Subgroups — C₃×#61659 #10680266

Order 768.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3326	C₂	1	2	yes	maximal, complemented
6	C₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#3301	C₂	1	2	yes	maximal, complemented
8	C₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3282	C₂	1	2	yes	maximal, complemented
11	C₃×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3275	C₂	1	2	yes	maximal, complemented
14	C₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3204	C₂	1	2	yes	maximal, complemented
18	C₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#3013	C₂	1	2	yes	maximal, complemented
22	C₃×#3010	C₂	1	2	yes	maximal, complemented
23	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	#61659	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
26	C₂×C₃×#137	C₂²	1	2	yes	complemented
27	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
28	C₂×C₃×#135	C₂²	1	2	yes	complemented
29	C₂²×C₃×SD₁₆	C₂²	1	2	yes	—
30	C₃×#560	—	2	2	no	—
31	C₃×#556	C₂²	1	1	yes	characteristic
32	C₃×#553	C₂²	1	2	yes	—
33	C₃×#550	—	2	1	no	—
34	C₃×#550	—	2	1	no	—
35	C₃×#550	C₂²	1	1	yes	characteristic
36	C₃×#550	C₂²	1	1	yes	characteristic
37	C₃×#550	C₂²	1	1	yes	characteristic, complemented
38	C₃×D₄×Q₈	—	2	1	no	—
39	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×#548	—	2	2	no	—
42	C₃×#548	C₂²	1	2	yes	complemented
43	C₃×#548	C₂²	1	2	yes	complemented
44	C₃×#547	C₂²	1	1	yes	characteristic
45	C₃×#546	—	2	1	no	—
46	C₃×#546	C₂²	1	2	yes	—
47	C₃×D₄²	C₂²	1	1	yes	characteristic
48	C₃×#542	—	2	1	no	—
49	C₃×#538	—	2	2	no	—
50	C₃×#537	—	2	2	no	—
51	C₃×#537	C₂²	1	2	yes	—
52	C₃×#537	C₂²	1	2	yes	complemented
53	C₃×#535	—	2	1	no	—
54	C₃×#535	C₂²	1	2	yes	—
55	C₃×#532	—	2	1	no	—
56	C₃×#532	—	2	1	no	—
57	C₃×#532	C₂²	1	1	yes	characteristic
58	C₃×#532	C₂²	1	1	yes	characteristic
59	C₃×#532	C₂²	1	1	yes	characteristic, complemented
60	C₃×#529	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₃×#495	C₂²	1	2	yes	—
63	C₃×#493	C₂²	1	1	yes	characteristic
64	C₃×#492	C₂²	1	1	yes	characteristic
65	C₃×#488	C₂²	1	2	yes	complemented
66	C₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₃×#485	C₂²	1	2	yes	complemented
69	C₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₃×#483	C₂²	1	2	yes	complemented
71	C₃×#482	C₂²	1	2	yes	complemented
72	C₃×#481	C₂²	1	2	yes	complemented
73	C₃×#481	C₂²	1	2	yes	complemented
74	C₃×#480	C₂²	1	1	yes	characteristic
75	C₃×#479	C₂²	1	1	yes	characteristic, complemented
76	C₃×#479	C₂²	1	1	yes	characteristic, complemented
77	C₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃×#475	C₂²	1	1	yes	characteristic, complemented
79	C₃×#470	C₂²	1	2	yes	complemented
80	C₃×#469	C₂²	1	2	yes	—
81	C₃×#469	C₂²	1	2	yes	—
82	C₃×#468	C₂²	1	2	yes	complemented
83	C₃×#466	C₂²	1	2	yes	complemented
84	C₃×#465	C₂²	1	2	yes	—
85	C₃×#465	C₂²	1	2	yes	—
86	C₃×#465	C₂²	1	2	yes	complemented
87	C₃×#464	C₂²	1	1	yes	characteristic
88	C₃×#464	C₂²	1	1	yes	characteristic
89	C₃×#463	C₂²	1	2	yes	complemented
90	C₃×#463	C₂²	1	2	yes	complemented
91	C₃×#462	C₂²	1	1	yes	characteristic, complemented
92	C₃×#461	C₂²	1	1	yes	characteristic
93	C₃×#460	C₂²	1	1	yes	characteristic
94	C₃×#460	C₂²	1	1	yes	characteristic
95	C₃×#460	C₂²	1	1	yes	characteristic, complemented
96	C₃×#459	C₂²	1	1	yes	characteristic
97	C₃×#452	C₂²	1	2	yes	complemented
98	C₃×#452	C₂²	1	2	yes	complemented
99	C₃×#452	C₂²	1	2	yes	complemented
100	C₃×#451	C₂²	1	1	yes	characteristic, complemented
101	C₃×#451	C₂²	1	2	yes	complemented
102	C₃×#450	C₂²	1	2	yes	—
103	C₃×#449	C₂²	1	2	yes	—
104	C₃×#449	C₂²	1	2	yes	—
105	C₃×#449	C₂²	1	2	yes	—
106	C₃×#449	C₂²	1	2	yes	complemented
107	C₃×#449	C₂²	1	2	yes	complemented
108	C₃×#449	C₂²	1	2	yes	complemented
109	C₃×#449	C₂²	1	2	yes	complemented
110	C₃×#448	C₂²	1	1	yes	characteristic
111	C₃×#448	C₂²	1	2	yes	—
112	C₃×#448	C₂²	1	2	yes	—
113	C₃×#448	C₂²	1	2	yes	complemented
114	C₃×#448	C₂²	1	2	yes	complemented
115	C₃×#447	C₂²	1	2	yes	—
116	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
119	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
121	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
122	C₃×#436	C₂²	1	1	yes	characteristic
123	C₃×#436	C₂²	1	2	yes	complemented
124	C₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
126	C₃×C₈×D₄	C₂²	1	2	yes	complemented
127	C₃×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	C₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃×#419	C₂²	1	2	yes	complemented
131	C₃×#417	C₂²	1	2	yes	complemented
132	C₃×#416	C₂²	1	2	yes	complemented
133	C₂×C₃×#103	C₂²	1	2	yes	complemented
134	C₃×#408	C₂²	1	2	yes	complemented
135	C₃×#408	C₂²	1	2	yes	complemented
136	#3546	C₂×C₃	1	1	yes	characteristic, complemented
137	#3497	C₂×C₃	1	1	yes	characteristic, complemented
138	#3332	C₂×C₃	1	1	yes	characteristic, complemented
139	#3328	C₂×C₃	1	1	yes	characteristic, complemented
140	#3326	C₂×C₃	1	2	yes	complemented
141	#3304	C₂×C₃	1	1	yes	characteristic, complemented
142	#3301	C₂×C₃	1	2	yes	complemented
143	#3298	C₂×C₃	1	1	yes	characteristic, complemented
144	#3287	C₂×C₃	1	1	yes	characteristic, complemented
145	#3282	C₂×C₃	1	2	yes	complemented
146	D₄×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
147	#3278	C₂×C₃	1	1	yes	characteristic, complemented
148	#3275	C₂×C₃	1	2	yes	complemented
149	#3274	C₂×C₃	1	1	yes	characteristic, complemented
150	#3212	C₂×C₃	1	1	yes	characteristic, complemented
151	#3207	C₂×C₃	1	1	yes	characteristic, complemented
152	#3204	C₂×C₃	1	2	yes	complemented
153	#3198	C₂×C₃	1	2	yes	complemented
154	#3108	C₂×C₃	1	1	yes	characteristic, complemented
155	#3103	C₂×C₃	1	1	yes	characteristic, complemented
156	#3013	C₂×C₃	1	2	yes	complemented
157	#3010	C₂×C₃	1	2	yes	complemented
158	#2979	C₂×C₃	1	1	yes	characteristic, complemented
159	C₃×2₋¹⁺⁴	—	4	4	no	—
160	C₃×2₋¹⁺⁴	—	4	4	no	—
161	C₂×C₃×#41	—	2	2	no	—
162	C₂×C₃×#41	—	2	2	no	—
163	C₂×C₃×#41	—	2	2	no	—
164	C₂×C₃×#41	—	2	1	no	—
165	C₂×C₃×#41	—	2	1	no	—
166	C₂×C₃×#41	C₂³	1	2	yes	—
167	C₂×C₃×#41	C₂³	1	2	yes	—
168	C₂×C₃×#41	C₂³	1	2	yes	—
169	C₂×C₃×#41	C₂³	1	2	yes	—
170	C₂×C₃×#41	C₂³	1	2	yes	—
171	C₂²×C₃×Q₈	—	2	2	no	—
172	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
173	C₂²×C₃×Q₈	C₂³	1	2	yes	—
174	C₂²×C₃×Q₈	C₂³	1	2	yes	—
175	C₂²×C₃×D₄	—	2	1	no	—
176	C₂²×C₃×D₄	C₂³	1	2	yes	—
177	C₃×#137	—	4	4	no	—
178	C₃×AGL(1,ℤ/8)	—	4	4	no	—
179	C₃×#135	—	4	4	no	—
180	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
181	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
182	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
183	C₂×C₃×SD₁₆	—	4	4	no	—
184	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
185	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
186	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
187	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
188	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
189	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
190	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
191	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
192	C₂×C₃×D₈	C₂³	1	2	yes	—
193	C₂×C₃×D₈	C₂³	1	2	yes	—
194	C₂×C₃×D₈	C₂³	1	2	yes	—
195	C₂×C₃×M₁₆	C₂³	1	2	yes	—
196	C₂×C₃×M₁₆	C₂³	1	2	yes	—
197	C₂²×C₃×C₈	C₂³	1	2	yes	—
198	C₂²×C₃×C₈	C₂³	1	2	yes	—
199	C₃×C₄⋊Q₈	—	2	1	no	—
200	C₃×C₄⋊Q₈	—	2	1	no	—
201	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
202	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
203	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
204	C₃×#127	—	2	2	no	—
205	C₃×#127	—	2	1	no	—
206	C₃×#127	—	2	1	no	—
207	C₃×#127	—	2	1	no	—
208	C₃×#127	D₄	1	1	yes	characteristic
209	C₃×#127	C₂³	1	1	yes	characteristic
210	C₃×#127	C₂³	1	1	yes	characteristic
211	C₃×#126	—	2	2	no	—
212	C₃×#126	—	2	2	no	—
213	C₃×#126	—	2	1	no	—
214	C₃×#125	C₂³	1	1	yes	characteristic
215	C₃×#124	—	2	2	no	—
216	C₃×#124	—	2	1	no	—
217	C₃×#124	—	2	2	no	—
218	C₃×#124	—	2	2	no	—
219	C₃×#124	—	2	1	no	—
220	C₃×#124	D₄	1	2	yes	—
221	C₃×#124	C₂³	1	2	yes	—
222	C₃×#124	C₂³	1	1	yes	characteristic
223	C₃×#123	—	2	1	no	—
224	C₃×#123	—	2	2	no	—
225	C₃×#123	—	2	2	no	—
226	C₃×#123	—	2	2	no	—
227	C₃×C₂²⋊Q₈	—	2	2	no	—
228	C₃×C₂²⋊Q₈	—	2	2	no	—
229	C₃×C₂²⋊Q₈	—	2	2	no	—
230	C₃×C₂²⋊Q₈	—	2	2	no	—
231	C₃×C₂²⋊Q₈	—	2	1	no	—
232	C₃×C₂²⋊Q₈	—	2	2	no	—
233	C₃×C₂²⋊Q₈	—	2	2	no	—
234	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
235	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
237	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
238	C₃×#121	—	2	2	no	—
239	C₃×#121	—	2	2	no	—
240	C₃×#121	—	2	2	no	—
241	C₃×#121	—	2	2	no	—
242	C₃×#121	—	2	2	no	—
243	C₃×#121	—	2	2	no	—
244	C₃×#121	—	2	2	no	—
245	C₃×#121	—	2	2	no	—
246	C₃×#121	—	2	2	no	—
247	C₃×#121	—	2	1	no	—
248	C₃×#121	—	2	1	no	—
249	C₃×#121	—	2	1	no	—
250	C₃×#121	—	2	1	no	—
251	C₃×#121	—	2	2	no	—
252	C₃×#121	—	2	2	no	—
253	C₃×#121	—	2	2	no	—
254	C₃×#121	—	2	2	no	—
255	C₃×#121	D₄	1	2	yes	—
256	C₃×#121	D₄	1	1	yes	characteristic
257	C₃×#121	D₄	1	1	yes	characteristic
258	C₃×#121	C₂³	1	2	yes	—
259	C₃×#121	C₂³	1	1	yes	characteristic
260	C₃×#121	C₂³	1	2	yes	—
261	C₃×#121	C₂³	1	2	yes	—
262	C₃×#121	C₂³	1	2	yes	—
263	C₃×#121	C₂³	1	2	yes	—
264	C₃×#121	C₂³	1	2	yes	—
265	C₃×#120	—	2	2	no	—
266	C₃×#120	—	2	2	no	—
267	C₃×#120	—	2	2	no	—
268	C₃×#120	—	2	2	no	—
269	C₃×C₄×Q₈	—	2	1	no	—
270	C₃×C₄×Q₈	—	2	1	no	—
271	C₃×C₄×Q₈	—	2	1	no	—
272	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
273	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
274	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
275	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
276	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
277	C₃×C₄×D₄	—	2	1	no	—
278	C₃×C₄×D₄	—	2	1	no	—
279	C₃×C₄×D₄	—	2	1	no	—
280	C₃×C₄×D₄	—	2	1	no	—
281	C₃×C₄×D₄	—	2	1	no	—
282	C₃×C₄×D₄	—	2	1	no	—
283	C₃×C₄×D₄	—	2	2	no	—
284	C₃×C₄×D₄	—	2	2	no	—
285	C₃×C₄×D₄	—	2	2	no	—
286	C₃×C₄×D₄	—	2	1	no	—
287	C₃×C₄×D₄	—	2	1	no	—
288	C₃×C₄×D₄	—	2	1	no	—
289	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
290	C₃×C₄×D₄	C₂³	1	2	yes	—
291	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
292	C₃×C₄×D₄	C₂³	1	2	yes	—
293	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
294	C₃×#117	—	2	1	no	—
295	C₃×#117	C₂³	1	2	yes	—
296	C₂×C₃×C₄⋊C₄	—	2	1	no	—
297	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
298	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₃×C₄²	—	2	1	no	—
301	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
302	C₃×#107	C₂³	1	1	yes	characteristic
303	C₃×#107	C₂³	1	1	yes	characteristic
304	C₃×#106	C₂³	1	1	yes	characteristic
305	C₃×#106	C₂³	1	1	yes	characteristic
306	C₃×#106	C₂³	1	2	yes	—
307	C₃×#106	C₂³	1	2	yes	—
308	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
309	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
310	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
311	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
312	C₃×#103	C₂³	1	1	yes	characteristic
313	C₃×#103	C₂³	1	2	yes	—
314	C₃×#103	C₂³	1	2	yes	—
315	C₃×#103	C₂³	1	2	yes	—
316	C₃×#103	C₂³	1	1	yes	characteristic
317	C₃×#103	C₂³	1	1	yes	characteristic
318	C₃×#103	C₂³	1	2	yes	—
319	C₃×#103	C₂³	1	1	yes	characteristic
320	C₃×#103	C₂³	1	2	yes	—
321	C₃×#103	C₂³	1	2	yes	—
322	C₃×#103	C₂³	1	1	yes	characteristic
323	C₃×#103	C₂³	1	1	yes	characteristic
324	C₃×#102	C₂³	1	2	yes	—
325	C₃×#102	C₂³	1	2	yes	—
326	C₃×#102	C₂³	1	2	yes	—
327	C₃×#102	C₂³	1	2	yes	—
328	C₃×#102	C₂³	1	1	yes	characteristic
329	C₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
334	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
340	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₃×C₄×C₈	C₂³	1	2	yes	—
342	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
343	C₂×#137	C₂²×C₃	1	2	yes	complemented
344	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
345	C₂×#135	C₂²×C₃	1	2	yes	complemented
346	C₂²×SD₁₆	C₂²×C₃	1	2	yes	—
347	#560	—	2	2	no	—
348	#556	C₂²×C₃	1	1	yes	characteristic
349	#553	C₂²×C₃	1	2	yes	—
350	#550	—	2	1	no	—
351	#550	—	2	1	no	—
352	#550	C₂²×C₃	1	1	yes	characteristic
353	#550	C₂²×C₃	1	1	yes	characteristic
354	#550	C₂²×C₃	1	1	yes	characteristic, complemented
355	D₄×Q₈	—	2	1	no	—
356	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
357	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
358	#548	—	2	2	no	—
359	#548	C₂²×C₃	1	2	yes	complemented
360	#548	C₂²×C₃	1	2	yes	complemented
361	#547	C₂²×C₃	1	1	yes	characteristic
362	#546	—	2	1	no	—
363	#546	C₂²×C₃	1	2	yes	—
364	D₄²	C₂²×C₃	1	1	yes	characteristic
365	#542	—	2	1	no	—
366	#538	—	2	2	no	—
367	#537	—	2	2	no	—
368	#537	C₂²×C₃	1	2	yes	—
369	#537	C₂²×C₃	1	2	yes	complemented
370	#535	—	2	1	no	—
371	#535	C₂²×C₃	1	2	yes	—
372	#532	—	2	1	no	—
373	#532	—	2	1	no	—
374	#532	C₂²×C₃	1	1	yes	characteristic
375	#532	C₂²×C₃	1	1	yes	characteristic
376	#532	C₂²×C₃	1	1	yes	characteristic, complemented
377	#529	C₂²×C₃	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
379	#495	C₂²×C₃	1	2	yes	—
380	#493	C₂²×C₃	1	1	yes	characteristic
381	#492	C₂²×C₃	1	1	yes	characteristic
382	#488	C₂²×C₃	1	2	yes	complemented
383	#487	C₂²×C₃	1	1	yes	characteristic, complemented
384	#486	C₂²×C₃	1	1	yes	characteristic, complemented
385	#485	C₂²×C₃	1	2	yes	complemented
386	#483	C₂²×C₃	1	1	yes	characteristic, complemented
387	#483	C₂²×C₃	1	2	yes	complemented
388	#482	C₂²×C₃	1	2	yes	complemented
389	#481	C₂²×C₃	1	2	yes	complemented
390	#481	C₂²×C₃	1	2	yes	complemented
391	#480	C₂²×C₃	1	1	yes	characteristic
392	#479	C₂²×C₃	1	1	yes	characteristic, complemented
393	#479	C₂²×C₃	1	1	yes	characteristic, complemented
394	#475	C₂²×C₃	1	1	yes	characteristic, complemented
395	#475	C₂²×C₃	1	1	yes	characteristic, complemented
396	#470	C₂²×C₃	1	2	yes	complemented
397	#469	C₂²×C₃	1	2	yes	—
398	#469	C₂²×C₃	1	2	yes	—
399	#468	C₂²×C₃	1	2	yes	complemented
400	#466	C₂²×C₃	1	2	yes	complemented
401	#465	C₂²×C₃	1	2	yes	—
402	#465	C₂²×C₃	1	2	yes	—
403	#465	C₂²×C₃	1	2	yes	complemented
404	#464	C₂²×C₃	1	1	yes	characteristic
405	#464	C₂²×C₃	1	1	yes	characteristic
406	#463	C₂²×C₃	1	2	yes	complemented
407	#463	C₂²×C₃	1	2	yes	complemented
408	#462	C₂²×C₃	1	1	yes	characteristic, complemented
409	#461	C₂²×C₃	1	1	yes	characteristic
410	#460	C₂²×C₃	1	1	yes	characteristic
411	#460	C₂²×C₃	1	1	yes	characteristic
412	#460	C₂²×C₃	1	1	yes	characteristic, complemented
413	#459	C₂²×C₃	1	1	yes	characteristic
414	#452	C₂²×C₃	1	2	yes	complemented
415	#452	C₂²×C₃	1	2	yes	complemented
416	#452	C₂²×C₃	1	2	yes	complemented
417	#451	C₂²×C₃	1	2	yes	complemented
418	#451	C₂²×C₃	1	1	yes	characteristic, complemented
419	#450	C₂²×C₃	1	2	yes	—
420	#449	C₂²×C₃	1	2	yes	—
421	#449	C₂²×C₃	1	2	yes	—
422	#449	C₂²×C₃	1	2	yes	—
423	#449	C₂²×C₃	1	2	yes	complemented
424	#449	C₂²×C₃	1	2	yes	complemented
425	#449	C₂²×C₃	1	2	yes	complemented
426	#449	C₂²×C₃	1	2	yes	complemented
427	#448	C₂²×C₃	1	1	yes	characteristic
428	#448	C₂²×C₃	1	2	yes	—
429	#448	C₂²×C₃	1	2	yes	—
430	#448	C₂²×C₃	1	2	yes	complemented
431	#448	C₂²×C₃	1	2	yes	complemented
432	#447	C₂²×C₃	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
434	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
435	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
436	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
437	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
438	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
439	#436	C₂²×C₃	1	1	yes	characteristic
440	#436	C₂²×C₃	1	1	yes	characteristic, complemented
441	#436	C₂²×C₃	1	2	yes	complemented
442	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
443	C₈×D₄	C₂²×C₃	1	2	yes	complemented
444	C₈×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
445	#431	C₂²×C₃	1	1	yes	characteristic, complemented
446	#431	C₂²×C₃	1	1	yes	characteristic, complemented
447	#419	C₂²×C₃	1	2	yes	complemented
448	#417	C₂²×C₃	1	2	yes	complemented
449	#416	C₂²×C₃	1	2	yes	complemented
450	C₂×#103	C₂²×C₃	1	2	yes	complemented
451	#408	C₂²×C₃	1	2	yes	complemented
452	#408	C₂²×C₃	1	2	yes	complemented
453	C₂⁴×C₃	—	2	2	no	—
454	C₃×#41	—	2	4	no	—
455	C₃×#41	—	2	4	no	—
456	C₃×#41	—	4	2	no	—
457	C₃×#41	—	4	2	no	—
458	C₃×#41	—	4	2	no	—
459	C₃×#41	—	4	2	no	—
460	C₃×#41	—	4	2	no	—
461	C₃×#41	—	4	2	no	—
462	C₃×#41	—	4	8	no	—
463	C₃×#41	—	4	8	no	—
464	C₃×#41	—	4	2	no	—
465	C₃×#41	—	4	2	no	—
466	C₃×#41	—	4	8	no	—
467	C₃×#41	—	8	2	no	—
468	C₃×#41	—	8	2	no	—
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	1	no	—
473	C₂×C₃×Q₈	—	2	2	no	—
474	C₂×C₃×Q₈	—	2	2	no	—
475	C₂×C₃×Q₈	—	2	4	no	—
476	C₂×C₃×Q₈	—	2	4	no	—
477	C₂×C₃×Q₈	—	4	2	no	—
478	C₂×C₃×Q₈	—	4	2	no	—
479	C₂×C₃×Q₈	—	4	8	no	—
480	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
481	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
482	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
483	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
484	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
485	C₂×C₃×D₄	—	2	2	no	—
486	C₂×C₃×D₄	—	2	2	no	—
487	C₂×C₃×D₄	—	2	2	no	—
488	C₂×C₃×D₄	—	2	1	no	—
489	C₂×C₃×D₄	—	2	2	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	—	2	2	no	—
495	C₂×C₃×D₄	—	2	2	no	—
496	C₂×C₃×D₄	—	2	1	no	—
497	C₂×C₃×D₄	—	2	1	no	—
498	C₂×C₃×D₄	—	2	1	no	—
499	C₂×C₃×D₄	—	2	1	no	—
500	C₂×C₃×D₄	—	2	2	no	—
501	C₂×C₃×D₄	—	4	2	no	—
502	C₂×C₃×D₄	—	4	2	no	—
503	C₂×C₃×D₄	—	8	2	no	—
504	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
505	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
506	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
507	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
508	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
509	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
510	C₂×C₃×D₄	C₂⁴	1	2	yes	—
511	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
512	C₂×C₃×D₄	C₂⁴	1	2	yes	—
513	C₂²×C₃×C₄	—	2	1	no	—
514	C₂²×C₃×C₄	—	2	2	no	—
515	C₂²×C₃×C₄	—	2	2	no	—
516	C₂²×C₃×C₄	—	2	1	no	—
517	C₂²×C₃×C₄	—	2	2	no	—
518	C₂²×C₃×C₄	—	2	1	no	—
519	C₂²×C₃×C₄	—	2	2	no	—
520	C₂²×C₃×C₄	—	2	2	no	—
521	C₂²×C₃×C₄	—	2	2	no	—
522	C₂²×C₃×C₄	—	2	2	no	—
523	C₂²×C₃×C₄	—	2	2	no	—
524	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
525	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
526	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
527	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
528	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
529	C₃×Q₁₆	—	2	2	no	—
530	C₃×Q₁₆	—	2	2	no	—
531	C₃×Q₁₆	—	4	2	no	—
532	C₃×SD₁₆	—	2	2	no	—
533	C₃×SD₁₆	—	2	4	no	—
534	C₃×SD₁₆	—	2	2	no	—
535	C₃×SD₁₆	—	2	4	no	—
536	C₃×SD₁₆	—	4	2	no	—
537	C₃×SD₁₆	—	4	2	no	—
538	C₃×SD₁₆	—	4	2	no	—
539	C₃×SD₁₆	—	4	2	no	—
540	C₃×D₈	—	4	2	no	—
541	C₃×D₈	—	4	2	no	—
542	C₃×D₈	—	4	2	no	—
543	C₃×M₁₆	—	4	2	no	—
544	C₃×M₁₆	—	4	2	no	—
545	C₂×C₃×C₈	—	4	2	no	—
546	C₂×C₃×C₈	—	4	2	no	—
547	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
548	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
549	C₂×C₃×C₈	C₂⁴	1	2	yes	—
550	C₂×C₃×C₈	C₂⁴	1	2	yes	—
551	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
552	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
553	C₃×C₄⋊C₄	—	2	1	no	—
554	C₃×C₄⋊C₄	—	2	1	no	—
555	C₃×C₄⋊C₄	—	2	1	no	—
556	C₃×C₄⋊C₄	—	2	1	no	—
557	C₃×C₄⋊C₄	—	2	1	no	—
558	C₃×C₄⋊C₄	—	2	2	no	—
559	C₃×C₄⋊C₄	—	2	1	no	—
560	C₃×C₄⋊C₄	—	2	1	no	—
561	C₃×C₄⋊C₄	—	2	1	no	—
562	C₃×C₄⋊C₄	—	2	1	no	—
563	C₃×C₄⋊C₄	—	2	1	no	—
564	C₃×C₄⋊C₄	—	2	2	no	—
565	C₃×C₄⋊C₄	—	2	2	no	—
566	C₃×C₄⋊C₄	—	2	1	no	—
567	C₃×C₄⋊C₄	—	2	2	no	—
568	C₃×C₄⋊C₄	—	2	1	no	—
569	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
570	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
571	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
572	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
573	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
574	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
575	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
576	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
577	C₃×C₂²⋊C₄	—	2	2	no	—
578	C₃×C₂²⋊C₄	—	2	2	no	—
579	C₃×C₂²⋊C₄	—	2	1	no	—
580	C₃×C₂²⋊C₄	—	2	2	no	—
581	C₃×C₂²⋊C₄	—	2	2	no	—
582	C₃×C₂²⋊C₄	—	2	1	no	—
583	C₃×C₂²⋊C₄	—	2	2	no	—
584	C₃×C₂²⋊C₄	—	2	1	no	—
585	C₃×C₂²⋊C₄	—	2	1	no	—
586	C₃×C₂²⋊C₄	—	2	2	no	—
587	C₃×C₂²⋊C₄	—	2	2	no	—
588	C₃×C₂²⋊C₄	—	2	2	no	—
589	C₃×C₂²⋊C₄	—	2	2	no	—
590	C₃×C₂²⋊C₄	—	2	2	no	—
591	C₃×C₂²⋊C₄	—	2	2	no	—
592	C₃×C₂²⋊C₄	—	2	2	no	—
593	C₃×C₂²⋊C₄	—	2	1	no	—
594	C₃×C₂²⋊C₄	—	2	2	no	—
595	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
596	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
597	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
598	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
599	C₃×C₄²	—	2	1	no	—
600	C₃×C₄²	—	2	1	no	—
601	C₃×C₄²	—	2	1	no	—
602	C₃×C₄²	—	2	1	no	—
603	C₃×C₄²	—	2	1	no	—
604	C₃×C₄²	—	2	2	no	—
605	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
606	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
607	C₃×C₄²	C₂⁴	1	1	yes	characteristic
608	C₃×C₄²	C₂⁴	1	1	yes	characteristic
609	2₋¹⁺⁴	—	4	4	no	—
610	2₋¹⁺⁴	—	4	4	no	—
611	C₂×#41	—	2	2	no	—
612	C₂×#41	—	2	2	no	—
613	C₂×#41	—	2	2	no	—
614	C₂×#41	—	2	1	no	—
615	C₂×#41	—	2	1	no	—
616	C₂×#41	C₂³×C₃	1	2	yes	—
617	C₂×#41	C₂³×C₃	1	2	yes	—
618	C₂×#41	C₂³×C₃	1	2	yes	—
619	C₂×#41	C₂³×C₃	1	2	yes	—
620	C₂×#41	C₂³×C₃	1	2	yes	—
621	C₂²×Q₈	—	2	2	no	—
622	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
623	C₂²×Q₈	C₂³×C₃	1	2	yes	—
624	C₂²×Q₈	C₂³×C₃	1	2	yes	—
625	C₂²×D₄	—	2	1	no	—
626	C₂²×D₄	C₂³×C₃	1	2	yes	—
627	#137	—	4	4	no	—
628	AGL(1,ℤ/8)	—	4	4	no	—
629	#135	—	4	4	no	—
630	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
631	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
632	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
633	C₂×SD₁₆	—	4	4	no	—
634	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
635	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
637	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
638	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
642	C₂×D₈	C₂³×C₃	1	2	yes	—
643	C₂×D₈	C₂³×C₃	1	2	yes	—
644	C₂×D₈	C₂³×C₃	1	2	yes	—
645	C₂×M₁₆	C₂³×C₃	1	2	yes	—
646	C₂×M₁₆	C₂³×C₃	1	2	yes	—
647	C₂²×C₈	C₂³×C₃	1	2	yes	—
648	C₂²×C₈	C₂³×C₃	1	2	yes	—
649	C₄⋊Q₈	—	2	1	no	—
650	C₄⋊Q₈	—	2	1	no	—
651	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
654	#127	—	2	1	no	—
655	#127	—	2	1	no	—
656	#127	—	2	1	no	—
657	#127	—	2	2	no	—
658	#127	C₃×D₄	1	1	yes	characteristic
659	#127	C₂³×C₃	1	1	yes	characteristic
660	#127	C₂³×C₃	1	1	yes	characteristic
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	—	2	1	no	—
664	#125	C₂³×C₃	1	1	yes	characteristic
665	#124	—	2	2	no	—
666	#124	—	2	1	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	1	no	—
670	#124	C₃×D₄	1	2	yes	—
671	#124	C₂³×C₃	1	1	yes	characteristic
672	#124	C₂³×C₃	1	2	yes	—
673	#123	—	2	1	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	C₃×D₄	1	1	yes	characteristic
706	#121	C₃×D₄	1	1	yes	characteristic
707	#121	C₃×D₄	1	2	yes	—
708	#121	C₂³×C₃	1	1	yes	characteristic
709	#121	C₂³×C₃	1	2	yes	—
710	#121	C₂³×C₃	1	2	yes	—
711	#121	C₂³×C₃	1	2	yes	—
712	#121	C₂³×C₃	1	2	yes	—
713	#121	C₂³×C₃	1	2	yes	—
714	#121	C₂³×C₃	1	2	yes	—
715	#120	—	2	2	no	—
716	#120	—	2	2	no	—
717	#120	—	2	2	no	—
718	#120	—	2	2	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	—	2	1	no	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
723	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
724	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
725	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
726	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	—	2	1	no	—
738	C₄×D₄	—	2	1	no	—
739	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
740	C₄×D₄	C₂³×C₃	1	2	yes	—
741	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
742	C₄×D₄	C₂³×C₃	1	2	yes	—
743	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
744	#117	—	2	1	no	—
745	#117	C₂³×C₃	1	2	yes	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
749	C₂×C₂²⋊C₄	—	2	2	no	—
750	C₂×C₄²	—	2	1	no	—
751	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
752	#107	C₂³×C₃	1	1	yes	characteristic
753	#107	C₂³×C₃	1	1	yes	characteristic
754	#106	C₂³×C₃	1	1	yes	characteristic
755	#106	C₂³×C₃	1	1	yes	characteristic
756	#106	C₂³×C₃	1	2	yes	—
757	#106	C₂³×C₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
759	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
760	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
761	C₄⋊C₈	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	1	yes	characteristic
767	#103	C₂³×C₃	1	1	yes	characteristic
768	#103	C₂³×C₃	1	2	yes	—
769	#103	C₂³×C₃	1	1	yes	characteristic
770	#103	C₂³×C₃	1	2	yes	—
771	#103	C₂³×C₃	1	2	yes	—
772	#103	C₂³×C₃	1	1	yes	characteristic
773	#103	C₂³×C₃	1	1	yes	characteristic
774	#102	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
779	#102	C₂³×C₃	1	1	yes	characteristic
780	#102	C₂³×C₃	1	2	yes	—
781	#102	C₂³×C₃	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
783	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
789	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
790	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
791	C₄×C₈	C₂³×C₃	1	2	yes	—
792	C₂³×C₃	—	2	1	no	—
793	C₂³×C₃	—	2	2	no	—
794	C₂³×C₃	—	2	2	no	—
795	C₂³×C₃	—	8	2	no	—
796	C₂³×C₃	—	8	2	no	—
797	C₂³×C₃	—	8	2	no	—
798	C₂³×C₃	C₂²×D₄	1	2	yes	—
799	C₂³×C₃	C₂²×D₄	1	2	yes	—
800	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
801	C₃×Q₈	—	2	4	no	—
802	C₃×Q₈	—	2	1	no	—
803	C₃×Q₈	—	2	1	no	—
804	C₃×Q₈	—	2	1	no	—
805	C₃×Q₈	—	2	2	no	—
806	C₃×Q₈	—	2	2	no	—
807	C₃×Q₈	—	2	1	no	—
808	C₃×Q₈	—	4	2	no	—
809	C₃×Q₈	—	4	4	no	—
810	C₃×Q₈	—	4	4	no	—
811	C₃×Q₈	—	4	2	no	—
812	C₃×Q₈	H(5,𝔽₂)	1	2	yes	—
813	C₃×Q₈	H(5,𝔽₂)	1	2	yes	—
814	C₃×D₄	—	2	2	no	—
815	C₃×D₄	—	2	2	no	—
816	C₃×D₄	—	2	1	no	—
817	C₃×D₄	—	2	2	no	—
818	C₃×D₄	—	2	2	no	—
819	C₃×D₄	—	2	2	no	—
820	C₃×D₄	—	2	2	no	—
821	C₃×D₄	—	2	1	no	—
822	C₃×D₄	—	4	2	no	—
823	C₃×D₄	—	4	2	no	—
824	C₃×D₄	—	4	2	no	—
825	C₃×D₄	—	4	2	no	—
826	C₃×D₄	—	4	4	no	—
827	C₃×D₄	—	4	4	no	—
828	C₃×D₄	—	4	4	no	—
829	C₃×D₄	—	4	2	no	—
830	C₃×D₄	—	4	2	no	—
831	C₃×D₄	—	8	1	no	—
832	C₃×D₄	—	8	1	no	—
833	C₃×D₄	—	8	2	no	—
834	C₃×D₄	—	8	2	no	—
835	C₃×D₄	—	8	2	no	—
836	C₃×D₄	—	8	1	no	—
837	C₃×D₄	—	8	2	no	—
838	C₃×D₄	—	8	2	no	—
839	C₃×D₄	—	8	2	no	—
840	C₃×D₄	—	8	2	no	—
841	C₃×D₄	—	8	2	no	—
842	C₂×C₃×C₄	—	2	4	no	—
843	C₂×C₃×C₄	—	2	1	no	—
844	C₂×C₃×C₄	—	2	1	no	—
845	C₂×C₃×C₄	—	2	2	no	—
846	C₂×C₃×C₄	—	2	2	no	—
847	C₂×C₃×C₄	—	2	2	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	1	no	—
854	C₂×C₃×C₄	—	2	1	no	—
855	C₂×C₃×C₄	—	2	1	no	—
856	C₂×C₃×C₄	—	2	2	no	—
857	C₂×C₃×C₄	—	2	1	no	—
858	C₂×C₃×C₄	—	2	2	no	—
859	C₂×C₃×C₄	—	4	1	no	—
860	C₂×C₃×C₄	—	4	4	no	—
861	C₂×C₃×C₄	—	4	4	no	—
862	C₂×C₃×C₄	—	4	4	no	—
863	C₂×C₃×C₄	—	4	4	no	—
864	C₂×C₃×C₄	—	4	4	no	—
865	C₂×C₃×C₄	—	4	2	no	—
866	C₂×C₃×C₄	—	8	2	no	—
867	C₂×C₃×C₄	—	8	2	no	—
868	C₂×C₃×C₄	—	8	1	no	—
869	C₂×C₃×C₄	—	8	2	no	—
870	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
872	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
876	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
878	C₃×C₈	—	2	1	no	—
879	C₃×C₈	—	2	1	no	—
880	C₃×C₈	—	2	2	no	—
881	C₃×C₈	—	2	1	no	—
882	C₃×C₈	—	2	2	no	—
883	C₃×C₈	—	2	1	no	—
884	C₂⁴	—	2	2	no	—
885	#41	—	2	4	no	—
886	#41	—	2	4	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	4	2	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	8	no	—
894	#41	—	4	8	no	—
895	#41	—	4	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	8	no	—
898	#41	—	8	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	4	no	—
907	C₂×Q₈	—	2	4	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	4	8	no	—
911	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
915	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	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	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	8	2	no	—
935	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
936	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
937	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
938	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
939	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
940	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
941	C₂×D₄	C₂⁴×C₃	1	2	yes	—
942	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
943	C₂×D₄	C₂⁴×C₃	1	2	yes	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
956	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
959	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
960	Q₁₆	—	2	2	no	—
961	Q₁₆	—	2	2	no	—
962	Q₁₆	—	4	2	no	—
963	SD₁₆	—	2	2	no	—
964	SD₁₆	—	2	4	no	—
965	SD₁₆	—	2	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	D₈	—	4	2	no	—
972	D₈	—	4	2	no	—
973	D₈	—	4	2	no	—
974	M₁₆	—	4	2	no	—
975	M₁₆	—	4	2	no	—
976	C₂×C₈	—	4	2	no	—
977	C₂×C₈	—	4	2	no	—
978	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₃	1	2	yes	—
981	C₂×C₈	C₂⁴×C₃	1	2	yes	—
982	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
1001	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1007	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1027	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1028	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1029	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1037	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1040	C₂²×C₃	—	2	1	no	—
1041	C₂²×C₃	—	2	2	no	—
1042	C₂²×C₃	—	2	2	no	—
1043	C₂²×C₃	—	2	1	no	—
1044	C₂²×C₃	—	2	2	no	—
1045	C₂²×C₃	—	2	2	no	—
1046	C₂²×C₃	—	2	1	no	—
1047	C₂²×C₃	—	2	2	no	—
1048	C₂²×C₃	—	2	2	no	—
1049	C₂²×C₃	—	4	2	no	—
1050	C₂²×C₃	—	4	2	no	—
1051	C₂²×C₃	—	4	1	no	—
1052	C₂²×C₃	—	4	2	no	—
1053	C₂²×C₃	—	4	2	no	—
1054	C₂²×C₃	—	4	1	no	—
1055	C₂²×C₃	—	4	1	no	—
1056	C₂²×C₃	—	4	2	no	—
1057	C₂²×C₃	—	4	2	no	—
1058	C₂²×C₃	—	16	4	no	—
1059	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1060	C₃×C₄	—	2	1	no	—
1061	C₃×C₄	—	2	1	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	2	1	no	—
1065	C₃×C₄	—	2	2	no	—
1066	C₃×C₄	—	2	2	no	—
1067	C₃×C₄	—	2	1	no	—
1068	C₃×C₄	—	4	1	no	—
1069	C₃×C₄	—	4	1	no	—
1070	C₃×C₄	—	4	1	no	—
1071	C₃×C₄	—	4	2	no	—
1072	C₃×C₄	—	4	1	no	—
1073	C₃×C₄	—	4	1	no	—
1074	C₃×C₄	—	4	2	no	—
1075	C₃×C₄	#577	1	2	yes	—
1076	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1077	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	C₂²×C₃×D₄	1	2	yes	—
1085	C₂³	C₂²×C₃×D₄	1	2	yes	—
1086	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1087	Q₈	—	2	4	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	1	no	—
1094	Q₈	—	4	2	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	4	no	—
1097	Q₈	—	4	2	no	—
1098	Q₈	C₃×H(5,𝔽₂)	1	2	yes	—
1099	Q₈	C₃×H(5,𝔽₂)	1	2	yes	—
1100	D₄	—	2	2	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	2	1	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	1	no	—
1127	D₄	—	8	2	no	—
1128	C₂×C₄	—	2	4	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	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	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	4	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	8	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	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	1	yes	characteristic
1160	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1161	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1162	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1163	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1164	C₈	—	2	1	no	—
1165	C₈	—	2	1	no	—
1166	C₈	—	2	2	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	1	no	—
1170	C₂×C₃	—	4	1	no	—
1171	C₂×C₃	—	4	2	no	—
1172	C₂×C₃	—	4	2	no	—
1173	C₂×C₃	—	8	2	no	—
1174	C₂×C₃	—	8	2	no	—
1175	C₂×C₃	—	8	1	no	—
1176	C₂×C₃	#3484	1	1	yes	characteristic
1177	C₂×C₃	C₂×#577	1	1	yes	characteristic
1178	C₂×C₃	#3584	1	1	yes	characteristic
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	16	4	no	—
1198	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1199	C₄	—	2	2	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	C₃×#577	1	2	yes	—
1215	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1217	C₃	#61659	1	1	yes	characteristic, direct product factor, Sylow
1218	C₂	—	4	2	no	—
1219	C₂	—	4	1	no	—
1220	C₂	—	4	2	no	—
1221	C₂	—	8	1	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	2	no	—
1224	C₂	C₃×#3484	1	1	yes	characteristic
1225	C₂	C₂×C₃×#577	1	1	yes	characteristic
1226	C₂	C₃×#3584	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 ◁ C₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3546	C₂	semidirect
2. C₃×#3497	C₂	semidirect
3. C₃×#3332	C₂	semidirect
4. C₃×#3328	C₂	semidirect
5. C₃×#3326	C₂	semidirect
6. C₃×#3304	C₂	semidirect
7. C₃×#3301	C₂	semidirect
8. C₃×#3298	C₂	semidirect
9. C₃×#3287	C₂	semidirect
10. C₃×#3282	C₂	semidirect
11. C₃×D₄×SD₁₆	C₂	semidirect
12. C₃×#3278	C₂	semidirect
13. C₃×#3275	C₂	semidirect
14. C₃×#3274	C₂	semidirect
15. C₃×#3212	C₂	semidirect
16. C₃×#3207	C₂	semidirect
17. C₃×#3204	C₂	semidirect
18. C₃×#3198	C₂	semidirect
19. C₃×#3108	C₂	semidirect
20. C₃×#3103	C₂	semidirect
21. C₃×#3013	C₂	semidirect
22. C₃×#3010	C₂	semidirect
23. C₃×#2979	C₂	semidirect
24. #61659	C₃	direct (N × H)
25. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
26. C₂×C₃×#137	C₂²	semidirect
28. C₂×C₃×#135	C₂²	semidirect
37. C₃×#550	C₂²	semidirect
40. C₃×D₄×Q₈	C₂²	semidirect
42. C₃×#548	C₂²	semidirect
43. C₃×#548	C₂²	semidirect
52. C₃×#537	C₂²	semidirect
59. C₃×#532	C₂²	semidirect
61. C₂×C₃×C₄×Q₈	C₂²	semidirect
65. C₃×#488	C₂²	semidirect
66. C₃×#487	C₂²	semidirect
67. C₃×#486	C₂²	semidirect
68. C₃×#485	C₂²	semidirect
69. C₃×#483	C₂²	semidirect
70. C₃×#483	C₂²	semidirect
71. C₃×#482	C₂²	semidirect
72. C₃×#481	C₂²	semidirect
73. C₃×#481	C₂²	semidirect
75. C₃×#479	C₂²	semidirect
76. C₃×#479	C₂²	semidirect
77. C₃×#475	C₂²	semidirect
78. C₃×#475	C₂²	semidirect
79. C₃×#470	C₂²	semidirect
82. C₃×#468	C₂²	semidirect
83. C₃×#466	C₂²	semidirect
86. C₃×#465	C₂²	semidirect
89. C₃×#463	C₂²	semidirect
90. C₃×#463	C₂²	semidirect
91. C₃×#462	C₂²	semidirect
95. C₃×#460	C₂²	semidirect
97. C₃×#452	C₂²	semidirect
98. C₃×#452	C₂²	semidirect
99. C₃×#452	C₂²	semidirect
100. C₃×#451	C₂²	semidirect
101. C₃×#451	C₂²	semidirect
106. C₃×#449	C₂²	semidirect
107. C₃×#449	C₂²	semidirect
108. C₃×#449	C₂²	semidirect
109. C₃×#449	C₂²	semidirect
113. C₃×#448	C₂²	semidirect
114. C₃×#448	C₂²	semidirect
116. C₃×C₄×Q₁₆	C₂²	semidirect
117. C₃×C₄×Q₁₆	C₂²	semidirect
120. C₃×C₄×SD₁₆	C₂²	semidirect
121. C₃×C₄×SD₁₆	C₂²	semidirect
123. C₃×#436	C₂²	semidirect
124. C₃×#436	C₂²	semidirect
126. C₃×C₈×D₄	C₂²	semidirect
127. C₃×C₈×D₄	C₂²	semidirect
128. C₃×#431	C₂²	semidirect
129. C₃×#431	C₂²	semidirect
130. C₃×#419	C₂²	semidirect
131. C₃×#417	C₂²	semidirect
132. C₃×#416	C₂²	semidirect
133. C₂×C₃×#103	C₂²	semidirect
134. C₃×#408	C₂²	semidirect
135. C₃×#408	C₂²	semidirect
136. #3546	C₂×C₃	semidirect
137. #3497	C₂×C₃	semidirect
138. #3332	C₂×C₃	semidirect
139. #3328	C₂×C₃	semidirect
140. #3326	C₂×C₃	semidirect
141. #3304	C₂×C₃	semidirect
142. #3301	C₂×C₃	semidirect
143. #3298	C₂×C₃	semidirect
144. #3287	C₂×C₃	semidirect
145. #3282	C₂×C₃	semidirect
146. D₄×SD₁₆	C₂×C₃	semidirect
147. #3278	C₂×C₃	semidirect
148. #3275	C₂×C₃	semidirect
149. #3274	C₂×C₃	semidirect
150. #3212	C₂×C₃	semidirect
151. #3207	C₂×C₃	semidirect
152. #3204	C₂×C₃	semidirect
153. #3198	C₂×C₃	semidirect
154. #3108	C₂×C₃	semidirect
155. #3103	C₂×C₃	semidirect
156. #3013	C₂×C₃	semidirect
157. #3010	C₂×C₃	semidirect
158. #2979	C₂×C₃	semidirect
342. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
343. C₂×#137	C₂²×C₃	semidirect
345. C₂×#135	C₂²×C₃	semidirect
354. #550	C₂²×C₃	semidirect
357. D₄×Q₈	C₂²×C₃	semidirect
359. #548	C₂²×C₃	semidirect
360. #548	C₂²×C₃	semidirect
369. #537	C₂²×C₃	semidirect
376. #532	C₂²×C₃	semidirect
378. C₂×C₄×Q₈	C₂²×C₃	semidirect
382. #488	C₂²×C₃	semidirect
383. #487	C₂²×C₃	semidirect
384. #486	C₂²×C₃	semidirect
385. #485	C₂²×C₃	semidirect
386. #483	C₂²×C₃	semidirect
387. #483	C₂²×C₃	semidirect
388. #482	C₂²×C₃	semidirect
389. #481	C₂²×C₃	semidirect
390. #481	C₂²×C₃	semidirect
392. #479	C₂²×C₃	semidirect
393. #479	C₂²×C₃	semidirect
394. #475	C₂²×C₃	semidirect
395. #475	C₂²×C₃	semidirect
396. #470	C₂²×C₃	semidirect
399. #468	C₂²×C₃	semidirect
400. #466	C₂²×C₃	semidirect
403. #465	C₂²×C₃	semidirect
406. #463	C₂²×C₃	semidirect
407. #463	C₂²×C₃	semidirect
408. #462	C₂²×C₃	semidirect
412. #460	C₂²×C₃	semidirect
414. #452	C₂²×C₃	semidirect
415. #452	C₂²×C₃	semidirect
416. #452	C₂²×C₃	semidirect
417. #451	C₂²×C₃	semidirect
418. #451	C₂²×C₃	semidirect
423. #449	C₂²×C₃	semidirect
424. #449	C₂²×C₃	semidirect
425. #449	C₂²×C₃	semidirect
426. #449	C₂²×C₃	semidirect
430. #448	C₂²×C₃	semidirect
431. #448	C₂²×C₃	semidirect
433. C₄×Q₁₆	C₂²×C₃	semidirect
434. C₄×Q₁₆	C₂²×C₃	semidirect
437. C₄×SD₁₆	C₂²×C₃	semidirect
438. C₄×SD₁₆	C₂²×C₃	semidirect
440. #436	C₂²×C₃	semidirect
441. #436	C₂²×C₃	semidirect
443. C₈×D₄	C₂²×C₃	semidirect
444. C₈×D₄	C₂²×C₃	semidirect
445. #431	C₂²×C₃	semidirect
446. #431	C₂²×C₃	semidirect
447. #419	C₂²×C₃	semidirect
448. #417	C₂²×C₃	semidirect
449. #416	C₂²×C₃	semidirect
450. C₂×#103	C₂²×C₃	semidirect
451. #408	C₂²×C₃	semidirect
452. #408	C₂²×C₃	semidirect
1217. C₃	#61659	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×#3546	2
C₃×#3497	2
C₃×#3332	2
C₃×#3328	2
C₃×#3326	2
C₃×#3304	2
C₃×#3301	2
C₃×#3298	2
C₃×#3287	2
C₃×#3282	2
C₃×D₄×SD₁₆	2
C₃×#3278	2
C₃×#3275	2
C₃×#3274	2
C₃×#3212	2
C₃×#3207	2
C₃×#3204	2
C₃×#3198	2
C₃×#3108	2
C₃×#3103	2
C₃×#3013	2
C₃×#3010	2
C₃×#2979	2
#61659	3

Subgroups — C3×#61659 #10680266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61659 #10680266