₃	C₂×#1004	1	2	yes	—
784	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
785	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
786	D₃	—	2	4	no	—
787	D₃	—	2	4	no	—
788	D₃	—	4	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	3	4	no	—
797	C₂²	—	3	4	no	—
798	C₂²	—	4	16	no	—
799	C₂²	—	4	8	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	6	8	no	—
802	C₂²	—	6	8	no	—
803	C₂²	—	6	4	no	—
804	C₂²	—	6	4	no	—
805	C₂²	—	6	2	no	—
806	C₂²	—	6	4	no	—
807	C₂²	—	12	16	no	—
808	C₂²	—	12	16	no	—
809	C₂²	—	12	4	no	—
810	C₂²	C₂×C₃×D₃×D₄	1	4	yes	—
811	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
812	C₂²	C₃×#1004	1	4	yes	—
813	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	4	no	—
816	C₄	—	6	2	no	—
817	C₄	—	6	4	no	—
818	C₄	—	6	4	no	—
819	C₃	—	2	1	no	—
820	C₃	C₂×#5589	1	1	yes	characteristic, direct product factor
821	C₃	C₂×C₃×#534	1	1	yes	characteristic, complemented
822	C₂	—	2	4	no	—
823	C₂	—	4	4	no	—
824	C₂	—	4	2	no	—
825	C₂	—	6	4	no	—
826	C₂	—	6	4	no	—
827	C₂	—	12	2	no	—
828	C₂	C₃×#5589	1	4	yes	direct product factor
829	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
830	C₂	C₂×C₃×#1004	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#120	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#120	D₃
hypocenter	C₃	C₂×C₃×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×#67	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₂×C₃²×#120	C₂	semidirect
4. C₂×C₃×#953	C₂	semidirect
5. C₂×C₃×#938	C₂	semidirect
6. C₂×C₃×#937	C₂	semidirect
7. C₂×C₃×#935	C₂	semidirect
8. C₃×#5589	C₂	direct (N × H)
9. C₂×C₃×#886	C₂	semidirect
10. C₂×C₃×#884	C₂	semidirect
11. C₂×C₃×#883	C₂	semidirect
12. C₂×C₃×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂×#5589	C₃	direct (N × H)
15. C₂⁵×C₃²	C₂²	semidirect
17. C₂⁴×C₃×D₃	C₂²	semidirect
19. C₂²×C₃²×D₄	C₂²	semidirect
23. C₂²×C₃×#67	C₂²	semidirect
24. C₂²×C₃×#67	C₂²	semidirect
25. C₂²×C₃×#67	C₂²	semidirect
26. C₂²×C₃×#67	C₂²	semidirect
27. C₂³×C₃×Dic₃	C₂²	semidirect
29. C₂×C₃×D₃×D₄	C₂²	semidirect
30. C₂²×C₃×D₁₂	C₂²	semidirect
31. C₂²×C₃×C₄×D₃	C₂²	semidirect
32. C₂²×C₃×C₄×D₃	C₂²	semidirect
33. C₃²×#120	C₂²	semidirect
34. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
36. C₃×#953	C₂²	semidirect
37. C₂×C₃×#217	C₂²	semidirect
38. C₂×C₃×#217	C₂²	semidirect
39. C₂×C₃×#217	C₂²	semidirect
40. C₃×#938	C₂²	semidirect
41. C₃×#937	C₂²	semidirect
42. C₃×#935	C₂²	semidirect
43. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
46. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
47. C₃×#886	C₂²	semidirect
48. C₃×#884	C₂²	semidirect
49. C₃×#883	C₂²	semidirect
50. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
53. C₂³×#67	C₂×C₃	semidirect
54. C₂²×D₃×D₄	C₂×C₃	semidirect
64. C₂×C₃×#120	D₃	semidirect
65. C₂×C₃×#120	C₂×C₃	semidirect
67. C₂×#953	C₂×C₃	semidirect
68. C₂×#938	C₂×C₃	semidirect
69. C₂×#937	C₂×C₃	semidirect
70. C₂×#935	C₂×C₃	semidirect
71. #5589	C₂×C₃	direct (N × H)
72. C₂×#886	C₂×C₃	semidirect
73. C₂×#884	C₂×C₃	semidirect
74. C₂×#883	C₂×C₃	semidirect
75. C₂×D₃×C₂²⋊C₄	C₂×C₃	semidirect
81. C₂⁴×C₃²	C₂³	semidirect
85. C₂³×C₃×D₃	D₄	semidirect
90. C₂³×C₃×D₃	C₂³	semidirect
94. C₂×C₃²×D₄	C₂³	semidirect
105. C₂×C₃×#67	C₂³	semidirect
106. C₂×C₃×#67	C₂³	semidirect
107. C₂×C₃×#67	C₂³	semidirect
112. C₂²×C₃×Dic₃	C₂³	semidirect
115. C₂×C₃×D₁₂	C₂³	semidirect
118. C₂×C₃×C₄×D₃	C₂³	semidirect
119. C₂×C₃×C₄×D₃	C₂³	semidirect
120. C₃²×C₂²⋊C₄	C₂³	semidirect
121. C₃²×C₂²⋊C₄	C₂³	semidirect
122. C₃×#217	C₂³	semidirect
123. C₃×#217	C₂³	semidirect
124. C₃×#217	C₂³	semidirect
125. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
126. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
127. C₃×C₄⋊Dic₃	C₂³	semidirect
128. C₃×Dic₃⋊C₄	C₂³	semidirect
133. C₂⁵×C₃	C₂×D₃	semidirect
134. C₂⁵×C₃	C₂²×C₃	semidirect
136. C₂⁴×D₃	C₂²×C₃	semidirect
150. C₂²×C₃×D₄	C₂×D₃	semidirect
152. C₂²×C₃×D₄	C₂²×C₃	semidirect
159. C₂²×#67	C₂²×C₃	semidirect
160. C₂²×#67	C₂²×C₃	semidirect
161. C₂²×#67	C₂²×C₃	semidirect
162. C₂²×#67	C₂²×C₃	semidirect
163. C₂³×Dic₃	C₂²×C₃	semidirect
165. C₂×D₃×D₄	C₂²×C₃	semidirect
166. C₂²×D₁₂	C₂²×C₃	semidirect
167. C₂²×C₄×D₃	C₂²×C₃	semidirect
168. C₂²×C₄×D₃	C₂²×C₃	semidirect
177. C₃×#120	C₂×D₃	semidirect
178. C₃×#120	C₂²×C₃	semidirect
189. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
190. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
191. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
192. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
193. #953	C₂²×C₃	semidirect
194. C₂×#217	C₂²×C₃	semidirect
195. C₂×#217	C₂²×C₃	semidirect
196. C₂×#217	C₂²×C₃	semidirect
197. #938	C₂²×C₃	semidirect
198. #937	C₂²×C₃	semidirect
199. #935	C₂²×C₃	semidirect
200. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
201. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
202. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
203. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
204. #886	C₂²×C₃	semidirect
205. #884	C₂²×C₃	semidirect
206. #883	C₂²×C₃	semidirect
207. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
233. C₂²×C₃×D₃	C₂×D₄	semidirect
268. C₂×#120	C₃×D₃	semidirect
292. C₂⁴×C₃	C₂²×D₃	semidirect
296. C₂⁴×C₃	C₂³×C₃	semidirect
300. C₂³×D₃	C₃×D₄	semidirect
305. C₂³×D₃	C₂³×C₃	semidirect
329. C₂×C₃×D₄	C₂²×D₃	semidirect
331. C₂×C₃×D₄	C₂³×C₃	semidirect
355. C₂×#67	C₂³×C₃	semidirect
356. C₂×#67	C₂³×C₃	semidirect
357. C₂×#67	C₂³×C₃	semidirect
362. C₂²×Dic₃	C₂³×C₃	semidirect
365. C₂×D₁₂	C₂³×C₃	semidirect
368. C₂×C₄×D₃	C₂³×C₃	semidirect
369. C₂×C₄×D₃	C₂³×C₃	semidirect
379. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
380. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
381. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
382. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
383. #217	C₂³×C₃	semidirect
384. #217	C₂³×C₃	semidirect
385. #217	C₂³×C₃	semidirect
386. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
387. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
388. C₄⋊Dic₃	C₂³×C₃	semidirect
389. Dic₃⋊C₄	C₂³×C₃	semidirect
422. C₂⁵	C₂×C₃×D₃	semidirect
434. C₂²×D₄	C₂×C₃×D₃	semidirect
445. #120	C₂×C₃×D₃	semidirect
454. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
455. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
524. C₂²×D₃	C₂×C₃×D₄	semidirect
579. C₂×C₃²	#534	semidirect
599. C₂⁴	C₂²×C₃×D₃	semidirect
617. C₂×D₄	C₂²×C₃×D₃	semidirect
636. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
637. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
714. C₃²	C₂×#534	semidirect
780. C₂×C₃	#5589	direct (N × H)
781. C₂×C₃	C₃×#534	semidirect
820. C₃	C₂×#5589	direct (N × H)
821. C₃	C₂×C₃×#534	semidirect
828. C₂	C₃×#5589	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×#67	2
C₂²×C₃×D₃×D₄	2
C₂×C₃²×#120	2
C₂×C₃×#953	2
C₂×C₃×#938	2
C₂×C₃×#937	2
C₂×C₃×#935	2
C₃×#5589	2
C₂×C₃×#886	2
C₂×C₃×#884	2
C₂×C₃×#883	2
C₂×C₃×D₃×C₂²⋊C₄	2
C₂×C₃×#534	3
C₂×#5589	3

Subgroups — C2×C3×#5589 #11900937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5589 #11900937