Subgroups — C₃×D₃×#540 #11901461

Order 1152.

2640 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5719	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5697	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5663	C₂	1	4	yes	maximal, complemented
7	C₃×D₃×#123	C₂	1	4	yes	maximal, complemented
8	C₃×#5619	C₂	1	2	yes	maximal, complemented
9	C₃×#5615	C₂	1	4	yes	maximal, complemented
10	C₃×D₃×#121	C₂	1	4	yes	maximal, complemented
11	C₃×D₃×#121	C₂	1	2	yes	maximal, complemented
12	C₃×#5562	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×D₃×D₄	C₂	1	2	yes	maximal, complemented
14	C₃×#5535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#540	—	3	1	no	maximal
17	D₃×#540	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
19	C₂×C₃×D₃×D₄	C₂²	1	4	yes	—
20	C₂×C₃×D₃×D₄	C₂²	1	4	yes	—
21	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	—
23	C₃²×#127	C₂²	1	1	yes	characteristic, complemented
24	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
25	C₃²×#123	C₂²	1	4	yes	complemented
26	C₃²×#121	C₂²	1	4	yes	complemented
27	C₃²×#121	C₂²	1	2	yes	complemented
28	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
29	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
30	C₃×#940	C₂²	1	2	yes	complemented
31	C₃×#940	C₂²	1	4	yes	complemented
32	C₃×#939	C₂²	1	4	yes	complemented
33	C₃×#939	C₂²	1	4	yes	complemented
34	C₃×#939	C₂²	1	4	yes	complemented
35	C₃×#938	C₂²	1	2	yes	complemented
36	C₃×#938	C₂²	1	4	yes	complemented
37	C₃×#935	C₂²	1	4	yes	complemented
38	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
39	C₃×#930	C₂²	1	2	yes	complemented
40	C₃×#930	C₂²	1	4	yes	complemented
41	C₃×#929	C₂²	1	4	yes	complemented
42	C₃×C₄×#67	C₂²	1	4	yes	complemented
43	C₃×#926	C₂²	1	1	yes	characteristic, complemented
44	C₃×#895	C₂²	1	2	yes	complemented
45	C₃×#895	C₂²	1	4	yes	complemented
46	C₃×#894	C₂²	1	4	yes	complemented
47	C₃×#894	C₂²	1	4	yes	complemented
48	C₃×#893	C₂²	1	2	yes	complemented
49	C₃×#892	C₂²	1	2	yes	complemented
50	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
51	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
52	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
53	C₃×#890	C₂²	1	2	yes	complemented
54	C₃×#889	C₂²	1	4	yes	complemented
55	C₃×#886	C₂²	1	4	yes	complemented
56	C₃×#884	C₂²	1	4	yes	complemented
57	C₃×#884	C₂²	1	4	yes	complemented
58	C₃×#884	C₂²	1	4	yes	complemented
59	C₃×#883	C₂²	1	4	yes	complemented
60	C₃×#883	C₂²	1	4	yes	complemented
61	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
62	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₃×#877	C₂²	1	2	yes	complemented
66	C₃×#874	C₂²	1	1	yes	characteristic, complemented
67	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
68	C₃×#872	C₂²	1	1	yes	characteristic, complemented
69	C₃×#872	C₂²	1	1	yes	characteristic, complemented
70	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
71	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
72	C₃×#870	C₂²	1	1	yes	characteristic, complemented
73	C₃×#540	—	2	1	no	—
74	C₃×#540	—	3	1	no	—
75	C₃×#540	—	3	1	no	—
76	C₃×#540	—	3	4	no	—
77	C₃×#540	—	3	4	no	—
78	C₃×#540	—	3	2	no	—
79	C₃×#540	—	3	2	no	—
80	C₃×#540	—	3	1	no	—
81	C₃×#540	D₃	1	1	yes	characteristic, direct product factor
82	C₃×#540	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#127	—	3	1	no	—
84	C₂×C₃×#125	—	3	1	no	—
85	C₂×C₃×#123	—	3	4	no	—
86	C₂×C₃×#121	—	3	4	no	—
87	C₂×C₃×#121	—	3	2	no	—
88	C₂×C₃×C₄×D₄	—	3	2	no	—
89	C₂×C₃×#117	—	3	1	no	—
90	#5719	C₂×C₃	1	1	yes	characteristic, complemented
91	D₃×#127	C₂×C₃	1	1	yes	characteristic, complemented
92	#5697	C₂×C₃	1	1	yes	characteristic, complemented
93	D₃×#125	C₂×C₃	1	1	yes	characteristic, complemented
94	#5663	C₂×C₃	1	4	yes	complemented
95	D₃×#123	C₂×C₃	1	4	yes	complemented
96	#5619	C₂×C₃	1	2	yes	complemented
97	#5615	C₂×C₃	1	4	yes	complemented
98	D₃×#121	C₂×C₃	1	2	yes	complemented
99	D₃×#121	C₂×C₃	1	4	yes	complemented
100	#5562	C₂×C₃	1	2	yes	complemented
101	C₄×D₃×D₄	C₂×C₃	1	2	yes	complemented
102	#5535	C₂×C₃	1	1	yes	characteristic, complemented
103	D₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
104	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
105	C₂³×C₃×D₃	C₂³	1	4	yes	—
106	C₂×C₃²×D₄	C₂³	1	2	yes	—
107	C₂×C₃²×D₄	C₂³	1	4	yes	—
108	C₂×C₃²×D₄	C₂³	1	4	yes	—
109	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
110	C₂²×C₃²×C₄	C₂³	1	4	yes	—
111	C₂×C₃×#67	C₂³	1	4	yes	—
112	C₂×C₃×#67	C₂³	1	4	yes	—
113	C₂×C₃×#67	C₂³	1	4	yes	—
114	C₂×C₃×#67	C₂³	1	4	yes	—
115	C₂×C₃×#67	C₂³	1	4	yes	—
116	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
117	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
118	C₃×D₃×D₄	—	2	8	no	—
119	C₃×D₃×D₄	—	4	8	no	—
120	C₃×D₃×D₄	—	4	8	no	—
121	C₂×C₃×D₁₂	C₂³	1	2	yes	—
122	C₂×C₃×D₁₂	C₂³	1	4	yes	—
123	C₂×C₃×D₁₂	C₂³	1	4	yes	—
124	C₂×C₃×C₄×D₃	—	2	4	no	—
125	C₂×C₃×C₄×D₃	—	4	8	no	—
126	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
128	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
129	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
130	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
133	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
134	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
135	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃²×C₄²	C₂³	1	1	yes	characteristic
142	C₃²×C₄²	C₂³	1	1	yes	characteristic
143	C₃×#217	C₂³	1	2	yes	—
144	C₃×#217	C₂³	1	4	yes	—
145	C₃×#217	C₂³	1	4	yes	—
146	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
147	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
148	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
149	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
150	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
151	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
152	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
153	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
154	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
155	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
156	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
157	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
158	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
159	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
160	C₃×C₄×Dic₃	C₂³	1	2	yes	—
161	C₃×C₄×Dic₃	C₂³	1	2	yes	—
162	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
163	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
164	C₂×#540	—	3	1	no	Sylow
165	C₂²×C₃×D₄	—	3	2	no	—
166	C₂²×C₃×D₄	—	3	4	no	—
167	C₂²×C₃×D₄	—	3	4	no	—
168	C₂³×C₃×C₄	—	3	1	no	—
169	C₂³×C₃×C₄	—	3	4	no	—
170	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
171	C₂×D₃×D₄	C₂²×C₃	1	4	yes	—
172	C₂×D₃×D₄	C₂²×C₃	1	4	yes	—
173	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
174	C₂²×C₄×D₃	C₂²×C₃	1	4	yes	—
175	C₃×#127	—	2	1	no	—
176	C₃×#127	—	3	4	no	—
177	C₃×#127	—	3	2	no	—
178	C₃×#127	—	3	1	no	—
179	C₃×#127	C₂×D₃	1	1	yes	characteristic, complemented
180	C₃×#127	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₃×#125	—	2	1	no	—
182	C₃×#125	—	3	4	no	—
183	C₃×#125	—	3	2	no	—
184	C₃×#125	—	3	1	no	—
185	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
186	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₃×#123	—	2	4	no	—
188	C₃×#123	—	3	4	no	—
189	C₃×#123	—	3	4	no	—
190	C₃×#123	—	3	4	no	—
191	C₃×#123	—	3	4	no	—
192	C₃×#123	—	3	4	no	—
193	C₃×#123	—	3	4	no	—
194	C₃×#123	—	3	4	no	—
195	C₃×#123	C₂×D₃	1	4	yes	complemented
196	C₃×#123	C₂²×C₃	1	4	yes	complemented
197	C₃×#121	—	2	4	no	—
198	C₃×#121	—	2	2	no	—
199	C₃×#121	—	3	4	no	—
200	C₃×#121	—	3	2	no	—
201	C₃×#121	—	3	4	no	—
202	C₃×#121	—	3	4	no	—
203	C₃×#121	—	3	4	no	—
204	C₃×#121	—	3	4	no	—
205	C₃×#121	—	3	2	no	—
206	C₃×#121	—	3	4	no	—
207	C₃×#121	—	3	2	no	—
208	C₃×#121	—	3	4	no	—
209	C₃×#121	—	3	4	no	—
210	C₃×#121	—	3	4	no	—
211	C₃×#121	C₂×D₃	1	4	yes	complemented
212	C₃×#121	C₂×D₃	1	2	yes	complemented
213	C₃×#121	C₂²×C₃	1	4	yes	complemented
214	C₃×#121	C₂²×C₃	1	2	yes	complemented
215	C₃×C₄×D₄	—	2	2	no	—
216	C₃×C₄×D₄	—	3	2	no	—
217	C₃×C₄×D₄	—	3	4	no	—
218	C₃×C₄×D₄	—	3	2	no	—
219	C₃×C₄×D₄	—	3	4	no	—
220	C₃×C₄×D₄	—	3	2	no	—
221	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
222	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
223	C₃×#117	—	2	1	no	—
224	C₃×#117	—	3	1	no	—
225	C₃×#117	—	3	2	no	—
226	C₃×#117	—	3	2	no	—
227	C₃×#117	—	3	1	no	—
228	C₃×#117	—	3	1	no	—
229	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
230	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
231	C₂×C₃×C₄⋊C₄	—	3	2	no	—
232	C₂×C₃×C₄⋊C₄	—	3	2	no	—
233	C₂×C₃×C₄⋊C₄	—	3	4	no	—
234	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
235	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
236	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
237	C₂×C₃×C₄²	—	3	1	no	—
238	C₂×C₃×C₄²	—	3	1	no	—
239	#940	C₂²×C₃	1	4	yes	complemented
240	#940	C₂²×C₃	1	2	yes	complemented
241	#939	C₂²×C₃	1	4	yes	complemented
242	#939	C₂²×C₃	1	4	yes	complemented
243	#939	C₂²×C₃	1	4	yes	complemented
244	#938	C₂²×C₃	1	2	yes	complemented
245	#938	C₂²×C₃	1	4	yes	complemented
246	#935	C₂²×C₃	1	4	yes	complemented
247	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
248	#930	C₂²×C₃	1	4	yes	complemented
249	#930	C₂²×C₃	1	2	yes	complemented
250	#929	C₂²×C₃	1	4	yes	complemented
251	C₄×#67	C₂²×C₃	1	4	yes	complemented
252	#926	C₂²×C₃	1	1	yes	characteristic, complemented
253	#895	C₂²×C₃	1	4	yes	complemented
254	#895	C₂²×C₃	1	2	yes	complemented
255	#894	C₂²×C₃	1	4	yes	complemented
256	#894	C₂²×C₃	1	4	yes	complemented
257	#893	C₂²×C₃	1	2	yes	complemented
258	#892	C₂²×C₃	1	2	yes	complemented
259	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
260	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
261	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
262	#890	C₂²×C₃	1	2	yes	complemented
263	#889	C₂²×C₃	1	4	yes	complemented
264	#886	C₂²×C₃	1	4	yes	complemented
265	#884	C₂²×C₃	1	4	yes	complemented
266	#884	C₂²×C₃	1	4	yes	complemented
267	#884	C₂²×C₃	1	4	yes	complemented
268	#883	C₂²×C₃	1	4	yes	complemented
269	#883	C₂²×C₃	1	4	yes	complemented
270	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
271	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
272	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
273	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
274	#877	C₂²×C₃	1	2	yes	complemented
275	#874	C₂²×C₃	1	1	yes	characteristic, complemented
276	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
277	#872	C₂²×C₃	1	1	yes	characteristic, complemented
278	#872	C₂²×C₃	1	1	yes	characteristic, complemented
279	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
280	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
281	#870	C₂²×C₃	1	1	yes	characteristic, complemented
282	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
283	C₂³×C₃²	C₂⁴	1	4	yes	—
284	C₂²×C₃×D₃	—	2	2	no	—
285	C₂²×C₃×D₃	—	2	8	no	—
286	C₂²×C₃×D₃	—	2	8	no	—
287	C₂²×C₃×D₃	—	2	4	no	—
288	C₂²×C₃×D₃	—	2	8	no	—
289	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
291	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
292	C₃²×D₄	—	2	4	no	—
293	C₃²×D₄	—	4	4	no	—
294	C₃²×D₄	—	4	4	no	—
295	C₂×C₃²×C₄	—	2	2	no	—
296	C₂×C₃²×C₄	—	4	4	no	—
297	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
298	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
299	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
300	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
301	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
302	C₃×#67	—	2	8	no	—
303	C₃×#67	—	4	4	no	—
304	C₃×#67	—	4	4	no	—
305	C₃×#67	—	4	4	no	—
306	C₃×#67	—	4	4	no	—
307	C₂×C₃×Dic₃	—	2	2	no	—
308	C₂×C₃×Dic₃	—	4	4	no	—
309	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
310	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
311	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
312	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
313	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
314	C₃×D₁₂	—	2	4	no	—
315	C₃×D₁₂	—	4	4	no	—
316	C₃×D₁₂	—	4	4	no	—
317	C₃×C₄×D₃	—	2	2	no	—
318	C₃×C₄×D₃	—	2	4	no	—
319	C₃×C₄×D₃	—	2	8	no	—
320	C₃×C₄×D₃	—	2	4	no	—
321	C₃×C₄×D₃	—	2	2	no	—
322	C₃×C₄×D₃	—	2	2	no	—
323	C₃×C₄×D₃	—	4	4	no	—
324	C₃×C₄×D₃	—	4	4	no	—
325	C₃×C₄×D₃	#41	1	4	yes	—
326	#540	—	3	1	no	—
327	#540	—	3	1	no	—
328	#540	—	3	4	no	—
329	#540	—	3	4	no	—
330	#540	—	3	2	no	—
331	#540	—	3	2	no	—
332	#540	—	3	1	no	—
333	#540	C₃×D₃	1	1	yes	characteristic, direct product factor
334	C₂×#127	—	3	1	no	—
335	C₂×#125	—	3	1	no	—
336	C₂×#123	—	3	4	no	—
337	C₂×#121	—	3	4	no	—
338	C₂×#121	—	3	2	no	—
339	C₂×C₄×D₄	—	3	2	no	—
340	C₂×#117	—	3	1	no	—
341	C₂⁴×C₃	—	3	1	no	—
342	C₂⁴×C₃	—	3	4	no	—
343	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
344	C₂³×D₃	C₂³×C₃	1	4	yes	—
345	C₂×C₃×D₄	—	2	2	no	—
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	2	4	no	—
348	C₂×C₃×D₄	—	3	4	no	—
349	C₂×C₃×D₄	—	3	4	no	—
350	C₂×C₃×D₄	—	3	4	no	—
351	C₂×C₃×D₄	—	3	4	no	—
352	C₂×C₃×D₄	—	3	4	no	—
353	C₂×C₃×D₄	—	3	2	no	—
354	C₂×C₃×D₄	—	3	4	no	—
355	C₂×C₃×D₄	—	3	4	no	—
356	C₂×C₃×D₄	—	6	8	no	—
357	C₂×C₃×D₄	—	12	8	no	—
358	C₂×C₃×D₄	—	12	8	no	—
359	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
360	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
361	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
362	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
363	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
364	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
365	C₂²×C₃×C₄	—	2	1	no	—
366	C₂²×C₃×C₄	—	2	4	no	—
367	C₂²×C₃×C₄	—	3	1	no	—
368	C₂²×C₃×C₄	—	3	1	no	—
369	C₂²×C₃×C₄	—	3	4	no	—
370	C₂²×C₃×C₄	—	3	2	no	—
371	C₂²×C₃×C₄	—	3	2	no	—
372	C₂²×C₃×C₄	—	3	1	no	—
373	C₂²×C₃×C₄	—	3	4	no	—
374	C₂²×C₃×C₄	—	3	1	no	—
375	C₂²×C₃×C₄	—	3	1	no	—
376	C₂²×C₃×C₄	—	3	4	no	—
377	C₂²×C₃×C₄	—	3	4	no	—
378	C₂²×C₃×C₄	—	6	4	no	—
379	C₂²×C₃×C₄	—	12	8	no	—
380	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
382	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
384	C₂×#67	C₂³×C₃	1	4	yes	—
385	C₂×#67	C₂³×C₃	1	4	yes	—
386	C₂×#67	C₂³×C₃	1	4	yes	—
387	C₂×#67	C₂³×C₃	1	4	yes	—
388	C₂×#67	C₂³×C₃	1	4	yes	—
389	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
390	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
391	D₃×D₄	—	2	8	no	—
392	D₃×D₄	—	4	8	no	—
393	D₃×D₄	—	4	8	no	—
394	C₂×D₁₂	C₂³×C₃	1	2	yes	—
395	C₂×D₁₂	C₂³×C₃	1	4	yes	—
396	C₂×D₁₂	C₂³×C₃	1	4	yes	—
397	C₂×C₄×D₃	—	2	4	no	—
398	C₂×C₄×D₃	—	4	8	no	—
399	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
400	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
401	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
404	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
405	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
406	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
407	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
408	C₃×C₄⋊C₄	—	2	2	no	—
409	C₃×C₄⋊C₄	—	2	2	no	—
410	C₃×C₄⋊C₄	—	2	4	no	—
411	C₃×C₄⋊C₄	—	3	2	no	—
412	C₃×C₄⋊C₄	—	3	2	no	—
413	C₃×C₄⋊C₄	—	3	4	no	—
414	C₃×C₄⋊C₄	—	3	4	no	—
415	C₃×C₄⋊C₄	—	3	4	no	—
416	C₃×C₄⋊C₄	—	3	2	no	—
417	C₃×C₄⋊C₄	—	3	2	no	—
418	C₃×C₄⋊C₄	—	3	4	no	—
419	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
420	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
421	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
422	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
423	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₃×C₂²⋊C₄	—	2	2	no	—
426	C₃×C₂²⋊C₄	—	2	4	no	—
427	C₃×C₂²⋊C₄	—	2	4	no	—
428	C₃×C₂²⋊C₄	—	3	2	no	—
429	C₃×C₂²⋊C₄	—	3	4	no	—
430	C₃×C₂²⋊C₄	—	3	4	no	—
431	C₃×C₂²⋊C₄	—	3	2	no	—
432	C₃×C₂²⋊C₄	—	3	2	no	—
433	C₃×C₂²⋊C₄	—	3	4	no	—
434	C₃×C₂²⋊C₄	—	3	4	no	—
435	C₃×C₂²⋊C₄	—	3	4	no	—
436	C₃×C₂²⋊C₄	—	3	4	no	—
437	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
438	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
439	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
440	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
442	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
443	C₃×C₄²	—	2	1	no	—
444	C₃×C₄²	—	2	1	no	—
445	C₃×C₄²	—	3	2	no	—
446	C₃×C₄²	—	3	1	no	—
447	C₃×C₄²	—	3	2	no	—
448	C₃×C₄²	—	3	1	no	—
449	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
450	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
451	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
452	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
453	#217	C₂³×C₃	1	2	yes	—
454	#217	C₂³×C₃	1	4	yes	—
455	#217	C₂³×C₃	1	4	yes	—
456	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
457	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
458	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
459	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
460	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
461	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
462	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
463	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
464	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
465	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
466	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
467	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
468	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
469	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
470	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
471	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
472	C₄×Dic₃	C₂³×C₃	1	2	yes	—
473	C₄×Dic₃	C₂³×C₃	1	2	yes	—
474	C₂²×C₃²	—	2	1	no	—
475	C₂²×C₃²	—	2	4	no	—
476	C₂²×C₃²	—	2	4	no	—
477	C₂²×C₃²	—	2	2	no	—
478	C₂²×C₃²	—	2	4	no	—
479	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
480	C₂×C₃×D₃	—	2	1	no	—
481	C₂×C₃×D₃	—	2	4	no	—
482	C₂×C₃×D₃	—	2	4	no	—
483	C₂×C₃×D₃	—	2	2	no	—
484	C₂×C₃×D₃	—	2	4	no	—
485	C₂×C₃×D₃	—	4	4	no	—
486	C₂×C₃×D₃	—	4	16	no	—
487	C₂×C₃×D₃	C₂×#41	1	2	yes	—
488	C₂×C₃×D₃	H(5,𝔽₂)	1	4	yes	—
489	C₃²×C₄	—	2	1	no	—
490	C₃²×C₄	—	2	2	no	—
491	C₃²×C₄	—	2	4	no	—
492	C₃²×C₄	—	2	2	no	—
493	C₃²×C₄	C₂×#41	1	2	yes	—
494	C₃×Dic₃	—	2	1	no	—
495	C₃×Dic₃	—	2	2	no	—
496	C₃×Dic₃	—	2	4	no	—
497	C₃×Dic₃	—	2	2	no	—
498	C₃×Dic₃	C₂×#41	1	2	yes	—
499	C₂²×D₄	—	3	2	no	—
500	C₂²×D₄	—	3	4	no	—
501	C₂²×D₄	—	3	4	no	—
502	C₂³×C₄	—	3	1	no	—
503	C₂³×C₄	—	3	4	no	—
504	#127	—	3	4	no	—
505	#127	—	3	2	no	—
506	#127	—	3	1	no	—
507	#127	C₂×C₃×D₃	1	1	yes	characteristic, complemented
508	#125	—	3	4	no	—
509	#125	—	3	2	no	—
510	#125	—	3	1	no	—
511	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
512	#123	—	3	4	no	—
513	#123	—	3	4	no	—
514	#123	—	3	4	no	—
515	#123	—	3	4	no	—
516	#123	—	3	4	no	—
517	#123	—	3	4	no	—
518	#123	—	3	4	no	—
519	#123	C₂×C₃×D₃	1	4	yes	complemented
520	#121	—	3	4	no	—
521	#121	—	3	2	no	—
522	#121	—	3	4	no	—
523	#121	—	3	4	no	—
524	#121	—	3	4	no	—
525	#121	—	3	4	no	—
526	#121	—	3	2	no	—
527	#121	—	3	4	no	—
528	#121	—	3	2	no	—
529	#121	—	3	4	no	—
530	#121	—	3	4	no	—
531	#121	—	3	4	no	—
532	#121	C₂×C₃×D₃	1	4	yes	complemented
533	#121	C₂×C₃×D₃	1	2	yes	complemented
534	C₄×D₄	—	3	2	no	—
535	C₄×D₄	—	3	4	no	—
536	C₄×D₄	—	3	2	no	—
537	C₄×D₄	—	3	4	no	—
538	C₄×D₄	—	3	2	no	—
539	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
540	#117	—	3	1	no	—
541	#117	—	3	2	no	—
542	#117	—	3	2	no	—
543	#117	—	3	1	no	—
544	#117	—	3	1	no	—
545	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
546	C₂×C₄⋊C₄	—	3	2	no	—
547	C₂×C₄⋊C₄	—	3	2	no	—
548	C₂×C₄⋊C₄	—	3	4	no	—
549	C₂×C₂²⋊C₄	—	3	2	no	—
550	C₂×C₂²⋊C₄	—	3	4	no	—
551	C₂×C₂²⋊C₄	—	3	4	no	—
552	C₂×C₄²	—	3	1	no	—
553	C₂×C₄²	—	3	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	4	no	—
556	C₂³×C₃	—	3	1	no	—
557	C₂³×C₃	—	3	1	no	—
558	C₂³×C₃	—	3	4	no	—
559	C₂³×C₃	—	6	2	no	—
560	C₂³×C₃	—	6	8	no	—
561	C₂³×C₃	—	6	8	no	—
562	C₂³×C₃	—	6	4	no	—
563	C₂³×C₃	—	6	8	no	—
564	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
565	C₂³×C₃	C₂³×D₃	1	4	yes	—
566	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
567	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
568	C₂²×D₃	—	2	2	no	—
569	C₂²×D₃	—	2	8	no	—
570	C₂²×D₃	—	2	8	no	—
571	C₂²×D₃	—	2	4	no	—
572	C₂²×D₃	—	2	8	no	—
573	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
574	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
575	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
576	C₃×D₄	—	2	4	no	—
577	C₃×D₄	—	2	4	no	—
578	C₃×D₄	—	4	4	no	—
579	C₃×D₄	—	4	4	no	—
580	C₃×D₄	—	4	4	no	—
581	C₃×D₄	—	4	4	no	—
582	C₃×D₄	—	4	4	no	—
583	C₃×D₄	—	6	8	no	—
584	C₃×D₄	—	6	4	no	—
585	C₃×D₄	—	8	4	no	—
586	C₃×D₄	—	8	4	no	—
587	C₃×D₄	—	12	4	no	—
588	C₃×D₄	—	12	4	no	—
589	C₃×D₄	—	12	4	no	—
590	C₃×D₄	—	12	4	no	—
591	C₃×D₄	—	12	4	no	—
592	C₃×D₄	—	12	4	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	4	no	—
600	C₂×C₃×C₄	—	3	1	no	—
601	C₂×C₃×C₄	—	3	4	no	—
602	C₂×C₃×C₄	—	3	2	no	—
603	C₂×C₃×C₄	—	3	2	no	—
604	C₂×C₃×C₄	—	3	1	no	—
605	C₂×C₃×C₄	—	3	4	no	—
606	C₂×C₃×C₄	—	4	2	no	—
607	C₂×C₃×C₄	—	4	4	no	—
608	C₂×C₃×C₄	—	4	4	no	—
609	C₂×C₃×C₄	—	6	2	no	—
610	C₂×C₃×C₄	—	6	2	no	—
611	C₂×C₃×C₄	—	6	4	no	—
612	C₂×C₃×C₄	—	6	8	no	—
613	C₂×C₃×C₄	—	6	4	no	—
614	C₂×C₃×C₄	—	6	2	no	—
615	C₂×C₃×C₄	—	6	2	no	—
616	C₂×C₃×C₄	—	8	4	no	—
617	C₂×C₃×C₄	—	12	4	no	—
618	C₂×C₃×C₄	—	12	4	no	—
619	C₂×C₃×C₄	—	12	4	no	—
620	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
621	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
622	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
624	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
625	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
626	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
627	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
628	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
629	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
630	#67	—	2	8	no	—
631	#67	—	4	4	no	—
632	#67	—	4	4	no	—
633	#67	—	4	4	no	—
634	#67	—	4	4	no	—
635	C₂×Dic₃	—	2	2	no	—
636	C₂×Dic₃	—	4	4	no	—
637	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
638	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
639	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
640	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
641	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
642	D₁₂	—	2	4	no	—
643	D₁₂	—	4	4	no	—
644	D₁₂	—	4	4	no	—
645	C₄×D₃	—	2	2	no	—
646	C₄×D₃	—	2	4	no	—
647	C₄×D₃	—	2	8	no	—
648	C₄×D₃	—	2	4	no	—
649	C₄×D₃	—	2	2	no	—
650	C₄×D₃	—	2	2	no	—
651	C₄×D₃	—	4	4	no	—
652	C₄×D₃	—	4	4	no	—
653	C₄×D₃	C₃×#41	1	4	yes	—
654	C₂×C₃²	—	4	1	no	—
655	C₂×C₃²	—	4	4	no	—
656	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
657	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
658	C₃×D₃	—	4	1	no	—
659	C₃×D₃	—	4	4	no	—
660	C₃×D₃	#540	1	4	yes	direct product factor
661	C₂⁴	—	3	1	no	—
662	C₂⁴	—	3	4	no	—
663	C₂×D₄	—	3	4	no	—
664	C₂×D₄	—	3	4	no	—
665	C₂×D₄	—	3	4	no	—
666	C₂×D₄	—	3	4	no	—
667	C₂×D₄	—	3	4	no	—
668	C₂×D₄	—	3	2	no	—
669	C₂×D₄	—	3	4	no	—
670	C₂×D₄	—	3	4	no	—
671	C₂×D₄	—	6	8	no	—
672	C₂×D₄	—	12	8	no	—
673	C₂×D₄	—	12	8	no	—
674	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
675	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
676	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
677	C₂²×C₄	—	3	1	no	—
678	C₂²×C₄	—	3	1	no	—
679	C₂²×C₄	—	3	4	no	—
680	C₂²×C₄	—	3	2	no	—
681	C₂²×C₄	—	3	2	no	—
682	C₂²×C₄	—	3	1	no	—
683	C₂²×C₄	—	3	4	no	—
684	C₂²×C₄	—	3	1	no	—
685	C₂²×C₄	—	3	1	no	—
686	C₂²×C₄	—	3	4	no	—
687	C₂²×C₄	—	3	4	no	—
688	C₂²×C₄	—	6	4	no	—
689	C₂²×C₄	—	12	8	no	—
690	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
691	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
692	C₄⋊C₄	—	3	2	no	—
693	C₄⋊C₄	—	3	2	no	—
694	C₄⋊C₄	—	3	2	no	—
695	C₄⋊C₄	—	3	4	no	—
696	C₄⋊C₄	—	3	2	no	—
697	C₄⋊C₄	—	3	4	no	—
698	C₄⋊C₄	—	3	4	no	—
699	C₄⋊C₄	—	3	4	no	—
700	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
701	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
702	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
703	C₂²⋊C₄	—	3	2	no	—
704	C₂²⋊C₄	—	3	4	no	—
705	C₂²⋊C₄	—	3	4	no	—
706	C₂²⋊C₄	—	3	2	no	—
707	C₂²⋊C₄	—	3	2	no	—
708	C₂²⋊C₄	—	3	4	no	—
709	C₂²⋊C₄	—	3	4	no	—
710	C₂²⋊C₄	—	3	4	no	—
711	C₂²⋊C₄	—	3	4	no	—
712	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
713	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
714	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
715	C₄²	—	3	2	no	—
716	C₄²	—	3	1	no	—
717	C₄²	—	3	2	no	—
718	C₄²	—	3	1	no	—
719	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
720	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
721	C₂²×C₃	—	2	1	no	—
722	C₂²×C₃	—	2	4	no	—
723	C₂²×C₃	—	2	4	no	—
724	C₂²×C₃	—	2	2	no	—
725	C₂²×C₃	—	2	4	no	—
726	C₂²×C₃	—	2	1	no	—
727	C₂²×C₃	—	2	4	no	—
728	C₂²×C₃	—	2	4	no	—
729	C₂²×C₃	—	2	2	no	—
730	C₂²×C₃	—	2	4	no	—
731	C₂²×C₃	—	2	1	no	—
732	C₂²×C₃	—	3	2	no	—
733	C₂²×C₃	—	3	4	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	4	no	—
736	C₂²×C₃	—	4	4	no	—
737	C₂²×C₃	—	4	2	no	—
738	C₂²×C₃	—	4	4	no	—
739	C₂²×C₃	—	6	1	no	—
740	C₂²×C₃	—	6	4	no	—
741	C₂²×C₃	—	6	4	no	—
742	C₂²×C₃	—	6	2	no	—
743	C₂²×C₃	—	6	4	no	—
744	C₂²×C₃	—	12	4	no	—
745	C₂²×C₃	—	12	16	no	—
746	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
747	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
748	C₂×D₃	—	2	1	no	—
749	C₂×D₃	—	2	4	no	—
750	C₂×D₃	—	2	4	no	—
751	C₂×D₃	—	2	2	no	—
752	C₂×D₃	—	2	4	no	—
753	C₂×D₃	—	4	4	no	—
754	C₂×D₃	—	4	16	no	—
755	C₂×D₃	C₂×C₃×#41	1	2	yes	—
756	C₂×D₃	C₃×H(5,𝔽₂)	1	4	yes	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	2	4	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	2	1	no	—
762	C₃×C₄	—	2	2	no	—
763	C₃×C₄	—	2	4	no	—
764	C₃×C₄	—	2	2	no	—
765	C₃×C₄	—	2	2	no	—
766	C₃×C₄	—	3	2	no	—
767	C₃×C₄	—	4	1	no	—
768	C₃×C₄	—	4	2	no	—
769	C₃×C₄	—	4	4	no	—
770	C₃×C₄	—	4	2	no	—
771	C₃×C₄	—	6	1	no	—
772	C₃×C₄	—	6	2	no	—
773	C₃×C₄	—	6	4	no	—
774	C₃×C₄	—	6	2	no	—
775	C₃×C₄	D₃×#41	1	2	yes	—
776	C₃×C₄	C₂×C₃×#41	1	2	yes	—
777	Dic₃	—	2	1	no	—
778	Dic₃	—	2	2	no	—
779	Dic₃	—	2	4	no	—
780	Dic₃	—	2	2	no	—
781	Dic₃	C₂×C₃×#41	1	2	yes	—
782	C₃²	C₂×#540	1	1	yes	characteristic, complemented, Sylow
783	C₂³	—	3	1	no	—
784	C₂³	—	3	1	no	—
785	C₂³	—	3	4	no	—
786	C₂³	—	6	2	no	—
787	C₂³	—	6	8	no	—
788	C₂³	—	6	8	no	—
789	C₂³	—	6	4	no	—
790	C₂³	—	6	8	no	—
791	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
792	C₂³	C₂³×C₃×D₃	1	4	yes	—
793	D₄	—	2	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	6	8	no	—
797	D₄	—	6	4	no	—
798	D₄	—	12	4	no	—
799	D₄	—	12	4	no	—
800	D₄	—	12	4	no	—
801	D₄	—	12	4	no	—
802	D₄	—	12	4	no	—
803	D₄	—	12	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	3	1	no	—
806	C₂×C₄	—	3	4	no	—
807	C₂×C₄	—	3	2	no	—
808	C₂×C₄	—	3	2	no	—
809	C₂×C₄	—	3	1	no	—
810	C₂×C₄	—	3	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	6	2	no	—
813	C₂×C₄	—	6	2	no	—
814	C₂×C₄	—	6	4	no	—
815	C₂×C₄	—	6	8	no	—
816	C₂×C₄	—	6	4	no	—
817	C₂×C₄	—	6	2	no	—
818	C₂×C₄	—	6	2	no	—
819	C₂×C₄	—	12	4	no	—
820	C₂×C₄	—	12	4	no	—
821	C₂×C₄	—	12	4	no	—
822	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
823	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
824	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
825	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
826	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
827	C₂×C₃	—	2	1	no	—
828	C₂×C₃	—	2	2	no	—
829	C₂×C₃	—	3	4	no	—
830	C₂×C₃	—	4	1	no	—
831	C₂×C₃	—	4	4	no	—
832	C₂×C₃	—	4	1	no	—
833	C₂×C₃	—	4	4	no	—
834	C₂×C₃	—	8	1	no	—
835	C₂×C₃	—	8	4	no	—
836	C₂×C₃	—	12	1	no	—
837	C₂×C₃	—	12	4	no	—
838	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
839	C₂×C₃	D₃×H(5,𝔽₂)	1	2	yes	—
840	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
841	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
842	D₃	—	4	1	no	—
843	D₃	—	4	4	no	—
844	D₃	C₃×#540	1	4	yes	direct product factor
845	C₂²	—	2	1	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	3	2	no	—
851	C₂²	—	3	4	no	—
852	C₂²	—	6	1	no	—
853	C₂²	—	6	4	no	—
854	C₂²	—	6	4	no	—
855	C₂²	—	6	2	no	—
856	C₂²	—	6	4	no	—
857	C₂²	—	12	4	no	—
858	C₂²	—	12	16	no	—
859	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	2	no	—
864	C₄	—	3	2	no	—
865	C₄	—	6	1	no	—
866	C₄	—	6	2	no	—
867	C₄	—	6	4	no	—
868	C₄	—	6	2	no	—
869	C₄	C₃×D₃×#41	1	2	yes	—
870	C₃	—	2	1	no	—
871	C₃	D₃×#540	1	1	yes	characteristic, direct product factor
872	C₃	C₂×C₃×#540	1	1	yes	characteristic, complemented
873	C₂	—	3	4	no	—
874	C₂	—	4	1	no	—
875	C₂	—	4	4	no	—
876	C₂	—	12	1	no	—
877	C₂	—	12	4	no	—
878	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
879	C₂	C₃×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#540	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#540	D₃
hypocenter	C₃	C₂×C₃×#540
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#540

Complements

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

N	H ≅ G/N	type
1. C₃²×#540	C₂	semidirect
2. C₃×#5719	C₂	semidirect
3. C₃×D₃×#127	C₂	semidirect
4. C₃×#5697	C₂	semidirect
5. C₃×D₃×#125	C₂	semidirect
6. C₃×#5663	C₂	semidirect
7. C₃×D₃×#123	C₂	semidirect
8. C₃×#5619	C₂	semidirect
9. C₃×#5615	C₂	semidirect
10. C₃×D₃×#121	C₂	semidirect
11. C₃×D₃×#121	C₂	semidirect
12. C₃×#5562	C₂	semidirect
13. C₃×C₄×D₃×D₄	C₂	semidirect
14. C₃×#5535	C₂	semidirect
15. C₃×D₃×#117	C₂	semidirect
17. D₃×#540	C₃	direct (N × H)
23. C₃²×#127	C₂²	semidirect
24. C₃²×#125	C₂²	semidirect
25. C₃²×#123	C₂²	semidirect
26. C₃²×#121	C₂²	semidirect
27. C₃²×#121	C₂²	semidirect
28. C₃²×C₄×D₄	C₂²	semidirect
29. C₃²×#117	C₂²	semidirect
30. C₃×#940	C₂²	semidirect
31. C₃×#940	C₂²	semidirect
32. C₃×#939	C₂²	semidirect
33. C₃×#939	C₂²	semidirect
34. C₃×#939	C₂²	semidirect
35. C₃×#938	C₂²	semidirect
36. C₃×#938	C₂²	semidirect
37. C₃×#935	C₂²	semidirect
38. C₃×D₄×Dic₃	C₂²	semidirect
39. C₃×#930	C₂²	semidirect
40. C₃×#930	C₂²	semidirect
41. C₃×#929	C₂²	semidirect
42. C₃×C₄×#67	C₂²	semidirect
43. C₃×#926	C₂²	semidirect
44. C₃×#895	C₂²	semidirect
45. C₃×#895	C₂²	semidirect
46. C₃×#894	C₂²	semidirect
47. C₃×#894	C₂²	semidirect
48. C₃×#893	C₂²	semidirect
49. C₃×#892	C₂²	semidirect
53. C₃×#890	C₂²	semidirect
54. C₃×#889	C₂²	semidirect
55. C₃×#886	C₂²	semidirect
56. C₃×#884	C₂²	semidirect
57. C₃×#884	C₂²	semidirect
58. C₃×#884	C₂²	semidirect
59. C₃×#883	C₂²	semidirect
60. C₃×#883	C₂²	semidirect
61. C₃×#67⋊C₄	C₂²	semidirect
65. C₃×#877	C₂²	semidirect
66. C₃×#874	C₂²	semidirect
67. C₃×C₄×D₁₂	C₂²	semidirect
68. C₃×#872	C₂²	semidirect
69. C₃×#872	C₂²	semidirect
72. C₃×#870	C₂²	semidirect
81. C₃×#540	D₃	direct (N × H)
82. C₃×#540	C₂×C₃	semidirect
90. #5719	C₂×C₃	semidirect
91. D₃×#127	C₂×C₃	semidirect
92. #5697	C₂×C₃	semidirect
93. D₃×#125	C₂×C₃	semidirect
94. #5663	C₂×C₃	semidirect
95. D₃×#123	C₂×C₃	semidirect
96. #5619	C₂×C₃	semidirect
97. #5615	C₂×C₃	semidirect
98. D₃×#121	C₂×C₃	semidirect
99. D₃×#121	C₂×C₃	semidirect
100. #5562	C₂×C₃	semidirect
101. C₄×D₃×D₄	C₂×C₃	semidirect
102. #5535	C₂×C₃	semidirect
103. D₃×#117	C₂×C₃	semidirect
179. C₃×#127	C₂×D₃	semidirect
180. C₃×#127	C₂²×C₃	semidirect
185. C₃×#125	C₂×D₃	semidirect
186. C₃×#125	C₂²×C₃	semidirect
195. C₃×#123	C₂×D₃	semidirect
196. C₃×#123	C₂²×C₃	semidirect
211. C₃×#121	C₂×D₃	semidirect
212. C₃×#121	C₂×D₃	semidirect
213. C₃×#121	C₂²×C₃	semidirect
214. C₃×#121	C₂²×C₃	semidirect
221. C₃×C₄×D₄	C₂×D₃	semidirect
222. C₃×C₄×D₄	C₂²×C₃	semidirect
229. C₃×#117	C₂×D₃	semidirect
230. C₃×#117	C₂²×C₃	semidirect
239. #940	C₂²×C₃	semidirect
240. #940	C₂²×C₃	semidirect
241. #939	C₂²×C₃	semidirect
242. #939	C₂²×C₃	semidirect
243. #939	C₂²×C₃	semidirect
244. #938	C₂²×C₃	semidirect
245. #938	C₂²×C₃	semidirect
246. #935	C₂²×C₃	semidirect
247. D₄×Dic₃	C₂²×C₃	semidirect
248. #930	C₂²×C₃	semidirect
249. #930	C₂²×C₃	semidirect
250. #929	C₂²×C₃	semidirect
251. C₄×#67	C₂²×C₃	semidirect
252. #926	C₂²×C₃	semidirect
253. #895	C₂²×C₃	semidirect
254. #895	C₂²×C₃	semidirect
255. #894	C₂²×C₃	semidirect
256. #894	C₂²×C₃	semidirect
257. #893	C₂²×C₃	semidirect
258. #892	C₂²×C₃	semidirect
262. #890	C₂²×C₃	semidirect
263. #889	C₂²×C₃	semidirect
264. #886	C₂²×C₃	semidirect
265. #884	C₂²×C₃	semidirect
266. #884	C₂²×C₃	semidirect
267. #884	C₂²×C₃	semidirect
268. #883	C₂²×C₃	semidirect
269. #883	C₂²×C₃	semidirect
270. #67⋊C₄	C₂²×C₃	semidirect
274. #877	C₂²×C₃	semidirect
275. #874	C₂²×C₃	semidirect
276. C₄×D₁₂	C₂²×C₃	semidirect
277. #872	C₂²×C₃	semidirect
278. #872	C₂²×C₃	semidirect
281. #870	C₂²×C₃	semidirect
333. #540	C₃×D₃	direct (N × H)
507. #127	C₂×C₃×D₃	semidirect
511. #125	C₂×C₃×D₃	semidirect
519. #123	C₂×C₃×D₃	semidirect
532. #121	C₂×C₃×D₃	semidirect
533. #121	C₂×C₃×D₃	semidirect
539. C₄×D₄	C₂×C₃×D₃	semidirect
545. #117	C₂×C₃×D₃	semidirect
660. C₃×D₃	#540	direct (N × H)
782. C₃²	C₂×#540	semidirect
844. D₃	C₃×#540	direct (N × H)
871. C₃	D₃×#540	direct (N × H)
872. C₃	C₂×C₃×#540	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#540	2
C₃×#5719	2
C₃×D₃×#127	2
C₃×#5697	2
C₃×D₃×#125	2
C₃×#5663	2
C₃×D₃×#123	2
C₃×#5619	2
C₃×#5615	2
C₃×D₃×#121	2
C₃×#5562	2
C₃×C₄×D₃×D₄	2
C₃×#5535	2
C₃×D₃×#117	2
C₂×C₃×#540	3
D₃×#540	3

Subgroups — C3×D3×#540 #11901461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#540 #11901461