Subgroups — C₃×#85868 #11904840

Order 1152.

2825 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#937	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5560	C₂	1	4	yes	maximal, complemented
5	C₃×#5556	C₂	1	4	yes	maximal, complemented
6	C₃×#5550	C₂	1	4	yes	maximal, complemented
7	C₃×#5547	C₂	1	4	yes	maximal, complemented
8	C₃×#5527	C₂	1	4	yes	maximal, complemented
9	C₃×#5490	C₂	1	4	yes	maximal, complemented
10	C₂×C₃×#882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5483	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3490	—	3	1	no	maximal
15	#85868	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#67	C₂²	1	2	yes	complemented
20	C₂×C₃×#235	C₂²	1	4	yes	complemented
21	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
23	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
24	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
25	C₃²×#117	C₂²	1	2	yes	complemented
26	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×#953	C₂²	1	2	yes	complemented
30	C₂×C₃×#217	C₂²	1	1	yes	characteristic
31	C₂×C₃×#217	C₂²	1	1	yes	characteristic
32	C₃×#939	C₂²	1	4	yes	complemented
33	C₃×#937	C₂²	1	4	yes	—
34	C₃×#937	C₂²	1	2	yes	complemented
35	C₃×#937	C₂²	1	2	yes	complemented
36	C₃×#937	C₂²	1	2	yes	complemented
37	C₃×#935	C₂²	1	2	yes	complemented
38	C₃×#930	C₂²	1	4	yes	complemented
39	C₃×#929	C₂²	1	4	yes	complemented
40	C₃×#929	C₂²	1	2	yes	complemented
41	C₃×C₄×#67	C₂²	1	4	yes	complemented
42	C₃×C₄×#67	C₂²	1	4	yes	complemented
43	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
46	C₃×#924	C₂²	1	4	yes	complemented
47	C₃×#898	C₂²	1	4	yes	complemented
48	C₃×#896	C₂²	1	4	yes	complemented
49	C₃×#894	C₂²	1	4	yes	complemented
50	C₃×#894	C₂²	1	4	yes	complemented
51	C₃×#885	C₂²	1	4	yes	complemented
52	C₃×#884	C₂²	1	4	yes	complemented
53	C₃×#884	C₂²	1	4	yes	complemented
54	C₃×#883	C₂²	1	4	yes	complemented
55	C₃×#882	C₂²	1	4	yes	—
56	C₃×#882	C₂²	1	2	yes	complemented
57	C₃×#882	C₂²	1	2	yes	complemented
58	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
59	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
60	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
61	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
62	C₃×#878	C₂²	1	4	yes	complemented
63	C₃×#878	C₂²	1	4	yes	complemented
64	C₃×#877	C₂²	1	2	yes	complemented
65	C₃×#876	C₂²	1	4	yes	complemented
66	C₃×#875	C₂²	1	4	yes	complemented
67	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
68	C₃×#872	C₂²	1	4	yes	complemented
69	C₃×#551	—	3	4	no	—
70	C₃×#551	—	3	4	no	—
71	C₃×#546	—	3	4	no	—
72	C₃×#546	—	3	4	no	—
73	C₃×#543	—	3	1	no	—
74	C₃×#538	—	3	4	no	—
75	C₃×#534	—	3	1	no	—
76	C₃×#525	—	3	4	no	—
77	C₂×C₃×#120	—	3	1	no	—
78	C₂×C₃×#120	—	3	1	no	—
79	C₃×#518	—	2	1	no	—
80	C₃×#518	—	3	1	no	—
81	C₃×#518	D₃	1	1	yes	characteristic, complemented
82	C₃×#518	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
84	#5804	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#937	C₂×C₃	1	1	yes	characteristic, complemented
86	#5560	C₂×C₃	1	4	yes	complemented
87	#5556	C₂×C₃	1	4	yes	complemented
88	#5550	C₂×C₃	1	4	yes	complemented
89	#5547	C₂×C₃	1	4	yes	complemented
90	#5527	C₂×C₃	1	4	yes	complemented
91	#5490	C₂×C₃	1	4	yes	complemented
92	C₂×#882	C₂×C₃	1	1	yes	characteristic, complemented
93	#5486	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
95	#5483	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
97	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
98	C₂³×C₃×D₃	—	2	4	no	—
99	C₂³×C₃×D₃	—	4	4	no	—
100	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
101	C₂³×C₃×D₃	C₂³	1	2	yes	—
102	C₂³×C₃×D₃	C₂³	1	2	yes	—
103	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
104	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
105	C₂×C₃²×D₄	—	2	4	no	—
106	C₂×C₃²×D₄	C₂³	1	2	yes	—
107	C₂×C₃²×D₄	C₂³	1	2	yes	—
108	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃²×C₄	C₂³	1	2	yes	—
110	C₂²×C₃²×C₄	C₂³	1	2	yes	—
111	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
112	C₂×C₃×#67	—	2	4	no	—
113	C₂×C₃×#67	—	4	4	no	—
114	C₂×C₃×#67	C₂³	1	2	yes	—
115	C₂×C₃×#67	C₂³	1	2	yes	—
116	C₂×C₃×#67	C₂³	1	4	yes	—
117	C₂×C₃×#67	C₂³	1	4	yes	—
118	C₂×C₃×#67	C₂³	1	4	yes	complemented
119	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
120	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
121	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
122	C₃×#235	—	4	8	no	—
123	C₂×C₃×D₁₂	—	4	4	no	—
124	C₂×C₃×D₁₂	C₂³	1	4	yes	—
125	C₂×C₃×D₁₂	C₂³	1	4	yes	—
126	C₂×C₃×C₄×D₃	—	4	4	no	—
127	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
128	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
129	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
130	C₂×C₃×Dic₆	C₂³	1	4	yes	complemented
131	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
132	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
137	C₃²×C₄²	C₂³	1	4	yes	complemented
138	C₃×#217	C₂³	1	2	yes	—
139	C₃×#217	C₂³	1	2	yes	—
140	C₃×#217	C₂³	1	2	yes	—
141	C₃×#217	C₂³	1	2	yes	—
142	C₃×#217	C₂³	1	4	yes	complemented
143	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
144	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
145	C₃×(C₂×D₃)⋊C₄	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	4	yes	complemented
150	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
151	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
152	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
153	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
154	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
155	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
156	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
157	#3490	—	3	1	no	Sylow
158	C₂⁵×C₃	—	3	1	no	—
159	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₃×#41	—	3	4	no	—
161	C₂²×C₃×D₄	—	2	1	no	—
162	C₂²×C₃×D₄	—	3	1	no	—
163	C₂²×C₃×D₄	—	3	2	no	—
164	C₂²×C₃×D₄	—	3	2	no	—
165	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
166	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
167	C₂³×C₃×C₄	—	3	2	no	—
168	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
169	C₂²×#67	C₂²×C₃	1	2	yes	complemented
170	C₂×#235	C₂²×C₃	1	4	yes	complemented
171	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
172	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
173	C₃×#126	—	3	4	no	—
174	C₃×#126	—	3	4	no	—
175	C₃×#124	—	3	4	no	—
176	C₃×#124	—	3	4	no	—
177	C₃×#123	—	3	2	no	—
178	C₃×#123	—	3	2	no	—
179	C₃×#123	—	3	4	no	—
180	C₃×#123	—	3	4	no	—
181	C₃×#123	—	3	4	no	—
182	C₃×#123	—	3	4	no	—
183	C₃×C₂²⋊Q₈	—	3	4	no	—
184	C₃×C₂²⋊Q₈	—	3	4	no	—
185	C₃×C₂²⋊Q₈	—	3	4	no	—
186	C₃×C₂²⋊Q₈	—	3	4	no	—
187	C₃×#121	—	3	4	no	—
188	C₃×#121	—	3	4	no	—
189	C₃×#121	—	3	4	no	—
190	C₃×#121	—	3	4	no	—
191	C₃×#120	—	3	2	no	—
192	C₃×#120	—	3	4	no	—
193	C₃×#120	—	3	2	no	—
194	C₃×#120	—	3	2	no	—
195	C₃×#120	—	3	2	no	—
196	C₃×#120	—	3	4	no	—
197	C₃×#120	—	3	2	no	—
198	C₃×#120	—	3	2	no	—
199	C₃×C₄×D₄	—	2	4	no	—
200	C₃×C₄×D₄	—	2	4	no	—
201	C₃×C₄×D₄	—	3	4	no	—
202	C₃×C₄×D₄	—	3	4	no	—
203	C₃×C₄×D₄	—	3	4	no	—
204	C₃×C₄×D₄	—	3	4	no	—
205	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
206	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
207	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
208	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
209	C₃×#117	—	2	2	no	—
210	C₃×#117	—	3	2	no	—
211	C₃×#117	—	3	4	no	—
212	C₃×#117	C₂×D₃	1	2	yes	complemented
213	C₃×#117	C₂²×C₃	1	2	yes	complemented
214	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
216	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
217	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
218	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
219	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
220	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
221	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
222	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
223	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
224	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
225	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
228	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
231	#953	C₂²×C₃	1	2	yes	complemented
232	C₂×#217	C₂²×C₃	1	1	yes	characteristic
233	C₂×#217	C₂²×C₃	1	1	yes	characteristic
234	#939	C₂²×C₃	1	4	yes	complemented
235	#937	C₂²×C₃	1	4	yes	—
236	#937	C₂²×C₃	1	2	yes	complemented
237	#937	C₂²×C₃	1	2	yes	complemented
238	#937	C₂²×C₃	1	2	yes	complemented
239	#935	C₂²×C₃	1	2	yes	complemented
240	#930	C₂²×C₃	1	4	yes	complemented
241	#929	C₂²×C₃	1	4	yes	complemented
242	#929	C₂²×C₃	1	2	yes	complemented
243	C₄×#67	C₂²×C₃	1	4	yes	complemented
244	C₄×#67	C₂²×C₃	1	4	yes	complemented
245	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
246	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
247	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
248	#924	C₂²×C₃	1	4	yes	complemented
249	#898	C₂²×C₃	1	4	yes	complemented
250	#896	C₂²×C₃	1	4	yes	complemented
251	#894	C₂²×C₃	1	4	yes	complemented
252	#894	C₂²×C₃	1	4	yes	complemented
253	#885	C₂²×C₃	1	4	yes	complemented
254	#884	C₂²×C₃	1	4	yes	complemented
255	#884	C₂²×C₃	1	4	yes	complemented
256	#883	C₂²×C₃	1	4	yes	complemented
257	#882	C₂²×C₃	1	4	yes	—
258	#882	C₂²×C₃	1	2	yes	complemented
259	#882	C₂²×C₃	1	2	yes	complemented
260	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
261	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
262	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
263	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
264	#878	C₂²×C₃	1	4	yes	complemented
265	#878	C₂²×C₃	1	4	yes	complemented
266	#877	C₂²×C₃	1	2	yes	complemented
267	#876	C₂²×C₃	1	4	yes	complemented
268	#875	C₂²×C₃	1	4	yes	complemented
269	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
270	#872	C₂²×C₃	1	4	yes	complemented
271	C₂³×C₃²	—	2	2	no	—
272	C₂³×C₃²	—	4	2	no	—
273	C₂³×C₃²	—	4	2	no	—
274	C₂³×C₃²	#41	1	4	yes	complemented
275	C₂³×C₃²	C₂⁴	1	2	yes	—
276	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
277	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
278	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
279	C₂²×C₃×D₃	—	2	2	no	—
280	C₂²×C₃×D₃	—	2	4	no	—
281	C₂²×C₃×D₃	—	2	4	no	—
282	C₂²×C₃×D₃	—	2	4	no	—
283	C₂²×C₃×D₃	—	2	2	no	—
284	C₂²×C₃×D₃	—	2	2	no	—
285	C₂²×C₃×D₃	—	2	4	no	—
286	C₂²×C₃×D₃	—	2	4	no	—
287	C₂²×C₃×D₃	—	4	2	no	—
288	C₂²×C₃×D₃	—	4	2	no	—
289	C₂²×C₃×D₃	—	4	2	no	—
290	C₂²×C₃×D₃	—	4	2	no	—
291	C₂²×C₃×D₃	—	4	16	no	—
292	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
293	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
294	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
295	C₃²×D₄	—	2	4	no	—
296	C₃²×D₄	—	2	4	no	—
297	C₂×C₃²×C₄	—	2	2	no	—
298	C₂×C₃²×C₄	—	4	2	no	—
299	C₂×C₃²×C₄	—	4	2	no	—
300	C₂×C₃²×C₄	—	4	4	no	—
301	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
302	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
303	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
304	C₃×#67	—	2	4	no	—
305	C₃×#67	—	2	4	no	—
306	C₃×#67	—	2	8	no	—
307	C₃×#67	—	4	4	no	—
308	C₃×#67	—	4	4	no	—
309	C₂×C₃×Dic₃	—	2	2	no	—
310	C₂×C₃×Dic₃	—	4	2	no	—
311	C₂×C₃×Dic₃	—	4	2	no	—
312	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
313	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
314	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
315	C₃×D₁₂	—	2	8	no	—
316	C₃×D₁₂	—	4	4	no	—
317	C₃×C₄×D₃	—	2	8	no	—
318	C₃×C₄×D₃	—	4	4	no	—
319	C₃×C₄×D₃	—	4	4	no	—
320	C₃×Dic₆	—	4	4	no	—
321	#551	—	3	4	no	—
322	#551	—	3	4	no	—
323	#546	—	3	4	no	—
324	#546	—	3	4	no	—
325	#543	—	3	1	no	—
326	#538	—	3	4	no	—
327	#534	—	3	1	no	—
328	#525	—	3	4	no	—
329	C₂×#120	—	3	1	no	—
330	C₂×#120	—	3	1	no	—
331	#518	—	3	1	no	—
332	#518	C₃×D₃	1	1	yes	characteristic, complemented
333	C₂²×C₂²⋊C₄	—	3	1	no	—
334	C₂⁴×C₃	—	2	1	no	—
335	C₂⁴×C₃	—	2	1	no	—
336	C₂⁴×C₃	—	3	1	no	—
337	C₂⁴×C₃	—	3	2	no	—
338	C₂⁴×C₃	—	3	2	no	—
339	C₂⁴×C₃	—	3	1	no	—
340	C₂⁴×C₃	—	3	1	no	—
341	C₂⁴×C₃	—	6	4	no	—
342	C₂⁴×C₃	—	12	4	no	—
343	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
344	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
345	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
346	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
347	C₂³×D₃	—	2	4	no	—
348	C₂³×D₃	—	4	4	no	—
349	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
350	C₂³×D₃	C₂³×C₃	1	2	yes	—
351	C₂³×D₃	C₂³×C₃	1	2	yes	—
352	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
353	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
354	C₃×#41	—	12	8	no	—
355	C₂×C₃×Q₈	—	3	4	no	—
356	C₂×C₃×D₄	—	2	8	no	—
357	C₂×C₃×D₄	—	2	4	no	—
358	C₂×C₃×D₄	—	2	4	no	—
359	C₂×C₃×D₄	—	2	2	no	—
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	—	3	2	no	—
362	C₂×C₃×D₄	—	3	2	no	—
363	C₂×C₃×D₄	—	3	4	no	—
364	C₂×C₃×D₄	—	3	4	no	—
365	C₂×C₃×D₄	—	3	4	no	—
366	C₂×C₃×D₄	—	3	4	no	—
367	C₂×C₃×D₄	—	3	4	no	—
368	C₂×C₃×D₄	—	6	4	no	—
369	C₂×C₃×D₄	—	12	4	no	—
370	C₂×C₃×D₄	—	12	4	no	—
371	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
372	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
373	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
374	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
375	C₂²×C₃×C₄	—	2	1	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	4	no	—
379	C₂²×C₃×C₄	—	3	1	no	—
380	C₂²×C₃×C₄	—	3	2	no	—
381	C₂²×C₃×C₄	—	3	2	no	—
382	C₂²×C₃×C₄	—	3	4	no	—
383	C₂²×C₃×C₄	—	3	4	no	—
384	C₂²×C₃×C₄	—	3	4	no	—
385	C₂²×C₃×C₄	—	12	4	no	—
386	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
388	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
389	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
390	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
392	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
393	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
394	C₂×#67	—	2	4	no	—
395	C₂×#67	—	4	4	no	—
396	C₂×#67	C₂³×C₃	1	2	yes	—
397	C₂×#67	C₂³×C₃	1	2	yes	—
398	C₂×#67	C₂³×C₃	1	4	yes	—
399	C₂×#67	C₂³×C₃	1	4	yes	—
400	C₂×#67	C₂³×C₃	1	4	yes	complemented
401	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
402	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
403	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
404	#235	—	4	8	no	—
405	C₂×D₁₂	—	4	4	no	—
406	C₂×D₁₂	C₂³×C₃	1	4	yes	—
407	C₂×D₁₂	C₂³×C₃	1	4	yes	—
408	C₂×C₄×D₃	—	4	4	no	—
409	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
410	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
411	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
412	C₂×Dic₆	C₂³×C₃	1	4	yes	complemented
413	C₃×C₄⋊C₄	—	2	4	no	—
414	C₃×C₄⋊C₄	—	3	4	no	—
415	C₃×C₄⋊C₄	—	3	4	no	—
416	C₃×C₄⋊C₄	—	3	4	no	—
417	C₃×C₄⋊C₄	—	3	4	no	—
418	C₃×C₄⋊C₄	—	3	4	no	—
419	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
420	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
421	C₃×C₂²⋊C₄	—	2	2	no	—
422	C₃×C₂²⋊C₄	—	2	2	no	—
423	C₃×C₂²⋊C₄	—	2	2	no	—
424	C₃×C₂²⋊C₄	—	2	2	no	—
425	C₃×C₂²⋊C₄	—	2	4	no	—
426	C₃×C₂²⋊C₄	—	3	2	no	—
427	C₃×C₂²⋊C₄	—	3	2	no	—
428	C₃×C₂²⋊C₄	—	3	2	no	—
429	C₃×C₂²⋊C₄	—	3	2	no	—
430	C₃×C₂²⋊C₄	—	3	4	no	—
431	C₃×C₂²⋊C₄	—	3	4	no	—
432	C₃×C₂²⋊C₄	—	3	4	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	—	3	4	no	—
438	C₃×C₂²⋊C₄	—	3	4	no	—
439	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
440	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
441	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
442	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
443	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
444	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
445	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
446	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
447	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
448	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
449	C₃×C₄²	—	2	4	no	—
450	C₃×C₄²	—	3	4	no	—
451	C₃×C₄²	C₂²×D₃	1	4	yes	complemented
452	C₃×C₄²	C₂³×C₃	1	4	yes	complemented
453	#217	C₂³×C₃	1	2	yes	—
454	#217	C₂³×C₃	1	2	yes	—
455	#217	C₂³×C₃	1	2	yes	—
456	#217	C₂³×C₃	1	2	yes	—
457	#217	C₂³×C₃	1	4	yes	complemented
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	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
463	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
464	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
465	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
466	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
467	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
468	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
469	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
470	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
471	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
472	C₂²×C₃²	—	2	2	no	—
473	C₂²×C₃²	—	2	2	no	—
474	C₂²×C₃²	—	2	2	no	—
475	C₂²×C₃²	—	2	2	no	—
476	C₂²×C₃²	—	2	4	no	—
477	C₂²×C₃²	—	4	4	no	—
478	C₂²×C₃²	—	8	2	no	—
479	C₂²×C₃²	C₂×#41	1	2	yes	—
480	C₂²×C₃²	C₂×#41	1	2	yes	—
481	C₂²×C₃²	C₂×#41	1	2	yes	—
482	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
483	C₂×C₃×D₃	—	2	8	no	—
484	C₂×C₃×D₃	—	2	2	no	—
485	C₂×C₃×D₃	—	2	2	no	—
486	C₂×C₃×D₃	—	2	2	no	—
487	C₂×C₃×D₃	—	2	2	no	—
488	C₂×C₃×D₃	—	2	4	no	—
489	C₂×C₃×D₃	—	2	2	no	—
490	C₂×C₃×D₃	—	2	2	no	—
491	C₂×C₃×D₃	—	4	8	no	—
492	C₂×C₃×D₃	—	4	8	no	—
493	C₂×C₃×D₃	—	4	4	no	—
494	C₂×C₃×D₃	—	8	2	no	—
495	C₂×C₃×D₃	H(5,𝔽₂)	1	4	yes	—
496	C₃²×C₄	—	2	2	no	—
497	C₃²×C₄	—	2	4	no	—
498	C₃²×C₄	—	2	4	no	—
499	C₃×Dic₃	—	2	2	no	—
500	C₃×Dic₃	—	2	4	no	—
501	C₃×Dic₃	—	2	4	no	—
502	C₂⁵	—	3	1	no	—
503	C₂×#41	—	3	4	no	—
504	C₂²×D₄	—	3	1	no	—
505	C₂²×D₄	—	3	2	no	—
506	C₂²×D₄	—	3	2	no	—
507	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
508	C₂³×C₄	—	3	2	no	—
509	#126	—	3	4	no	—
510	#126	—	3	4	no	—
511	#124	—	3	4	no	—
512	#124	—	3	4	no	—
513	#123	—	3	2	no	—
514	#123	—	3	2	no	—
515	#123	—	3	4	no	—
516	#123	—	3	4	no	—
517	#123	—	3	4	no	—
518	#123	—	3	4	no	—
519	C₂²⋊Q₈	—	3	4	no	—
520	C₂²⋊Q₈	—	3	4	no	—
521	C₂²⋊Q₈	—	3	4	no	—
522	C₂²⋊Q₈	—	3	4	no	—
523	#121	—	3	4	no	—
524	#121	—	3	4	no	—
525	#121	—	3	4	no	—
526	#121	—	3	4	no	—
527	#120	—	3	2	no	—
528	#120	—	3	2	no	—
529	#120	—	3	2	no	—
530	#120	—	3	4	no	—
531	#120	—	3	2	no	—
532	#120	—	3	2	no	—
533	#120	—	3	2	no	—
534	#120	—	3	4	no	—
535	C₄×D₄	—	3	4	no	—
536	C₄×D₄	—	3	4	no	—
537	C₄×D₄	—	3	4	no	—
538	C₄×D₄	—	3	4	no	—
539	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
540	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
541	#117	—	3	2	no	—
542	#117	—	3	4	no	—
543	#117	C₂×C₃×D₃	1	2	yes	complemented
544	C₂×C₂²⋊C₄	—	3	1	no	—
545	C₂×C₂²⋊C₄	—	3	1	no	—
546	C₂×C₂²⋊C₄	—	3	2	no	—
547	C₂×C₂²⋊C₄	—	3	2	no	—
548	C₂×C₂²⋊C₄	—	3	2	no	—
549	C₂×C₂²⋊C₄	—	3	4	no	—
550	C₂×C₂²⋊C₄	—	3	4	no	—
551	C₂×C₂²⋊C₄	—	3	2	no	—
552	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
555	C₂³×C₃	—	2	4	no	—
556	C₂³×C₃	—	2	2	no	—
557	C₂³×C₃	—	2	2	no	—
558	C₂³×C₃	—	2	1	no	—
559	C₂³×C₃	—	2	2	no	—
560	C₂³×C₃	—	2	1	no	—
561	C₂³×C₃	—	2	1	no	—
562	C₂³×C₃	—	2	4	no	—
563	C₂³×C₃	—	3	2	no	—
564	C₂³×C₃	—	3	2	no	—
565	C₂³×C₃	—	3	2	no	—
566	C₂³×C₃	—	4	2	no	—
567	C₂³×C₃	—	4	2	no	—
568	C₂³×C₃	—	4	2	no	—
569	C₂³×C₃	—	4	2	no	—
570	C₂³×C₃	—	6	4	no	—
571	C₂³×C₃	—	6	4	no	—
572	C₂³×C₃	—	6	4	no	—
573	C₂³×C₃	—	6	2	no	—
574	C₂³×C₃	—	6	4	no	—
575	C₂³×C₃	—	6	4	no	—
576	C₂³×C₃	—	6	2	no	—
577	C₂³×C₃	—	6	2	no	—
578	C₂³×C₃	—	8	2	no	—
579	C₂³×C₃	—	8	2	no	—
580	C₂³×C₃	—	12	2	no	—
581	C₂³×C₃	—	12	2	no	—
582	C₂³×C₃	—	12	2	no	—
583	C₂³×C₃	—	12	2	no	—
584	C₂³×C₃	—	12	16	no	—
585	C₂³×C₃	#235	1	4	yes	complemented
586	C₂³×C₃	C₃×#41	1	4	yes	complemented
587	C₂³×C₃	C₂³×D₃	1	2	yes	—
588	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
589	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
590	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
591	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
592	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
593	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
594	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
595	C₂²×D₃	—	2	2	no	—
596	C₂²×D₃	—	2	4	no	—
597	C₂²×D₃	—	2	4	no	—
598	C₂²×D₃	—	2	4	no	—
599	C₂²×D₃	—	2	2	no	—
600	C₂²×D₃	—	2	2	no	—
601	C₂²×D₃	—	2	4	no	—
602	C₂²×D₃	—	2	4	no	—
603	C₂²×D₃	—	4	2	no	—
604	C₂²×D₃	—	4	2	no	—
605	C₂²×D₃	—	4	2	no	—
606	C₂²×D₃	—	4	2	no	—
607	C₂²×D₃	—	4	16	no	—
608	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
609	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
610	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
611	C₃×Q₈	—	12	4	no	—
612	C₃×D₄	—	2	8	no	—
613	C₃×D₄	—	2	8	no	—
614	C₃×D₄	—	2	4	no	—
615	C₃×D₄	—	2	4	no	—
616	C₃×D₄	—	2	4	no	—
617	C₃×D₄	—	2	4	no	—
618	C₃×D₄	—	6	8	no	—
619	C₃×D₄	—	6	8	no	—
620	C₃×D₄	—	6	4	no	—
621	C₃×D₄	—	6	4	no	—
622	C₃×D₄	—	12	4	no	—
623	C₃×D₄	—	12	4	no	—
624	C₃×D₄	—	12	4	no	—
625	C₂×C₃×C₄	—	2	4	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	4	no	—
630	C₂×C₃×C₄	—	2	4	no	—
631	C₂×C₃×C₄	—	3	2	no	—
632	C₂×C₃×C₄	—	3	4	no	—
633	C₂×C₃×C₄	—	3	4	no	—
634	C₂×C₃×C₄	—	4	2	no	—
635	C₂×C₃×C₄	—	4	2	no	—
636	C₂×C₃×C₄	—	4	4	no	—
637	C₂×C₃×C₄	—	4	2	no	—
638	C₂×C₃×C₄	—	4	2	no	—
639	C₂×C₃×C₄	—	4	4	no	—
640	C₂×C₃×C₄	—	6	8	no	—
641	C₂×C₃×C₄	—	6	2	no	—
642	C₂×C₃×C₄	—	8	2	no	—
643	C₂×C₃×C₄	—	8	2	no	—
644	C₂×C₃×C₄	—	8	4	no	—
645	C₂×C₃×C₄	—	12	4	no	—
646	C₂×C₃×C₄	—	12	4	no	—
647	C₂×C₃×C₄	—	12	2	no	—
648	C₂×C₃×C₄	—	12	2	no	—
649	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
650	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
651	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
652	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
653	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
654	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
655	#67	—	2	4	no	—
656	#67	—	2	4	no	—
657	#67	—	2	8	no	—
658	#67	—	4	4	no	—
659	#67	—	4	4	no	—
660	C₂×Dic₃	—	2	2	no	—
661	C₂×Dic₃	—	4	2	no	—
662	C₂×Dic₃	—	4	2	no	—
663	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
664	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
665	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
666	D₁₂	—	2	8	no	—
667	D₁₂	—	4	4	no	—
668	C₄×D₃	—	2	8	no	—
669	C₄×D₃	—	4	4	no	—
670	C₄×D₃	—	4	4	no	—
671	Dic₆	—	4	4	no	—
672	C₂×C₃²	—	2	2	no	—
673	C₂×C₃²	—	2	2	no	—
674	C₂×C₃²	—	2	2	no	—
675	C₂×C₃²	—	4	2	no	—
676	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
677	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
678	C₃×D₃	—	2	4	no	—
679	C₃×D₃	—	4	2	no	—
680	C₃×D₃	—	4	2	no	—
681	C₂⁴	—	3	1	no	—
682	C₂⁴	—	3	2	no	—
683	C₂⁴	—	3	2	no	—
684	C₂⁴	—	3	1	no	—
685	C₂⁴	—	3	1	no	—
686	C₂⁴	—	6	4	no	—
687	C₂⁴	—	12	4	no	—
688	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
689	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
690	#41	—	12	8	no	—
691	C₂×Q₈	—	3	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	3	2	no	—
694	C₂×D₄	—	3	2	no	—
695	C₂×D₄	—	3	4	no	—
696	C₂×D₄	—	3	4	no	—
697	C₂×D₄	—	3	4	no	—
698	C₂×D₄	—	3	4	no	—
699	C₂×D₄	—	3	4	no	—
700	C₂×D₄	—	6	4	no	—
701	C₂×D₄	—	12	4	no	—
702	C₂×D₄	—	12	4	no	—
703	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
704	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
705	C₂²×C₄	—	3	1	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	—	12	4	no	—
712	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
713	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
714	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
715	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
716	C₄⋊C₄	—	3	4	no	—
717	C₄⋊C₄	—	3	4	no	—
718	C₄⋊C₄	—	3	4	no	—
719	C₄⋊C₄	—	3	4	no	—
720	C₄⋊C₄	—	3	4	no	—
721	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
722	C₂²⋊C₄	—	3	2	no	—
723	C₂²⋊C₄	—	3	2	no	—
724	C₂²⋊C₄	—	3	2	no	—
725	C₂²⋊C₄	—	3	2	no	—
726	C₂²⋊C₄	—	3	4	no	—
727	C₂²⋊C₄	—	3	4	no	—
728	C₂²⋊C₄	—	3	4	no	—
729	C₂²⋊C₄	—	3	4	no	—
730	C₂²⋊C₄	—	3	4	no	—
731	C₂²⋊C₄	—	3	4	no	—
732	C₂²⋊C₄	—	3	4	no	—
733	C₂²⋊C₄	—	3	4	no	—
734	C₂²⋊C₄	—	3	4	no	—
735	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
736	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
737	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
738	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
739	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
740	C₄²	—	3	4	no	—
741	C₄²	C₂²×C₃×D₃	1	4	yes	complemented
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	2	2	no	—
744	C₂²×C₃	—	2	2	no	—
745	C₂²×C₃	—	2	2	no	—
746	C₂²×C₃	—	2	2	no	—
747	C₂²×C₃	—	2	2	no	—
748	C₂²×C₃	—	2	4	no	—
749	C₂²×C₃	—	2	2	no	—
750	C₂²×C₃	—	2	4	no	—
751	C₂²×C₃	—	2	2	no	—
752	C₂²×C₃	—	2	4	no	—
753	C₂²×C₃	—	2	2	no	—
754	C₂²×C₃	—	2	2	no	—
755	C₂²×C₃	—	2	2	no	—
756	C₂²×C₃	—	2	1	no	—
757	C₂²×C₃	—	3	4	no	—
758	C₂²×C₃	—	4	2	no	—
759	C₂²×C₃	—	4	2	no	—
760	C₂²×C₃	—	4	4	no	—
761	C₂²×C₃	—	4	2	no	—
762	C₂²×C₃	—	4	4	no	—
763	C₂²×C₃	—	4	4	no	—
764	C₂²×C₃	—	6	8	no	—
765	C₂²×C₃	—	6	2	no	—
766	C₂²×C₃	—	6	2	no	—
767	C₂²×C₃	—	6	2	no	—
768	C₂²×C₃	—	6	2	no	—
769	C₂²×C₃	—	6	4	no	—
770	C₂²×C₃	—	6	2	no	—
771	C₂²×C₃	—	6	2	no	—
772	C₂²×C₃	—	8	4	no	—
773	C₂²×C₃	—	8	2	no	—
774	C₂²×C₃	—	8	2	no	—
775	C₂²×C₃	—	8	4	no	—
776	C₂²×C₃	—	12	8	no	—
777	C₂²×C₃	—	12	8	no	—
778	C₂²×C₃	—	12	4	no	—
779	C₂²×C₃	—	24	2	no	—
780	C₂²×C₃	C₂×#235	1	2	yes	—
781	C₂²×C₃	C₂×#235	1	2	yes	—
782	C₂²×C₃	C₂×#235	1	2	yes	—
783	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
784	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
785	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
786	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
787	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
788	C₂×D₃	—	2	8	no	—
789	C₂×D₃	—	2	2	no	—
790	C₂×D₃	—	2	2	no	—
791	C₂×D₃	—	2	2	no	—
792	C₂×D₃	—	2	2	no	—
793	C₂×D₃	—	2	4	no	—
794	C₂×D₃	—	2	2	no	—
795	C₂×D₃	—	2	2	no	—
796	C₂×D₃	—	4	8	no	—
797	C₂×D₃	—	4	8	no	—
798	C₂×D₃	—	4	4	no	—
799	C₂×D₃	—	8	2	no	—
800	C₂×D₃	C₃×H(5,𝔽₂)	1	4	yes	—
801	C₃×C₄	—	2	4	no	—
802	C₃×C₄	—	2	2	no	—
803	C₃×C₄	—	2	4	no	—
804	C₃×C₄	—	2	4	no	—
805	C₃×C₄	—	2	2	no	—
806	C₃×C₄	—	2	4	no	—
807	C₃×C₄	—	2	4	no	—
808	C₃×C₄	—	4	4	no	—
809	C₃×C₄	—	4	4	no	—
810	C₃×C₄	—	6	2	no	—
811	C₃×C₄	—	6	4	no	—
812	C₃×C₄	—	6	4	no	—
813	Dic₃	—	2	2	no	—
814	Dic₃	—	2	4	no	—
815	Dic₃	—	2	4	no	—
816	C₃²	#3490	1	1	yes	characteristic, complemented, Sylow
817	C₂³	—	2	2	no	—
818	C₂³	—	3	2	no	—
819	C₂³	—	3	2	no	—
820	C₂³	—	3	2	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	4	2	no	—
823	C₂³	—	6	4	no	—
824	C₂³	—	6	4	no	—
825	C₂³	—	6	4	no	—
826	C₂³	—	6	2	no	—
827	C₂³	—	6	4	no	—
828	C₂³	—	6	4	no	—
829	C₂³	—	6	2	no	—
830	C₂³	—	6	2	no	—
831	C₂³	—	12	2	no	—
832	C₂³	—	12	2	no	—
833	C₂³	—	12	2	no	—
834	C₂³	—	12	2	no	—
835	C₂³	—	12	16	no	—
836	C₂³	C₃×#235	1	4	yes	complemented
837	C₂³	C₂³×C₃×D₃	1	2	yes	—
838	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
839	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
840	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
841	Q₈	—	12	4	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	4	no	—
844	D₄	—	6	8	no	—
845	D₄	—	6	8	no	—
846	D₄	—	6	4	no	—
847	D₄	—	6	4	no	—
848	D₄	—	12	4	no	—
849	D₄	—	12	4	no	—
850	D₄	—	12	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	3	2	no	—
853	C₂×C₄	—	3	4	no	—
854	C₂×C₄	—	3	4	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	6	8	no	—
859	C₂×C₄	—	6	2	no	—
860	C₂×C₄	—	12	4	no	—
861	C₂×C₄	—	12	4	no	—
862	C₂×C₄	—	12	2	no	—
863	C₂×C₄	—	12	2	no	—
864	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
865	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
866	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
867	C₂×C₃	—	2	2	no	—
868	C₂×C₃	—	2	2	no	—
869	C₂×C₃	—	2	2	no	—
870	C₂×C₃	—	2	2	no	—
871	C₂×C₃	—	2	2	no	—
872	C₂×C₃	—	2	2	no	—
873	C₂×C₃	—	2	1	no	—
874	C₂×C₃	—	2	2	no	—
875	C₂×C₃	—	4	2	no	—
876	C₂×C₃	—	4	2	no	—
877	C₂×C₃	—	4	2	no	—
878	C₂×C₃	—	4	4	no	—
879	C₂×C₃	—	4	2	no	—
880	C₂×C₃	—	4	2	no	—
881	C₂×C₃	—	6	4	no	—
882	C₂×C₃	—	12	2	no	—
883	C₂×C₃	—	12	2	no	—
884	C₂×C₃	C₂²×#235	1	1	yes	characteristic
885	C₂×C₃	D₃×H(5,𝔽₂)	1	2	yes	—
886	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
887	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
888	D₃	—	2	4	no	—
889	D₃	—	4	2	no	—
890	D₃	—	4	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	3	4	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	6	8	no	—
899	C₂²	—	6	2	no	—
900	C₂²	—	6	2	no	—
901	C₂²	—	6	2	no	—
902	C₂²	—	6	2	no	—
903	C₂²	—	6	4	no	—
904	C₂²	—	6	2	no	—
905	C₂²	—	6	2	no	—
906	C₂²	—	8	2	no	—
907	C₂²	—	12	8	no	—
908	C₂²	—	12	8	no	—
909	C₂²	—	12	4	no	—
910	C₂²	—	24	2	no	—
911	C₂²	C₂×C₃×#235	1	2	yes	—
912	C₂²	C₂×C₃×#235	1	2	yes	—
913	C₂²	C₂×C₃×#235	1	2	yes	—
914	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
915	C₄	—	2	2	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	4	no	—
918	C₄	—	6	2	no	—
919	C₄	—	6	4	no	—
920	C₄	—	6	4	no	—
921	C₃	—	2	1	no	—
922	C₃	#85868	1	1	yes	characteristic, direct product factor
923	C₃	C₃×#3490	1	1	yes	characteristic, complemented
924	C₂	—	2	2	no	—
925	C₂	—	2	2	no	—
926	C₂	—	2	2	no	—
927	C₂	—	4	2	no	—
928	C₂	—	6	4	no	—
929	C₂	—	12	2	no	—
930	C₂	—	12	2	no	—
931	C₂	C₂²×C₃×#235	1	1	yes	characteristic
932	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×#518	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#518	D₃
hypocenter	C₃	C₃×#3490
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#518

Complements

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

N	H ≅ G/N	type
1. C₃²×#518	C₂	semidirect
2. C₃×#5804	C₂	semidirect
3. C₂×C₃×#937	C₂	semidirect
4. C₃×#5560	C₂	semidirect
5. C₃×#5556	C₂	semidirect
6. C₃×#5550	C₂	semidirect
7. C₃×#5547	C₂	semidirect
8. C₃×#5527	C₂	semidirect
9. C₃×#5490	C₂	semidirect
10. C₂×C₃×#882	C₂	semidirect
11. C₃×#5486	C₂	semidirect
12. C₂×C₃×D₃×C₂²⋊C₄	C₂	semidirect
13. C₃×#5483	C₂	semidirect
15. #85868	C₃	direct (N × H)
19. C₂²×C₃×#67	C₂²	semidirect
20. C₂×C₃×#235	C₂²	semidirect
21. C₂²×C₃×D₁₂	C₂²	semidirect
22. C₂²×C₃×C₄×D₃	C₂²	semidirect
23. C₃²×C₄×D₄	C₂²	semidirect
24. C₃²×C₄×D₄	C₂²	semidirect
25. C₃²×#117	C₂²	semidirect
28. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
29. C₃×#953	C₂²	semidirect
32. C₃×#939	C₂²	semidirect
34. C₃×#937	C₂²	semidirect
35. C₃×#937	C₂²	semidirect
36. C₃×#937	C₂²	semidirect
37. C₃×#935	C₂²	semidirect
38. C₃×#930	C₂²	semidirect
39. C₃×#929	C₂²	semidirect
40. C₃×#929	C₂²	semidirect
41. C₃×C₄×#67	C₂²	semidirect
42. C₃×C₄×#67	C₂²	semidirect
43. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
46. C₃×#924	C₂²	semidirect
47. C₃×#898	C₂²	semidirect
48. C₃×#896	C₂²	semidirect
49. C₃×#894	C₂²	semidirect
50. C₃×#894	C₂²	semidirect
51. C₃×#885	C₂²	semidirect
52. C₃×#884	C₂²	semidirect
53. C₃×#884	C₂²	semidirect
54. C₃×#883	C₂²	semidirect
56. C₃×#882	C₂²	semidirect
57. C₃×#882	C₂²	semidirect
58. C₃×#67⋊C₄	C₂²	semidirect
59. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
60. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
61. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
62. C₃×#878	C₂²	semidirect
63. C₃×#878	C₂²	semidirect
64. C₃×#877	C₂²	semidirect
65. C₃×#876	C₂²	semidirect
66. C₃×#875	C₂²	semidirect
67. C₃×C₄×D₁₂	C₂²	semidirect
68. C₃×#872	C₂²	semidirect
81. C₃×#518	D₃	semidirect
82. C₃×#518	C₂×C₃	semidirect
84. #5804	C₂×C₃	semidirect
85. C₂×#937	C₂×C₃	semidirect
86. #5560	C₂×C₃	semidirect
87. #5556	C₂×C₃	semidirect
88. #5550	C₂×C₃	semidirect
89. #5547	C₂×C₃	semidirect
90. #5527	C₂×C₃	semidirect
91. #5490	C₂×C₃	semidirect
92. C₂×#882	C₂×C₃	semidirect
93. #5486	C₂×C₃	semidirect
94. C₂×D₃×C₂²⋊C₄	C₂×C₃	semidirect
95. #5483	C₂×C₃	semidirect
111. C₂²×C₃²×C₄	C₂³	semidirect
118. C₂×C₃×#67	C₂³	semidirect
129. C₂×C₃×C₄×D₃	C₂³	semidirect
130. C₂×C₃×Dic₆	C₂³	semidirect
131. C₃²×C₄⋊C₄	C₂³	semidirect
136. C₃²×C₂²⋊C₄	C₂³	semidirect
137. C₃²×C₄²	C₂³	semidirect
142. C₃×#217	C₂³	semidirect
149. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
150. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
151. C₃×C₄⋊Dic₃	C₂³	semidirect
152. C₃×Dic₃⋊C₄	C₂³	semidirect
153. C₃×Dic₃⋊C₄	C₂³	semidirect
154. C₃×Dic₃⋊C₄	C₂³	semidirect
155. C₃×Dic₃⋊C₄	C₂³	semidirect
156. C₃×C₄×Dic₃	C₂³	semidirect
169. C₂²×#67	C₂²×C₃	semidirect
170. C₂×#235	C₂²×C₃	semidirect
171. C₂²×D₁₂	C₂²×C₃	semidirect
172. C₂²×C₄×D₃	C₂²×C₃	semidirect
205. C₃×C₄×D₄	C₂×D₃	semidirect
206. C₃×C₄×D₄	C₂×D₃	semidirect
207. C₃×C₄×D₄	C₂²×C₃	semidirect
208. C₃×C₄×D₄	C₂²×C₃	semidirect
212. C₃×#117	C₂×D₃	semidirect
213. C₃×#117	C₂²×C₃	semidirect
227. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
230. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
231. #953	C₂²×C₃	semidirect
234. #939	C₂²×C₃	semidirect
236. #937	C₂²×C₃	semidirect
237. #937	C₂²×C₃	semidirect
238. #937	C₂²×C₃	semidirect
239. #935	C₂²×C₃	semidirect
240. #930	C₂²×C₃	semidirect
241. #929	C₂²×C₃	semidirect
242. #929	C₂²×C₃	semidirect
243. C₄×#67	C₂²×C₃	semidirect
244. C₄×#67	C₂²×C₃	semidirect
245. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
246. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
247. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
248. #924	C₂²×C₃	semidirect
249. #898	C₂²×C₃	semidirect
250. #896	C₂²×C₃	semidirect
251. #894	C₂²×C₃	semidirect
252. #894	C₂²×C₃	semidirect
253. #885	C₂²×C₃	semidirect
254. #884	C₂²×C₃	semidirect
255. #884	C₂²×C₃	semidirect
256. #883	C₂²×C₃	semidirect
258. #882	C₂²×C₃	semidirect
259. #882	C₂²×C₃	semidirect
260. #67⋊C₄	C₂²×C₃	semidirect
261. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
262. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
263. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
264. #878	C₂²×C₃	semidirect
265. #878	C₂²×C₃	semidirect
266. #877	C₂²×C₃	semidirect
267. #876	C₂²×C₃	semidirect
268. #875	C₂²×C₃	semidirect
269. C₄×D₁₂	C₂²×C₃	semidirect
270. #872	C₂²×C₃	semidirect
274. C₂³×C₃²	#41	semidirect
332. #518	C₃×D₃	semidirect
389. C₂²×C₃×C₄	C₂²×D₃	semidirect
393. C₂²×C₃×C₄	C₂³×C₃	semidirect
400. C₂×#67	C₂³×C₃	semidirect
411. C₂×C₄×D₃	C₂³×C₃	semidirect
412. C₂×Dic₆	C₂³×C₃	semidirect
419. C₃×C₄⋊C₄	C₂²×D₃	semidirect
420. C₃×C₄⋊C₄	C₂³×C₃	semidirect
443. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
448. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
451. C₃×C₄²	C₂²×D₃	semidirect
452. C₃×C₄²	C₂³×C₃	semidirect
457. #217	C₂³×C₃	semidirect
464. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
465. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
466. C₄⋊Dic₃	C₂³×C₃	semidirect
467. Dic₃⋊C₄	C₂³×C₃	semidirect
468. Dic₃⋊C₄	C₂³×C₃	semidirect
469. Dic₃⋊C₄	C₂³×C₃	semidirect
470. Dic₃⋊C₄	C₂³×C₃	semidirect
471. C₄×Dic₃	C₂³×C₃	semidirect
539. C₄×D₄	C₂×C₃×D₃	semidirect
540. C₄×D₄	C₂×C₃×D₃	semidirect
543. #117	C₂×C₃×D₃	semidirect
554. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
585. C₂³×C₃	#235	semidirect
586. C₂³×C₃	C₃×#41	semidirect
715. C₂²×C₄	C₂²×C₃×D₃	semidirect
721. C₄⋊C₄	C₂²×C₃×D₃	semidirect
739. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
741. C₄²	C₂²×C₃×D₃	semidirect
816. C₃²	#3490	semidirect
836. C₂³	C₃×#235	semidirect
922. C₃	#85868	direct (N × H)
923. C₃	C₃×#3490	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#518	2
C₃×#5804	2
C₂×C₃×#937	2
C₃×#5560	2
C₃×#5556	2
C₃×#5550	2
C₃×#5547	2
C₃×#5527	2
C₃×#5490	2
C₂×C₃×#882	2
C₃×#5486	2
C₂×C₃×D₃×C₂²⋊C₄	2
C₃×#5483	2
C₃×#3490	3
#85868	3

Subgroups — C3×#85868 #11904840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85868 #11904840