Subgroups — C₃×D₃×#1004 #13181549

Order 1728.

4214 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64361	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#1004	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64330	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×D₃×#67	C₂	1	4	yes	maximal, complemented
6	C₃×#64314	C₂	1	4	yes	maximal, complemented
7	C₃×#64313	C₂	1	4	yes	maximal, complemented
8	C₃×D₃×#237	C₂	1	4	yes	maximal, complemented
9	C₃×D₃²×D₄	C₂	1	4	yes	maximal, complemented
10	C₃×#64307	C₂	1	2	yes	maximal, complemented
11	C₃×D₃×#235	C₂	1	2	yes	maximal, complemented
12	C₃×D₃×H(5,𝔽₂)	—	3	1	no	maximal
13	C₂×C₃×#1004	—	3	1	no	maximal
14	D₃×#1004	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂³×C₃²×D₃	C₂²	1	2	yes	complemented
16	C₂²×C₃×D₃²	C₂²	1	4	yes	complemented
17	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×#638	C₂²	1	4	yes	complemented
19	C₃×#3830	C₂²	1	4	yes	complemented
20	C₃×D₄×C₃⋊D₃	C₂²	1	4	yes	complemented
21	C₃×#3828	C₂²	1	2	yes	complemented
22	C₂×C₃²×#67	C₂²	1	4	yes	complemented
23	C₂×C₃²×#67	C₂²	1	2	yes	complemented
24	C₃²×#237	C₂²	1	4	yes	complemented
25	C₃²×D₃×D₄	C₂²	1	4	yes	complemented
26	C₃²×D₃×D₄	C₂²	1	4	yes	complemented
27	C₃²×D₃×D₄	C₂²	1	4	yes	complemented
28	C₃²×#235	C₂²	1	2	yes	complemented
29	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₃×#3811	C₂²	1	8	yes	complemented
32	C₃×D₃×#67	C₂²	1	4	yes	complemented
33	C₃×D₃×#67	C₂²	1	8	yes	complemented
34	C₃×D₃×#67	C₂²	1	8	yes	complemented
35	C₃×D₃×#67	C₂²	1	8	yes	complemented
36	C₃×D₃×#67	C₂²	1	8	yes	complemented
37	C₂×C₃×#626	C₂²	1	4	yes	complemented
38	C₂×C₃×#625	C₂²	1	4	yes	complemented
39	C₃×#3805	C₂²	1	8	yes	complemented
40	C₃×#3804	C₂²	1	4	yes	complemented
41	C₃×#3804	C₂²	1	8	yes	complemented
42	C₂×C₃×D₃×Dic₃	C₂²	1	4	yes	complemented
43	C₃×#3802	C₂²	1	4	yes	complemented
44	C₃×D₃×D₁₂	C₂²	1	2	yes	complemented
45	C₃×D₃×D₁₂	C₂²	1	4	yes	complemented
46	C₃×C₄×D₃²	C₂²	1	4	yes	complemented
47	C₃×#3799	C₂²	1	2	yes	complemented
48	C₃×#3798	C₂²	1	4	yes	complemented
49	C₃×#3796	C₂²	1	4	yes	complemented
50	C₃×#3795	C₂²	1	2	yes	complemented
51	C₃×#3795	C₂²	1	4	yes	complemented
52	C₃×D₃×Dic₆	C₂²	1	2	yes	complemented
53	C₃²×H(5,𝔽₂)	—	3	1	no	—
54	C₂²×C₃²×D₄	—	3	1	no	—
55	#64361	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₃×#67	—	3	4	no	—
57	C₃×#1009	—	3	4	no	—
58	C₃×#1009	—	3	2	no	—
59	C₃×D₃×#41	—	3	4	no	—
60	C₃×D₃×#41	—	3	2	no	—
61	C₃×#1004	—	2	1	no	—
62	C₃×#1004	—	3	1	no	—
63	C₃×#1004	—	3	1	no	—
64	C₃×#1004	—	3	4	no	—
65	C₃×#1004	—	3	4	no	—
66	C₃×#1004	—	3	4	no	—
67	C₃×#1004	—	3	4	no	—
68	C₃×#1004	—	3	4	no	—
69	C₃×#1004	—	3	2	no	—
70	C₃×#1004	—	6	1	no	—
71	C₃×#1004	D₃	1	1	yes	characteristic, direct product factor
72	C₃×#1004	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×C₃×#237	—	3	4	no	—
74	C₂×C₃×D₃×D₄	—	2	1	no	—
75	C₂×C₃×D₃×D₄	—	3	4	no	—
76	C₂×C₃×D₃×D₄	—	3	4	no	—
77	C₂×C₃×D₃×D₄	—	3	4	no	—
78	C₂×C₃×D₃×D₄	D₃	1	1	yes	characteristic, complemented
79	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂×C₃×#235	—	3	2	no	—
81	#64330	C₂×C₃	1	4	yes	complemented
82	C₂×D₃×#67	C₂×C₃	1	4	yes	complemented
83	#64314	C₂×C₃	1	4	yes	complemented
84	#64313	C₂×C₃	1	4	yes	complemented
85	D₃×#237	C₂×C₃	1	4	yes	complemented
86	D₃²×D₄	C₂×C₃	1	4	yes	complemented
87	#64307	C₂×C₃	1	2	yes	complemented
88	D₃×#235	C₂×C₃	1	2	yes	complemented
89	C₂³×C₃³	C₂³	1	2	yes	complemented
90	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	complemented
91	C₂²×C₃²×D₃	—	4	4	no	—
92	C₂²×C₃²×D₃	C₂³	1	4	yes	—
93	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
94	C₂²×C₃²×D₃	C₂³	1	4	yes	complemented
95	C₂²×C₃²×D₃	C₂³	1	4	yes	complemented
96	C₂²×C₃²×D₃	C₂³	1	2	yes	complemented
97	C₂×C₃×D₃²	—	4	8	no	—
98	C₂×C₃×D₃²	C₂³	1	4	yes	—
99	C₂×C₃×D₃²	C₂³	1	8	yes	complemented
100	C₃³×D₄	C₂³	1	4	yes	complemented
101	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic, complemented
102	C₃×#638	C₂³	1	4	yes	complemented
103	C₃×#638	C₂³	1	8	yes	complemented
104	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	complemented
105	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	complemented
106	C₃×C₄×C₃⋊D₃	C₂³	1	4	yes	complemented
107	C₃×#634	C₂³	1	2	yes	complemented
108	C₃²×#67	C₂³	1	8	yes	complemented
109	C₃²×#67	C₂³	1	4	yes	complemented
110	C₃²×#67	C₂³	1	8	yes	complemented
111	C₂×C₃²×Dic₃	C₂³	1	4	yes	complemented
112	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic, complemented
113	C₃²×D₁₂	C₂³	1	4	yes	complemented
114	C₃²×D₁₂	C₂³	1	2	yes	complemented
115	C₃²×C₄×D₃	C₂³	1	2	yes	—
116	C₃²×C₄×D₃	C₂³	1	2	yes	complemented
117	C₃²×C₄×D₃	C₂³	1	4	yes	complemented
118	C₃²×Dic₆	C₂³	1	2	yes	complemented
119	C₃×#627	C₂³	1	4	yes	complemented
120	C₃×#626	C₂³	1	8	yes	complemented
121	C₃×#626	C₂³	1	4	yes	complemented
122	C₃×#626	C₂³	1	4	yes	complemented
123	C₃×#625	C₂³	1	4	yes	complemented
124	C₃×#625	C₂³	1	8	yes	complemented
125	C₃×#624	C₂³	1	4	yes	complemented
126	C₃×D₃×Dic₃	C₂³	1	4	yes	—
127	C₃×D₃×Dic₃	C₂³	1	8	yes	complemented
128	C₃×D₃×Dic₃	C₂³	1	4	yes	complemented
129	C₂×C₃×H(5,𝔽₂)	—	9	1	no	—
130	D₃×H(5,𝔽₂)	—	3	1	no	—
131	C₂×#1004	—	3	1	no	—
132	C₂⁴×C₃²	—	3	2	no	—
133	C₂³×C₃×D₃	—	2	2	no	—
134	C₂³×C₃×D₃	—	3	4	no	—
135	C₂³×C₃×D₃	—	3	4	no	—
136	C₂³×C₃×D₃	C₂×D₃	1	2	yes	complemented
137	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	complemented
138	C₂²×D₃²	C₂²×C₃	1	4	yes	complemented
139	C₃²×#41	—	3	4	no	—
140	C₃²×#41	—	3	2	no	—
141	C₂×C₃²×D₄	—	2	1	no	—
142	C₂×C₃²×D₄	—	2	1	no	—
143	C₂×C₃²×D₄	—	2	1	no	—
144	C₂×C₃²×D₄	—	3	4	no	—
145	C₂×C₃²×D₄	—	3	2	no	—
146	C₂×C₃²×D₄	—	3	4	no	—
147	C₂×C₃²×D₄	—	3	4	no	—
148	C₂×C₃²×D₄	—	3	4	no	—
149	C₂×C₃²×D₄	—	3	1	no	—
150	C₂×C₃²×D₄	—	4	1	no	—
151	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
152	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
153	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₂²×C₃²×C₄	—	3	1	no	—
155	C₂×#638	C₂²×C₃	1	4	yes	complemented
156	#3830	C₂²×C₃	1	4	yes	complemented
157	D₄×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
158	#3828	C₂²×C₃	1	2	yes	complemented
159	C₂×C₃×#67	—	2	2	no	—
160	C₂×C₃×#67	—	2	4	no	—
161	C₂×C₃×#67	—	3	4	no	—
162	C₂×C₃×#67	—	3	4	no	—
163	C₂×C₃×#67	—	3	4	no	—
164	C₂×C₃×#67	—	3	4	no	—
165	C₂×C₃×#67	—	3	4	no	—
166	C₂×C₃×#67	—	3	8	no	—
167	C₂×C₃×#67	—	3	8	no	—
168	C₂×C₃×#67	—	3	8	no	—
169	C₂×C₃×#67	—	3	8	no	—
170	C₂×C₃×#67	—	3	4	no	—
171	C₂×C₃×#67	—	6	4	no	—
172	C₂×C₃×#67	C₂×D₃	1	2	yes	complemented
173	C₂×C₃×#67	C₂×D₃	1	4	yes	complemented
174	C₂×C₃×#67	C₂²×C₃	1	4	yes	complemented
175	C₂×C₃×#67	C₂²×C₃	1	2	yes	complemented
176	C₂²×C₃×Dic₃	—	3	4	no	—
177	C₃×#239	—	3	4	no	—
178	C₃×#239	—	3	2	no	—
179	C₃×D₃×Q₈	—	3	2	no	—
180	C₃×#237	—	2	4	no	—
181	C₃×#237	—	3	4	no	—
182	C₃×#237	—	3	4	no	—
183	C₃×#237	—	3	8	no	—
184	C₃×#237	—	3	8	no	—
185	C₃×#237	—	3	8	no	—
186	C₃×#237	—	3	4	no	—
187	C₃×#237	—	3	4	no	—
188	C₃×#237	—	3	2	no	—
189	C₃×#237	—	3	4	no	—
190	C₃×#237	—	6	4	no	—
191	C₃×#237	C₂×D₃	1	4	yes	complemented
192	C₃×#237	C₂²×C₃	1	4	yes	complemented
193	C₃×D₃×D₄	—	2	4	no	—
194	C₃×D₃×D₄	—	2	4	no	—
195	C₃×D₃×D₄	—	2	4	no	—
196	C₃×D₃×D₄	—	3	8	no	—
197	C₃×D₃×D₄	—	3	4	no	—
198	C₃×D₃×D₄	—	3	8	no	—
199	C₃×D₃×D₄	—	3	8	no	—
200	C₃×D₃×D₄	—	3	8	no	—
201	C₃×D₃×D₄	—	3	4	no	—
202	C₃×D₃×D₄	—	3	4	no	—
203	C₃×D₃×D₄	—	3	8	no	—
204	C₃×D₃×D₄	—	3	8	no	—
205	C₃×D₃×D₄	—	3	4	no	—
206	C₃×D₃×D₄	—	3	4	no	—
207	C₃×D₃×D₄	—	3	2	no	—
208	C₃×D₃×D₄	—	3	4	no	—
209	C₃×D₃×D₄	—	6	4	no	—
210	C₃×D₃×D₄	C₂×D₃	1	4	yes	complemented
211	C₃×D₃×D₄	C₂×D₃	1	4	yes	complemented
212	C₃×D₃×D₄	C₂×D₃	1	4	yes	complemented
213	C₃×D₃×D₄	C₂²×C₃	1	4	yes	complemented
214	C₃×D₃×D₄	C₂²×C₃	1	4	yes	complemented
215	C₃×D₃×D₄	C₂²×C₃	1	4	yes	complemented
216	C₃×#235	—	2	2	no	—
217	C₃×#235	—	3	2	no	—
218	C₃×#235	—	3	2	no	—
219	C₃×#235	—	3	4	no	—
220	C₃×#235	—	3	8	no	—
221	C₃×#235	—	3	2	no	—
222	C₃×#235	—	3	4	no	—
223	C₃×#235	—	3	4	no	—
224	C₃×#235	—	3	4	no	—
225	C₃×#235	—	3	2	no	—
226	C₃×#235	—	6	2	no	—
227	C₃×#235	C₂×D₃	1	2	yes	complemented
228	C₃×#235	C₂²×C₃	1	2	yes	complemented
229	C₂×C₃×D₁₂	—	2	1	no	—
230	C₂×C₃×D₁₂	—	3	4	no	—
231	C₂×C₃×D₁₂	—	3	2	no	—
232	C₂×C₃×D₁₂	—	3	4	no	—
233	C₂×C₃×D₁₂	C₂×D₃	1	1	yes	characteristic, complemented
234	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
235	C₂×C₃×C₄×D₃	—	2	1	no	—
236	C₂×C₃×C₄×D₃	—	3	4	no	—
237	C₂×C₃×C₄×D₃	—	3	4	no	—
238	C₂×C₃×C₄×D₃	—	3	4	no	—
239	C₂×C₃×C₄×D₃	C₂×D₃	1	1	yes	characteristic, complemented
240	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
241	C₂×C₃×Dic₆	—	3	2	no	—
242	#3811	C₂²×C₃	1	8	yes	complemented
243	D₃×#67	C₂²×C₃	1	4	yes	complemented
244	D₃×#67	C₂²×C₃	1	8	yes	complemented
245	D₃×#67	C₂²×C₃	1	8	yes	complemented
246	D₃×#67	C₂²×C₃	1	8	yes	complemented
247	D₃×#67	C₂²×C₃	1	8	yes	complemented
248	C₂×#626	C₂²×C₃	1	4	yes	complemented
249	C₂×#625	C₂²×C₃	1	4	yes	complemented
250	#3805	C₂²×C₃	1	8	yes	complemented
251	#3804	C₂²×C₃	1	4	yes	complemented
252	#3804	C₂²×C₃	1	8	yes	complemented
253	C₂×D₃×Dic₃	C₂²×C₃	1	4	yes	complemented
254	#3802	C₂²×C₃	1	4	yes	complemented
255	D₃×D₁₂	C₂²×C₃	1	2	yes	complemented
256	D₃×D₁₂	C₂²×C₃	1	4	yes	complemented
257	C₄×D₃²	C₂²×C₃	1	4	yes	complemented
258	#3799	C₂²×C₃	1	2	yes	complemented
259	#3798	C₂²×C₃	1	4	yes	complemented
260	#3796	C₂²×C₃	1	4	yes	complemented
261	#3795	C₂²×C₃	1	2	yes	complemented
262	#3795	C₂²×C₃	1	4	yes	complemented
263	D₃×Dic₆	C₂²×C₃	1	2	yes	complemented
264	C₂²×C₃³	—	4	2	no	—
265	C₂²×C₃³	C₂⁴	1	4	yes	—
266	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
267	C₂×C₃×C₃⋊D₃	—	4	4	no	—
268	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
269	C₂×C₃²×D₃	—	2	2	no	—
270	C₂×C₃²×D₃	—	2	8	no	—
271	C₂×C₃²×D₃	—	4	4	no	—
272	C₂×C₃²×D₃	—	4	2	no	—
273	C₂×C₃²×D₃	—	4	4	no	—
274	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
275	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
276	C₂×C₃²×D₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₃²×D₃	C₂⁴	1	1	yes	characteristic
278	C₃×D₃²	—	2	8	no	—
279	C₃×D₃²	—	4	8	no	—
280	C₃³×C₄	C₂⁴	1	2	yes	—
281	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	—
282	C₃²×Dic₃	C₂⁴	1	4	yes	—
283	C₃²×Dic₃	C₂⁴	1	2	yes	—
284	C₃×H(5,𝔽₂)	—	3	1	no	—
285	C₃×H(5,𝔽₂)	—	3	1	no	—
286	C₃×H(5,𝔽₂)	—	6	1	no	—
287	C₃×H(5,𝔽₂)	—	9	4	no	—
288	C₃×H(5,𝔽₂)	—	9	4	no	—
289	C₃×H(5,𝔽₂)	—	9	4	no	—
290	C₃×H(5,𝔽₂)	—	9	2	no	—
291	C₃×H(5,𝔽₂)	—	9	1	no	—
292	C₂×C₃×#41	—	9	2	no	—
293	C₂×C₃×#41	—	9	4	no	—
294	C₂²×C₃×D₄	—	3	1	no	—
295	C₂²×C₃×D₄	—	3	1	no	—
296	C₂²×C₃×D₄	—	6	1	no	—
297	C₂²×C₃×D₄	—	9	4	no	—
298	C₂²×C₃×D₄	—	9	4	no	—
299	C₂²×#67	—	3	4	no	—
300	#1009	—	3	4	no	—
301	#1009	—	3	2	no	—
302	D₃×#41	—	3	4	no	—
303	D₃×#41	—	3	2	no	—
304	#1004	—	3	1	no	—
305	#1004	—	3	1	no	—
306	#1004	—	3	4	no	—
307	#1004	—	3	4	no	—
308	#1004	—	3	4	no	—
309	#1004	—	3	4	no	—
310	#1004	—	3	4	no	—
311	#1004	—	3	2	no	—
312	#1004	—	6	1	no	—
313	#1004	C₃×D₃	1	1	yes	characteristic, direct product factor
314	C₂×#237	—	3	4	no	—
315	C₂×D₃×D₄	—	3	4	no	—
316	C₂×D₃×D₄	—	3	4	no	—
317	C₂×D₃×D₄	—	3	4	no	—
318	C₂×D₃×D₄	C₃×D₃	1	1	yes	characteristic, complemented
319	C₂×#235	—	3	2	no	—
320	C₂³×C₃²	—	2	2	no	—
321	C₂³×C₃²	—	2	2	no	—
322	C₂³×C₃²	—	2	2	no	—
323	C₂³×C₃²	—	3	4	no	—
324	C₂³×C₃²	—	3	1	no	—
325	C₂³×C₃²	—	3	4	no	—
326	C₂³×C₃²	—	3	2	no	—
327	C₂³×C₃²	—	3	4	no	—
328	C₂³×C₃²	—	4	2	no	—
329	C₂³×C₃²	—	12	4	no	—
330	C₂³×C₃²	C₂²×D₃	1	2	yes	complemented
331	C₂³×C₃²	C₂²×D₃	1	2	yes	complemented
332	C₂³×C₃²	C₂³×C₃	1	2	yes	complemented
333	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	complemented
334	C₂²×C₃×D₃	—	2	1	no	—
335	C₂²×C₃×D₃	—	2	4	no	—
336	C₂²×C₃×D₃	—	2	2	no	—
337	C₂²×C₃×D₃	—	2	4	no	—
338	C₂²×C₃×D₃	—	2	4	no	—
339	C₂²×C₃×D₃	—	3	4	no	—
340	C₂²×C₃×D₃	—	3	4	no	—
341	C₂²×C₃×D₃	—	3	4	no	—
342	C₂²×C₃×D₃	—	3	4	no	—
343	C₂²×C₃×D₃	—	3	8	no	—
344	C₂²×C₃×D₃	—	3	8	no	—
345	C₂²×C₃×D₃	—	4	4	no	—
346	C₂²×C₃×D₃	—	4	4	no	—
347	C₂²×C₃×D₃	—	4	8	no	—
348	C₂²×C₃×D₃	—	6	4	no	—
349	C₂²×C₃×D₃	—	12	8	no	—
350	C₂²×C₃×D₃	—	12	8	no	—
351	C₂²×C₃×D₃	C₂²×D₃	1	4	yes	—
352	C₂²×C₃×D₃	C₂²×D₃	1	1	yes	characteristic
353	C₂²×C₃×D₃	C₂²×D₃	1	4	yes	complemented
354	C₂²×C₃×D₃	C₂²×D₃	1	4	yes	complemented
355	C₂²×C₃×D₃	C₂²×D₃	1	2	yes	complemented
356	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
357	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
358	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	complemented
359	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	complemented
360	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	complemented
361	C₂×D₃²	—	4	8	no	—
362	C₂×D₃²	C₂³×C₃	1	4	yes	—
363	C₂×D₃²	C₂³×C₃	1	8	yes	complemented
364	C₃²×Q₈	—	3	2	no	—
365	C₃²×D₄	—	2	4	no	—
366	C₃²×D₄	—	2	4	no	—
367	C₃²×D₄	—	2	4	no	—
368	C₃²×D₄	—	3	8	no	—
369	C₃²×D₄	—	3	4	no	—
370	C₃²×D₄	—	3	8	no	—
371	C₃²×D₄	—	3	2	no	—
372	C₃²×D₄	—	3	4	no	—
373	C₃²×D₄	—	4	4	no	—
374	C₃²×D₄	C₂²×D₃	1	4	yes	complemented
375	C₃²×D₄	C₂²×D₃	1	4	yes	complemented
376	C₃²×D₄	C₂³×C₃	1	4	yes	complemented
377	C₂×C₃²×C₄	—	2	1	no	—
378	C₂×C₃²×C₄	—	2	1	no	—
379	C₂×C₃²×C₄	—	2	1	no	—
380	C₂×C₃²×C₄	—	3	4	no	—
381	C₂×C₃²×C₄	—	3	1	no	—
382	C₂×C₃²×C₄	—	3	2	no	—
383	C₂×C₃²×C₄	—	3	4	no	—
384	C₂×C₃²×C₄	—	3	2	no	—
385	C₂×C₃²×C₄	—	4	1	no	—
386	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic, complemented
387	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic, complemented
388	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic, complemented
389	#638	C₂³×C₃	1	4	yes	complemented
390	#638	C₂³×C₃	1	8	yes	complemented
391	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	complemented
392	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	complemented
393	C₄×C₃⋊D₃	C₂³×C₃	1	4	yes	complemented
394	#634	C₂³×C₃	1	2	yes	complemented
395	C₃×#67	—	2	4	no	—
396	C₃×#67	—	2	8	no	—
397	C₃×#67	—	2	8	no	—
398	C₃×#67	—	3	4	no	—
399	C₃×#67	—	3	8	no	—
400	C₃×#67	—	3	4	no	—
401	C₃×#67	—	3	8	no	—
402	C₃×#67	—	3	4	no	—
403	C₃×#67	—	3	8	no	—
404	C₃×#67	—	3	4	no	—
405	C₃×#67	—	3	8	no	—
406	C₃×#67	—	3	4	no	—
407	C₃×#67	—	3	4	no	—
408	C₃×#67	—	3	8	no	—
409	C₃×#67	—	6	4	no	—
410	C₃×#67	—	6	8	no	—
411	C₃×#67	C₂²×D₃	1	4	yes	complemented
412	C₃×#67	C₂²×D₃	1	8	yes	complemented
413	C₃×#67	C₂²×D₃	1	8	yes	complemented
414	C₃×#67	C₂³×C₃	1	8	yes	complemented
415	C₃×#67	C₂³×C₃	1	4	yes	complemented
416	C₃×#67	C₂³×C₃	1	8	yes	complemented
417	C₂×C₃×Dic₃	—	2	1	no	—
418	C₂×C₃×Dic₃	—	2	4	no	—
419	C₂×C₃×Dic₃	—	3	4	no	—
420	C₂×C₃×Dic₃	—	3	4	no	—
421	C₂×C₃×Dic₃	—	3	4	no	—
422	C₂×C₃×Dic₃	—	3	4	no	—
423	C₂×C₃×Dic₃	—	3	8	no	—
424	C₂×C₃×Dic₃	—	6	4	no	—
425	C₂×C₃×Dic₃	C₂²×D₃	1	1	yes	characteristic, complemented
426	C₂×C₃×Dic₃	C₂²×D₃	1	4	yes	complemented
427	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	complemented
428	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic, complemented
429	C₃×D₁₂	—	2	4	no	—
430	C₃×D₁₂	—	2	2	no	—
431	C₃×D₁₂	—	3	8	no	—
432	C₃×D₁₂	—	3	4	no	—
433	C₃×D₁₂	—	3	4	no	—
434	C₃×D₁₂	—	3	2	no	—
435	C₃×D₁₂	—	3	2	no	—
436	C₃×D₁₂	—	6	2	no	—
437	C₃×D₁₂	C₂²×D₃	1	4	yes	complemented
438	C₃×D₁₂	C₂²×D₃	1	2	yes	complemented
439	C₃×D₁₂	C₂³×C₃	1	4	yes	complemented
440	C₃×D₁₂	C₂³×C₃	1	2	yes	complemented
441	C₃×C₄×D₃	—	2	2	no	—
442	C₃×C₄×D₃	—	2	2	no	—
443	C₃×C₄×D₃	—	2	4	no	—
444	C₃×C₄×D₃	—	3	4	no	—
445	C₃×C₄×D₃	—	3	4	no	—
446	C₃×C₄×D₃	—	3	8	no	—
447	C₃×C₄×D₃	—	3	4	no	—
448	C₃×C₄×D₃	—	3	4	no	—
449	C₃×C₄×D₃	—	3	4	no	—
450	C₃×C₄×D₃	—	3	4	no	—
451	C₃×C₄×D₃	—	6	4	no	—
452	C₃×C₄×D₃	C₂²×D₃	1	2	yes	—
453	C₃×C₄×D₃	C₂²×D₃	1	4	yes	complemented
454	C₃×C₄×D₃	C₂²×D₃	1	2	yes	complemented
455	C₃×C₄×D₃	C₂³×C₃	1	2	yes	—
456	C₃×C₄×D₃	C₂³×C₃	1	2	yes	complemented
457	C₃×C₄×D₃	C₂³×C₃	1	4	yes	complemented
458	C₃×Dic₆	—	2	2	no	—
459	C₃×Dic₆	—	3	2	no	—
460	C₃×Dic₆	—	3	2	no	—
461	C₃×Dic₆	—	3	4	no	—
462	C₃×Dic₆	—	3	4	no	—
463	C₃×Dic₆	—	6	2	no	—
464	C₃×Dic₆	C₂²×D₃	1	2	yes	complemented
465	C₃×Dic₆	C₂³×C₃	1	2	yes	complemented
466	#627	C₂³×C₃	1	4	yes	complemented
467	#626	C₂³×C₃	1	8	yes	complemented
468	#626	C₂³×C₃	1	4	yes	complemented
469	#626	C₂³×C₃	1	4	yes	complemented
470	#625	C₂³×C₃	1	4	yes	complemented
471	#625	C₂³×C₃	1	8	yes	complemented
472	#624	C₂³×C₃	1	4	yes	complemented
473	D₃×Dic₃	C₂³×C₃	1	4	yes	—
474	D₃×Dic₃	C₂³×C₃	1	8	yes	complemented
475	D₃×Dic₃	C₂³×C₃	1	4	yes	complemented
476	C₂×H(5,𝔽₂)	—	9	1	no	Sylow
477	C₂×C₃³	—	2	1	no	—
478	C₂×C₃³	—	2	4	no	—
479	C₂×C₃³	C₂⁵	1	1	yes	characteristic
480	C₃×C₃⋊D₃	—	2	4	no	—
481	C₃²×D₃	—	2	1	no	—
482	C₃²×D₃	—	2	4	no	—
483	C₃²×D₃	—	2	4	no	—
484	C₃²×D₃	H(5,𝔽₂)	1	2	yes	complemented
485	C₂⁴×C₃	—	3	2	no	—
486	C₂⁴×C₃	—	3	2	no	—
487	C₂⁴×C₃	—	6	2	no	—
488	C₂⁴×C₃	—	9	4	no	—
489	C₂³×D₃	—	3	4	no	—
490	C₂³×D₃	—	3	4	no	—
491	C₂³×D₃	C₂×C₃×D₃	1	2	yes	complemented
492	C₃×#41	—	3	4	no	—
493	C₃×#41	—	3	4	no	—
494	C₃×#41	—	3	2	no	—
495	C₃×#41	—	3	2	no	—
496	C₃×#41	—	6	2	no	—
497	C₃×#41	—	6	4	no	—
498	C₃×#41	—	9	4	no	—
499	C₃×#41	—	9	4	no	—
500	C₃×#41	—	9	8	no	—
501	C₃×#41	—	9	2	no	—
502	C₃×#41	—	9	4	no	—
503	C₃×#41	—	9	2	no	—
504	C₃×#41	—	9	8	no	—
505	C₃×#41	—	9	4	no	—
506	C₃×#41	—	9	4	no	—
507	C₃×#41	—	9	2	no	—
508	C₂×C₃×Q₈	—	9	2	no	—
509	C₂×C₃×D₄	—	2	1	no	—
510	C₂×C₃×D₄	—	2	1	no	—
511	C₂×C₃×D₄	—	2	1	no	—
512	C₂×C₃×D₄	—	3	2	no	—
513	C₂×C₃×D₄	—	3	4	no	—
514	C₂×C₃×D₄	—	3	4	no	—
515	C₂×C₃×D₄	—	3	2	no	—
516	C₂×C₃×D₄	—	3	4	no	—
517	C₂×C₃×D₄	—	3	4	no	—
518	C₂×C₃×D₄	—	3	4	no	—
519	C₂×C₃×D₄	—	3	4	no	—
520	C₂×C₃×D₄	—	3	4	no	—
521	C₂×C₃×D₄	—	3	4	no	—
522	C₂×C₃×D₄	—	3	1	no	—
523	C₂×C₃×D₄	—	3	1	no	—
524	C₂×C₃×D₄	—	4	1	no	—
525	C₂×C₃×D₄	—	6	1	no	—
526	C₂×C₃×D₄	—	6	4	no	—
527	C₂×C₃×D₄	—	6	4	no	—
528	C₂×C₃×D₄	—	6	4	no	—
529	C₂×C₃×D₄	—	6	2	no	—
530	C₂×C₃×D₄	—	6	4	no	—
531	C₂×C₃×D₄	—	9	2	no	—
532	C₂×C₃×D₄	—	9	4	no	—
533	C₂×C₃×D₄	—	9	4	no	—
534	C₂×C₃×D₄	—	9	8	no	—
535	C₂×C₃×D₄	—	9	4	no	—
536	C₂×C₃×D₄	—	9	4	no	—
537	C₂×C₃×D₄	—	9	8	no	—
538	C₂×C₃×D₄	—	9	8	no	—
539	C₂×C₃×D₄	—	9	8	no	—
540	C₂×C₃×D₄	—	9	8	no	—
541	C₂×C₃×D₄	—	9	4	no	—
542	C₂×C₃×D₄	—	9	4	no	—
543	C₂×C₃×D₄	—	9	4	no	—
544	C₂×C₃×D₄	D₃²	1	1	yes	characteristic, complemented
545	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
546	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
547	C₂²×C₃×C₄	—	3	1	no	—
548	C₂²×C₃×C₄	—	3	1	no	—
549	C₂²×C₃×C₄	—	6	1	no	—
550	C₂²×C₃×C₄	—	9	4	no	—
551	C₂²×C₃×C₄	—	9	4	no	—
552	C₂×#67	—	3	4	no	—
553	C₂×#67	—	3	4	no	—
554	C₂×#67	—	3	4	no	—
555	C₂×#67	—	3	4	no	—
556	C₂×#67	—	3	4	no	—
557	C₂×#67	—	3	8	no	—
558	C₂×#67	—	3	8	no	—
559	C₂×#67	—	3	8	no	—
560	C₂×#67	—	3	8	no	—
561	C₂×#67	—	3	4	no	—
562	C₂×#67	—	6	4	no	—
563	C₂×#67	C₂×C₃×D₃	1	2	yes	complemented
564	C₂×#67	C₂×C₃×D₃	1	4	yes	complemented
565	C₂²×Dic₃	—	3	4	no	—
566	#239	—	3	4	no	—
567	#239	—	3	2	no	—
568	D₃×Q₈	—	3	2	no	—
569	#237	—	3	4	no	—
570	#237	—	3	4	no	—
571	#237	—	3	8	no	—
572	#237	—	3	8	no	—
573	#237	—	3	8	no	—
574	#237	—	3	4	no	—
575	#237	—	3	4	no	—
576	#237	—	3	2	no	—
577	#237	—	3	4	no	—
578	#237	—	6	4	no	—
579	#237	C₂×C₃×D₃	1	4	yes	complemented
580	D₃×D₄	—	3	8	no	—
581	D₃×D₄	—	3	4	no	—
582	D₃×D₄	—	3	8	no	—
583	D₃×D₄	—	3	8	no	—
584	D₃×D₄	—	3	8	no	—
585	D₃×D₄	—	3	4	no	—
586	D₃×D₄	—	3	4	no	—
587	D₃×D₄	—	3	8	no	—
588	D₃×D₄	—	3	8	no	—
589	D₃×D₄	—	3	4	no	—
590	D₃×D₄	—	3	4	no	—
591	D₃×D₄	—	3	2	no	—
592	D₃×D₄	—	3	4	no	—
593	D₃×D₄	—	6	4	no	—
594	D₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
595	D₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
596	D₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
597	#235	—	3	2	no	—
598	#235	—	3	2	no	—
599	#235	—	3	4	no	—
600	#235	—	3	8	no	—
601	#235	—	3	2	no	—
602	#235	—	3	4	no	—
603	#235	—	3	4	no	—
604	#235	—	3	4	no	—
605	#235	—	3	2	no	—
606	#235	—	6	2	no	—
607	#235	C₂×C₃×D₃	1	2	yes	complemented
608	C₂×D₁₂	—	3	4	no	—
609	C₂×D₁₂	—	3	2	no	—
610	C₂×D₁₂	—	3	4	no	—
611	C₂×D₁₂	C₂×C₃×D₃	1	1	yes	characteristic, complemented
612	C₂×C₄×D₃	—	3	4	no	—
613	C₂×C₄×D₃	—	3	4	no	—
614	C₂×C₄×D₃	—	3	4	no	—
615	C₂×C₄×D₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented
616	C₂×Dic₆	—	3	2	no	—
617	C₂²×C₃²	—	2	4	no	—
618	C₂²×C₃²	—	2	1	no	—
619	C₂²×C₃²	—	2	1	no	—
620	C₂²×C₃²	—	2	4	no	—
621	C₂²×C₃²	—	2	1	no	—
622	C₂²×C₃²	—	2	4	no	—
623	C₂²×C₃²	—	3	1	no	—
624	C₂²×C₃²	—	3	4	no	—
625	C₂²×C₃²	—	3	4	no	—
626	C₂²×C₃²	—	3	1	no	—
627	C₂²×C₃²	—	4	1	no	—
628	C₂²×C₃²	—	4	4	no	—
629	C₂²×C₃²	—	4	2	no	—
630	C₂²×C₃²	—	4	2	no	—
631	C₂²×C₃²	—	4	2	no	—
632	C₂²×C₃²	—	4	4	no	—
633	C₂²×C₃²	—	6	2	no	—
634	C₂²×C₃²	—	6	8	no	—
635	C₂²×C₃²	—	8	2	no	—
636	C₂²×C₃²	—	8	2	no	—
637	C₂²×C₃²	—	8	4	no	—
638	C₂²×C₃²	—	12	2	no	—
639	C₂²×C₃²	—	12	4	no	—
640	C₂²×C₃²	—	12	4	no	—
641	C₂²×C₃²	C₂³×D₃	1	4	yes	—
642	C₂²×C₃²	C₂³×D₃	1	4	yes	—
643	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
644	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
645	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
646	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
647	C₂×C₃⋊D₃	—	4	4	no	—
648	C₂×C₃⋊D₃	C₂⁴×C₃	1	4	yes	—
649	C₂×C₃×D₃	—	2	4	no	—
650	C₂×C₃×D₃	—	2	2	no	—
651	C₂×C₃×D₃	—	2	8	no	—
652	C₂×C₃×D₃	—	2	8	no	—
653	C₂×C₃×D₃	—	2	2	no	—
654	C₂×C₃×D₃	—	2	1	no	—
655	C₂×C₃×D₃	—	2	1	no	—
656	C₂×C₃×D₃	—	2	4	no	—
657	C₂×C₃×D₃	—	2	4	no	—
658	C₂×C₃×D₃	—	3	4	no	—
659	C₂×C₃×D₃	—	3	4	no	—
660	C₂×C₃×D₃	—	4	8	no	—
661	C₂×C₃×D₃	—	4	4	no	—
662	C₂×C₃×D₃	—	4	4	no	—
663	C₂×C₃×D₃	—	4	2	no	—
664	C₂×C₃×D₃	—	4	2	no	—
665	C₂×C₃×D₃	—	4	4	no	—
666	C₂×C₃×D₃	—	4	4	no	—
667	C₂×C₃×D₃	—	4	8	no	—
668	C₂×C₃×D₃	—	4	4	no	—
669	C₂×C₃×D₃	—	6	4	no	—
670	C₂×C₃×D₃	—	6	8	no	—
671	C₂×C₃×D₃	—	6	8	no	—
672	C₂×C₃×D₃	—	8	4	no	—
673	C₂×C₃×D₃	—	12	8	no	—
674	C₂×C₃×D₃	—	12	8	no	—
675	C₂×C₃×D₃	—	12	4	no	—
676	C₂×C₃×D₃	—	12	4	no	—
677	C₂×C₃×D₃	—	24	4	no	—
678	C₂×C₃×D₃	C₂³×D₃	1	4	yes	—
679	C₂×C₃×D₃	C₂³×D₃	1	4	yes	—
680	C₂×C₃×D₃	C₂³×D₃	1	1	yes	characteristic
681	C₂×C₃×D₃	C₂³×D₃	1	1	yes	characteristic
682	C₂×C₃×D₃	C₂⁴×C₃	1	4	yes	—
683	C₂×C₃×D₃	C₂⁴×C₃	1	4	yes	—
684	C₂×C₃×D₃	C₂⁴×C₃	1	1	yes	characteristic
685	C₂×C₃×D₃	C₂⁴×C₃	1	1	yes	characteristic
686	D₃²	—	2	8	no	—
687	D₃²	—	4	8	no	—
688	C₃²×C₄	—	2	2	no	—
689	C₃²×C₄	—	2	2	no	—
690	C₃²×C₄	—	2	2	no	—
691	C₃²×C₄	—	3	2	no	—
692	C₃²×C₄	—	3	4	no	—
693	C₃²×C₄	—	4	2	no	—
694	C₃²×C₄	C₂³×D₃	1	2	yes	—
695	C₃²×C₄	C₂³×D₃	1	2	yes	—
696	C₃²×C₄	C₂⁴×C₃	1	2	yes	—
697	C₃⋊Dic₃	C₂⁴×C₃	1	4	yes	—
698	C₃×Dic₃	—	2	4	no	—
699	C₃×Dic₃	—	2	2	no	—
700	C₃×Dic₃	—	3	4	no	—
701	C₃×Dic₃	—	3	4	no	—
702	C₃×Dic₃	—	6	4	no	—
703	C₃×Dic₃	C₂³×D₃	1	2	yes	—
704	C₃×Dic₃	C₂³×D₃	1	4	yes	—
705	C₃×Dic₃	C₂⁴×C₃	1	4	yes	—
706	C₃×Dic₃	C₂⁴×C₃	1	2	yes	—
707	H(5,𝔽₂)	—	3	1	no	—
708	H(5,𝔽₂)	—	9	4	no	—
709	H(5,𝔽₂)	—	9	4	no	—
710	H(5,𝔽₂)	—	9	4	no	—
711	H(5,𝔽₂)	—	9	2	no	—
712	H(5,𝔽₂)	—	9	1	no	—
713	C₂×#41	—	9	2	no	—
714	C₂×#41	—	9	4	no	—
715	C₂²×D₄	—	3	1	no	—
716	C₂²×D₄	—	9	4	no	—
717	C₂²×D₄	—	9	4	no	—
718	C₃³	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
719	C₂³×C₃	—	2	2	no	—
720	C₂³×C₃	—	2	2	no	—
721	C₂³×C₃	—	2	2	no	—
722	C₂³×C₃	—	3	1	no	—
723	C₂³×C₃	—	3	4	no	—
724	C₂³×C₃	—	3	4	no	—
725	C₂³×C₃	—	3	1	no	—
726	C₂³×C₃	—	3	4	no	—
727	C₂³×C₃	—	3	4	no	—
728	C₂³×C₃	—	3	2	no	—
729	C₂³×C₃	—	3	2	no	—
730	C₂³×C₃	—	3	4	no	—
731	C₂³×C₃	—	3	4	no	—
732	C₂³×C₃	—	4	2	no	—
733	C₂³×C₃	—	6	1	no	—
734	C₂³×C₃	—	6	4	no	—
735	C₂³×C₃	—	6	2	no	—
736	C₂³×C₃	—	6	4	no	—
737	C₂³×C₃	—	6	4	no	—
738	C₂³×C₃	—	9	4	no	—
739	C₂³×C₃	—	9	8	no	—
740	C₂³×C₃	—	9	4	no	—
741	C₂³×C₃	—	12	4	no	—
742	C₂³×C₃	—	12	4	no	—
743	C₂³×C₃	—	12	8	no	—
744	C₂³×C₃	—	36	8	no	—
745	C₂³×C₃	C₂×D₃²	1	2	yes	complemented
746	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	complemented
747	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	complemented
748	C₂²×D₃	—	3	4	no	—
749	C₂²×D₃	—	3	4	no	—
750	C₂²×D₃	—	3	4	no	—
751	C₂²×D₃	—	3	4	no	—
752	C₂²×D₃	—	3	8	no	—
753	C₂²×D₃	—	3	8	no	—
754	C₂²×D₃	—	4	4	no	—
755	C₂²×D₃	—	6	4	no	—
756	C₂²×D₃	—	12	8	no	—
757	C₂²×D₃	—	12	8	no	—
758	C₂²×D₃	C₂²×C₃×D₃	1	4	yes	—
759	C₂²×D₃	C₂²×C₃×D₃	1	1	yes	characteristic
760	C₂²×D₃	C₂²×C₃×D₃	1	4	yes	complemented
761	C₂²×D₃	C₂²×C₃×D₃	1	2	yes	complemented
762	C₂²×D₃	C₂²×C₃×D₃	1	4	yes	complemented
763	C₃×Q₈	—	3	2	no	—
764	C₃×Q₈	—	3	2	no	—
765	C₃×Q₈	—	6	2	no	—
766	C₃×Q₈	—	9	4	no	—
767	C₃×Q₈	—	9	2	no	—
768	C₃×D₄	—	2	4	no	—
769	C₃×D₄	—	2	4	no	—
770	C₃×D₄	—	2	4	no	—
771	C₃×D₄	—	3	8	no	—
772	C₃×D₄	—	3	8	no	—
773	C₃×D₄	—	3	4	no	—
774	C₃×D₄	—	3	8	no	—
775	C₃×D₄	—	3	4	no	—
776	C₃×D₄	—	3	8	no	—
777	C₃×D₄	—	3	4	no	—
778	C₃×D₄	—	3	2	no	—
779	C₃×D₄	—	3	2	no	—
780	C₃×D₄	—	3	4	no	—
781	C₃×D₄	—	4	4	no	—
782	C₃×D₄	—	6	4	no	—
783	C₃×D₄	—	6	2	no	—
784	C₃×D₄	—	6	8	no	—
785	C₃×D₄	—	6	4	no	—
786	C₃×D₄	—	6	8	no	—
787	C₃×D₄	—	9	4	no	—
788	C₃×D₄	—	9	4	no	—
789	C₃×D₄	—	9	8	no	—
790	C₃×D₄	—	9	4	no	—
791	C₃×D₄	—	9	8	no	—
792	C₃×D₄	—	9	8	no	—
793	C₃×D₄	—	9	4	no	—
794	C₃×D₄	—	9	2	no	—
795	C₃×D₄	C₂×D₃²	1	4	yes	complemented
796	C₃×D₄	C₂²×C₃×D₃	1	4	yes	complemented
797	C₃×D₄	C₂²×C₃×D₃	1	4	yes	complemented
798	C₂×C₃×C₄	—	2	1	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	1	no	—
801	C₂×C₃×C₄	—	3	1	no	—
802	C₂×C₃×C₄	—	3	4	no	—
803	C₂×C₃×C₄	—	3	4	no	—
804	C₂×C₃×C₄	—	3	1	no	—
805	C₂×C₃×C₄	—	3	2	no	—
806	C₂×C₃×C₄	—	3	2	no	—
807	C₂×C₃×C₄	—	3	4	no	—
808	C₂×C₃×C₄	—	3	2	no	—
809	C₂×C₃×C₄	—	3	4	no	—
810	C₂×C₃×C₄	—	3	2	no	—
811	C₂×C₃×C₄	—	4	1	no	—
812	C₂×C₃×C₄	—	6	2	no	—
813	C₂×C₃×C₄	—	6	2	no	—
814	C₂×C₃×C₄	—	6	4	no	—
815	C₂×C₃×C₄	—	6	1	no	—
816	C₂×C₃×C₄	—	6	4	no	—
817	C₂×C₃×C₄	—	9	4	no	—
818	C₂×C₃×C₄	—	9	4	no	—
819	C₂×C₃×C₄	—	9	4	no	—
820	C₂×C₃×C₄	—	9	8	no	—
821	C₂×C₃×C₄	—	9	4	no	—
822	C₂×C₃×C₄	—	9	4	no	—
823	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic, complemented
824	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
825	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
826	#67	—	3	4	no	—
827	#67	—	3	8	no	—
828	#67	—	3	4	no	—
829	#67	—	3	8	no	—
830	#67	—	3	4	no	—
831	#67	—	3	8	no	—
832	#67	—	3	4	no	—
833	#67	—	3	8	no	—
834	#67	—	3	4	no	—
835	#67	—	3	4	no	—
836	#67	—	3	8	no	—
837	#67	—	6	4	no	—
838	#67	—	6	8	no	—
839	#67	C₂²×C₃×D₃	1	4	yes	complemented
840	#67	C₂²×C₃×D₃	1	8	yes	complemented
841	#67	C₂²×C₃×D₃	1	8	yes	complemented
842	C₂×Dic₃	—	3	4	no	—
843	C₂×Dic₃	—	3	4	no	—
844	C₂×Dic₃	—	3	4	no	—
845	C₂×Dic₃	—	3	4	no	—
846	C₂×Dic₃	—	3	8	no	—
847	C₂×Dic₃	—	6	4	no	—
848	C₂×Dic₃	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
849	C₂×Dic₃	C₂²×C₃×D₃	1	4	yes	complemented
850	D₁₂	—	3	8	no	—
851	D₁₂	—	3	4	no	—
852	D₁₂	—	3	4	no	—
853	D₁₂	—	3	2	no	—
854	D₁₂	—	3	2	no	—
855	D₁₂	—	6	2	no	—
856	D₁₂	C₂²×C₃×D₃	1	4	yes	complemented
857	D₁₂	C₂²×C₃×D₃	1	2	yes	complemented
858	C₄×D₃	—	3	4	no	—
859	C₄×D₃	—	3	4	no	—
860	C₄×D₃	—	3	8	no	—
861	C₄×D₃	—	3	4	no	—
862	C₄×D₃	—	3	4	no	—
863	C₄×D₃	—	3	4	no	—
864	C₄×D₃	—	3	4	no	—
865	C₄×D₃	—	6	4	no	—
866	C₄×D₃	C₂²×C₃×D₃	1	2	yes	—
867	C₄×D₃	C₂²×C₃×D₃	1	4	yes	complemented
868	C₄×D₃	C₂²×C₃×D₃	1	2	yes	complemented
869	Dic₆	—	3	2	no	—
870	Dic₆	—	3	2	no	—
871	Dic₆	—	3	4	no	—
872	Dic₆	—	3	4	no	—
873	Dic₆	—	6	2	no	—
874	Dic₆	C₂²×C₃×D₃	1	2	yes	complemented
875	C₂×C₃²	—	2	1	no	—
876	C₂×C₃²	—	2	2	no	—
877	C₂×C₃²	—	2	1	no	—
878	C₂×C₃²	—	2	4	no	—
879	C₂×C₃²	—	2	4	no	—
880	C₂×C₃²	—	2	4	no	—
881	C₂×C₃²	—	2	1	no	—
882	C₂×C₃²	—	2	1	no	—
883	C₂×C₃²	—	2	1	no	—
884	C₂×C₃²	—	2	1	no	—
885	C₂×C₃²	—	3	2	no	—
886	C₂×C₃²	—	4	1	no	—
887	C₂×C₃²	—	4	1	no	—
888	C₂×C₃²	—	4	1	no	—
889	C₂×C₃²	—	4	2	no	—
890	C₂×C₃²	—	4	4	no	—
891	C₂×C₃²	—	4	4	no	—
892	C₂×C₃²	—	4	4	no	—
893	C₂×C₃²	—	6	1	no	—
894	C₂×C₃²	—	6	4	no	—
895	C₂×C₃²	—	6	4	no	—
896	C₂×C₃²	—	8	4	no	—
897	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
898	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
899	C₂×C₃²	C₂⁵×C₃	1	1	yes	characteristic
900	C₃⋊D₃	—	2	4	no	—
901	C₃×D₃	—	2	2	no	—
902	C₃×D₃	—	2	1	no	—
903	C₃×D₃	—	2	4	no	—
904	C₃×D₃	—	2	4	no	—
905	C₃×D₃	—	2	4	no	—
906	C₃×D₃	—	2	4	no	—
907	C₃×D₃	—	2	1	no	—
908	C₃×D₃	—	2	2	no	—
909	C₃×D₃	—	4	4	no	—
910	C₃×D₃	—	4	4	no	—
911	C₃×D₃	—	6	4	no	—
912	C₃×D₃	—	6	4	no	—
913	C₃×D₃	—	12	4	no	—
914	C₃×D₃	#1004	1	2	yes	direct product factor
915	C₃×D₃	C₃×H(5,𝔽₂)	1	2	yes	complemented
916	C₂⁴	—	3	2	no	—
917	C₂⁴	—	9	4	no	—
918	#41	—	3	4	no	—
919	#41	—	3	2	no	—
920	#41	—	9	4	no	—
921	#41	—	9	4	no	—
922	#41	—	9	8	no	—
923	#41	—	9	2	no	—
924	#41	—	9	4	no	—
925	#41	—	9	2	no	—
926	#41	—	9	8	no	—
927	#41	—	9	4	no	—
928	#41	—	9	4	no	—
929	#41	—	9	2	no	—
930	C₂×Q₈	—	9	2	no	—
931	C₂×D₄	—	3	2	no	—
932	C₂×D₄	—	3	4	no	—
933	C₂×D₄	—	3	4	no	—
934	C₂×D₄	—	3	4	no	—
935	C₂×D₄	—	3	4	no	—
936	C₂×D₄	—	3	1	no	—
937	C₂×D₄	—	9	2	no	—
938	C₂×D₄	—	9	4	no	—
939	C₂×D₄	—	9	4	no	—
940	C₂×D₄	—	9	8	no	—
941	C₂×D₄	—	9	4	no	—
942	C₂×D₄	—	9	4	no	—
943	C₂×D₄	—	9	8	no	—
944	C₂×D₄	—	9	8	no	—
945	C₂×D₄	—	9	8	no	—
946	C₂×D₄	—	9	8	no	—
947	C₂×D₄	—	9	4	no	—
948	C₂×D₄	—	9	4	no	—
949	C₂×D₄	—	9	4	no	—
950	C₂×D₄	C₃×D₃²	1	1	yes	characteristic, complemented
951	C₂²×C₄	—	3	1	no	—
952	C₂²×C₄	—	9	4	no	—
953	C₂²×C₄	—	9	4	no	—
954	C₂²×C₃	—	2	1	no	—
955	C₂²×C₃	—	2	4	no	—
956	C₂²×C₃	—	2	1	no	—
957	C₂²×C₃	—	2	1	no	—
958	C₂²×C₃	—	2	4	no	—
959	C₂²×C₃	—	2	4	no	—
960	C₂²×C₃	—	3	1	no	—
961	C₂²×C₃	—	3	1	no	—
962	C₂²×C₃	—	3	1	no	—
963	C₂²×C₃	—	3	4	no	—
964	C₂²×C₃	—	3	4	no	—
965	C₂²×C₃	—	3	4	no	—
966	C₂²×C₃	—	3	4	no	—
967	C₂²×C₃	—	3	1	no	—
968	C₂²×C₃	—	4	2	no	—
969	C₂²×C₃	—	4	2	no	—
970	C₂²×C₃	—	4	2	no	—
971	C₂²×C₃	—	4	4	no	—
972	C₂²×C₃	—	4	1	no	—
973	C₂²×C₃	—	4	4	no	—
974	C₂²×C₃	—	6	1	no	—
975	C₂²×C₃	—	6	1	no	—
976	C₂²×C₃	—	6	4	no	—
977	C₂²×C₃	—	6	4	no	—
978	C₂²×C₃	—	6	8	no	—
979	C₂²×C₃	—	6	2	no	—
980	C₂²×C₃	—	6	2	no	—
981	C₂²×C₃	—	6	8	no	—
982	C₂²×C₃	—	6	4	no	—
983	C₂²×C₃	—	8	2	no	—
984	C₂²×C₃	—	8	2	no	—
985	C₂²×C₃	—	8	4	no	—
986	C₂²×C₃	—	9	4	no	—
987	C₂²×C₃	—	12	8	no	—
988	C₂²×C₃	—	12	4	no	—
989	C₂²×C₃	—	12	2	no	—
990	C₂²×C₃	—	12	4	no	—
991	C₂²×C₃	—	12	4	no	—
992	C₂²×C₃	—	12	2	no	—
993	C₂²×C₃	—	12	4	no	—
994	C₂²×C₃	—	12	4	no	—
995	C₂²×C₃	—	12	8	no	—
996	C₂²×C₃	—	18	8	no	—
997	C₂²×C₃	—	24	4	no	—
998	C₂²×C₃	—	36	4	no	—
999	C₂²×C₃	—	36	8	no	—
1000	C₂²×C₃	C₂²×D₃²	1	4	yes	—
1001	C₂²×C₃	C₂²×D₃²	1	1	yes	characteristic
1002	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
1003	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
1004	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
1005	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
1006	C₂×D₃	—	2	2	no	—
1007	C₂×D₃	—	2	8	no	—
1008	C₂×D₃	—	3	4	no	—
1009	C₂×D₃	—	3	4	no	—
1010	C₂×D₃	—	4	4	no	—
1011	C₂×D₃	—	4	2	no	—
1012	C₂×D₃	—	4	4	no	—
1013	C₂×D₃	—	6	4	no	—
1014	C₂×D₃	—	6	8	no	—
1015	C₂×D₃	—	6	8	no	—
1016	C₂×D₃	—	12	8	no	—
1017	C₂×D₃	—	12	8	no	—
1018	C₂×D₃	—	12	4	no	—
1019	C₂×D₃	—	12	4	no	—
1020	C₂×D₃	—	24	4	no	—
1021	C₂×D₃	C₂³×C₃×D₃	1	4	yes	—
1022	C₂×D₃	C₂³×C₃×D₃	1	4	yes	—
1023	C₂×D₃	C₂³×C₃×D₃	1	1	yes	characteristic
1024	C₂×D₃	C₂³×C₃×D₃	1	1	yes	characteristic
1025	C₃×C₄	—	2	2	no	—
1026	C₃×C₄	—	2	2	no	—
1027	C₃×C₄	—	2	2	no	—
1028	C₃×C₄	—	3	2	no	—
1029	C₃×C₄	—	3	4	no	—
1030	C₃×C₄	—	3	2	no	—
1031	C₃×C₄	—	3	4	no	—
1032	C₃×C₄	—	4	2	no	—
1033	C₃×C₄	—	6	2	no	—
1034	C₃×C₄	—	6	4	no	—
1035	C₃×C₄	—	9	4	no	—
1036	C₃×C₄	C₂²×D₃²	1	2	yes	—
1037	C₃×C₄	C₂³×C₃×D₃	1	2	yes	—
1038	C₃×C₄	C₂³×C₃×D₃	1	2	yes	—
1039	Dic₃	—	3	4	no	—
1040	Dic₃	—	3	4	no	—
1041	Dic₃	—	6	4	no	—
1042	Dic₃	C₂³×C₃×D₃	1	2	yes	—
1043	Dic₃	C₂³×C₃×D₃	1	4	yes	—
1044	C₃²	—	2	1	no	—
1045	C₃²	—	2	1	no	—
1046	C₃²	—	2	1	no	—
1047	C₃²	—	4	1	no	—
1048	C₃²	C₂×#1004	1	1	yes	characteristic, complemented
1049	C₃²	D₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
1050	C₃²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
1051	C₂³	—	3	1	no	—
1052	C₂³	—	3	4	no	—
1053	C₂³	—	3	4	no	—
1054	C₂³	—	3	4	no	—
1055	C₂³	—	3	2	no	—
1056	C₂³	—	9	4	no	—
1057	C₂³	—	9	8	no	—
1058	C₂³	—	9	4	no	—
1059	C₂³	—	12	4	no	—
1060	C₂³	—	36	8	no	—
1061	C₂³	C₂×C₃×D₃²	1	2	yes	complemented
1062	Q₈	—	3	2	no	—
1063	Q₈	—	9	4	no	—
1064	Q₈	—	9	2	no	—
1065	D₄	—	3	8	no	—
1066	D₄	—	3	8	no	—
1067	D₄	—	3	4	no	—
1068	D₄	—	3	4	no	—
1069	D₄	—	3	2	no	—
1070	D₄	—	9	4	no	—
1071	D₄	—	9	4	no	—
1072	D₄	—	9	8	no	—
1073	D₄	—	9	4	no	—
1074	D₄	—	9	8	no	—
1075	D₄	—	9	8	no	—
1076	D₄	—	9	4	no	—
1077	D₄	—	9	2	no	—
1078	D₄	C₂×C₃×D₃²	1	4	yes	complemented
1079	C₂×C₄	—	3	1	no	—
1080	C₂×C₄	—	3	4	no	—
1081	C₂×C₄	—	3	2	no	—
1082	C₂×C₄	—	3	2	no	—
1083	C₂×C₄	—	3	4	no	—
1084	C₂×C₄	—	9	4	no	—
1085	C₂×C₄	—	9	4	no	—
1086	C₂×C₄	—	9	4	no	—
1087	C₂×C₄	—	9	8	no	—
1088	C₂×C₄	—	9	4	no	—
1089	C₂×C₄	—	9	4	no	—
1090	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic, complemented
1091	C₂×C₃	—	2	2	no	—
1092	C₂×C₃	—	2	1	no	—
1093	C₂×C₃	—	2	4	no	—
1094	C₂×C₃	—	2	1	no	—
1095	C₂×C₃	—	2	4	no	—
1096	C₂×C₃	—	2	4	no	—
1097	C₂×C₃	—	2	1	no	—
1098	C₂×C₃	—	2	1	no	—
1099	C₂×C₃	—	2	1	no	—
1100	C₂×C₃	—	2	1	no	—
1101	C₂×C₃	—	3	2	no	—
1102	C₂×C₃	—	3	2	no	—
1103	C₂×C₃	—	4	4	no	—
1104	C₂×C₃	—	4	4	no	—
1105	C₂×C₃	—	4	1	no	—
1106	C₂×C₃	—	4	1	no	—
1107	C₂×C₃	—	4	4	no	—
1108	C₂×C₃	—	4	2	no	—
1109	C₂×C₃	—	4	1	no	—
1110	C₂×C₃	—	6	2	no	—
1111	C₂×C₃	—	6	2	no	—
1112	C₂×C₃	—	6	1	no	—
1113	C₂×C₃	—	6	4	no	—
1114	C₂×C₃	—	6	4	no	—
1115	C₂×C₃	—	6	4	no	—
1116	C₂×C₃	—	6	4	no	—
1117	C₂×C₃	—	6	1	no	—
1118	C₂×C₃	—	8	4	no	—
1119	C₂×C₃	—	12	4	no	—
1120	C₂×C₃	—	12	4	no	—
1121	C₂×C₃	—	18	4	no	—
1122	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
1123	C₂×C₃	C₂⁴×C₃×D₃	1	1	yes	characteristic
1124	C₂×C₃	C₂⁴×C₃×D₃	1	1	yes	characteristic
1125	D₃	—	2	1	no	—
1126	D₃	—	2	4	no	—
1127	D₃	—	2	4	no	—
1128	D₃	—	6	4	no	—
1129	D₃	—	6	4	no	—
1130	D₃	—	12	4	no	—
1131	D₃	C₃×#1004	1	2	yes	direct product factor
1132	C₂²	—	3	1	no	—
1133	C₂²	—	3	1	no	—
1134	C₂²	—	3	4	no	—
1135	C₂²	—	3	4	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	6	2	no	—
1138	C₂²	—	6	8	no	—
1139	C₂²	—	9	4	no	—
1140	C₂²	—	12	2	no	—
1141	C₂²	—	12	4	no	—
1142	C₂²	—	12	4	no	—
1143	C₂²	—	18	8	no	—
1144	C₂²	—	36	4	no	—
1145	C₂²	—	36	8	no	—
1146	C₂²	C₂²×C₃×D₃²	1	4	yes	—
1147	C₂²	C₂²×C₃×D₃²	1	1	yes	characteristic
1148	C₄	—	3	2	no	—
1149	C₄	—	3	4	no	—
1150	C₄	—	9	4	no	—
1151	C₄	C₂²×C₃×D₃²	1	2	yes	—
1152	C₃	—	2	1	no	—
1153	C₃	—	2	1	no	—
1154	C₃	—	2	1	no	—
1155	C₃	—	4	1	no	—
1156	C₃	D₃×#1004	1	1	yes	characteristic, direct product factor
1157	C₃	C₂×C₃×#1004	1	1	yes	characteristic, complemented
1158	C₃	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
1159	C₂	—	2	1	no	—
1160	C₂	—	2	4	no	—
1161	C₂	—	3	2	no	—
1162	C₂	—	6	1	no	—
1163	C₂	—	6	4	no	—
1164	C₂	—	6	4	no	—
1165	C₂	—	18	4	no	—
1166	C₂	C₂³×C₃×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂³×D₃²
commutator, cosocle	C₂×C₃²	C₂⁵×C₃
Frattini	C₂	C₂³×C₃×D₃²
Fitting	C₂×C₃³×D₄	C₂²
socle	C₂×C₃³	C₂⁵
hypercenter	C₂×C₃×D₄	D₃²
hypocenter	C₃²	C₂×C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×#64361	C₂	semidirect
2. C₃²×#1004	C₂	semidirect
3. C₂×C₃²×D₃×D₄	C₂	semidirect
4. C₃×#64330	C₂	semidirect
5. C₂×C₃×D₃×#67	C₂	semidirect
6. C₃×#64314	C₂	semidirect
7. C₃×#64313	C₂	semidirect
8. C₃×D₃×#237	C₂	semidirect
9. C₃×D₃²×D₄	C₂	semidirect
10. C₃×#64307	C₂	semidirect
11. C₃×D₃×#235	C₂	semidirect
14. D₃×#1004	C₃	direct (N × H)
15. C₂³×C₃²×D₃	C₂²	semidirect
16. C₂²×C₃×D₃²	C₂²	semidirect
17. C₂×C₃³×D₄	C₂²	semidirect
18. C₂×C₃×#638	C₂²	semidirect
19. C₃×#3830	C₂²	semidirect
20. C₃×D₄×C₃⋊D₃	C₂²	semidirect
21. C₃×#3828	C₂²	semidirect
22. C₂×C₃²×#67	C₂²	semidirect
23. C₂×C₃²×#67	C₂²	semidirect
24. C₃²×#237	C₂²	semidirect
25. C₃²×D₃×D₄	C₂²	semidirect
26. C₃²×D₃×D₄	C₂²	semidirect
27. C₃²×D₃×D₄	C₂²	semidirect
28. C₃²×#235	C₂²	semidirect
29. C₂×C₃²×D₁₂	C₂²	semidirect
30. C₂×C₃²×C₄×D₃	C₂²	semidirect
31. C₃×#3811	C₂²	semidirect
32. C₃×D₃×#67	C₂²	semidirect
33. C₃×D₃×#67	C₂²	semidirect
34. C₃×D₃×#67	C₂²	semidirect
35. C₃×D₃×#67	C₂²	semidirect
36. C₃×D₃×#67	C₂²	semidirect
37. C₂×C₃×#626	C₂²	semidirect
38. C₂×C₃×#625	C₂²	semidirect
39. C₃×#3805	C₂²	semidirect
40. C₃×#3804	C₂²	semidirect
41. C₃×#3804	C₂²	semidirect
42. C₂×C₃×D₃×Dic₃	C₂²	semidirect
43. C₃×#3802	C₂²	semidirect
44. C₃×D₃×D₁₂	C₂²	semidirect
45. C₃×D₃×D₁₂	C₂²	semidirect
46. C₃×C₄×D₃²	C₂²	semidirect
47. C₃×#3799	C₂²	semidirect
48. C₃×#3798	C₂²	semidirect
49. C₃×#3796	C₂²	semidirect
50. C₃×#3795	C₂²	semidirect
51. C₃×#3795	C₂²	semidirect
52. C₃×D₃×Dic₆	C₂²	semidirect
55. #64361	C₂×C₃	semidirect
71. C₃×#1004	D₃	direct (N × H)
72. C₃×#1004	C₂×C₃	semidirect
78. C₂×C₃×D₃×D₄	D₃	semidirect
79. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
81. #64330	C₂×C₃	semidirect
82. C₂×D₃×#67	C₂×C₃	semidirect
83. #64314	C₂×C₃	semidirect
84. #64313	C₂×C₃	semidirect
85. D₃×#237	C₂×C₃	semidirect
86. D₃²×D₄	C₂×C₃	semidirect
87. #64307	C₂×C₃	semidirect
88. D₃×#235	C₂×C₃	semidirect
89. C₂³×C₃³	C₂³	semidirect
90. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
94. C₂²×C₃²×D₃	C₂³	semidirect
95. C₂²×C₃²×D₃	C₂³	semidirect
96. C₂²×C₃²×D₃	C₂³	semidirect
99. C₂×C₃×D₃²	C₂³	semidirect
100. C₃³×D₄	C₂³	semidirect
101. C₂×C₃³×C₄	C₂³	semidirect
102. C₃×#638	C₂³	semidirect
103. C₃×#638	C₂³	semidirect
104. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
105. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
106. C₃×C₄×C₃⋊D₃	C₂³	semidirect
107. C₃×#634	C₂³	semidirect
108. C₃²×#67	C₂³	semidirect
109. C₃²×#67	C₂³	semidirect
110. C₃²×#67	C₂³	semidirect
111. C₂×C₃²×Dic₃	C₂³	semidirect
112. C₂×C₃²×Dic₃	C₂³	semidirect
113. C₃²×D₁₂	C₂³	semidirect
114. C₃²×D₁₂	C₂³	semidirect
116. C₃²×C₄×D₃	C₂³	semidirect
117. C₃²×C₄×D₃	C₂³	semidirect
118. C₃²×Dic₆	C₂³	semidirect
119. C₃×#627	C₂³	semidirect
120. C₃×#626	C₂³	semidirect
121. C₃×#626	C₂³	semidirect
122. C₃×#626	C₂³	semidirect
123. C₃×#625	C₂³	semidirect
124. C₃×#625	C₂³	semidirect
125. C₃×#624	C₂³	semidirect
127. C₃×D₃×Dic₃	C₂³	semidirect
128. C₃×D₃×Dic₃	C₂³	semidirect
136. C₂³×C₃×D₃	C₂×D₃	semidirect
137. C₂³×C₃×D₃	C₂²×C₃	semidirect
138. C₂²×D₃²	C₂²×C₃	semidirect
151. C₂×C₃²×D₄	C₂×D₃	semidirect
152. C₂×C₃²×D₄	C₂×D₃	semidirect
153. C₂×C₃²×D₄	C₂²×C₃	semidirect
155. C₂×#638	C₂²×C₃	semidirect
156. #3830	C₂²×C₃	semidirect
157. D₄×C₃⋊D₃	C₂²×C₃	semidirect
158. #3828	C₂²×C₃	semidirect
172. C₂×C₃×#67	C₂×D₃	semidirect
173. C₂×C₃×#67	C₂×D₃	semidirect
174. C₂×C₃×#67	C₂²×C₃	semidirect
175. C₂×C₃×#67	C₂²×C₃	semidirect
191. C₃×#237	C₂×D₃	semidirect
192. C₃×#237	C₂²×C₃	semidirect
210. C₃×D₃×D₄	C₂×D₃	semidirect
211. C₃×D₃×D₄	C₂×D₃	semidirect
212. C₃×D₃×D₄	C₂×D₃	semidirect
213. C₃×D₃×D₄	C₂²×C₃	semidirect
214. C₃×D₃×D₄	C₂²×C₃	semidirect
215. C₃×D₃×D₄	C₂²×C₃	semidirect
227. C₃×#235	C₂×D₃	semidirect
228. C₃×#235	C₂²×C₃	semidirect
233. C₂×C₃×D₁₂	C₂×D₃	semidirect
234. C₂×C₃×D₁₂	C₂²×C₃	semidirect
239. C₂×C₃×C₄×D₃	C₂×D₃	semidirect
240. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
242. #3811	C₂²×C₃	semidirect
243. D₃×#67	C₂²×C₃	semidirect
244. D₃×#67	C₂²×C₃	semidirect
245. D₃×#67	C₂²×C₃	semidirect
246. D₃×#67	C₂²×C₃	semidirect
247. D₃×#67	C₂²×C₃	semidirect
248. C₂×#626	C₂²×C₃	semidirect
249. C₂×#625	C₂²×C₃	semidirect
250. #3805	C₂²×C₃	semidirect
251. #3804	C₂²×C₃	semidirect
252. #3804	C₂²×C₃	semidirect
253. C₂×D₃×Dic₃	C₂²×C₃	semidirect
254. #3802	C₂²×C₃	semidirect
255. D₃×D₁₂	C₂²×C₃	semidirect
256. D₃×D₁₂	C₂²×C₃	semidirect
257. C₄×D₃²	C₂²×C₃	semidirect
258. #3799	C₂²×C₃	semidirect
259. #3798	C₂²×C₃	semidirect
260. #3796	C₂²×C₃	semidirect
261. #3795	C₂²×C₃	semidirect
262. #3795	C₂²×C₃	semidirect
263. D₃×Dic₆	C₂²×C₃	semidirect
313. #1004	C₃×D₃	direct (N × H)
318. C₂×D₃×D₄	C₃×D₃	semidirect
330. C₂³×C₃²	C₂²×D₃	semidirect
331. C₂³×C₃²	C₂²×D₃	semidirect
332. C₂³×C₃²	C₂³×C₃	semidirect
333. C₂²×C₃⋊D₃	C₂³×C₃	semidirect
353. C₂²×C₃×D₃	C₂²×D₃	semidirect
354. C₂²×C₃×D₃	C₂²×D₃	semidirect
355. C₂²×C₃×D₃	C₂²×D₃	semidirect
358. C₂²×C₃×D₃	C₂³×C₃	semidirect
359. C₂²×C₃×D₃	C₂³×C₃	semidirect
360. C₂²×C₃×D₃	C₂³×C₃	semidirect
363. C₂×D₃²	C₂³×C₃	semidirect
374. C₃²×D₄	C₂²×D₃	semidirect
375. C₃²×D₄	C₂²×D₃	semidirect
376. C₃²×D₄	C₂³×C₃	semidirect
386. C₂×C₃²×C₄	C₂²×D₃	semidirect
387. C₂×C₃²×C₄	C₂²×D₃	semidirect
388. C₂×C₃²×C₄	C₂³×C₃	semidirect
389. #638	C₂³×C₃	semidirect
390. #638	C₂³×C₃	semidirect
391. C₂×C₃⋊Dic₃	C₂³×C₃	semidirect
392. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
393. C₄×C₃⋊D₃	C₂³×C₃	semidirect
394. #634	C₂³×C₃	semidirect
411. C₃×#67	C₂²×D₃	semidirect
412. C₃×#67	C₂²×D₃	semidirect
413. C₃×#67	C₂²×D₃	semidirect
414. C₃×#67	C₂³×C₃	semidirect
415. C₃×#67	C₂³×C₃	semidirect
416. C₃×#67	C₂³×C₃	semidirect
425. C₂×C₃×Dic₃	C₂²×D₃	semidirect
426. C₂×C₃×Dic₃	C₂²×D₃	semidirect
427. C₂×C₃×Dic₃	C₂³×C₃	semidirect
428. C₂×C₃×Dic₃	C₂³×C₃	semidirect
437. C₃×D₁₂	C₂²×D₃	semidirect
438. C₃×D₁₂	C₂²×D₃	semidirect
439. C₃×D₁₂	C₂³×C₃	semidirect
440. C₃×D₁₂	C₂³×C₃	semidirect
453. C₃×C₄×D₃	C₂²×D₃	semidirect
454. C₃×C₄×D₃	C₂²×D₃	semidirect
456. C₃×C₄×D₃	C₂³×C₃	semidirect
457. C₃×C₄×D₃	C₂³×C₃	semidirect
464. C₃×Dic₆	C₂²×D₃	semidirect
465. C₃×Dic₆	C₂³×C₃	semidirect
466. #627	C₂³×C₃	semidirect
467. #626	C₂³×C₃	semidirect
468. #626	C₂³×C₃	semidirect
469. #626	C₂³×C₃	semidirect
470. #625	C₂³×C₃	semidirect
471. #625	C₂³×C₃	semidirect
472. #624	C₂³×C₃	semidirect
474. D₃×Dic₃	C₂³×C₃	semidirect
475. D₃×Dic₃	C₂³×C₃	semidirect
484. C₃²×D₃	H(5,𝔽₂)	semidirect
491. C₂³×D₃	C₂×C₃×D₃	semidirect
544. C₂×C₃×D₄	D₃²	semidirect
545. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
546. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
563. C₂×#67	C₂×C₃×D₃	semidirect
564. C₂×#67	C₂×C₃×D₃	semidirect
579. #237	C₂×C₃×D₃	semidirect
594. D₃×D₄	C₂×C₃×D₃	semidirect
595. D₃×D₄	C₂×C₃×D₃	semidirect
596. D₃×D₄	C₂×C₃×D₃	semidirect
607. #235	C₂×C₃×D₃	semidirect
611. C₂×D₁₂	C₂×C₃×D₃	semidirect
615. C₂×C₄×D₃	C₂×C₃×D₃	semidirect
718. C₃³	C₂×H(5,𝔽₂)	semidirect
745. C₂³×C₃	C₂×D₃²	semidirect
746. C₂³×C₃	C₂²×C₃×D₃	semidirect
747. C₂³×C₃	C₂²×C₃×D₃	semidirect
760. C₂²×D₃	C₂²×C₃×D₃	semidirect
761. C₂²×D₃	C₂²×C₃×D₃	semidirect
762. C₂²×D₃	C₂²×C₃×D₃	semidirect
795. C₃×D₄	C₂×D₃²	semidirect
796. C₃×D₄	C₂²×C₃×D₃	semidirect
797. C₃×D₄	C₂²×C₃×D₃	semidirect
823. C₂×C₃×C₄	C₂×D₃²	semidirect
824. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
825. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
839. #67	C₂²×C₃×D₃	semidirect
840. #67	C₂²×C₃×D₃	semidirect
841. #67	C₂²×C₃×D₃	semidirect
848. C₂×Dic₃	C₂²×C₃×D₃	semidirect
849. C₂×Dic₃	C₂²×C₃×D₃	semidirect
856. D₁₂	C₂²×C₃×D₃	semidirect
857. D₁₂	C₂²×C₃×D₃	semidirect
867. C₄×D₃	C₂²×C₃×D₃	semidirect
868. C₄×D₃	C₂²×C₃×D₃	semidirect
874. Dic₆	C₂²×C₃×D₃	semidirect
914. C₃×D₃	#1004	direct (N × H)
915. C₃×D₃	C₃×H(5,𝔽₂)	semidirect
950. C₂×D₄	C₃×D₃²	semidirect
1048. C₃²	C₂×#1004	semidirect
1049. C₃²	D₃×H(5,𝔽₂)	semidirect
1050. C₃²	C₂×C₃×H(5,𝔽₂)	semidirect
1061. C₂³	C₂×C₃×D₃²	semidirect
1078. D₄	C₂×C₃×D₃²	semidirect
1090. C₂×C₄	C₂×C₃×D₃²	semidirect
1131. D₃	C₃×#1004	direct (N × H)
1156. C₃	D₃×#1004	direct (N × H)
1157. C₃	C₂×C₃×#1004	semidirect
1158. C₃	C₃×D₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₃×#64361	2
C₃²×#1004	2
C₂×C₃²×D₃×D₄	2
C₃×#64330	2
C₂×C₃×D₃×#67	2
C₃×#64314	2
C₃×#64313	2
C₃×D₃×#237	2
C₃×D₃²×D₄	2
C₃×#64307	2
C₃×D₃×#235	2
C₃×D₃×H(5,𝔽₂)	3
C₂×C₃×#1004	3
D₃×#1004	3

Subgroups — C3×D3×#1004 #13181549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#1004 #13181549