Subgroups — C₃×#85913 #11904846

Order 1152.

2987 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#953	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5806	C₂	1	4	yes	maximal, complemented
5	C₃×#5804	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5798	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5593	C₂	1	4	yes	maximal, complemented
8	C₃×#5591	C₂	1	4	yes	maximal, complemented
9	C₃×#5587	C₂	1	4	yes	maximal, complemented
10	C₃×#5586	C₂	1	4	yes	maximal, complemented
11	C₃×#5495	C₂	1	4	yes	maximal, complemented
12	C₃×#5486	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	#85913	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
19	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#67	C₂²	1	2	yes	complemented
21	C₂³×C₃×Dic₃	C₂²	1	2	yes	complemented
22	C₂×C₃×#237	C₂²	1	4	yes	complemented
23	C₃²×#120	C₂²	1	4	yes	—
24	C₃²×#120	C₂²	1	2	yes	complemented
25	C₃²×#120	C₂²	1	2	yes	complemented
26	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₃×#953	C₂²	1	4	yes	—
29	C₃×#953	C₂²	1	2	yes	complemented
30	C₃×#953	C₂²	1	2	yes	complemented
31	C₃×#953	C₂²	1	2	yes	complemented
32	C₂×C₃×#217	C₂²	1	1	yes	characteristic
33	C₂×C₃×#217	C₂²	1	1	yes	characteristic
34	C₂×C₃×#217	C₂²	1	1	yes	characteristic
35	C₂×C₃×#217	C₂²	1	4	yes	complemented
36	C₂×C₃×#217	C₂²	1	4	yes	complemented
37	C₂×C₃×#217	C₂²	1	2	yes	complemented
38	C₂×C₃×#217	C₂²	1	2	yes	complemented
39	C₂×C₃×#217	C₂²	1	2	yes	complemented
40	C₃×#939	C₂²	1	4	yes	complemented
41	C₃×#939	C₂²	1	4	yes	complemented
42	C₃×#939	C₂²	1	4	yes	complemented
43	C₃×#938	C₂²	1	4	yes	complemented
44	C₃×#937	C₂²	1	2	yes	complemented
45	C₃×#936	C₂²	1	4	yes	complemented
46	C₃×#935	C₂²	1	4	yes	complemented
47	C₃×#935	C₂²	1	2	yes	complemented
48	C₃×#935	C₂²	1	4	yes	complemented
49	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
50	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
51	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
52	C₃×#929	C₂²	1	2	yes	complemented
53	C₃×C₄×#67	C₂²	1	4	yes	complemented
54	C₃×#926	C₂²	1	2	yes	complemented
55	C₃×#924	C₂²	1	4	yes	complemented
56	C₃×#886	C₂²	1	4	yes	complemented
57	C₃×#885	C₂²	1	4	yes	complemented
58	C₃×#883	C₂²	1	4	yes	complemented
59	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
60	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
61	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
62	C₃×#879	C₂²	1	4	yes	complemented
63	C₃×#879	C₂²	1	4	yes	complemented
64	C₃×#878	C₂²	1	4	yes	complemented
65	C₃×#878	C₂²	1	4	yes	complemented
66	C₃×#878	C₂²	1	4	yes	complemented
67	C₃×#877	C₂²	1	4	yes	complemented
68	C₃×#877	C₂²	1	2	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	—	2	1	no	—
78	C₂×C₃×#120	—	3	1	no	—
79	C₂×C₃×#120	D₃	1	1	yes	characteristic, complemented
80	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic, complemented
81	C₃×#518	—	3	1	no	—
82	C₃×#518	—	3	1	no	—
83	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
84	C₂×#953	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂²×#217	C₂×C₃	1	1	yes	characteristic, complemented
86	#5806	C₂×C₃	1	4	yes	complemented
87	#5804	C₂×C₃	1	1	yes	characteristic, complemented
88	#5798	C₂×C₃	1	1	yes	characteristic, complemented
89	#5593	C₂×C₃	1	4	yes	complemented
90	#5591	C₂×C₃	1	4	yes	complemented
91	#5587	C₂×C₃	1	4	yes	complemented
92	#5586	C₂×C₃	1	4	yes	complemented
93	#5495	C₂×C₃	1	4	yes	complemented
94	#5486	C₂×C₃	1	1	yes	characteristic, complemented
95	#5483	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂⁴×C₃²	—	2	4	no	—
97	C₂⁴×C₃²	—	4	4	no	—
98	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
99	C₂⁴×C₃²	C₂³	1	2	yes	—
100	C₂⁴×C₃²	C₂³	1	2	yes	—
101	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
102	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
103	C₂⁴×C₃²	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	—	4	4	no	—
107	C₂×C₃²×D₄	C₂³	1	2	yes	—
108	C₂×C₃²×D₄	C₂³	1	2	yes	—
109	C₂×C₃²×D₄	C₂³	1	4	yes	—
110	C₂×C₃²×D₄	C₂³	1	4	yes	—
111	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃²×C₄	C₂³	1	2	yes	—
113	C₂×C₃×#67	—	2	4	no	—
114	C₂×C₃×#67	—	4	4	no	—
115	C₂×C₃×#67	C₂³	1	2	yes	—
116	C₂×C₃×#67	C₂³	1	4	yes	—
117	C₂×C₃×#67	C₂³	1	2	yes	—
118	C₂×C₃×#67	C₂³	1	4	yes	—
119	C₂×C₃×#67	C₂³	1	4	yes	complemented
120	C₂²×C₃×Dic₃	—	4	4	no	—
121	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
122	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
123	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
124	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
125	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
126	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
127	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
128	C₃×#237	—	4	8	no	—
129	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
130	C₂×C₃×Dic₆	C₂³	1	4	yes	complemented
131	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₃×#217	C₂³	1	4	yes	—
136	C₃×#217	C₂³	1	2	yes	—
137	C₃×#217	C₂³	1	2	yes	—
138	C₃×#217	C₂³	1	2	yes	—
139	C₃×#217	C₂³	1	4	yes	—
140	C₃×#217	C₂³	1	4	yes	—
141	C₃×#217	C₂³	1	4	yes	—
142	C₃×#217	C₂³	1	2	yes	—
143	C₃×#217	C₂³	1	2	yes	—
144	C₃×#217	C₂³	1	2	yes	—
145	C₃×#217	C₂³	1	4	yes	complemented
146	C₃×#217	C₂³	1	4	yes	complemented
147	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
148	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
149	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
150	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
151	C₃×Dic₃⋊C₄	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×C₄×Dic₃	C₂³	1	4	yes	complemented
156	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
157	#3490	—	3	1	no	Sylow
158	C₂⁵×C₃	—	2	1	no	—
159	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
160	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₃×#41	—	3	4	no	—
162	C₂²×C₃×D₄	—	2	1	no	—
163	C₂²×C₃×D₄	—	2	2	no	—
164	C₂²×C₃×D₄	—	3	1	no	—
165	C₂²×C₃×D₄	—	3	2	no	—
166	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
168	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
169	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
170	C₂³×C₃×C₄	—	3	2	no	—
171	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
172	C₂²×#67	C₂²×C₃	1	2	yes	complemented
173	C₂³×Dic₃	C₂²×C₃	1	2	yes	complemented
174	C₂×#237	C₂²×C₃	1	4	yes	complemented
175	C₃×#126	—	3	4	no	—
176	C₃×#126	—	3	4	no	—
177	C₃×#124	—	3	4	no	—
178	C₃×#124	—	3	4	no	—
179	C₃×#123	—	3	4	no	—
180	C₃×#123	—	3	2	no	—
181	C₃×#123	—	3	4	no	—
182	C₃×#123	—	3	2	no	—
183	C₃×#123	—	3	4	no	—
184	C₃×#123	—	3	4	no	—
185	C₃×C₂²⋊Q₈	—	3	4	no	—
186	C₃×C₂²⋊Q₈	—	3	4	no	—
187	C₃×C₂²⋊Q₈	—	3	4	no	—
188	C₃×C₂²⋊Q₈	—	3	4	no	—
189	C₃×#121	—	3	4	no	—
190	C₃×#121	—	3	4	no	—
191	C₃×#121	—	3	4	no	—
192	C₃×#121	—	3	4	no	—
193	C₃×#120	—	2	4	no	—
194	C₃×#120	—	2	2	no	—
195	C₃×#120	—	2	2	no	—
196	C₃×#120	—	3	4	no	—
197	C₃×#120	—	3	2	no	—
198	C₃×#120	—	3	2	no	—
199	C₃×#120	—	3	2	no	—
200	C₃×#120	—	3	2	no	—
201	C₃×#120	C₂×D₃	1	4	yes	—
202	C₃×#120	C₂×D₃	1	2	yes	complemented
203	C₃×#120	C₂×D₃	1	2	yes	complemented
204	C₃×#120	C₂²×C₃	1	4	yes	—
205	C₃×#120	C₂²×C₃	1	2	yes	complemented
206	C₃×#120	C₂²×C₃	1	2	yes	complemented
207	C₃×C₄×D₄	—	3	4	no	—
208	C₃×C₄×D₄	—	3	4	no	—
209	C₃×C₄×D₄	—	3	4	no	—
210	C₃×C₄×D₄	—	3	4	no	—
211	C₃×C₄×D₄	—	3	4	no	—
212	C₃×C₄×D₄	—	3	4	no	—
213	C₃×#117	—	3	2	no	—
214	C₃×#117	—	3	2	no	—
215	C₃×#117	—	3	4	no	—
216	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
217	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
219	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
220	C₂×C₃×C₂²⋊C₄	—	3	1	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	—	3	2	no	—
226	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
227	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
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	4	yes	—
232	#953	C₂²×C₃	1	2	yes	complemented
233	#953	C₂²×C₃	1	2	yes	complemented
234	#953	C₂²×C₃	1	2	yes	complemented
235	C₂×#217	C₂²×C₃	1	1	yes	characteristic
236	C₂×#217	C₂²×C₃	1	1	yes	characteristic
237	C₂×#217	C₂²×C₃	1	1	yes	characteristic
238	C₂×#217	C₂²×C₃	1	4	yes	complemented
239	C₂×#217	C₂²×C₃	1	4	yes	complemented
240	C₂×#217	C₂²×C₃	1	2	yes	complemented
241	C₂×#217	C₂²×C₃	1	2	yes	complemented
242	C₂×#217	C₂²×C₃	1	2	yes	complemented
243	#939	C₂²×C₃	1	4	yes	complemented
244	#939	C₂²×C₃	1	4	yes	complemented
245	#939	C₂²×C₃	1	4	yes	complemented
246	#938	C₂²×C₃	1	4	yes	complemented
247	#937	C₂²×C₃	1	2	yes	complemented
248	#936	C₂²×C₃	1	4	yes	complemented
249	#935	C₂²×C₃	1	4	yes	complemented
250	#935	C₂²×C₃	1	2	yes	complemented
251	#935	C₂²×C₃	1	4	yes	complemented
252	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
253	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
254	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
255	#929	C₂²×C₃	1	2	yes	complemented
256	C₄×#67	C₂²×C₃	1	4	yes	complemented
257	#926	C₂²×C₃	1	2	yes	complemented
258	#924	C₂²×C₃	1	4	yes	complemented
259	#886	C₂²×C₃	1	4	yes	complemented
260	#885	C₂²×C₃	1	4	yes	complemented
261	#883	C₂²×C₃	1	4	yes	complemented
262	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
263	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
264	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
265	#879	C₂²×C₃	1	4	yes	complemented
266	#879	C₂²×C₃	1	4	yes	complemented
267	#878	C₂²×C₃	1	4	yes	complemented
268	#878	C₂²×C₃	1	4	yes	complemented
269	#878	C₂²×C₃	1	4	yes	complemented
270	#877	C₂²×C₃	1	2	yes	complemented
271	#877	C₂²×C₃	1	4	yes	complemented
272	C₂³×C₃²	—	2	4	no	—
273	C₂³×C₃²	—	2	2	no	—
274	C₂³×C₃²	—	2	4	no	—
275	C₂³×C₃²	—	2	4	no	—
276	C₂³×C₃²	—	2	4	no	—
277	C₂³×C₃²	—	2	2	no	—
278	C₂³×C₃²	—	2	4	no	—
279	C₂³×C₃²	—	2	2	no	—
280	C₂³×C₃²	—	4	2	no	—
281	C₂³×C₃²	—	4	2	no	—
282	C₂³×C₃²	—	4	2	no	—
283	C₂³×C₃²	—	4	2	no	—
284	C₂³×C₃²	—	4	2	no	—
285	C₂³×C₃²	—	4	16	no	—
286	C₂³×C₃²	#41	1	4	yes	complemented
287	C₂³×C₃²	C₂⁴	1	2	yes	—
288	C₂³×C₃²	C₂⁴	1	2	yes	—
289	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
290	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
291	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
292	C₂³×C₃²	C₂⁴	1	2	yes	—
293	C₂²×C₃×D₃	—	2	2	no	—
294	C₂²×C₃×D₃	—	4	2	no	—
295	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
296	C₃²×D₄	—	2	4	no	—
297	C₃²×D₄	—	2	4	no	—
298	C₃²×D₄	—	2	8	no	—
299	C₃²×D₄	—	4	4	no	—
300	C₂×C₃²×C₄	—	2	2	no	—
301	C₂×C₃²×C₄	—	4	2	no	—
302	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
303	C₂×C₃²×C₄	C₂⁴	1	4	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	—	2	8	no	—
311	C₂×C₃×Dic₃	—	4	4	no	—
312	C₂×C₃×Dic₃	—	4	2	no	—
313	C₂×C₃×Dic₃	—	4	4	no	—
314	C₂×C₃×Dic₃	—	4	2	no	—
315	C₂×C₃×Dic₃	—	4	2	no	—
316	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
317	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
318	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
319	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
320	C₃×C₄×D₃	—	4	4	no	—
321	C₃×Dic₆	—	4	4	no	—
322	#551	—	3	4	no	—
323	#551	—	3	4	no	—
324	#546	—	3	4	no	—
325	#546	—	3	4	no	—
326	#543	—	3	1	no	—
327	#538	—	3	4	no	—
328	#534	—	3	1	no	—
329	#525	—	3	4	no	—
330	C₂×#120	—	3	1	no	—
331	C₂×#120	C₃×D₃	1	1	yes	characteristic, complemented
332	#518	—	3	1	no	—
333	#518	—	3	1	no	—
334	C₂²×C₂²⋊C₄	—	3	1	no	—
335	C₂⁴×C₃	—	2	4	no	—
336	C₂⁴×C₃	—	2	4	no	—
337	C₂⁴×C₃	—	2	2	no	—
338	C₂⁴×C₃	—	2	1	no	—
339	C₂⁴×C₃	—	2	1	no	—
340	C₂⁴×C₃	—	2	2	no	—
341	C₂⁴×C₃	—	2	1	no	—
342	C₂⁴×C₃	—	2	1	no	—
343	C₂⁴×C₃	—	3	1	no	—
344	C₂⁴×C₃	—	4	4	no	—
345	C₂⁴×C₃	—	4	4	no	—
346	C₂⁴×C₃	—	4	4	no	—
347	C₂⁴×C₃	—	4	8	no	—
348	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
349	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
350	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
351	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
352	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
353	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
354	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
355	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
356	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
357	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
358	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
359	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
360	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
361	C₃×#41	—	12	8	no	—
362	C₂×C₃×Q₈	—	3	4	no	—
363	C₂×C₃×D₄	—	2	4	no	—
364	C₂×C₃×D₄	—	2	4	no	—
365	C₂×C₃×D₄	—	2	2	no	—
366	C₂×C₃×D₄	—	2	2	no	—
367	C₂×C₃×D₄	—	2	4	no	—
368	C₂×C₃×D₄	—	2	4	no	—
369	C₂×C₃×D₄	—	3	2	no	—
370	C₂×C₃×D₄	—	3	2	no	—
371	C₂×C₃×D₄	—	3	4	no	—
372	C₂×C₃×D₄	—	3	4	no	—
373	C₂×C₃×D₄	—	3	4	no	—
374	C₂×C₃×D₄	—	4	4	no	—
375	C₂×C₃×D₄	—	4	4	no	—
376	C₂×C₃×D₄	—	4	4	no	—
377	C₂×C₃×D₄	—	4	8	no	—
378	C₂×C₃×D₄	—	6	4	no	—
379	C₂×C₃×D₄	—	12	4	no	—
380	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
381	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
382	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
383	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
384	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
385	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
386	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
387	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
388	C₂²×C₃×C₄	—	2	1	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	3	1	no	—
391	C₂²×C₃×C₄	—	3	4	no	—
392	C₂²×C₃×C₄	—	3	2	no	—
393	C₂²×C₃×C₄	—	3	4	no	—
394	C₂²×C₃×C₄	—	3	2	no	—
395	C₂²×C₃×C₄	—	3	2	no	—
396	C₂²×C₃×C₄	—	3	4	no	—
397	C₂²×C₃×C₄	—	3	4	no	—
398	C₂²×C₃×C₄	—	12	4	no	—
399	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
401	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
403	C₂×#67	—	2	4	no	—
404	C₂×#67	—	4	4	no	—
405	C₂×#67	C₂³×C₃	1	2	yes	—
406	C₂×#67	C₂³×C₃	1	4	yes	—
407	C₂×#67	C₂³×C₃	1	2	yes	—
408	C₂×#67	C₂³×C₃	1	4	yes	—
409	C₂×#67	C₂³×C₃	1	4	yes	complemented
410	C₂²×Dic₃	—	4	4	no	—
411	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
412	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
413	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
414	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
415	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
416	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
417	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
418	#237	—	4	8	no	—
419	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
420	C₂×Dic₆	C₂³×C₃	1	4	yes	complemented
421	C₃×C₄⋊C₄	—	3	4	no	—
422	C₃×C₄⋊C₄	—	3	4	no	—
423	C₃×C₄⋊C₄	—	3	4	no	—
424	C₃×C₄⋊C₄	—	3	4	no	—
425	C₃×C₄⋊C₄	—	3	4	no	—
426	C₃×C₄⋊C₄	—	3	4	no	—
427	C₃×C₂²⋊C₄	—	2	2	no	—
428	C₃×C₂²⋊C₄	—	2	2	no	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	2	4	no	—
431	C₃×C₂²⋊C₄	—	3	2	no	—
432	C₃×C₂²⋊C₄	—	3	2	no	—
433	C₃×C₂²⋊C₄	—	3	2	no	—
434	C₃×C₂²⋊C₄	—	3	2	no	—
435	C₃×C₂²⋊C₄	—	3	4	no	—
436	C₃×C₂²⋊C₄	—	3	4	no	—
437	C₃×C₂²⋊C₄	—	3	2	no	—
438	C₃×C₂²⋊C₄	—	3	4	no	—
439	C₃×C₂²⋊C₄	—	3	2	no	—
440	C₃×C₂²⋊C₄	—	3	4	no	—
441	C₃×C₂²⋊C₄	—	3	4	no	—
442	C₃×C₂²⋊C₄	—	3	4	no	—
443	C₃×C₂²⋊C₄	—	3	4	no	—
444	C₃×C₂²⋊C₄	—	3	4	no	—
445	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
446	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
447	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
448	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
449	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
450	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
451	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
453	C₃×C₄²	—	3	4	no	—
454	C₃×C₄²	—	3	4	no	—
455	#217	C₂³×C₃	1	4	yes	—
456	#217	C₂³×C₃	1	2	yes	—
457	#217	C₂³×C₃	1	2	yes	—
458	#217	C₂³×C₃	1	2	yes	—
459	#217	C₂³×C₃	1	4	yes	—
460	#217	C₂³×C₃	1	4	yes	—
461	#217	C₂³×C₃	1	4	yes	—
462	#217	C₂³×C₃	1	2	yes	—
463	#217	C₂³×C₃	1	2	yes	—
464	#217	C₂³×C₃	1	2	yes	—
465	#217	C₂³×C₃	1	4	yes	complemented
466	#217	C₂³×C₃	1	4	yes	complemented
467	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
468	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
469	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
470	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
471	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
472	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
473	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
474	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
475	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
476	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
477	C₂²×C₃²	—	2	2	no	—
478	C₂²×C₃²	—	2	2	no	—
479	C₂²×C₃²	—	2	8	no	—
480	C₂²×C₃²	—	2	2	no	—
481	C₂²×C₃²	—	2	2	no	—
482	C₂²×C₃²	—	2	2	no	—
483	C₂²×C₃²	—	2	2	no	—
484	C₂²×C₃²	—	2	2	no	—
485	C₂²×C₃²	—	2	2	no	—
486	C₂²×C₃²	—	2	4	no	—
487	C₂²×C₃²	—	2	2	no	—
488	C₂²×C₃²	—	4	4	no	—
489	C₂²×C₃²	—	4	8	no	—
490	C₂²×C₃²	—	4	8	no	—
491	C₂²×C₃²	—	4	4	no	—
492	C₂²×C₃²	—	8	2	no	—
493	C₂²×C₃²	C₂×#41	1	2	yes	—
494	C₂²×C₃²	C₂×#41	1	2	yes	—
495	C₂²×C₃²	C₂×#41	1	2	yes	—
496	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
497	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
498	C₂×C₃×D₃	—	2	2	no	—
499	C₂×C₃×D₃	—	2	4	no	—
500	C₂×C₃×D₃	—	8	2	no	—
501	C₃²×C₄	—	2	2	no	—
502	C₃²×C₄	—	2	4	no	—
503	C₃×Dic₃	—	2	2	no	—
504	C₃×Dic₃	—	2	4	no	—
505	C₃×Dic₃	—	2	4	no	—
506	C₃×Dic₃	—	2	4	no	—
507	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
508	C₂×#41	—	3	4	no	—
509	C₂²×D₄	—	3	1	no	—
510	C₂²×D₄	—	3	2	no	—
511	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
512	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
513	C₂³×C₄	—	3	2	no	—
514	#126	—	3	4	no	—
515	#126	—	3	4	no	—
516	#124	—	3	4	no	—
517	#124	—	3	4	no	—
518	#123	—	3	4	no	—
519	#123	—	3	2	no	—
520	#123	—	3	4	no	—
521	#123	—	3	2	no	—
522	#123	—	3	4	no	—
523	#123	—	3	4	no	—
524	C₂²⋊Q₈	—	3	4	no	—
525	C₂²⋊Q₈	—	3	4	no	—
526	C₂²⋊Q₈	—	3	4	no	—
527	C₂²⋊Q₈	—	3	4	no	—
528	#121	—	3	4	no	—
529	#121	—	3	4	no	—
530	#121	—	3	4	no	—
531	#121	—	3	4	no	—
532	#120	—	3	2	no	—
533	#120	—	3	2	no	—
534	#120	—	3	4	no	—
535	#120	—	3	2	no	—
536	#120	—	3	2	no	—
537	#120	C₂×C₃×D₃	1	4	yes	—
538	#120	C₂×C₃×D₃	1	2	yes	complemented
539	#120	C₂×C₃×D₃	1	2	yes	complemented
540	C₄×D₄	—	3	4	no	—
541	C₄×D₄	—	3	4	no	—
542	C₄×D₄	—	3	4	no	—
543	C₄×D₄	—	3	4	no	—
544	C₄×D₄	—	3	4	no	—
545	C₄×D₄	—	3	4	no	—
546	#117	—	3	2	no	—
547	#117	—	3	2	no	—
548	#117	—	3	4	no	—
549	C₂×C₂²⋊C₄	—	3	1	no	—
550	C₂×C₂²⋊C₄	—	3	1	no	—
551	C₂×C₂²⋊C₄	—	3	2	no	—
552	C₂×C₂²⋊C₄	—	3	4	no	—
553	C₂×C₂²⋊C₄	—	3	4	no	—
554	C₂×C₂²⋊C₄	—	3	1	no	—
555	C₂×C₂²⋊C₄	—	3	2	no	—
556	C₂×C₂²⋊C₄	—	3	2	no	—
557	C₂×C₂²⋊C₄	—	3	2	no	—
558	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
560	C₂³×C₃	—	2	2	no	—
561	C₂³×C₃	—	2	4	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	4	no	—
564	C₂³×C₃	—	2	8	no	—
565	C₂³×C₃	—	2	4	no	—
566	C₂³×C₃	—	2	4	no	—
567	C₂³×C₃	—	2	2	no	—
568	C₂³×C₃	—	2	4	no	—
569	C₂³×C₃	—	2	4	no	—
570	C₂³×C₃	—	2	4	no	—
571	C₂³×C₃	—	2	4	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	4	no	—
574	C₂³×C₃	—	2	4	no	—
575	C₂³×C₃	—	2	2	no	—
576	C₂³×C₃	—	2	2	no	—
577	C₂³×C₃	—	2	1	no	—
578	C₂³×C₃	—	2	2	no	—
579	C₂³×C₃	—	2	1	no	—
580	C₂³×C₃	—	2	1	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	4	no	—
584	C₂³×C₃	—	3	2	no	—
585	C₂³×C₃	—	4	2	no	—
586	C₂³×C₃	—	4	4	no	—
587	C₂³×C₃	—	4	4	no	—
588	C₂³×C₃	—	4	4	no	—
589	C₂³×C₃	—	4	2	no	—
590	C₂³×C₃	—	4	4	no	—
591	C₂³×C₃	—	4	2	no	—
592	C₂³×C₃	—	4	2	no	—
593	C₂³×C₃	—	4	2	no	—
594	C₂³×C₃	—	4	2	no	—
595	C₂³×C₃	—	4	2	no	—
596	C₂³×C₃	—	4	2	no	—
597	C₂³×C₃	—	4	2	no	—
598	C₂³×C₃	—	4	2	no	—
599	C₂³×C₃	—	4	2	no	—
600	C₂³×C₃	—	4	2	no	—
601	C₂³×C₃	—	4	2	no	—
602	C₂³×C₃	—	4	4	no	—
603	C₂³×C₃	—	4	4	no	—
604	C₂³×C₃	—	4	4	no	—
605	C₂³×C₃	—	4	4	no	—
606	C₂³×C₃	—	4	16	no	—
607	C₂³×C₃	—	4	16	no	—
608	C₂³×C₃	—	4	4	no	—
609	C₂³×C₃	—	4	32	no	—
610	C₂³×C₃	—	6	2	no	—
611	C₂³×C₃	—	12	2	no	—
612	C₂³×C₃	#237	1	4	yes	complemented
613	C₂³×C₃	C₃×#41	1	4	yes	complemented
614	C₂³×C₃	C₂³×D₃	1	2	yes	—
615	C₂³×C₃	C₂³×D₃	1	2	yes	—
616	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
617	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
618	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
619	C₂³×C₃	C₂³×D₃	1	2	yes	—
620	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
621	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
622	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
623	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
624	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
625	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
626	C₂²×D₃	—	2	2	no	—
627	C₂²×D₃	—	4	2	no	—
628	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
629	C₃×Q₈	—	12	4	no	—
630	C₃×D₄	—	2	4	no	—
631	C₃×D₄	—	2	4	no	—
632	C₃×D₄	—	2	8	no	—
633	C₃×D₄	—	2	4	no	—
634	C₃×D₄	—	2	4	no	—
635	C₃×D₄	—	2	8	no	—
636	C₃×D₄	—	4	4	no	—
637	C₃×D₄	—	4	4	no	—
638	C₃×D₄	—	4	8	no	—
639	C₃×D₄	—	4	4	no	—
640	C₃×D₄	—	4	4	no	—
641	C₃×D₄	—	4	8	no	—
642	C₃×D₄	—	6	4	no	—
643	C₃×D₄	—	6	4	no	—
644	C₃×D₄	—	6	8	no	—
645	C₃×D₄	—	12	4	no	—
646	C₃×D₄	—	12	4	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	4	no	—
651	C₂×C₃×C₄	—	3	2	no	—
652	C₂×C₃×C₄	—	3	4	no	—
653	C₂×C₃×C₄	—	3	4	no	—
654	C₂×C₃×C₄	—	3	4	no	—
655	C₂×C₃×C₄	—	4	2	no	—
656	C₂×C₃×C₄	—	4	2	no	—
657	C₂×C₃×C₄	—	4	2	no	—
658	C₂×C₃×C₄	—	4	4	no	—
659	C₂×C₃×C₄	—	6	2	no	—
660	C₂×C₃×C₄	—	6	8	no	—
661	C₂×C₃×C₄	—	12	4	no	—
662	C₂×C₃×C₄	—	12	2	no	—
663	C₂×C₃×C₄	—	12	4	no	—
664	C₂×C₃×C₄	—	12	2	no	—
665	C₂×C₃×C₄	—	12	2	no	—
666	C₂×C₃×C₄	—	12	4	no	—
667	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
668	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
669	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
670	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
671	#67	—	2	4	no	—
672	#67	—	2	4	no	—
673	#67	—	2	8	no	—
674	#67	—	4	4	no	—
675	#67	—	4	4	no	—
676	C₂×Dic₃	—	2	2	no	—
677	C₂×Dic₃	—	2	8	no	—
678	C₂×Dic₃	—	4	4	no	—
679	C₂×Dic₃	—	4	2	no	—
680	C₂×Dic₃	—	4	4	no	—
681	C₂×Dic₃	—	4	2	no	—
682	C₂×Dic₃	—	4	2	no	—
683	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
684	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
685	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
686	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
687	C₄×D₃	—	4	4	no	—
688	Dic₆	—	4	4	no	—
689	C₂×C₃²	—	2	2	no	—
690	C₂×C₃²	—	2	2	no	—
691	C₂×C₃²	—	2	2	no	—
692	C₂×C₃²	—	2	4	no	—
693	C₂×C₃²	—	4	2	no	—
694	C₂×C₃²	—	4	2	no	—
695	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
696	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
697	C₃×D₃	—	4	2	no	—
698	C₂⁴	—	2	4	no	—
699	C₂⁴	—	3	1	no	—
700	C₂⁴	—	4	4	no	—
701	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
702	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
703	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
704	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
705	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
706	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
707	#41	—	12	8	no	—
708	C₂×Q₈	—	3	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	3	2	no	—
711	C₂×D₄	—	3	2	no	—
712	C₂×D₄	—	3	4	no	—
713	C₂×D₄	—	3	4	no	—
714	C₂×D₄	—	3	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	6	4	no	—
717	C₂×D₄	—	12	4	no	—
718	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
719	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
720	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
721	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
722	C₂²×C₄	—	3	1	no	—
723	C₂²×C₄	—	3	4	no	—
724	C₂²×C₄	—	3	2	no	—
725	C₂²×C₄	—	3	4	no	—
726	C₂²×C₄	—	3	2	no	—
727	C₂²×C₄	—	3	2	no	—
728	C₂²×C₄	—	3	4	no	—
729	C₂²×C₄	—	3	4	no	—
730	C₂²×C₄	—	12	4	no	—
731	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
732	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
733	C₄⋊C₄	—	3	4	no	—
734	C₄⋊C₄	—	3	4	no	—
735	C₄⋊C₄	—	3	4	no	—
736	C₄⋊C₄	—	3	4	no	—
737	C₄⋊C₄	—	3	4	no	—
738	C₄⋊C₄	—	3	4	no	—
739	C₂²⋊C₄	—	3	2	no	—
740	C₂²⋊C₄	—	3	2	no	—
741	C₂²⋊C₄	—	3	2	no	—
742	C₂²⋊C₄	—	3	2	no	—
743	C₂²⋊C₄	—	3	4	no	—
744	C₂²⋊C₄	—	3	4	no	—
745	C₂²⋊C₄	—	3	2	no	—
746	C₂²⋊C₄	—	3	4	no	—
747	C₂²⋊C₄	—	3	2	no	—
748	C₂²⋊C₄	—	3	4	no	—
749	C₂²⋊C₄	—	3	4	no	—
750	C₂²⋊C₄	—	3	4	no	—
751	C₂²⋊C₄	—	3	4	no	—
752	C₂²⋊C₄	—	3	4	no	—
753	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
754	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
755	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
756	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
757	C₄²	—	3	4	no	—
758	C₄²	—	3	4	no	—
759	C₂²×C₃	—	2	4	no	—
760	C₂²×C₃	—	2	8	no	—
761	C₂²×C₃	—	2	8	no	—
762	C₂²×C₃	—	2	2	no	—
763	C₂²×C₃	—	2	2	no	—
764	C₂²×C₃	—	2	2	no	—
765	C₂²×C₃	—	2	2	no	—
766	C₂²×C₃	—	2	2	no	—
767	C₂²×C₃	—	2	2	no	—
768	C₂²×C₃	—	2	2	no	—
769	C₂²×C₃	—	2	2	no	—
770	C₂²×C₃	—	2	2	no	—
771	C₂²×C₃	—	2	2	no	—
772	C₂²×C₃	—	2	4	no	—
773	C₂²×C₃	—	2	2	no	—
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	2	4	no	—
776	C₂²×C₃	—	2	2	no	—
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	4	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	2	no	—
785	C₂²×C₃	—	2	2	no	—
786	C₂²×C₃	—	2	4	no	—
787	C₂²×C₃	—	2	1	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	4	2	no	—
790	C₂²×C₃	—	4	2	no	—
791	C₂²×C₃	—	4	2	no	—
792	C₂²×C₃	—	4	2	no	—
793	C₂²×C₃	—	4	2	no	—
794	C₂²×C₃	—	4	2	no	—
795	C₂²×C₃	—	4	4	no	—
796	C₂²×C₃	—	4	8	no	—
797	C₂²×C₃	—	4	4	no	—
798	C₂²×C₃	—	4	4	no	—
799	C₂²×C₃	—	4	8	no	—
800	C₂²×C₃	—	4	8	no	—
801	C₂²×C₃	—	4	8	no	—
802	C₂²×C₃	—	4	8	no	—
803	C₂²×C₃	—	4	8	no	—
804	C₂²×C₃	—	4	16	no	—
805	C₂²×C₃	—	4	4	no	—
806	C₂²×C₃	—	4	4	no	—
807	C₂²×C₃	—	4	16	no	—
808	C₂²×C₃	—	4	8	no	—
809	C₂²×C₃	—	6	2	no	—
810	C₂²×C₃	—	6	4	no	—
811	C₂²×C₃	—	8	2	no	—
812	C₂²×C₃	—	8	2	no	—
813	C₂²×C₃	—	8	4	no	—
814	C₂²×C₃	—	24	2	no	—
815	C₂²×C₃	C₂×#237	1	2	yes	—
816	C₂²×C₃	C₂×#237	1	2	yes	—
817	C₂²×C₃	C₂×#237	1	2	yes	—
818	C₂²×C₃	#1004	1	4	yes	—
819	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
820	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
821	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
822	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
823	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
824	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
825	C₂×D₃	—	2	2	no	—
826	C₂×D₃	—	2	4	no	—
827	C₂×D₃	—	8	2	no	—
828	C₃×C₄	—	2	2	no	—
829	C₃×C₄	—	2	4	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	2	4	no	—
832	C₃×C₄	—	4	2	no	—
833	C₃×C₄	—	4	4	no	—
834	C₃×C₄	—	6	2	no	—
835	C₃×C₄	—	6	4	no	—
836	C₃×C₄	—	6	4	no	—
837	C₃×C₄	—	6	4	no	—
838	Dic₃	—	2	2	no	—
839	Dic₃	—	2	4	no	—
840	Dic₃	—	2	4	no	—
841	Dic₃	—	2	4	no	—
842	C₃²	#3490	1	1	yes	characteristic, complemented, Sylow
843	C₂³	—	2	2	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	4	no	—
846	C₂³	—	2	4	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	4	no	—
849	C₂³	—	2	4	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	3	2	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	16	no	—
858	C₂³	—	6	2	no	—
859	C₂³	—	12	2	no	—
860	C₂³	C₃×#237	1	4	yes	complemented
861	C₂³	C₂³×C₃×D₃	1	2	yes	—
862	C₂³	C₂³×C₃×D₃	1	2	yes	—
863	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
864	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
865	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
866	C₂³	C₂³×C₃×D₃	1	2	yes	—
867	Q₈	—	12	4	no	—
868	D₄	—	2	4	no	—
869	D₄	—	2	4	no	—
870	D₄	—	2	8	no	—
871	D₄	—	4	4	no	—
872	D₄	—	6	4	no	—
873	D₄	—	6	4	no	—
874	D₄	—	6	8	no	—
875	D₄	—	12	4	no	—
876	D₄	—	12	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	3	2	no	—
879	C₂×C₄	—	3	4	no	—
880	C₂×C₄	—	3	4	no	—
881	C₂×C₄	—	3	4	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	—	6	2	no	—
884	C₂×C₄	—	6	8	no	—
885	C₂×C₄	—	12	4	no	—
886	C₂×C₄	—	12	2	no	—
887	C₂×C₄	—	12	4	no	—
888	C₂×C₄	—	12	2	no	—
889	C₂×C₄	—	12	2	no	—
890	C₂×C₄	—	12	4	no	—
891	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
892	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
893	C₂×C₃	—	2	4	no	—
894	C₂×C₃	—	2	2	no	—
895	C₂×C₃	—	2	2	no	—
896	C₂×C₃	—	2	4	no	—
897	C₂×C₃	—	2	2	no	—
898	C₂×C₃	—	2	2	no	—
899	C₂×C₃	—	2	4	no	—
900	C₂×C₃	—	2	2	no	—
901	C₂×C₃	—	2	2	no	—
902	C₂×C₃	—	2	1	no	—
903	C₂×C₃	—	2	2	no	—
904	C₂×C₃	—	4	2	no	—
905	C₂×C₃	—	4	4	no	—
906	C₂×C₃	—	4	2	no	—
907	C₂×C₃	—	4	4	no	—
908	C₂×C₃	—	4	2	no	—
909	C₂×C₃	—	4	2	no	—
910	C₂×C₃	—	4	2	no	—
911	C₂×C₃	—	4	2	no	—
912	C₂×C₃	—	8	2	no	—
913	C₂×C₃	—	12	2	no	—
914	C₂×C₃	C₂²×#237	1	1	yes	characteristic
915	C₂×C₃	C₂×#1004	1	2	yes	—
916	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
917	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
918	D₃	—	4	2	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	4	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	4	4	no	—
931	C₂²	—	4	8	no	—
932	C₂²	—	4	8	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	6	2	no	—
935	C₂²	—	6	4	no	—
936	C₂²	—	8	2	no	—
937	C₂²	—	24	2	no	—
938	C₂²	C₂×C₃×#237	1	2	yes	—
939	C₂²	C₂×C₃×#237	1	2	yes	—
940	C₂²	C₂×C₃×#237	1	2	yes	—
941	C₂²	C₃×#1004	1	4	yes	—
942	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
943	C₄	—	2	2	no	—
944	C₄	—	2	4	no	—
945	C₄	—	6	2	no	—
946	C₄	—	6	4	no	—
947	C₄	—	6	4	no	—
948	C₄	—	6	4	no	—
949	C₃	—	2	1	no	—
950	C₃	#85913	1	1	yes	characteristic, direct product factor
951	C₃	C₃×#3490	1	1	yes	characteristic, complemented
952	C₂	—	2	2	no	—
953	C₂	—	2	4	no	—
954	C₂	—	2	2	no	—
955	C₂	—	2	2	no	—
956	C₂	—	4	2	no	—
957	C₂	—	4	2	no	—
958	C₂	—	12	2	no	—
959	C₂	C₂²×C₃×#237	1	1	yes	characteristic
960	C₂	C₂×C₃×#1004	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#120	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×#120	D₃
hypocenter	C₃	C₃×#3490
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#120	C₂	semidirect
2. C₂×C₃×#953	C₂	semidirect
3. C₂²×C₃×#217	C₂	semidirect
4. C₃×#5806	C₂	semidirect
5. C₃×#5804	C₂	semidirect
6. C₃×#5798	C₂	semidirect
7. C₃×#5593	C₂	semidirect
8. C₃×#5591	C₂	semidirect
9. C₃×#5587	C₂	semidirect
10. C₃×#5586	C₂	semidirect
11. C₃×#5495	C₂	semidirect
12. C₃×#5486	C₂	semidirect
13. C₃×#5483	C₂	semidirect
15. #85913	C₃	direct (N × H)
18. C₂²×C₃²×D₄	C₂²	semidirect
20. C₂²×C₃×#67	C₂²	semidirect
21. C₂³×C₃×Dic₃	C₂²	semidirect
22. C₂×C₃×#237	C₂²	semidirect
24. C₃²×#120	C₂²	semidirect
25. C₃²×#120	C₂²	semidirect
27. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
29. C₃×#953	C₂²	semidirect
30. C₃×#953	C₂²	semidirect
31. C₃×#953	C₂²	semidirect
35. C₂×C₃×#217	C₂²	semidirect
36. C₂×C₃×#217	C₂²	semidirect
37. C₂×C₃×#217	C₂²	semidirect
38. C₂×C₃×#217	C₂²	semidirect
39. C₂×C₃×#217	C₂²	semidirect
40. C₃×#939	C₂²	semidirect
41. C₃×#939	C₂²	semidirect
42. C₃×#939	C₂²	semidirect
43. C₃×#938	C₂²	semidirect
44. C₃×#937	C₂²	semidirect
45. C₃×#936	C₂²	semidirect
46. C₃×#935	C₂²	semidirect
47. C₃×#935	C₂²	semidirect
48. C₃×#935	C₂²	semidirect
49. C₃×D₄×Dic₃	C₂²	semidirect
50. C₃×D₄×Dic₃	C₂²	semidirect
51. C₃×D₄×Dic₃	C₂²	semidirect
52. C₃×#929	C₂²	semidirect
53. C₃×C₄×#67	C₂²	semidirect
54. C₃×#926	C₂²	semidirect
55. C₃×#924	C₂²	semidirect
56. C₃×#886	C₂²	semidirect
57. C₃×#885	C₂²	semidirect
58. C₃×#883	C₂²	semidirect
59. C₃×#67⋊C₄	C₂²	semidirect
60. C₃×#67⋊C₄	C₂²	semidirect
61. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
62. C₃×#879	C₂²	semidirect
63. C₃×#879	C₂²	semidirect
64. C₃×#878	C₂²	semidirect
65. C₃×#878	C₂²	semidirect
66. C₃×#878	C₂²	semidirect
67. C₃×#877	C₂²	semidirect
68. C₃×#877	C₂²	semidirect
79. C₂×C₃×#120	D₃	semidirect
80. C₂×C₃×#120	C₂×C₃	semidirect
84. C₂×#953	C₂×C₃	semidirect
85. C₂²×#217	C₂×C₃	semidirect
86. #5806	C₂×C₃	semidirect
87. #5804	C₂×C₃	semidirect
88. #5798	C₂×C₃	semidirect
89. #5593	C₂×C₃	semidirect
90. #5591	C₂×C₃	semidirect
91. #5587	C₂×C₃	semidirect
92. #5586	C₂×C₃	semidirect
93. #5495	C₂×C₃	semidirect
94. #5486	C₂×C₃	semidirect
95. #5483	C₂×C₃	semidirect
119. C₂×C₃×#67	C₂³	semidirect
127. C₂²×C₃×Dic₃	C₂³	semidirect
129. C₂×C₃×C₄×D₃	C₂³	semidirect
130. C₂×C₃×Dic₆	C₂³	semidirect
145. C₃×#217	C₂³	semidirect
146. C₃×#217	C₂³	semidirect
147. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
148. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
149. C₃×C₄⋊Dic₃	C₂³	semidirect
150. C₃×C₄⋊Dic₃	C₂³	semidirect
151. C₃×Dic₃⋊C₄	C₂³	semidirect
152. C₃×Dic₃⋊C₄	C₂³	semidirect
153. C₃×Dic₃⋊C₄	C₂³	semidirect
154. C₃×Dic₃⋊C₄	C₂³	semidirect
155. C₃×C₄×Dic₃	C₂³	semidirect
156. C₃×C₄×Dic₃	C₂³	semidirect
167. C₂²×C₃×D₄	C₂×D₃	semidirect
169. C₂²×C₃×D₄	C₂²×C₃	semidirect
172. C₂²×#67	C₂²×C₃	semidirect
173. C₂³×Dic₃	C₂²×C₃	semidirect
174. C₂×#237	C₂²×C₃	semidirect
202. C₃×#120	C₂×D₃	semidirect
203. C₃×#120	C₂×D₃	semidirect
205. C₃×#120	C₂²×C₃	semidirect
206. C₃×#120	C₂²×C₃	semidirect
228. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
230. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
232. #953	C₂²×C₃	semidirect
233. #953	C₂²×C₃	semidirect
234. #953	C₂²×C₃	semidirect
238. C₂×#217	C₂²×C₃	semidirect
239. C₂×#217	C₂²×C₃	semidirect
240. C₂×#217	C₂²×C₃	semidirect
241. C₂×#217	C₂²×C₃	semidirect
242. C₂×#217	C₂²×C₃	semidirect
243. #939	C₂²×C₃	semidirect
244. #939	C₂²×C₃	semidirect
245. #939	C₂²×C₃	semidirect
246. #938	C₂²×C₃	semidirect
247. #937	C₂²×C₃	semidirect
248. #936	C₂²×C₃	semidirect
249. #935	C₂²×C₃	semidirect
250. #935	C₂²×C₃	semidirect
251. #935	C₂²×C₃	semidirect
252. D₄×Dic₃	C₂²×C₃	semidirect
253. D₄×Dic₃	C₂²×C₃	semidirect
254. D₄×Dic₃	C₂²×C₃	semidirect
255. #929	C₂²×C₃	semidirect
256. C₄×#67	C₂²×C₃	semidirect
257. #926	C₂²×C₃	semidirect
258. #924	C₂²×C₃	semidirect
259. #886	C₂²×C₃	semidirect
260. #885	C₂²×C₃	semidirect
261. #883	C₂²×C₃	semidirect
262. #67⋊C₄	C₂²×C₃	semidirect
263. #67⋊C₄	C₂²×C₃	semidirect
264. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
265. #879	C₂²×C₃	semidirect
266. #879	C₂²×C₃	semidirect
267. #878	C₂²×C₃	semidirect
268. #878	C₂²×C₃	semidirect
269. #878	C₂²×C₃	semidirect
270. #877	C₂²×C₃	semidirect
271. #877	C₂²×C₃	semidirect
286. C₂³×C₃²	#41	semidirect
331. C₂×#120	C₃×D₃	semidirect
409. C₂×#67	C₂³×C₃	semidirect
417. C₂²×Dic₃	C₂³×C₃	semidirect
419. C₂×C₄×D₃	C₂³×C₃	semidirect
420. C₂×Dic₆	C₂³×C₃	semidirect
465. #217	C₂³×C₃	semidirect
466. #217	C₂³×C₃	semidirect
467. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
468. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
469. C₄⋊Dic₃	C₂³×C₃	semidirect
470. C₄⋊Dic₃	C₂³×C₃	semidirect
471. Dic₃⋊C₄	C₂³×C₃	semidirect
472. Dic₃⋊C₄	C₂³×C₃	semidirect
473. Dic₃⋊C₄	C₂³×C₃	semidirect
474. Dic₃⋊C₄	C₂³×C₃	semidirect
475. C₄×Dic₃	C₂³×C₃	semidirect
476. C₄×Dic₃	C₂³×C₃	semidirect
512. C₂²×D₄	C₂×C₃×D₃	semidirect
538. #120	C₂×C₃×D₃	semidirect
539. #120	C₂×C₃×D₃	semidirect
559. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
612. C₂³×C₃	#237	semidirect
613. C₂³×C₃	C₃×#41	semidirect
842. C₃²	#3490	semidirect
860. C₂³	C₃×#237	semidirect
950. C₃	#85913	direct (N × H)
951. 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
C₂×C₃²×#120	2
C₂×C₃×#953	2
C₂²×C₃×#217	2
C₃×#5806	2
C₃×#5804	2
C₃×#5798	2
C₃×#5593	2
C₃×#5591	2
C₃×#5587	2
C₃×#5586	2
C₃×#5495	2
C₃×#5486	2
C₃×#5483	2
C₃×#3490	3
#85913	3

Subgroups — C3×#85913 #11904846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85913 #11904846