Subgroups — C₃×#60587 #10679194

Order 768.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3126	C₂	1	2	yes	maximal, complemented
4	C₃×#3122	C₂	1	2	yes	maximal, complemented
5	C₃×#3121	C₂	1	2	yes	maximal, complemented
6	C₃×#3118	C₂	1	2	yes	maximal, complemented
7	C₃×#3115	C₂	1	2	yes	maximal, complemented
8	C₃×#3111	C₂	1	2	yes	maximal, complemented
9	C₃×#3106	C₂	1	2	yes	maximal, complemented
10	C₃×#3102	C₂	1	2	yes	maximal, complemented
11	C₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#60587	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₃×#135	C₂²	1	1	yes	characteristic
30	C₃×#555	—	2	1	no	—
31	C₃×#553	—	2	1	no	—
32	C₃×#553	—	2	1	no	—
33	C₃×#551	—	2	2	no	—
34	C₃×#547	—	2	1	no	—
35	C₃×#546	—	2	2	no	—
36	C₃×#544	C₂²	1	1	yes	characteristic, complemented
37	C₃×#542	C₂²	1	2	yes	—
38	C₃×#540	C₂²	1	2	yes	—
39	C₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₃×#532	C₂²	1	2	yes	complemented
41	C₃×#529	C₂²	1	2	yes	complemented
42	C₃×#525	C₂²	1	1	yes	characteristic
43	C₂×C₃×#121	C₂²	1	1	yes	characteristic
44	C₃×#520	—	2	1	no	—
45	C₃×#520	—	2	1	no	—
46	C₃×#520	C₂²	1	1	yes	characteristic
47	C₃×#520	C₂²	1	1	yes	characteristic
48	C₃×#520	C₂²	1	1	yes	characteristic
49	C₃×#520	C₂²	1	1	yes	characteristic
50	C₃×#520	C₂²	1	1	yes	characteristic, complemented
51	C₃×#519	C₂²	1	2	yes	complemented
52	C₃×#518	—	2	2	no	—
53	C₃×#518	C₂²	1	2	yes	complemented
54	C₃×#518	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₄×#41	—	2	2	no	—
56	C₃×C₄×#41	C₂²	1	2	yes	complemented
57	C₃×C₄×#41	C₂²	1	2	yes	complemented
58	C₂×C₃×#117	—	2	1	no	—
59	C₂×C₃×#117	—	2	1	no	—
60	C₂×C₃×#117	C₂²	1	1	yes	characteristic
61	C₂×C₃×#117	C₂²	1	1	yes	characteristic
62	C₃×#485	C₂²	1	2	yes	complemented
63	C₃×#485	C₂²	1	2	yes	complemented
64	C₃×#482	C₂²	1	2	yes	—
65	C₃×#482	C₂²	1	2	yes	—
66	C₃×#482	C₂²	1	2	yes	complemented
67	C₃×#482	C₂²	1	2	yes	complemented
68	C₃×#482	C₂²	1	2	yes	complemented
69	C₃×#482	C₂²	1	2	yes	complemented
70	C₃×#479	C₂²	1	2	yes	complemented
71	C₃×#479	C₂²	1	2	yes	complemented
72	C₃×#478	C₂²	1	2	yes	complemented
73	C₃×#478	C₂²	1	2	yes	complemented
74	C₃×#477	C₂²	1	2	yes	complemented
75	C₃×#476	C₂²	1	2	yes	complemented
76	C₃×#475	C₂²	1	2	yes	complemented
77	C₃×#474	C₂²	1	2	yes	complemented
78	C₃×#464	C₂²	1	2	yes	complemented
79	C₃×#464	C₂²	1	2	yes	complemented
80	C₃×#463	C₂²	1	2	yes	complemented
81	C₃×#463	C₂²	1	2	yes	complemented
82	C₃×#460	C₂²	1	2	yes	complemented
83	C₃×#460	C₂²	1	2	yes	complemented
84	C₃×#459	C₂²	1	2	yes	complemented
85	C₃×#459	C₂²	1	2	yes	complemented
86	C₃×#452	C₂²	1	1	yes	characteristic, complemented
87	C₃×#452	C₂²	1	1	yes	characteristic, complemented
88	C₃×#451	C₂²	1	1	yes	characteristic, complemented
89	C₃×#450	C₂²	1	1	yes	characteristic, complemented
90	C₃×#449	C₂²	1	2	yes	—
91	C₃×#449	C₂²	1	2	yes	—
92	C₃×#449	C₂²	1	1	yes	characteristic, complemented
93	C₃×#449	C₂²	1	1	yes	characteristic, complemented
94	C₃×#448	C₂²	1	2	yes	—
95	C₃×#448	C₂²	1	1	yes	characteristic, complemented
96	C₃×#447	C₂²	1	2	yes	—
97	C₃×#447	C₂²	1	1	yes	characteristic, complemented
98	C₃×#442	C₂²	1	2	yes	complemented
99	C₃×#442	C₂²	1	2	yes	complemented
100	C₃×#442	C₂²	1	2	yes	complemented
101	C₃×#441	C₂²	1	2	yes	complemented
102	C₃×#440	C₂²	1	2	yes	complemented
103	C₃×#440	C₂²	1	2	yes	complemented
104	C₃×#440	C₂²	1	2	yes	complemented
105	C₃×#440	C₂²	1	2	yes	complemented
106	C₃×C₄×Q₁₆	C₂²	1	2	yes	complemented
107	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
108	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
109	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
110	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
111	C₃×C₄×D₈	C₂²	1	2	yes	complemented
112	C₃×C₄×D₈	C₂²	1	2	yes	complemented
113	C₃×C₄×D₈	C₂²	1	2	yes	complemented
114	C₃×#433	C₂²	1	2	yes	complemented
115	C₃×#433	C₂²	1	2	yes	complemented
116	C₃×#432	C₂²	1	2	yes	complemented
117	C₃×#431	C₂²	1	2	yes	complemented
118	C₃×#428	C₂²	1	1	yes	characteristic, complemented
119	C₃×#428	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃×#107	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₃×#106	C₂²	1	1	yes	characteristic, complemented
122	C₃×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃×#424	C₂²	1	1	yes	characteristic, complemented
124	C₃×#417	C₂²	1	1	yes	characteristic
125	C₃×#417	C₂²	1	1	yes	characteristic
126	C₃×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃×#417	C₂²	1	1	yes	characteristic, complemented
128	C₃×#416	C₂²	1	1	yes	characteristic
129	C₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₃×#102	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃×#102	C₂²	1	1	yes	characteristic, complemented
132	C₃×#407	C₂²	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₃×#405	C₂²	1	1	yes	characteristic, complemented
136	#3494	C₂×C₃	1	1	yes	characteristic, complemented
137	#3428	C₂×C₃	1	1	yes	characteristic, complemented
138	#3126	C₂×C₃	1	2	yes	complemented
139	#3122	C₂×C₃	1	2	yes	complemented
140	#3121	C₂×C₃	1	2	yes	complemented
141	#3118	C₂×C₃	1	2	yes	complemented
142	#3115	C₂×C₃	1	2	yes	complemented
143	#3111	C₂×C₃	1	2	yes	complemented
144	#3106	C₂×C₃	1	2	yes	complemented
145	#3102	C₂×C₃	1	2	yes	complemented
146	#3093	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#482	C₂×C₃	1	1	yes	characteristic, complemented
148	#3084	C₂×C₃	1	1	yes	characteristic, complemented
149	#3083	C₂×C₃	1	1	yes	characteristic, complemented
150	#3045	C₂×C₃	1	1	yes	characteristic, complemented
151	#3045	C₂×C₃	1	1	yes	characteristic, complemented
152	#3006	C₂×C₃	1	1	yes	characteristic, complemented
153	#3002	C₂×C₃	1	1	yes	characteristic, complemented
154	#2952	C₂×C₃	1	1	yes	characteristic, complemented
155	#2951	C₂×C₃	1	1	yes	characteristic, complemented
156	#2946	C₂×C₃	1	1	yes	characteristic, complemented
157	#2946	C₂×C₃	1	1	yes	characteristic, complemented
158	#2924	C₂×C₃	1	1	yes	characteristic, complemented
159	C₂×C₃×#41	—	2	4	no	—
160	C₂×C₃×#41	—	2	4	no	—
161	C₂×C₃×#41	—	2	1	no	—
162	C₂×C₃×#41	—	2	1	no	—
163	C₂×C₃×#41	—	2	2	no	—
164	C₂×C₃×#41	C₂³	1	1	yes	characteristic
165	C₂×C₃×#41	C₂³	1	1	yes	characteristic
166	C₂×C₃×#41	C₂³	1	1	yes	characteristic
167	C₂×C₃×#41	C₂³	1	1	yes	characteristic
168	C₂×C₃×#41	C₂³	1	1	yes	characteristic
169	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
170	C₂²×C₃×D₄	—	2	1	no	—
171	C₂²×C₃×D₄	—	2	1	no	—
172	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
174	C₂³×C₃×C₄	—	2	1	no	—
175	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
176	C₃×AGL(1,ℤ/8)	—	2	4	no	—
177	C₃×AGL(1,ℤ/8)	—	2	4	no	—
178	C₃×#135	—	2	4	no	—
179	C₃×#135	—	2	4	no	—
180	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
181	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
182	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
183	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
184	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
185	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
186	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
187	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
188	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
189	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
190	C₂×C₃×D₈	C₂³	1	2	yes	—
191	C₂×C₃×D₈	C₂³	1	2	yes	—
192	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
193	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
194	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
195	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊Q₈	—	2	1	no	—
197	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
198	C₃×#127	C₂³	1	2	yes	—
199	C₃×#126	—	2	2	no	—
200	C₃×#126	—	2	2	no	—
201	C₃×#125	—	2	1	no	—
202	C₃×#125	C₂³	1	2	yes	—
203	C₃×#124	—	2	2	no	—
204	C₃×#124	—	2	2	no	—
205	C₃×#124	C₂³	1	2	yes	—
206	C₃×#123	—	2	1	no	—
207	C₃×#123	—	2	2	no	—
208	C₃×#123	—	2	2	no	—
209	C₃×#123	—	2	2	no	—
210	C₃×#123	—	2	2	no	—
211	C₃×C₂²⋊Q₈	—	2	2	no	—
212	C₃×C₂²⋊Q₈	—	2	2	no	—
213	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₃×#121	—	2	1	no	—
216	C₃×#121	—	2	1	no	—
217	C₃×#121	—	2	2	no	—
218	C₃×#121	—	2	1	no	—
219	C₃×#121	—	2	1	no	—
220	C₃×#121	—	2	2	no	—
221	C₃×#121	—	2	2	no	—
222	C₃×#121	C₂³	1	2	yes	—
223	C₃×#121	C₂³	1	1	yes	characteristic
224	C₃×#121	C₂³	1	2	yes	—
225	C₃×#121	C₂³	1	1	yes	characteristic
226	C₃×#120	—	2	1	no	—
227	C₃×#120	—	2	2	no	—
228	C₃×C₄×Q₈	—	2	2	no	—
229	C₃×C₄×Q₈	—	2	2	no	—
230	C₃×C₄×Q₈	C₂³	1	2	yes	—
231	C₃×C₄×Q₈	C₂³	1	2	yes	—
232	C₃×C₄×Q₈	C₂³	1	2	yes	—
233	C₃×C₄×Q₈	C₂³	1	2	yes	—
234	C₃×C₄×Q₈	C₂³	1	2	yes	—
235	C₃×C₄×D₄	—	2	2	no	—
236	C₃×C₄×D₄	—	2	2	no	—
237	C₃×C₄×D₄	—	2	2	no	—
238	C₃×C₄×D₄	—	2	2	no	—
239	C₃×C₄×D₄	—	2	1	no	—
240	C₃×C₄×D₄	—	2	1	no	—
241	C₃×C₄×D₄	—	2	2	no	—
242	C₃×C₄×D₄	—	2	2	no	—
243	C₃×C₄×D₄	—	2	2	no	—
244	C₃×C₄×D₄	—	2	1	no	—
245	C₃×C₄×D₄	—	2	1	no	—
246	C₃×C₄×D₄	—	2	2	no	—
247	C₃×C₄×D₄	—	2	2	no	—
248	C₃×C₄×D₄	—	2	2	no	—
249	C₃×C₄×D₄	—	2	2	no	—
250	C₃×C₄×D₄	—	2	2	no	—
251	C₃×C₄×D₄	—	2	2	no	—
252	C₃×C₄×D₄	C₂³	1	2	yes	—
253	C₃×C₄×D₄	C₂³	1	2	yes	—
254	C₃×C₄×D₄	C₂³	1	2	yes	—
255	C₃×C₄×D₄	C₂³	1	2	yes	—
256	C₃×C₄×D₄	C₂³	1	2	yes	—
257	C₃×C₄×D₄	C₂³	1	2	yes	—
258	C₃×C₄×D₄	C₂³	1	2	yes	—
259	C₃×#117	—	2	1	no	—
260	C₃×#117	—	2	1	no	—
261	C₃×#117	—	2	1	no	—
262	C₃×#117	—	2	1	no	—
263	C₃×#117	—	2	1	no	—
264	C₃×#117	—	2	1	no	—
265	C₃×#117	—	2	1	no	—
266	C₃×#117	—	2	2	no	—
267	C₃×#117	—	2	2	no	—
268	C₃×#117	—	2	2	no	—
269	C₃×#117	—	2	2	no	—
270	C₃×#117	—	2	2	no	—
271	C₃×#117	D₄	1	1	yes	characteristic
272	C₃×#117	D₄	1	1	yes	characteristic
273	C₃×#117	D₄	1	2	yes	—
274	C₃×#117	C₂³	1	1	yes	characteristic
275	C₃×#117	C₂³	1	2	yes	—
276	C₃×#117	C₂³	1	2	yes	—
277	C₃×#117	C₂³	1	1	yes	characteristic
278	C₃×#117	C₂³	1	1	yes	characteristic
279	C₃×#117	C₂³	1	2	yes	—
280	C₂×C₃×C₄⋊C₄	—	2	1	no	—
281	C₂×C₃×C₄⋊C₄	—	2	1	no	—
282	C₂×C₃×C₄⋊C₄	—	2	1	no	—
283	C₂×C₃×C₄⋊C₄	—	2	1	no	—
284	C₂×C₃×C₄⋊C₄	—	2	1	no	—
285	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
286	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
287	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
296	C₂×C₃×C₄²	—	2	1	no	—
297	C₂×C₃×C₄²	—	2	2	no	—
298	C₂×C₃×C₄²	—	2	2	no	—
299	C₂×C₃×C₄²	C₂³	1	2	yes	—
300	C₃×#107	C₂³	1	2	yes	—
301	C₃×#107	C₂³	1	2	yes	—
302	C₃×#107	C₂³	1	2	yes	—
303	C₃×#107	C₂³	1	2	yes	—
304	C₃×#106	C₂³	1	2	yes	—
305	C₃×#106	C₂³	1	2	yes	—
306	C₃×#106	C₂³	1	2	yes	—
307	C₃×#106	C₂³	1	2	yes	—
308	C₃×C₄⋊C₈	C₂³	1	2	yes	—
309	C₃×C₄⋊C₈	C₂³	1	2	yes	—
310	C₃×C₄⋊C₈	C₂³	1	2	yes	—
311	C₃×C₄⋊C₈	C₂³	1	2	yes	—
312	C₃×#103	C₂³	1	1	yes	characteristic
313	C₃×#103	C₂³	1	1	yes	characteristic
314	C₃×#103	C₂³	1	1	yes	characteristic
315	C₃×#103	C₂³	1	1	yes	characteristic
316	C₃×#103	C₂³	1	2	yes	—
317	C₃×#103	C₂³	1	2	yes	—
318	C₃×#103	C₂³	1	2	yes	—
319	C₃×#103	C₂³	1	2	yes	—
320	C₃×#102	C₂³	1	2	yes	—
321	C₃×#102	C₂³	1	2	yes	—
322	C₃×#102	C₂³	1	2	yes	—
323	C₃×#102	C₂³	1	2	yes	—
324	C₃×#102	C₂³	1	1	yes	characteristic
325	C₃×#102	C₂³	1	1	yes	characteristic
326	C₃×#102	C₂³	1	1	yes	characteristic
327	C₃×#102	C₂³	1	1	yes	characteristic
328	C₃×#102	C₂³	1	2	yes	—
329	C₃×#102	C₂³	1	2	yes	—
330	C₃×#102	C₂³	1	2	yes	—
331	C₃×#102	C₂³	1	2	yes	—
332	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃×#97	C₂³	1	2	yes	—
339	C₃×#97	C₂³	1	2	yes	—
340	C₃×C₄×C₈	C₂³	1	2	yes	—
341	C₃×C₄×C₈	C₂³	1	2	yes	—
342	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
343	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic
344	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic
345	C₂×#135	C₂²×C₃	1	1	yes	characteristic
346	C₂×#135	C₂²×C₃	1	1	yes	characteristic
347	#555	—	2	1	no	—
348	#553	—	2	1	no	—
349	#553	—	2	1	no	—
350	#551	—	2	2	no	—
351	#547	—	2	1	no	—
352	#546	—	2	2	no	—
353	#544	C₂²×C₃	1	1	yes	characteristic, complemented
354	#542	C₂²×C₃	1	2	yes	—
355	#540	C₂²×C₃	1	2	yes	—
356	#535	C₂²×C₃	1	1	yes	characteristic, complemented
357	#532	C₂²×C₃	1	2	yes	complemented
358	#529	C₂²×C₃	1	2	yes	complemented
359	#525	C₂²×C₃	1	1	yes	characteristic
360	C₂×#121	C₂²×C₃	1	1	yes	characteristic
361	#520	—	2	1	no	—
362	#520	—	2	1	no	—
363	#520	C₂²×C₃	1	1	yes	characteristic
364	#520	C₂²×C₃	1	1	yes	characteristic
365	#520	C₂²×C₃	1	1	yes	characteristic
366	#520	C₂²×C₃	1	1	yes	characteristic
367	#520	C₂²×C₃	1	1	yes	characteristic, complemented
368	#519	C₂²×C₃	1	2	yes	complemented
369	#518	—	2	2	no	—
370	#518	C₂²×C₃	1	2	yes	complemented
371	#518	C₂²×C₃	1	1	yes	characteristic, complemented
372	C₄×#41	—	2	2	no	—
373	C₄×#41	C₂²×C₃	1	2	yes	complemented
374	C₄×#41	C₂²×C₃	1	2	yes	complemented
375	C₂×#117	—	2	1	no	—
376	C₂×#117	—	2	1	no	—
377	C₂×#117	C₂²×C₃	1	1	yes	characteristic
378	C₂×#117	C₂²×C₃	1	1	yes	characteristic
379	#485	C₂²×C₃	1	2	yes	complemented
380	#485	C₂²×C₃	1	2	yes	complemented
381	#482	C₂²×C₃	1	2	yes	—
382	#482	C₂²×C₃	1	2	yes	—
383	#482	C₂²×C₃	1	2	yes	complemented
384	#482	C₂²×C₃	1	2	yes	complemented
385	#482	C₂²×C₃	1	2	yes	complemented
386	#482	C₂²×C₃	1	2	yes	complemented
387	#479	C₂²×C₃	1	2	yes	complemented
388	#479	C₂²×C₃	1	2	yes	complemented
389	#478	C₂²×C₃	1	2	yes	complemented
390	#478	C₂²×C₃	1	2	yes	complemented
391	#477	C₂²×C₃	1	2	yes	complemented
392	#476	C₂²×C₃	1	2	yes	complemented
393	#475	C₂²×C₃	1	2	yes	complemented
394	#474	C₂²×C₃	1	2	yes	complemented
395	#464	C₂²×C₃	1	2	yes	complemented
396	#464	C₂²×C₃	1	2	yes	complemented
397	#463	C₂²×C₃	1	2	yes	complemented
398	#463	C₂²×C₃	1	2	yes	complemented
399	#460	C₂²×C₃	1	2	yes	complemented
400	#460	C₂²×C₃	1	2	yes	complemented
401	#459	C₂²×C₃	1	2	yes	complemented
402	#459	C₂²×C₃	1	2	yes	complemented
403	#452	C₂²×C₃	1	1	yes	characteristic, complemented
404	#452	C₂²×C₃	1	1	yes	characteristic, complemented
405	#451	C₂²×C₃	1	1	yes	characteristic, complemented
406	#450	C₂²×C₃	1	1	yes	characteristic, complemented
407	#449	C₂²×C₃	1	2	yes	—
408	#449	C₂²×C₃	1	2	yes	—
409	#449	C₂²×C₃	1	1	yes	characteristic, complemented
410	#449	C₂²×C₃	1	1	yes	characteristic, complemented
411	#448	C₂²×C₃	1	2	yes	—
412	#448	C₂²×C₃	1	1	yes	characteristic, complemented
413	#447	C₂²×C₃	1	2	yes	—
414	#447	C₂²×C₃	1	1	yes	characteristic, complemented
415	#442	C₂²×C₃	1	2	yes	complemented
416	#442	C₂²×C₃	1	2	yes	complemented
417	#442	C₂²×C₃	1	2	yes	complemented
418	#441	C₂²×C₃	1	2	yes	complemented
419	#440	C₂²×C₃	1	2	yes	complemented
420	#440	C₂²×C₃	1	2	yes	complemented
421	#440	C₂²×C₃	1	2	yes	complemented
422	#440	C₂²×C₃	1	2	yes	complemented
423	C₄×Q₁₆	C₂²×C₃	1	2	yes	complemented
424	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
425	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
426	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
427	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
428	C₄×D₈	C₂²×C₃	1	2	yes	complemented
429	C₄×D₈	C₂²×C₃	1	2	yes	complemented
430	C₄×D₈	C₂²×C₃	1	2	yes	complemented
431	#433	C₂²×C₃	1	2	yes	complemented
432	#433	C₂²×C₃	1	2	yes	complemented
433	#432	C₂²×C₃	1	2	yes	complemented
434	#431	C₂²×C₃	1	2	yes	complemented
435	#428	C₂²×C₃	1	1	yes	characteristic, complemented
436	#428	C₂²×C₃	1	1	yes	characteristic, complemented
437	C₂×#107	C₂²×C₃	1	1	yes	characteristic, complemented
438	C₂×#106	C₂²×C₃	1	1	yes	characteristic, complemented
439	#424	C₂²×C₃	1	1	yes	characteristic, complemented
440	#424	C₂²×C₃	1	1	yes	characteristic, complemented
441	#417	C₂²×C₃	1	1	yes	characteristic
442	#417	C₂²×C₃	1	1	yes	characteristic
443	#417	C₂²×C₃	1	1	yes	characteristic, complemented
444	#417	C₂²×C₃	1	1	yes	characteristic, complemented
445	#416	C₂²×C₃	1	1	yes	characteristic
446	#416	C₂²×C₃	1	1	yes	characteristic
447	C₂×#102	C₂²×C₃	1	1	yes	characteristic, complemented
448	C₂×#102	C₂²×C₃	1	1	yes	characteristic, complemented
449	#407	C₂²×C₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
451	#405	C₂²×C₃	1	1	yes	characteristic, complemented
452	#405	C₂²×C₃	1	1	yes	characteristic, complemented
453	C₂⁴×C₃	—	2	1	no	—
454	C₂⁴×C₃	—	2	1	no	—
455	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
456	C₃×#41	—	2	8	no	—
457	C₃×#41	—	2	8	no	—
458	C₃×#41	—	2	2	no	—
459	C₃×#41	—	2	2	no	—
460	C₃×#41	—	2	2	no	—
461	C₃×#41	—	2	2	no	—
462	C₃×#41	—	2	2	no	—
463	C₃×#41	—	2	2	no	—
464	C₃×#41	—	2	2	no	—
465	C₃×#41	—	2	2	no	—
466	C₃×#41	—	8	4	no	—
467	C₃×#41	#41	1	4	yes	complemented
468	C₃×#41	#41	1	4	yes	complemented
469	C₂×C₃×Q₈	—	2	2	no	—
470	C₂×C₃×Q₈	—	2	2	no	—
471	C₂×C₃×Q₈	—	2	1	no	—
472	C₂×C₃×Q₈	—	2	2	no	—
473	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
474	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
475	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
476	C₂×C₃×D₄	—	2	8	no	—
477	C₂×C₃×D₄	—	2	1	no	—
478	C₂×C₃×D₄	—	2	1	no	—
479	C₂×C₃×D₄	—	2	1	no	—
480	C₂×C₃×D₄	—	2	1	no	—
481	C₂×C₃×D₄	—	2	2	no	—
482	C₂×C₃×D₄	—	2	2	no	—
483	C₂×C₃×D₄	—	2	1	no	—
484	C₂×C₃×D₄	—	2	1	no	—
485	C₂×C₃×D₄	—	2	2	no	—
486	C₂×C₃×D₄	—	2	1	no	—
487	C₂×C₃×D₄	—	2	2	no	—
488	C₂×C₃×D₄	—	2	1	no	—
489	C₂×C₃×D₄	—	2	1	no	—
490	C₂×C₃×D₄	—	2	2	no	—
491	C₂×C₃×D₄	—	2	2	no	—
492	C₂×C₃×D₄	—	2	2	no	—
493	C₂×C₃×D₄	—	2	2	no	—
494	C₂×C₃×D₄	—	8	2	no	—
495	C₂×C₃×D₄	C₂⁴	1	2	yes	—
496	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
497	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
498	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
499	C₂²×C₃×C₄	—	2	8	no	—
500	C₂²×C₃×C₄	—	2	1	no	—
501	C₂²×C₃×C₄	—	2	1	no	—
502	C₂²×C₃×C₄	—	2	1	no	—
503	C₂²×C₃×C₄	—	2	1	no	—
504	C₂²×C₃×C₄	—	2	1	no	—
505	C₂²×C₃×C₄	—	2	2	no	—
506	C₂²×C₃×C₄	—	2	2	no	—
507	C₂²×C₃×C₄	—	2	1	no	—
508	C₂²×C₃×C₄	—	2	1	no	—
509	C₂²×C₃×C₄	—	2	1	no	—
510	C₂²×C₃×C₄	—	2	1	no	—
511	C₂²×C₃×C₄	—	2	2	no	—
512	C₂²×C₃×C₄	—	2	2	no	—
513	C₂²×C₃×C₄	—	2	2	no	—
514	C₂²×C₃×C₄	—	2	2	no	—
515	C₂²×C₃×C₄	—	2	2	no	—
516	C₂²×C₃×C₄	—	2	2	no	—
517	C₂²×C₃×C₄	—	2	2	no	—
518	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
519	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
520	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
521	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
522	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
523	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
524	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
525	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
526	C₃×Q₁₆	—	2	2	no	—
527	C₃×Q₁₆	—	2	2	no	—
528	C₃×SD₁₆	—	2	2	no	—
529	C₃×SD₁₆	—	2	2	no	—
530	C₃×SD₁₆	—	2	4	no	—
531	C₃×SD₁₆	—	2	4	no	—
532	C₃×SD₁₆	—	2	2	no	—
533	C₃×SD₁₆	—	2	2	no	—
534	C₃×D₈	—	2	2	no	—
535	C₃×D₈	—	2	2	no	—
536	C₃×D₈	—	2	4	no	—
537	C₃×D₈	—	2	4	no	—
538	C₃×M₁₆	—	2	2	no	—
539	C₃×M₁₆	—	2	2	no	—
540	C₂×C₃×C₈	—	2	2	no	—
541	C₂×C₃×C₈	—	2	2	no	—
542	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
543	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
544	C₂×C₃×C₈	C₂⁴	1	2	yes	—
545	C₂×C₃×C₈	C₂⁴	1	2	yes	—
546	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
547	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
548	C₃×C₄⋊C₄	—	2	1	no	—
549	C₃×C₄⋊C₄	—	2	1	no	—
550	C₃×C₄⋊C₄	—	2	1	no	—
551	C₃×C₄⋊C₄	—	2	2	no	—
552	C₃×C₄⋊C₄	—	2	2	no	—
553	C₃×C₄⋊C₄	—	2	2	no	—
554	C₃×C₄⋊C₄	—	2	2	no	—
555	C₃×C₄⋊C₄	—	2	2	no	—
556	C₃×C₄⋊C₄	—	2	1	no	—
557	C₃×C₄⋊C₄	—	2	2	no	—
558	C₃×C₄⋊C₄	—	2	2	no	—
559	C₃×C₄⋊C₄	—	2	2	no	—
560	C₃×C₄⋊C₄	—	2	1	no	—
561	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
562	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
563	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
564	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
565	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
566	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
567	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
568	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
569	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
570	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
571	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
572	C₃×C₂²⋊C₄	—	2	2	no	—
573	C₃×C₂²⋊C₄	—	2	1	no	—
574	C₃×C₂²⋊C₄	—	2	2	no	—
575	C₃×C₂²⋊C₄	—	2	1	no	—
576	C₃×C₂²⋊C₄	—	2	1	no	—
577	C₃×C₂²⋊C₄	—	2	2	no	—
578	C₃×C₂²⋊C₄	—	2	2	no	—
579	C₃×C₂²⋊C₄	—	2	2	no	—
580	C₃×C₂²⋊C₄	—	2	2	no	—
581	C₃×C₂²⋊C₄	—	2	2	no	—
582	C₃×C₂²⋊C₄	—	2	2	no	—
583	C₃×C₂²⋊C₄	—	2	2	no	—
584	C₃×C₂²⋊C₄	—	2	2	no	—
585	C₃×C₂²⋊C₄	—	2	2	no	—
586	C₃×C₂²⋊C₄	—	2	2	no	—
587	C₃×C₂²⋊C₄	—	2	1	no	—
588	C₃×C₂²⋊C₄	—	2	2	no	—
589	C₃×C₂²⋊C₄	—	2	1	no	—
590	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
591	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
592	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
593	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
594	C₃×C₄²	—	2	2	no	—
595	C₃×C₄²	—	2	2	no	—
596	C₃×C₄²	—	2	2	no	—
597	C₃×C₄²	—	2	2	no	—
598	C₃×C₄²	—	2	2	no	—
599	C₃×C₄²	—	2	2	no	—
600	C₃×C₄²	—	2	2	no	—
601	C₃×C₄²	—	2	1	no	—
602	C₃×C₄²	C₂×D₄	1	2	yes	—
603	C₃×C₄²	C₂×D₄	1	2	yes	—
604	C₃×C₄²	C₂⁴	1	2	yes	—
605	C₃×C₄²	C₂⁴	1	2	yes	—
606	C₂×#41	—	2	4	no	—
607	C₂×#41	—	2	4	no	—
608	C₂×#41	—	2	1	no	—
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	2	no	—
611	C₂×#41	C₂³×C₃	1	1	yes	characteristic
612	C₂×#41	C₂³×C₃	1	1	yes	characteristic
613	C₂×#41	C₂³×C₃	1	1	yes	characteristic
614	C₂×#41	C₂³×C₃	1	1	yes	characteristic
615	C₂×#41	C₂³×C₃	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
621	C₂³×C₄	—	2	1	no	—
622	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
623	AGL(1,ℤ/8)	—	2	4	no	—
624	AGL(1,ℤ/8)	—	2	4	no	—
625	#135	—	2	4	no	—
626	#135	—	2	4	no	—
627	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
628	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
629	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
630	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
631	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
632	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
633	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
635	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
636	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
637	C₂×D₈	C₂³×C₃	1	2	yes	—
638	C₂×D₈	C₂³×C₃	1	2	yes	—
639	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
640	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
641	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
642	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
645	#127	C₂³×C₃	1	2	yes	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#125	—	2	1	no	—
649	#125	C₂³×C₃	1	2	yes	—
650	#124	—	2	2	no	—
651	#124	—	2	2	no	—
652	#124	C₂³×C₃	1	2	yes	—
653	#123	—	2	1	no	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
661	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
662	#121	—	2	1	no	—
663	#121	—	2	1	no	—
664	#121	—	2	2	no	—
665	#121	—	2	1	no	—
666	#121	—	2	1	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	C₂³×C₃	1	2	yes	—
670	#121	C₂³×C₃	1	2	yes	—
671	#121	C₂³×C₃	1	1	yes	characteristic
672	#121	C₂³×C₃	1	1	yes	characteristic
673	#120	—	2	1	no	—
674	#120	—	2	2	no	—
675	C₄×Q₈	—	2	2	no	—
676	C₄×Q₈	—	2	2	no	—
677	C₄×Q₈	C₂³×C₃	1	2	yes	—
678	C₄×Q₈	C₂³×C₃	1	2	yes	—
679	C₄×Q₈	C₂³×C₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₃	1	2	yes	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	C₂³×C₃	1	2	yes	—
700	C₄×D₄	C₂³×C₃	1	2	yes	—
701	C₄×D₄	C₂³×C₃	1	2	yes	—
702	C₄×D₄	C₂³×C₃	1	2	yes	—
703	C₄×D₄	C₂³×C₃	1	2	yes	—
704	C₄×D₄	C₂³×C₃	1	2	yes	—
705	C₄×D₄	C₂³×C₃	1	2	yes	—
706	#117	—	2	1	no	—
707	#117	—	2	1	no	—
708	#117	—	2	1	no	—
709	#117	—	2	1	no	—
710	#117	—	2	1	no	—
711	#117	—	2	1	no	—
712	#117	—	2	1	no	—
713	#117	—	2	2	no	—
714	#117	—	2	2	no	—
715	#117	—	2	2	no	—
716	#117	—	2	2	no	—
717	#117	—	2	2	no	—
718	#117	C₃×D₄	1	1	yes	characteristic
719	#117	C₃×D₄	1	1	yes	characteristic
720	#117	C₃×D₄	1	2	yes	—
721	#117	C₂³×C₃	1	2	yes	—
722	#117	C₂³×C₃	1	2	yes	—
723	#117	C₂³×C₃	1	1	yes	characteristic
724	#117	C₂³×C₃	1	2	yes	—
725	#117	C₂³×C₃	1	1	yes	characteristic
726	#117	C₂³×C₃	1	1	yes	characteristic
727	C₂×C₄⋊C₄	—	2	1	no	—
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	1	no	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	—	2	1	no	—
738	C₂×C₂²⋊C₄	—	2	1	no	—
739	C₂×C₂²⋊C₄	—	2	2	no	—
740	C₂×C₂²⋊C₄	—	2	2	no	—
741	C₂×C₂²⋊C₄	—	2	2	no	—
742	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
743	C₂×C₄²	—	2	1	no	—
744	C₂×C₄²	—	2	2	no	—
745	C₂×C₄²	—	2	2	no	—
746	C₂×C₄²	C₂³×C₃	1	2	yes	—
747	#107	C₂³×C₃	1	2	yes	—
748	#107	C₂³×C₃	1	2	yes	—
749	#107	C₂³×C₃	1	2	yes	—
750	#107	C₂³×C₃	1	2	yes	—
751	#106	C₂³×C₃	1	2	yes	—
752	#106	C₂³×C₃	1	2	yes	—
753	#106	C₂³×C₃	1	2	yes	—
754	#106	C₂³×C₃	1	2	yes	—
755	C₄⋊C₈	C₂³×C₃	1	2	yes	—
756	C₄⋊C₈	C₂³×C₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₃	1	2	yes	—
759	#103	C₂³×C₃	1	1	yes	characteristic
760	#103	C₂³×C₃	1	1	yes	characteristic
761	#103	C₂³×C₃	1	1	yes	characteristic
762	#103	C₂³×C₃	1	1	yes	characteristic
763	#103	C₂³×C₃	1	2	yes	—
764	#103	C₂³×C₃	1	2	yes	—
765	#103	C₂³×C₃	1	2	yes	—
766	#103	C₂³×C₃	1	2	yes	—
767	#102	C₂³×C₃	1	2	yes	—
768	#102	C₂³×C₃	1	2	yes	—
769	#102	C₂³×C₃	1	2	yes	—
770	#102	C₂³×C₃	1	2	yes	—
771	#102	C₂³×C₃	1	1	yes	characteristic
772	#102	C₂³×C₃	1	1	yes	characteristic
773	#102	C₂³×C₃	1	1	yes	characteristic
774	#102	C₂³×C₃	1	1	yes	characteristic
775	#102	C₂³×C₃	1	2	yes	—
776	#102	C₂³×C₃	1	2	yes	—
777	#102	C₂³×C₃	1	2	yes	—
778	#102	C₂³×C₃	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
780	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
781	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
782	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
783	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
785	#97	C₂³×C₃	1	2	yes	—
786	#97	C₂³×C₃	1	2	yes	—
787	C₄×C₈	C₂³×C₃	1	2	yes	—
788	C₄×C₈	C₂³×C₃	1	2	yes	—
789	C₂³×C₃	—	2	4	no	—
790	C₂³×C₃	—	2	1	no	—
791	C₂³×C₃	—	2	1	no	—
792	C₂³×C₃	—	2	2	no	—
793	C₂³×C₃	—	2	2	no	—
794	C₂³×C₃	—	2	1	no	—
795	C₂³×C₃	—	4	1	no	—
796	C₂³×C₃	—	4	1	no	—
797	C₂³×C₃	—	4	2	no	—
798	C₂³×C₃	—	8	1	no	—
799	C₂³×C₃	—	8	1	no	—
800	C₂³×C₃	—	8	1	no	—
801	C₂³×C₃	—	8	1	no	—
802	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
803	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
804	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
805	C₃×Q₈	—	2	4	no	—
806	C₃×Q₈	—	2	1	no	—
807	C₃×Q₈	—	2	1	no	—
808	C₃×Q₈	—	2	1	no	—
809	C₃×Q₈	—	2	1	no	—
810	C₃×Q₈	—	8	2	no	—
811	C₃×Q₈	C₂×#41	1	2	yes	—
812	C₃×Q₈	C₂×#41	1	2	yes	—
813	C₃×D₄	—	2	4	no	—
814	C₃×D₄	—	2	4	no	—
815	C₃×D₄	—	2	4	no	—
816	C₃×D₄	—	2	4	no	—
817	C₃×D₄	—	2	4	no	—
818	C₃×D₄	—	2	1	no	—
819	C₃×D₄	—	2	1	no	—
820	C₃×D₄	—	2	2	no	—
821	C₃×D₄	—	2	2	no	—
822	C₃×D₄	—	2	1	no	—
823	C₃×D₄	—	2	1	no	—
824	C₃×D₄	—	4	4	no	—
825	C₃×D₄	—	4	2	no	—
826	C₃×D₄	—	4	2	no	—
827	C₃×D₄	—	4	2	no	—
828	C₃×D₄	—	8	2	no	—
829	C₃×D₄	—	8	2	no	—
830	C₃×D₄	—	8	1	no	—
831	C₃×D₄	—	8	2	no	—
832	C₃×D₄	C₂×#41	1	2	yes	—
833	C₃×D₄	C₂×#41	1	2	yes	—
834	C₂×C₃×C₄	—	2	4	no	—
835	C₂×C₃×C₄	—	2	4	no	—
836	C₂×C₃×C₄	—	2	4	no	—
837	C₂×C₃×C₄	—	2	2	no	—
838	C₂×C₃×C₄	—	2	1	no	—
839	C₂×C₃×C₄	—	2	1	no	—
840	C₂×C₃×C₄	—	2	2	no	—
841	C₂×C₃×C₄	—	2	4	no	—
842	C₂×C₃×C₄	—	2	4	no	—
843	C₂×C₃×C₄	—	2	2	no	—
844	C₂×C₃×C₄	—	2	1	no	—
845	C₂×C₃×C₄	—	2	1	no	—
846	C₂×C₃×C₄	—	2	1	no	—
847	C₂×C₃×C₄	—	2	1	no	—
848	C₂×C₃×C₄	—	2	2	no	—
849	C₂×C₃×C₄	—	2	2	no	—
850	C₂×C₃×C₄	—	2	1	no	—
851	C₂×C₃×C₄	—	2	1	no	—
852	C₂×C₃×C₄	—	2	1	no	—
853	C₂×C₃×C₄	—	2	2	no	—
854	C₂×C₃×C₄	—	4	2	no	—
855	C₂×C₃×C₄	—	4	2	no	—
856	C₂×C₃×C₄	—	4	2	no	—
857	C₂×C₃×C₄	—	8	2	no	—
858	C₂×C₃×C₄	—	8	2	no	—
859	C₂×C₃×C₄	—	8	2	no	—
860	C₂×C₃×C₄	—	8	2	no	—
861	C₂×C₃×C₄	—	8	2	no	—
862	C₂×C₃×C₄	—	8	2	no	—
863	C₂×C₃×C₄	—	8	2	no	—
864	C₂×C₃×C₄	—	8	1	no	—
865	C₂×C₃×C₄	—	8	1	no	—
866	C₂×C₃×C₄	—	8	1	no	—
867	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
868	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
869	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
871	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
872	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
873	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂×C₃×C₄	C₂×#41	1	2	yes	—
875	C₂×C₃×C₄	C₂×#41	1	2	yes	—
876	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
877	C₃×C₈	—	2	1	no	—
878	C₃×C₈	—	2	1	no	—
879	C₃×C₈	—	2	1	no	—
880	C₃×C₈	—	2	1	no	—
881	C₃×C₈	—	2	2	no	—
882	C₃×C₈	—	2	2	no	—
883	C₂⁴	—	2	1	no	—
884	C₂⁴	—	2	1	no	—
885	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
886	#41	—	2	8	no	—
887	#41	—	2	8	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	8	4	no	—
897	#41	C₃×#41	1	4	yes	complemented
898	#41	C₃×#41	1	4	yes	complemented
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
906	C₂×D₄	—	2	8	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	8	2	no	—
925	C₂×D₄	C₂⁴×C₃	1	2	yes	—
926	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
929	C₂²×C₄	—	2	8	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
949	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
950	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
951	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
952	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
956	Q₁₆	—	2	2	no	—
957	Q₁₆	—	2	2	no	—
958	SD₁₆	—	2	2	no	—
959	SD₁₆	—	2	2	no	—
960	SD₁₆	—	2	4	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	2	no	—
963	SD₁₆	—	2	2	no	—
964	D₈	—	2	2	no	—
965	D₈	—	2	2	no	—
966	D₈	—	2	4	no	—
967	D₈	—	2	4	no	—
968	M₁₆	—	2	2	no	—
969	M₁₆	—	2	2	no	—
970	C₂×C₈	—	2	2	no	—
971	C₂×C₈	—	2	2	no	—
972	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₃	1	2	yes	—
975	C₂×C₈	C₂⁴×C₃	1	2	yes	—
976	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
992	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
993	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
994	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
995	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
996	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1021	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1022	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1023	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	C₂×C₃×D₄	1	2	yes	—
1033	C₄²	C₂×C₃×D₄	1	2	yes	—
1034	C₄²	C₂⁴×C₃	1	2	yes	—
1035	C₄²	C₂⁴×C₃	1	2	yes	—
1036	C₂²×C₃	—	2	1	no	—
1037	C₂²×C₃	—	2	1	no	—
1038	C₂²×C₃	—	2	1	no	—
1039	C₂²×C₃	—	2	1	no	—
1040	C₂²×C₃	—	2	1	no	—
1041	C₂²×C₃	—	2	1	no	—
1042	C₂²×C₃	—	2	1	no	—
1043	C₂²×C₃	—	2	1	no	—
1044	C₂²×C₃	—	2	2	no	—
1045	C₂²×C₃	—	2	2	no	—
1046	C₂²×C₃	—	4	1	no	—
1047	C₂²×C₃	—	4	1	no	—
1048	C₂²×C₃	—	4	1	no	—
1049	C₂²×C₃	—	4	1	no	—
1050	C₂²×C₃	—	4	2	no	—
1051	C₂²×C₃	—	4	1	no	—
1052	C₂²×C₃	—	4	1	no	—
1053	C₂²×C₃	—	4	2	no	—
1054	C₂²×C₃	—	4	1	no	—
1055	C₂²×C₃	—	4	2	no	—
1056	C₂²×C₃	—	8	2	no	—
1057	C₂²×C₃	—	8	4	no	—
1058	C₂²×C₃	—	16	2	no	—
1059	C₂²×C₃	#525	1	2	yes	—
1060	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1061	C₃×C₄	—	2	2	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	2	2	no	—
1065	C₃×C₄	—	2	1	no	—
1066	C₃×C₄	—	2	2	no	—
1067	C₃×C₄	—	2	2	no	—
1068	C₃×C₄	—	2	1	no	—
1069	C₃×C₄	—	4	2	no	—
1070	C₃×C₄	—	4	1	no	—
1071	C₃×C₄	—	4	2	no	—
1072	C₃×C₄	—	4	2	no	—
1073	C₃×C₄	—	4	1	no	—
1074	C₃×C₄	—	4	1	no	—
1075	C₃×C₄	#525	1	2	yes	—
1076	C₃×C₄	C₂²×#41	1	1	yes	characteristic
1077	C₃×C₄	C₂²×#41	1	1	yes	characteristic
1078	C₂³	—	2	4	no	—
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	2	no	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	4	1	no	—
1085	C₂³	—	4	1	no	—
1086	C₂³	—	4	2	no	—
1087	C₂³	—	8	1	no	—
1088	C₂³	—	8	1	no	—
1089	C₂³	—	8	1	no	—
1090	C₂³	—	8	1	no	—
1091	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1092	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1093	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1094	Q₈	—	2	4	no	—
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	1	no	—
1097	Q₈	—	2	1	no	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	8	2	no	—
1100	Q₈	C₂×C₃×#41	1	2	yes	—
1101	Q₈	C₂×C₃×#41	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	4	no	—
1104	D₄	—	2	4	no	—
1105	D₄	—	2	4	no	—
1106	D₄	—	2	4	no	—
1107	D₄	—	2	1	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	1	no	—
1121	D₄	C₂×C₃×#41	1	2	yes	—
1122	D₄	C₂×C₃×#41	1	2	yes	—
1123	C₂×C₄	—	2	4	no	—
1124	C₂×C₄	—	2	4	no	—
1125	C₂×C₄	—	2	4	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	2	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	2	no	—
1150	C₂×C₄	—	8	2	no	—
1151	C₂×C₄	—	8	2	no	—
1152	C₂×C₄	—	8	2	no	—
1153	C₂×C₄	—	8	1	no	—
1154	C₂×C₄	—	8	1	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1157	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1158	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1159	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1160	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1161	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1162	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1163	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1164	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1165	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	2	no	—
1172	C₂×C₃	—	2	2	no	—
1173	C₂×C₃	—	4	1	no	—
1174	C₂×C₃	—	4	1	no	—
1175	C₂×C₃	—	4	2	no	—
1176	C₂×C₃	—	4	2	no	—
1177	C₂×C₃	—	8	1	no	—
1178	C₂×C₃	—	8	2	no	—
1179	C₂×C₃	C₂×#525	1	1	yes	characteristic
1180	C₂×C₃	#3584	1	1	yes	characteristic
1181	C₂×C₃	#3585	1	1	yes	characteristic
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	8	2	no	—
1203	C₂²	—	8	4	no	—
1204	C₂²	—	16	2	no	—
1205	C₂²	C₃×#525	1	2	yes	—
1206	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1207	C₄	—	2	1	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	C₃×#525	1	2	yes	—
1222	C₄	C₂²×C₃×#41	1	1	yes	characteristic
1223	C₄	C₂²×C₃×#41	1	1	yes	characteristic
1224	C₃	#60587	1	1	yes	characteristic, direct product factor, Sylow
1225	C₂	—	2	2	no	—
1226	C₂	—	4	1	no	—
1227	C₂	—	4	1	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	—	8	2	no	—
1231	C₂	—	8	1	no	—
1232	C₂	C₂×C₃×#525	1	1	yes	characteristic
1233	C₂	C₃×#3584	1	1	yes	characteristic
1234	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3494	C₂	semidirect
2. C₃×#3428	C₂	semidirect
3. C₃×#3126	C₂	semidirect
4. C₃×#3122	C₂	semidirect
5. C₃×#3121	C₂	semidirect
6. C₃×#3118	C₂	semidirect
7. C₃×#3115	C₂	semidirect
8. C₃×#3111	C₂	semidirect
9. C₃×#3106	C₂	semidirect
10. C₃×#3102	C₂	semidirect
11. C₃×#3093	C₂	semidirect
12. C₂×C₃×#482	C₂	semidirect
13. C₃×#3084	C₂	semidirect
14. C₃×#3083	C₂	semidirect
15. C₃×#3045	C₂	semidirect
16. C₃×#3045	C₂	semidirect
17. C₃×#3006	C₂	semidirect
18. C₃×#3002	C₂	semidirect
19. C₃×#2952	C₂	semidirect
20. C₃×#2951	C₂	semidirect
21. C₃×#2946	C₂	semidirect
22. C₃×#2946	C₂	semidirect
23. C₃×#2924	C₂	semidirect
24. #60587	C₃	direct (N × H)
36. C₃×#544	C₂²	semidirect
39. C₃×#535	C₂²	semidirect
40. C₃×#532	C₂²	semidirect
41. C₃×#529	C₂²	semidirect
50. C₃×#520	C₂²	semidirect
51. C₃×#519	C₂²	semidirect
53. C₃×#518	C₂²	semidirect
54. C₃×#518	C₂²	semidirect
56. C₃×C₄×#41	C₂²	semidirect
57. C₃×C₄×#41	C₂²	semidirect
62. C₃×#485	C₂²	semidirect
63. C₃×#485	C₂²	semidirect
66. C₃×#482	C₂²	semidirect
67. C₃×#482	C₂²	semidirect
68. C₃×#482	C₂²	semidirect
69. C₃×#482	C₂²	semidirect
70. C₃×#479	C₂²	semidirect
71. C₃×#479	C₂²	semidirect
72. C₃×#478	C₂²	semidirect
73. C₃×#478	C₂²	semidirect
74. C₃×#477	C₂²	semidirect
75. C₃×#476	C₂²	semidirect
76. C₃×#475	C₂²	semidirect
77. C₃×#474	C₂²	semidirect
78. C₃×#464	C₂²	semidirect
79. C₃×#464	C₂²	semidirect
80. C₃×#463	C₂²	semidirect
81. C₃×#463	C₂²	semidirect
82. C₃×#460	C₂²	semidirect
83. C₃×#460	C₂²	semidirect
84. C₃×#459	C₂²	semidirect
85. C₃×#459	C₂²	semidirect
86. C₃×#452	C₂²	semidirect
87. C₃×#452	C₂²	semidirect
88. C₃×#451	C₂²	semidirect
89. C₃×#450	C₂²	semidirect
92. C₃×#449	C₂²	semidirect
93. C₃×#449	C₂²	semidirect
95. C₃×#448	C₂²	semidirect
97. C₃×#447	C₂²	semidirect
98. C₃×#442	C₂²	semidirect
99. C₃×#442	C₂²	semidirect
100. C₃×#442	C₂²	semidirect
101. C₃×#441	C₂²	semidirect
102. C₃×#440	C₂²	semidirect
103. C₃×#440	C₂²	semidirect
104. C₃×#440	C₂²	semidirect
105. C₃×#440	C₂²	semidirect
106. C₃×C₄×Q₁₆	C₂²	semidirect
107. C₃×C₄×SD₁₆	C₂²	semidirect
108. C₃×C₄×SD₁₆	C₂²	semidirect
109. C₃×C₄×SD₁₆	C₂²	semidirect
110. C₃×C₄×SD₁₆	C₂²	semidirect
111. C₃×C₄×D₈	C₂²	semidirect
112. C₃×C₄×D₈	C₂²	semidirect
113. C₃×C₄×D₈	C₂²	semidirect
114. C₃×#433	C₂²	semidirect
115. C₃×#433	C₂²	semidirect
116. C₃×#432	C₂²	semidirect
117. C₃×#431	C₂²	semidirect
118. C₃×#428	C₂²	semidirect
119. C₃×#428	C₂²	semidirect
120. C₂×C₃×#107	C₂²	semidirect
121. C₂×C₃×#106	C₂²	semidirect
122. C₃×#424	C₂²	semidirect
123. C₃×#424	C₂²	semidirect
126. C₃×#417	C₂²	semidirect
127. C₃×#417	C₂²	semidirect
130. C₂×C₃×#102	C₂²	semidirect
131. C₂×C₃×#102	C₂²	semidirect
134. C₃×#405	C₂²	semidirect
135. C₃×#405	C₂²	semidirect
136. #3494	C₂×C₃	semidirect
137. #3428	C₂×C₃	semidirect
138. #3126	C₂×C₃	semidirect
139. #3122	C₂×C₃	semidirect
140. #3121	C₂×C₃	semidirect
141. #3118	C₂×C₃	semidirect
142. #3115	C₂×C₃	semidirect
143. #3111	C₂×C₃	semidirect
144. #3106	C₂×C₃	semidirect
145. #3102	C₂×C₃	semidirect
146. #3093	C₂×C₃	semidirect
147. C₂×#482	C₂×C₃	semidirect
148. #3084	C₂×C₃	semidirect
149. #3083	C₂×C₃	semidirect
150. #3045	C₂×C₃	semidirect
151. #3045	C₂×C₃	semidirect
152. #3006	C₂×C₃	semidirect
153. #3002	C₂×C₃	semidirect
154. #2952	C₂×C₃	semidirect
155. #2951	C₂×C₃	semidirect
156. #2946	C₂×C₃	semidirect
157. #2946	C₂×C₃	semidirect
158. #2924	C₂×C₃	semidirect
353. #544	C₂²×C₃	semidirect
356. #535	C₂²×C₃	semidirect
357. #532	C₂²×C₃	semidirect
358. #529	C₂²×C₃	semidirect
367. #520	C₂²×C₃	semidirect
368. #519	C₂²×C₃	semidirect
370. #518	C₂²×C₃	semidirect
371. #518	C₂²×C₃	semidirect
373. C₄×#41	C₂²×C₃	semidirect
374. C₄×#41	C₂²×C₃	semidirect
379. #485	C₂²×C₃	semidirect
380. #485	C₂²×C₃	semidirect
383. #482	C₂²×C₃	semidirect
384. #482	C₂²×C₃	semidirect
385. #482	C₂²×C₃	semidirect
386. #482	C₂²×C₃	semidirect
387. #479	C₂²×C₃	semidirect
388. #479	C₂²×C₃	semidirect
389. #478	C₂²×C₃	semidirect
390. #478	C₂²×C₃	semidirect
391. #477	C₂²×C₃	semidirect
392. #476	C₂²×C₃	semidirect
393. #475	C₂²×C₃	semidirect
394. #474	C₂²×C₃	semidirect
395. #464	C₂²×C₃	semidirect
396. #464	C₂²×C₃	semidirect
397. #463	C₂²×C₃	semidirect
398. #463	C₂²×C₃	semidirect
399. #460	C₂²×C₃	semidirect
400. #460	C₂²×C₃	semidirect
401. #459	C₂²×C₃	semidirect
402. #459	C₂²×C₃	semidirect
403. #452	C₂²×C₃	semidirect
404. #452	C₂²×C₃	semidirect
405. #451	C₂²×C₃	semidirect
406. #450	C₂²×C₃	semidirect
409. #449	C₂²×C₃	semidirect
410. #449	C₂²×C₃	semidirect
412. #448	C₂²×C₃	semidirect
414. #447	C₂²×C₃	semidirect
415. #442	C₂²×C₃	semidirect
416. #442	C₂²×C₃	semidirect
417. #442	C₂²×C₃	semidirect
418. #441	C₂²×C₃	semidirect
419. #440	C₂²×C₃	semidirect
420. #440	C₂²×C₃	semidirect
421. #440	C₂²×C₃	semidirect
422. #440	C₂²×C₃	semidirect
423. C₄×Q₁₆	C₂²×C₃	semidirect
424. C₄×SD₁₆	C₂²×C₃	semidirect
425. C₄×SD₁₆	C₂²×C₃	semidirect
426. C₄×SD₁₆	C₂²×C₃	semidirect
427. C₄×SD₁₆	C₂²×C₃	semidirect
428. C₄×D₈	C₂²×C₃	semidirect
429. C₄×D₈	C₂²×C₃	semidirect
430. C₄×D₈	C₂²×C₃	semidirect
431. #433	C₂²×C₃	semidirect
432. #433	C₂²×C₃	semidirect
433. #432	C₂²×C₃	semidirect
434. #431	C₂²×C₃	semidirect
435. #428	C₂²×C₃	semidirect
436. #428	C₂²×C₃	semidirect
437. C₂×#107	C₂²×C₃	semidirect
438. C₂×#106	C₂²×C₃	semidirect
439. #424	C₂²×C₃	semidirect
440. #424	C₂²×C₃	semidirect
443. #417	C₂²×C₃	semidirect
444. #417	C₂²×C₃	semidirect
447. C₂×#102	C₂²×C₃	semidirect
448. C₂×#102	C₂²×C₃	semidirect
451. #405	C₂²×C₃	semidirect
452. #405	C₂²×C₃	semidirect
467. C₃×#41	#41	semidirect
468. C₃×#41	#41	semidirect
897. #41	C₃×#41	semidirect
898. #41	C₃×#41	semidirect
1224. C₃	#60587	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3494	2
C₃×#3428	2
C₃×#3126	2
C₃×#3122	2
C₃×#3121	2
C₃×#3118	2
C₃×#3115	2
C₃×#3111	2
C₃×#3106	2
C₃×#3102	2
C₃×#3093	2
C₂×C₃×#482	2
C₃×#3084	2
C₃×#3083	2
C₃×#3045	2
C₃×#3006	2
C₃×#3002	2
C₃×#2952	2
C₃×#2951	2
C₃×#2946	2
C₃×#2924	2
#60587	3

Subgroups — C3×#60587 #10679194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60587 #10679194