Subgroups — C₃×#10596018 #13179301

Order 1728.

2356 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64148	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64146	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64105	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64093	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64092	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#64091	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#64087	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64081	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596018	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₃×#5547	—	3	4	no	maximal
18	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#638	C₂²	1	1	yes	characteristic
23	C₂×C₃×#638	C₂²	1	1	yes	characteristic
24	C₂×C₃×#638	C₂²	1	1	yes	characteristic
25	C₂×C₃×#638	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₃×#3828	—	2	4	no	—
28	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×C₃⋊D₃	—	2	4	no	—
31	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
37	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
41	C₃×#3757	C₂²	1	1	yes	characteristic
42	C₃×#3757	C₂²	1	1	yes	characteristic, complemented
43	C₃×#3752	C₂²	1	1	yes	characteristic
44	C₃×#3752	C₂²	1	1	yes	characteristic
45	C₃×#3752	C₂²	1	1	yes	characteristic
46	C₃×#3752	C₂²	1	1	yes	characteristic
47	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
48	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
50	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
51	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
52	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₃×#235	—	3	4	no	—
58	C₂²×C₃×C₄×D₃	—	3	4	no	—
59	C₃²×C₄×D₄	—	2	4	no	—
60	C₃²×C₄×D₄	D₃	1	4	yes	complemented
61	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
62	#64148	C₂×C₃	1	1	yes	characteristic, complemented
63	#64146	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
65	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
66	#64105	C₂×C₃	1	1	yes	characteristic, complemented
67	#64103	C₂×C₃	1	1	yes	characteristic, complemented
68	#64093	C₂×C₃	1	1	yes	characteristic, complemented
69	#64092	C₂×C₃	1	1	yes	characteristic, complemented
70	#64091	C₂×C₃	1	1	yes	characteristic, complemented
71	#64087	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
73	#64081	C₂×C₃	1	1	yes	characteristic, complemented
74	C₃×#939	—	3	4	no	—
75	C₃×#937	—	3	4	no	—
76	C₃×C₄×#67	—	3	4	no	—
77	C₃×C₄×#67	—	3	4	no	—
78	C₃×#896	—	3	4	no	—
79	C₃×#894	—	3	4	no	—
80	C₃×#884	—	3	4	no	—
81	C₃×#883	—	3	4	no	—
82	C₃×#882	—	3	4	no	—
83	C₃×#878	—	3	4	no	—
84	C₃×C₄×D₁₂	—	3	4	no	—
85	C₃×#872	—	3	4	no	—
86	C₂³×C₃³	C₂³	1	1	yes	characteristic
87	C₂³×C₃³	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
89	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
90	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
91	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
94	C₃³×D₄	—	2	2	no	—
95	C₂×C₃³×C₄	—	2	2	no	—
96	C₂×C₃³×C₄	—	2	2	no	—
97	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
98	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
99	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
100	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
101	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
102	C₃×#638	—	2	2	no	—
103	C₃×#638	—	2	2	no	—
104	C₃×#638	—	2	2	no	—
105	C₃×#638	—	2	2	no	—
106	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
107	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
112	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
113	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
114	C₃×C₄×C₃⋊D₃	—	2	2	no	—
115	C₃×C₄×C₃⋊D₃	—	2	2	no	—
116	C₃×C₄×C₃⋊D₃	—	2	2	no	—
117	C₃×C₄×C₃⋊D₃	—	2	2	no	—
118	C₃×C₄×C₃⋊D₃	D₄	1	4	yes	complemented
119	C₃×#634	—	2	2	no	—
120	C₃×#525	—	9	1	no	—
121	#5547	—	3	4	no	—
122	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
123	C₂³×C₃×D₃	—	3	4	no	—
124	C₂×C₃²×D₄	—	2	4	no	—
125	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
126	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
127	C₂²×C₃²×C₄	—	2	4	no	—
128	C₂²×C₃²×C₄	—	2	4	no	—
129	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
130	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
131	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₂×#638	C₂²×C₃	1	1	yes	characteristic
134	C₂×#638	C₂²×C₃	1	1	yes	characteristic
135	C₂×#638	C₂²×C₃	1	1	yes	characteristic
136	C₂×#638	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
138	#3828	—	2	4	no	—
139	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₄×C₃⋊D₃	—	2	4	no	—
142	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₂×C₃×#67	—	3	4	no	—
149	C₂×C₃×#67	—	3	4	no	—
150	C₂×C₃×#67	—	3	4	no	—
151	C₂×C₃×#67	—	3	4	no	—
152	C₂²×C₃×Dic₃	—	3	4	no	—
153	C₃×#235	—	6	16	no	—
154	C₂×C₃×D₁₂	—	3	4	no	—
155	C₂×C₃×D₁₂	—	3	4	no	—
156	C₂×C₃×C₄×D₃	—	3	4	no	—
157	C₂×C₃×C₄×D₃	—	3	4	no	—
158	C₂×C₃×C₄×D₃	—	3	4	no	—
159	C₂×C₃×C₄×D₃	—	3	4	no	—
160	C₂×C₃×C₄×D₃	—	3	4	no	—
161	C₂×C₃×C₄×D₃	—	6	16	no	—
162	C₂×C₃×Dic₆	—	3	4	no	—
163	C₃²×C₄⋊C₄	—	2	4	no	—
164	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
165	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₃²×C₂²⋊C₄	—	2	4	no	—
167	C₃²×C₂²⋊C₄	—	2	4	no	—
168	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
169	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
170	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₃²×C₄²	—	2	4	no	—
173	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
174	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
175	#3757	C₂²×C₃	1	1	yes	characteristic
176	#3757	C₂²×C₃	1	1	yes	characteristic, complemented
177	#3752	C₂²×C₃	1	1	yes	characteristic
178	#3752	C₂²×C₃	1	1	yes	characteristic
179	#3752	C₂²×C₃	1	1	yes	characteristic
180	#3752	C₂²×C₃	1	1	yes	characteristic
181	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
182	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
184	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
185	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
186	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
187	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₃×#217	—	3	4	no	—
190	C₃×#217	—	3	4	no	—
191	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
192	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
193	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
194	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
195	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
196	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
197	C₃×C₄⋊Dic₃	—	3	4	no	—
198	C₃×Dic₃⋊C₄	—	3	4	no	—
199	C₃×Dic₃⋊C₄	—	3	4	no	—
200	C₃×Dic₃⋊C₄	—	3	4	no	—
201	C₃×Dic₃⋊C₄	—	3	4	no	—
202	C₃×C₄×Dic₃	—	3	4	no	—
203	C₂²×C₃³	—	2	1	no	—
204	C₂²×C₃³	—	2	1	no	—
205	C₂²×C₃³	—	2	1	no	—
206	C₂²×C₃³	—	2	1	no	—
207	C₂²×C₃³	—	2	1	no	—
208	C₂²×C₃³	#41	1	2	yes	complemented
209	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
210	C₂×C₃×C₃⋊D₃	—	2	8	no	—
211	C₂×C₃×C₃⋊D₃	—	2	1	no	—
212	C₂×C₃×C₃⋊D₃	—	2	1	no	—
213	C₂×C₃×C₃⋊D₃	—	2	1	no	—
214	C₂×C₃×C₃⋊D₃	—	2	1	no	—
215	C₂×C₃×C₃⋊D₃	—	2	1	no	—
216	C₂×C₃×C₃⋊D₃	—	2	1	no	—
217	C₂×C₃×C₃⋊D₃	—	2	1	no	—
218	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
219	C₂×C₃×C₃⋊D₃	#41	1	2	yes	complemented
220	C₃³×C₄	—	2	1	no	—
221	C₃³×C₄	—	2	1	no	—
222	C₃³×C₄	—	2	1	no	—
223	C₃³×C₄	—	2	1	no	—
224	C₃³×C₄	C₂×D₄	1	2	yes	—
225	C₃×C₃⋊Dic₃	—	2	1	no	—
226	C₃×C₃⋊Dic₃	—	2	1	no	—
227	C₃×C₃⋊Dic₃	—	2	1	no	—
228	C₃×C₃⋊Dic₃	—	2	1	no	—
229	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
230	C₂×C₃×#41	—	9	1	no	—
231	C₂³×C₃×C₄	—	9	1	no	—
232	C₂×#235	—	3	4	no	—
233	C₂²×C₄×D₃	—	3	4	no	—
234	C₃×#123	—	9	1	no	—
235	C₃×#123	—	9	1	no	—
236	C₃×C₂²⋊Q₈	—	9	1	no	—
237	C₃×C₂²⋊Q₈	—	9	1	no	—
238	C₃×#121	—	9	1	no	—
239	C₃×#121	—	9	1	no	—
240	C₃×#120	—	9	1	no	—
241	C₃×#120	—	9	1	no	—
242	C₃×C₄×D₄	—	2	4	no	—
243	C₃×C₄×D₄	—	9	1	no	—
244	C₃×C₄×D₄	—	9	1	no	—
245	C₃×C₄×D₄	—	9	1	no	—
246	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
247	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
248	C₃×#117	—	9	1	no	—
249	#939	—	3	4	no	—
250	#937	—	3	4	no	—
251	C₄×#67	—	3	4	no	—
252	C₄×#67	—	3	4	no	—
253	#896	—	3	4	no	—
254	#894	—	3	4	no	—
255	#884	—	3	4	no	—
256	#883	—	3	4	no	—
257	#882	—	3	4	no	—
258	#878	—	3	4	no	—
259	C₄×D₁₂	—	3	4	no	—
260	#872	—	3	4	no	—
261	C₂³×C₃²	—	2	4	no	—
262	C₂³×C₃²	—	2	4	no	—
263	C₂³×C₃²	C₂²×D₃	1	4	yes	—
264	C₂³×C₃²	C₂²×D₃	1	4	yes	—
265	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
266	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
267	C₂²×C₃⋊D₃	—	2	2	no	—
268	C₂²×C₃⋊D₃	—	2	2	no	—
269	C₂²×C₃⋊D₃	—	2	2	no	—
270	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
271	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
273	C₂²×C₃×D₃	—	3	4	no	—
274	C₂²×C₃×D₃	—	3	4	no	—
275	C₂²×C₃×D₃	—	3	4	no	—
276	C₂²×C₃×D₃	—	6	8	no	—
277	C₂²×C₃×D₃	—	6	8	no	—
278	C₂²×C₃×D₃	—	6	8	no	—
279	C₃²×D₄	—	2	16	no	—
280	C₃²×D₄	—	2	8	no	—
281	C₃²×D₄	—	2	2	no	—
282	C₂×C₃²×C₄	—	2	2	no	—
283	C₂×C₃²×C₄	—	2	2	no	—
284	C₂×C₃²×C₄	—	2	4	no	—
285	C₂×C₃²×C₄	—	2	4	no	—
286	C₂×C₃²×C₄	—	2	4	no	—
287	C₂×C₃²×C₄	—	2	4	no	—
288	C₂×C₃²×C₄	—	2	4	no	—
289	C₂×C₃²×C₄	—	2	8	no	—
290	C₂×C₃²×C₄	—	2	8	no	—
291	C₂×C₃²×C₄	—	4	8	no	—
292	C₂×C₃²×C₄	—	4	8	no	—
293	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
294	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
295	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
296	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
297	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
298	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
303	#638	—	2	2	no	—
304	#638	—	2	2	no	—
305	#638	—	2	2	no	—
306	#638	—	2	2	no	—
307	C₂×C₃⋊Dic₃	—	2	2	no	—
308	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
313	C₄⋊(C₃⋊D₃)	—	2	2	no	—
314	C₄⋊(C₃⋊D₃)	—	2	2	no	—
315	C₄×C₃⋊D₃	—	2	2	no	—
316	C₄×C₃⋊D₃	—	2	2	no	—
317	C₄×C₃⋊D₃	—	2	2	no	—
318	C₄×C₃⋊D₃	—	2	2	no	—
319	C₄×C₃⋊D₃	C₃×D₄	1	4	yes	complemented
320	#634	—	2	2	no	—
321	C₃×#67	—	6	8	no	—
322	C₃×#67	—	6	8	no	—
323	C₃×#67	—	6	8	no	—
324	C₃×#67	—	6	8	no	—
325	C₂×C₃×Dic₃	—	3	4	no	—
326	C₂×C₃×Dic₃	—	3	4	no	—
327	C₂×C₃×Dic₃	—	3	4	no	—
328	C₂×C₃×Dic₃	—	3	4	no	—
329	C₂×C₃×Dic₃	—	3	4	no	—
330	C₂×C₃×Dic₃	—	6	8	no	—
331	C₃×D₁₂	—	6	8	no	—
332	C₃×D₁₂	—	6	8	no	—
333	C₃×C₄×D₃	—	3	16	no	—
334	C₃×C₄×D₃	—	6	8	no	—
335	C₃×C₄×D₃	—	6	8	no	—
336	C₃×C₄×D₃	—	6	8	no	—
337	C₃×C₄×D₃	—	6	8	no	—
338	C₃×Dic₆	—	6	8	no	—
339	#525	—	9	1	no	Sylow
340	C₂×C₃³	—	2	2	no	—
341	C₂×C₃³	—	4	1	no	—
342	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₃³	C₂×#41	1	1	yes	characteristic
344	C₂×C₃³	C₂×#41	1	1	yes	characteristic
345	C₃×C₃⋊D₃	—	2	2	no	—
346	C₃×C₃⋊D₃	—	2	2	no	—
347	C₃×C₃⋊D₃	—	4	1	no	—
348	C₂⁴×C₃	—	9	1	no	—
349	C₂³×D₃	—	3	4	no	—
350	C₃×#41	—	18	4	no	—
351	C₂×C₃×Q₈	—	9	1	no	—
352	C₂×C₃×D₄	—	2	4	no	—
353	C₂×C₃×D₄	—	9	1	no	—
354	C₂×C₃×D₄	—	9	1	no	—
355	C₂×C₃×D₄	—	9	1	no	—
356	C₂×C₃×D₄	—	9	1	no	—
357	C₂×C₃×D₄	—	9	1	no	—
358	C₂×C₃×D₄	—	9	1	no	—
359	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
360	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
361	C₂²×C₃×C₄	—	2	4	no	—
362	C₂²×C₃×C₄	—	2	4	no	—
363	C₂²×C₃×C₄	—	9	1	no	—
364	C₂²×C₃×C₄	—	9	1	no	—
365	C₂²×C₃×C₄	—	9	1	no	—
366	C₂²×C₃×C₄	—	9	1	no	—
367	C₂²×C₃×C₄	—	9	1	no	—
368	C₂²×C₃×C₄	—	9	1	no	—
369	C₂²×C₃×C₄	—	18	4	no	—
370	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
371	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
372	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
374	C₂×#67	—	3	4	no	—
375	C₂×#67	—	3	4	no	—
376	C₂×#67	—	3	4	no	—
377	C₂×#67	—	3	4	no	—
378	C₂²×Dic₃	—	3	4	no	—
379	#235	—	6	16	no	—
380	C₂×D₁₂	—	3	4	no	—
381	C₂×D₁₂	—	3	4	no	—
382	C₂×C₄×D₃	—	3	4	no	—
383	C₂×C₄×D₃	—	3	4	no	—
384	C₂×C₄×D₃	—	3	4	no	—
385	C₂×C₄×D₃	—	3	4	no	—
386	C₂×C₄×D₃	—	3	4	no	—
387	C₂×C₄×D₃	—	6	16	no	—
388	C₂×Dic₆	—	3	4	no	—
389	C₃×C₄⋊C₄	—	2	4	no	—
390	C₃×C₄⋊C₄	—	9	1	no	—
391	C₃×C₄⋊C₄	—	9	1	no	—
392	C₃×C₄⋊C₄	—	9	1	no	—
393	C₃×C₄⋊C₄	—	9	1	no	—
394	C₃×C₄⋊C₄	—	9	1	no	—
395	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
396	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
397	C₃×C₂²⋊C₄	—	2	4	no	—
398	C₃×C₂²⋊C₄	—	2	4	no	—
399	C₃×C₂²⋊C₄	—	9	1	no	—
400	C₃×C₂²⋊C₄	—	9	1	no	—
401	C₃×C₂²⋊C₄	—	9	1	no	—
402	C₃×C₂²⋊C₄	—	9	1	no	—
403	C₃×C₂²⋊C₄	—	9	1	no	—
404	C₃×C₂²⋊C₄	—	9	1	no	—
405	C₃×C₂²⋊C₄	—	9	1	no	—
406	C₃×C₂²⋊C₄	—	9	1	no	—
407	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
408	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
409	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
410	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
411	C₃×C₄²	—	2	4	no	—
412	C₃×C₄²	—	9	1	no	—
413	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
414	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
415	#217	—	3	4	no	—
416	#217	—	3	4	no	—
417	(C₂×D₃)⋊C₄	—	3	4	no	—
418	(C₂×D₃)⋊C₄	—	3	4	no	—
419	(C₂×D₃)⋊C₄	—	3	4	no	—
420	(C₂×D₃)⋊C₄	—	3	4	no	—
421	(C₂×D₃)⋊C₄	—	3	4	no	—
422	(C₂×D₃)⋊C₄	—	3	4	no	—
423	C₄⋊Dic₃	—	3	4	no	—
424	Dic₃⋊C₄	—	3	4	no	—
425	Dic₃⋊C₄	—	3	4	no	—
426	Dic₃⋊C₄	—	3	4	no	—
427	Dic₃⋊C₄	—	3	4	no	—
428	C₄×Dic₃	—	3	4	no	—
429	C₂²×C₃²	—	2	1	no	—
430	C₂²×C₃²	—	2	1	no	—
431	C₂²×C₃²	—	2	8	no	—
432	C₂²×C₃²	—	2	4	no	—
433	C₂²×C₃²	—	2	1	no	—
434	C₂²×C₃²	—	2	1	no	—
435	C₂²×C₃²	—	2	1	no	—
436	C₂²×C₃²	—	2	4	no	—
437	C₂²×C₃²	—	2	8	no	—
438	C₂²×C₃²	—	2	4	no	—
439	C₂²×C₃²	—	2	4	no	—
440	C₂²×C₃²	—	2	4	no	—
441	C₂²×C₃²	—	2	4	no	—
442	C₂²×C₃²	—	4	4	no	—
443	C₂²×C₃²	—	4	4	no	—
444	C₂²×C₃²	—	4	4	no	—
445	C₂²×C₃²	—	4	4	no	—
446	C₂²×C₃²	#235	1	8	yes	complemented
447	C₂²×C₃²	C₃×#41	1	2	yes	complemented
448	C₂²×C₃²	C₂³×D₃	1	4	yes	—
449	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
450	C₂×C₃⋊D₃	—	2	8	no	—
451	C₂×C₃⋊D₃	—	2	1	no	—
452	C₂×C₃⋊D₃	—	2	1	no	—
453	C₂×C₃⋊D₃	—	2	1	no	—
454	C₂×C₃⋊D₃	—	2	1	no	—
455	C₂×C₃⋊D₃	—	2	1	no	—
456	C₂×C₃⋊D₃	—	2	1	no	—
457	C₂×C₃⋊D₃	—	2	1	no	—
458	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
459	C₂×C₃⋊D₃	C₃×#41	1	2	yes	complemented
460	C₂×C₃×D₃	—	3	8	no	—
461	C₂×C₃×D₃	—	3	8	no	—
462	C₂×C₃×D₃	—	6	32	no	—
463	C₂×C₃×D₃	—	6	4	no	—
464	C₂×C₃×D₃	—	6	4	no	—
465	C₂×C₃×D₃	—	6	4	no	—
466	C₂×C₃×D₃	—	6	4	no	—
467	C₂×C₃×D₃	—	6	4	no	—
468	C₂×C₃×D₃	—	6	4	no	—
469	C₂×C₃×D₃	—	6	4	no	—
470	C₃²×C₄	—	2	8	no	—
471	C₃²×C₄	—	2	4	no	—
472	C₃²×C₄	—	2	1	no	—
473	C₃²×C₄	—	2	1	no	—
474	C₃²×C₄	—	2	1	no	—
475	C₃²×C₄	—	2	1	no	—
476	C₃²×C₄	—	2	8	no	—
477	C₃²×C₄	—	2	4	no	—
478	C₃²×C₄	—	2	4	no	—
479	C₃²×C₄	—	2	4	no	—
480	C₃²×C₄	—	4	4	no	—
481	C₃²×C₄	—	4	4	no	—
482	C₃²×C₄	—	4	4	no	—
483	C₃²×C₄	D₃×D₄	1	8	yes	—
484	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
485	C₃⋊Dic₃	—	2	1	no	—
486	C₃⋊Dic₃	—	2	1	no	—
487	C₃⋊Dic₃	—	2	1	no	—
488	C₃⋊Dic₃	—	2	1	no	—
489	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
490	C₃×Dic₃	—	3	8	no	—
491	C₃×Dic₃	—	6	4	no	—
492	C₃×Dic₃	—	6	4	no	—
493	C₃×Dic₃	—	6	4	no	—
494	C₃×Dic₃	—	6	4	no	—
495	C₂×#41	—	9	1	no	—
496	C₂³×C₄	—	9	1	no	—
497	#123	—	9	1	no	—
498	#123	—	9	1	no	—
499	C₂²⋊Q₈	—	9	1	no	—
500	C₂²⋊Q₈	—	9	1	no	—
501	#121	—	9	1	no	—
502	#121	—	9	1	no	—
503	#120	—	9	1	no	—
504	#120	—	9	1	no	—
505	C₄×D₄	—	9	1	no	—
506	C₄×D₄	—	9	1	no	—
507	C₄×D₄	—	9	1	no	—
508	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
509	#117	—	9	1	no	—
510	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
511	C₂³×C₃	—	2	4	no	—
512	C₂³×C₃	—	2	4	no	—
513	C₂³×C₃	—	9	1	no	—
514	C₂³×C₃	—	9	1	no	—
515	C₂³×C₃	—	9	1	no	—
516	C₂³×C₃	—	18	2	no	—
517	C₂³×C₃	—	18	2	no	—
518	C₂³×C₃	—	18	2	no	—
519	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
520	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
521	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
522	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
523	C₂²×D₃	—	3	4	no	—
524	C₂²×D₃	—	3	4	no	—
525	C₂²×D₃	—	3	4	no	—
526	C₂²×D₃	—	6	8	no	—
527	C₂²×D₃	—	6	8	no	—
528	C₂²×D₃	—	6	8	no	—
529	C₃×Q₈	—	18	2	no	—
530	C₃×D₄	—	2	16	no	—
531	C₃×D₄	—	2	8	no	—
532	C₃×D₄	—	2	2	no	—
533	C₃×D₄	—	18	2	no	—
534	C₃×D₄	—	18	2	no	—
535	C₃×D₄	—	18	2	no	—
536	C₃×D₄	—	18	2	no	—
537	C₃×D₄	—	18	2	no	—
538	C₃×D₄	—	18	2	no	—
539	C₂×C₃×C₄	—	2	8	no	—
540	C₂×C₃×C₄	—	2	8	no	—
541	C₂×C₃×C₄	—	2	2	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	4	no	—
546	C₂×C₃×C₄	—	2	4	no	—
547	C₂×C₃×C₄	—	2	4	no	—
548	C₂×C₃×C₄	—	4	8	no	—
549	C₂×C₃×C₄	—	4	8	no	—
550	C₂×C₃×C₄	—	9	1	no	—
551	C₂×C₃×C₄	—	9	4	no	—
552	C₂×C₃×C₄	—	9	1	no	—
553	C₂×C₃×C₄	—	9	1	no	—
554	C₂×C₃×C₄	—	9	1	no	—
555	C₂×C₃×C₄	—	9	1	no	—
556	C₂×C₃×C₄	—	18	2	no	—
557	C₂×C₃×C₄	—	18	2	no	—
558	C₂×C₃×C₄	—	18	2	no	—
559	C₂×C₃×C₄	—	18	2	no	—
560	C₂×C₃×C₄	—	18	2	no	—
561	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
562	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
563	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
564	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
565	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
566	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
570	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
571	#67	—	6	8	no	—
572	#67	—	6	8	no	—
573	#67	—	6	8	no	—
574	#67	—	6	8	no	—
575	C₂×Dic₃	—	3	4	no	—
576	C₂×Dic₃	—	3	4	no	—
577	C₂×Dic₃	—	3	4	no	—
578	C₂×Dic₃	—	3	4	no	—
579	C₂×Dic₃	—	3	4	no	—
580	C₂×Dic₃	—	6	8	no	—
581	D₁₂	—	6	8	no	—
582	D₁₂	—	6	8	no	—
583	C₄×D₃	—	3	16	no	—
584	C₄×D₃	—	6	8	no	—
585	C₄×D₃	—	6	8	no	—
586	C₄×D₃	—	6	8	no	—
587	C₄×D₃	—	6	8	no	—
588	Dic₆	—	6	8	no	—
589	C₂×C₃²	—	2	2	no	—
590	C₂×C₃²	—	2	4	no	—
591	C₂×C₃²	—	2	4	no	—
592	C₂×C₃²	—	2	4	no	—
593	C₂×C₃²	—	2	8	no	—
594	C₂×C₃²	—	4	8	no	—
595	C₂×C₃²	—	4	8	no	—
596	C₂×C₃²	—	4	4	no	—
597	C₂×C₃²	—	4	1	no	—
598	C₂×C₃²	C₂×#235	1	4	yes	—
599	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
600	C₂×C₃²	D₃×#41	1	4	yes	—
601	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
602	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
603	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
604	C₃⋊D₃	—	2	2	no	—
605	C₃⋊D₃	—	2	2	no	—
606	C₃⋊D₃	—	4	1	no	—
607	C₃×D₃	—	6	8	no	—
608	C₃×D₃	—	6	8	no	—
609	C₃×D₃	—	12	4	no	—
610	C₂⁴	—	9	1	no	—
611	#41	—	18	4	no	—
612	C₂×Q₈	—	9	1	no	—
613	C₂×D₄	—	9	1	no	—
614	C₂×D₄	—	9	1	no	—
615	C₂×D₄	—	9	1	no	—
616	C₂×D₄	—	9	1	no	—
617	C₂×D₄	—	9	1	no	—
618	C₂×D₄	—	9	1	no	—
619	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
620	C₂²×C₄	—	9	1	no	—
621	C₂²×C₄	—	9	1	no	—
622	C₂²×C₄	—	9	1	no	—
623	C₂²×C₄	—	9	1	no	—
624	C₂²×C₄	—	9	1	no	—
625	C₂²×C₄	—	9	1	no	—
626	C₂²×C₄	—	18	4	no	—
627	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
628	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
629	C₄⋊C₄	—	9	1	no	—
630	C₄⋊C₄	—	9	1	no	—
631	C₄⋊C₄	—	9	1	no	—
632	C₄⋊C₄	—	9	1	no	—
633	C₄⋊C₄	—	9	1	no	—
634	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
635	C₂²⋊C₄	—	9	1	no	—
636	C₂²⋊C₄	—	9	1	no	—
637	C₂²⋊C₄	—	9	1	no	—
638	C₂²⋊C₄	—	9	1	no	—
639	C₂²⋊C₄	—	9	1	no	—
640	C₂²⋊C₄	—	9	1	no	—
641	C₂²⋊C₄	—	9	1	no	—
642	C₂²⋊C₄	—	9	1	no	—
643	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
644	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
645	C₄²	—	9	1	no	—
646	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
647	C₂²×C₃	—	2	4	no	—
648	C₂²×C₃	—	2	4	no	—
649	C₂²×C₃	—	2	1	no	—
650	C₂²×C₃	—	2	1	no	—
651	C₂²×C₃	—	2	8	no	—
652	C₂²×C₃	—	2	4	no	—
653	C₂²×C₃	—	2	4	no	—
654	C₂²×C₃	—	2	4	no	—
655	C₂²×C₃	—	2	1	no	—
656	C₂²×C₃	—	2	1	no	—
657	C₂²×C₃	—	2	1	no	—
658	C₂²×C₃	—	2	4	no	—
659	C₂²×C₃	—	2	8	no	—
660	C₂²×C₃	—	4	4	no	—
661	C₂²×C₃	—	4	4	no	—
662	C₂²×C₃	—	4	4	no	—
663	C₂²×C₃	—	4	4	no	—
664	C₂²×C₃	—	9	2	no	—
665	C₂²×C₃	—	9	2	no	—
666	C₂²×C₃	—	18	8	no	—
667	C₂²×C₃	—	18	1	no	—
668	C₂²×C₃	—	18	1	no	—
669	C₂²×C₃	—	18	1	no	—
670	C₂²×C₃	—	18	1	no	—
671	C₂²×C₃	—	18	1	no	—
672	C₂²×C₃	—	18	1	no	—
673	C₂²×C₃	—	18	1	no	—
674	C₂²×C₃	C₃×#235	1	8	yes	complemented
675	C₂²×C₃	#3828	1	2	yes	complemented
676	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
677	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
678	C₂×D₃	—	3	8	no	—
679	C₂×D₃	—	3	8	no	—
680	C₂×D₃	—	6	32	no	—
681	C₂×D₃	—	6	4	no	—
682	C₂×D₃	—	6	4	no	—
683	C₂×D₃	—	6	4	no	—
684	C₂×D₃	—	6	4	no	—
685	C₂×D₃	—	6	4	no	—
686	C₂×D₃	—	6	4	no	—
687	C₂×D₃	—	6	4	no	—
688	C₃×C₄	—	2	8	no	—
689	C₃×C₄	—	2	4	no	—
690	C₃×C₄	—	2	4	no	—
691	C₃×C₄	—	2	4	no	—
692	C₃×C₄	—	2	4	no	—
693	C₃×C₄	—	2	1	no	—
694	C₃×C₄	—	2	1	no	—
695	C₃×C₄	—	2	1	no	—
696	C₃×C₄	—	2	1	no	—
697	C₃×C₄	—	2	8	no	—
698	C₃×C₄	—	4	4	no	—
699	C₃×C₄	—	4	4	no	—
700	C₃×C₄	—	4	4	no	—
701	C₃×C₄	—	9	2	no	—
702	C₃×C₄	—	18	1	no	—
703	C₃×C₄	—	18	1	no	—
704	C₃×C₄	—	18	1	no	—
705	C₃×C₄	—	18	1	no	—
706	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
707	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
708	Dic₃	—	3	8	no	—
709	Dic₃	—	6	4	no	—
710	Dic₃	—	6	4	no	—
711	Dic₃	—	6	4	no	—
712	Dic₃	—	6	4	no	—
713	C₃²	—	2	4	no	—
714	C₃²	#5547	1	4	yes	complemented
715	C₃²	C₃×#525	1	1	yes	characteristic, complemented
716	C₂³	—	9	1	no	—
717	C₂³	—	9	1	no	—
718	C₂³	—	9	1	no	—
719	C₂³	—	18	2	no	—
720	C₂³	—	18	2	no	—
721	C₂³	—	18	2	no	—
722	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
723	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
724	Q₈	—	18	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	18	2	no	—
727	D₄	—	18	2	no	—
728	D₄	—	18	2	no	—
729	D₄	—	18	2	no	—
730	D₄	—	18	2	no	—
731	D₄	—	18	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	9	1	no	—
735	C₂×C₄	—	9	4	no	—
736	C₂×C₄	—	9	1	no	—
737	C₂×C₄	—	9	1	no	—
738	C₂×C₄	—	9	1	no	—
739	C₂×C₄	—	9	1	no	—
740	C₂×C₄	—	18	2	no	—
741	C₂×C₄	—	18	2	no	—
742	C₂×C₄	—	18	2	no	—
743	C₂×C₄	—	18	2	no	—
744	C₂×C₄	—	18	2	no	—
745	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
747	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
748	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
749	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
750	C₂×C₃	—	2	8	no	—
751	C₂×C₃	—	2	2	no	—
752	C₂×C₃	—	2	4	no	—
753	C₂×C₃	—	2	4	no	—
754	C₂×C₃	—	2	4	no	—
755	C₂×C₃	—	4	8	no	—
756	C₂×C₃	—	4	8	no	—
757	C₂×C₃	—	4	4	no	—
758	C₂×C₃	—	4	1	no	—
759	C₂×C₃	—	18	2	no	—
760	C₂×C₃	—	18	2	no	—
761	C₂×C₃	—	36	1	no	—
762	C₂×C₃	C₂×C₃×#235	1	4	yes	—
763	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
764	C₂×C₃	C₃×D₃×#41	1	4	yes	—
765	C₂×C₃	C₂×#3828	1	1	yes	characteristic
766	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
767	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
768	D₃	—	6	8	no	—
769	D₃	—	6	8	no	—
770	D₃	—	12	4	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	9	2	no	—
777	C₂²	—	9	2	no	—
778	C₂²	—	18	8	no	—
779	C₂²	—	18	1	no	—
780	C₂²	—	18	1	no	—
781	C₂²	—	18	1	no	—
782	C₂²	—	18	1	no	—
783	C₂²	—	18	1	no	—
784	C₂²	—	18	1	no	—
785	C₂²	—	18	1	no	—
786	C₂²	C₃×#3828	1	2	yes	complemented
787	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	9	2	no	—
793	C₄	—	18	1	no	—
794	C₄	—	18	1	no	—
795	C₄	—	18	1	no	—
796	C₄	—	18	1	no	—
797	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
798	C₃	—	2	4	no	—
799	C₃	C₃×#5547	1	4	yes	complemented
800	C₃	#10596018	1	1	yes	characteristic, direct product factor
801	C₂	—	2	2	no	—
802	C₂	—	4	1	no	—
803	C₂	—	18	2	no	—
804	C₂	—	18	2	no	—
805	C₂	—	36	1	no	—
806	C₂	C₂×C₃×#3828	1	1	yes	characteristic
807	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
808	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#525
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3828	C₂	semidirect
2. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
3. C₃³×C₄×D₄	C₂	semidirect
4. C₃×#64148	C₂	semidirect
5. C₃×#64146	C₂	semidirect
6. C₃×C₄×#638	C₂	semidirect
7. C₃×C₄×#638	C₂	semidirect
8. C₃×#64105	C₂	semidirect
9. C₃×#64103	C₂	semidirect
10. C₃×#64093	C₂	semidirect
11. C₃×#64092	C₂	semidirect
12. C₃×#64091	C₂	semidirect
13. C₃×#64087	C₂	semidirect
14. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
15. C₃×#64081	C₂	semidirect
16. #10596018	C₃	direct (N × H)
21. C₂²×C₃³×C₄	C₂²	semidirect
25. C₂×C₃×#638	C₂²	semidirect
35. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
36. C₂×C₃×#634	C₂²	semidirect
37. C₃³×C₄⋊C₄	C₂²	semidirect
39. C₃³×C₂²⋊C₄	C₂²	semidirect
40. C₃³×C₄²	C₂²	semidirect
42. C₃×#3757	C₂²	semidirect
47. C₃×#3752	C₂²	semidirect
48. C₃×#3752	C₂²	semidirect
49. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
50. C₃×#3750	C₂²	semidirect
51. C₃×#3750	C₂²	semidirect
52. C₃×#3750	C₂²	semidirect
53. C₃×#3750	C₂²	semidirect
54. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
55. C₂×#3828	C₂×C₃	semidirect
56. C₂²×C₄×C₃⋊D₃	C₂×C₃	semidirect
60. C₃²×C₄×D₄	D₃	semidirect
61. C₃²×C₄×D₄	C₂×C₃	semidirect
62. #64148	C₂×C₃	semidirect
63. #64146	C₂×C₃	semidirect
64. C₄×#638	C₂×C₃	semidirect
65. C₄×#638	C₂×C₃	semidirect
66. #64105	C₂×C₃	semidirect
67. #64103	C₂×C₃	semidirect
68. #64093	C₂×C₃	semidirect
69. #64092	C₂×C₃	semidirect
70. #64091	C₂×C₃	semidirect
71. #64087	C₂×C₃	semidirect
72. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
73. #64081	C₂×C₃	semidirect
118. C₃×C₄×C₃⋊D₃	D₄	semidirect
130. C₂²×C₃²×C₄	C₂×D₃	semidirect
132. C₂²×C₃²×C₄	C₂²×C₃	semidirect
136. C₂×#638	C₂²×C₃	semidirect
146. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
147. C₂×#634	C₂²×C₃	semidirect
164. C₃²×C₄⋊C₄	C₂×D₃	semidirect
165. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
169. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
171. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
173. C₃²×C₄²	C₂×D₃	semidirect
174. C₃²×C₄²	C₂²×C₃	semidirect
176. #3757	C₂²×C₃	semidirect
181. #3752	C₂²×C₃	semidirect
182. #3752	C₂²×C₃	semidirect
183. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
184. #3750	C₂²×C₃	semidirect
185. #3750	C₂²×C₃	semidirect
186. #3750	C₂²×C₃	semidirect
187. #3750	C₂²×C₃	semidirect
188. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
208. C₂²×C₃³	#41	semidirect
219. C₂×C₃×C₃⋊D₃	#41	semidirect
246. C₃×C₄×D₄	C₃×D₃	semidirect
247. C₃×C₄×D₄	C₃⋊D₃	semidirect
319. C₄×C₃⋊D₃	C₃×D₄	semidirect
371. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
373. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
395. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
396. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
408. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
410. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
413. C₃×C₄²	C₂×C₃×D₃	semidirect
414. C₃×C₄²	C₂×C₃⋊D₃	semidirect
446. C₂²×C₃²	#235	semidirect
447. C₂²×C₃²	C₃×#41	semidirect
459. C₂×C₃⋊D₃	C₃×#41	semidirect
508. C₄×D₄	C₃×C₃⋊D₃	semidirect
510. C₃³	#525	semidirect
628. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
634. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
644. C₂²⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
646. C₄²	C₂×C₃×C₃⋊D₃	semidirect
674. C₂²×C₃	C₃×#235	semidirect
675. C₂²×C₃	#3828	semidirect
714. C₃²	#5547	semidirect
715. C₃²	C₃×#525	semidirect
786. C₂²	C₃×#3828	semidirect
799. C₃	C₃×#5547	semidirect
800. C₃	#10596018	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×C₃×#3828	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₃³×C₄×D₄	2
C₃×#64148	2
C₃×#64146	2
C₃×C₄×#638	2
C₃×#64105	2
C₃×#64103	2
C₃×#64093	2
C₃×#64092	2
C₃×#64091	2
C₃×#64087	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64081	2
#10596018	3
C₃×#5547	3

Subgroups — C3×#10596018 #13179301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596018 #13179301