Subgroups — C₃×#61671 #10680278

Order 768.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1118 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×#3320	C₂	1	2	yes	maximal, complemented
4	C₃×#3313	C₂	1	2	yes	maximal, complemented
5	C₃×#3309	C₂	1	2	yes	maximal, complemented
6	C₃×#3308	C₂	1	2	yes	maximal, complemented
7	C₃×#3271	C₂	1	2	yes	maximal, complemented
8	C₃×#3268	C₂	1	2	yes	maximal, complemented
9	C₃×#3266	C₂	1	2	yes	maximal, complemented
10	C₃×#3265	C₂	1	2	yes	maximal, complemented
11	C₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3203	C₂	1	2	yes	maximal, complemented
14	C₃×#3198	C₂	1	2	yes	maximal, complemented
15	C₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3013	C₂	1	2	yes	maximal, complemented
18	C₃×#3010	C₂	1	2	yes	maximal, complemented
19	C₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	#61671	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
22	C₂×C₃×#137	C₂²	1	2	yes	complemented
23	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
24	C₂×C₃×#135	C₂²	1	2	yes	complemented
25	C₂²×C₃×SD₁₆	C₂²	1	2	yes	—
26	C₃×#560	—	2	2	no	—
27	C₃×#556	C₂²	1	1	yes	characteristic
28	C₃×#553	C₂²	1	2	yes	—
29	C₃×#550	—	2	1	no	—
30	C₃×#550	—	2	1	no	—
31	C₃×#550	C₂²	1	1	yes	characteristic
32	C₃×#550	C₂²	1	2	yes	complemented
33	C₃×D₄×Q₈	—	2	1	no	—
34	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
35	C₃×#548	—	2	2	no	—
36	C₃×#548	C₂²	1	2	yes	—
37	C₃×#548	C₂²	1	2	yes	complemented
38	C₃×#547	C₂²	1	1	yes	characteristic
39	C₃×#546	—	2	1	no	—
40	C₃×#546	C₂²	1	2	yes	—
41	C₃×D₄²	C₂²	1	1	yes	characteristic
42	C₃×#542	—	2	1	no	—
43	C₃×#538	—	2	2	no	—
44	C₃×#537	—	2	1	no	—
45	C₃×#537	—	2	1	no	—
46	C₃×#537	C₂²	1	2	yes	—
47	C₃×#537	C₂²	1	2	yes	complemented
48	C₃×#535	—	2	1	no	—
49	C₃×#535	C₂²	1	2	yes	—
50	C₃×#532	—	2	2	no	—
51	C₃×#532	C₂²	1	1	yes	characteristic
52	C₃×#532	C₂²	1	1	yes	characteristic
53	C₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₃×#529	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₃×#497	C₂²	1	1	yes	characteristic
57	C₃×#496	C₂²	1	2	yes	—
58	C₃×#496	C₂²	1	1	yes	characteristic
59	C₃×#491	C₂²	1	1	yes	characteristic, complemented
60	C₃×#490	C₂²	1	1	yes	characteristic, complemented
61	C₃×#489	C₂²	1	2	yes	complemented
62	C₃×#485	C₂²	1	2	yes	complemented
63	C₃×#484	C₂²	1	1	yes	characteristic, complemented
64	C₃×#484	C₂²	1	2	yes	complemented
65	C₃×#482	C₂²	1	2	yes	complemented
66	C₃×#481	C₂²	1	1	yes	characteristic
67	C₃×#480	C₂²	1	2	yes	complemented
68	C₃×#480	C₂²	1	2	yes	complemented
69	C₃×#479	C₂²	1	2	yes	complemented
70	C₃×#477	C₂²	1	2	yes	complemented
71	C₃×#469	C₂²	1	2	yes	complemented
72	C₃×#468	C₂²	1	2	yes	—
73	C₃×#468	C₂²	1	2	yes	—
74	C₃×#468	C₂²	1	2	yes	complemented
75	C₃×#467	C₂²	1	2	yes	complemented
76	C₃×#466	C₂²	1	2	yes	—
77	C₃×#466	C₂²	1	2	yes	—
78	C₃×#465	C₂²	1	2	yes	complemented
79	C₃×#464	C₂²	1	2	yes	—
80	C₃×#464	C₂²	1	2	yes	complemented
81	C₃×#463	C₂²	1	2	yes	—
82	C₃×#461	C₂²	1	2	yes	complemented
83	C₃×#460	C₂²	1	2	yes	—
84	C₃×#459	C₂²	1	2	yes	complemented
85	C₃×#452	C₂²	1	2	yes	complemented
86	C₃×#452	C₂²	1	2	yes	complemented
87	C₃×#452	C₂²	1	2	yes	complemented
88	C₃×#451	C₂²	1	2	yes	complemented
89	C₃×#451	C₂²	1	1	yes	characteristic, complemented
90	C₃×#450	C₂²	1	2	yes	—
91	C₃×#449	C₂²	1	2	yes	—
92	C₃×#449	C₂²	1	2	yes	—
93	C₃×#449	C₂²	1	2	yes	—
94	C₃×#449	C₂²	1	2	yes	complemented
95	C₃×#449	C₂²	1	2	yes	complemented
96	C₃×#449	C₂²	1	2	yes	complemented
97	C₃×#449	C₂²	1	2	yes	complemented
98	C₃×#448	C₂²	1	2	yes	—
99	C₃×#448	C₂²	1	1	yes	characteristic
100	C₃×#448	C₂²	1	2	yes	—
101	C₃×#448	C₂²	1	2	yes	complemented
102	C₃×#448	C₂²	1	2	yes	complemented
103	C₃×#447	C₂²	1	2	yes	—
104	C₃×#441	C₂²	1	2	yes	complemented
105	C₃×#440	C₂²	1	2	yes	—
106	C₃×#440	C₂²	1	2	yes	complemented
107	C₃×#440	C₂²	1	2	yes	complemented
108	C₃×#435	C₂²	1	2	yes	—
109	C₃×#435	C₂²	1	2	yes	complemented
110	C₃×#435	C₂²	1	2	yes	complemented
111	C₃×#435	C₂²	1	2	yes	complemented
112	C₃×#432	C₂²	1	1	yes	characteristic, complemented
113	C₃×#432	C₂²	1	1	yes	characteristic, complemented
114	C₃×#419	C₂²	1	2	yes	complemented
115	C₃×#417	C₂²	1	2	yes	complemented
116	C₃×#416	C₂²	1	2	yes	complemented
117	C₂×C₃×#103	C₂²	1	2	yes	complemented
118	C₃×#408	C₂²	1	2	yes	complemented
119	C₃×#408	C₂²	1	2	yes	complemented
120	#3546	C₂×C₃	1	1	yes	characteristic, complemented
121	#3497	C₂×C₃	1	1	yes	characteristic, complemented
122	#3320	C₂×C₃	1	2	yes	complemented
123	#3313	C₂×C₃	1	2	yes	complemented
124	#3309	C₂×C₃	1	2	yes	complemented
125	#3308	C₂×C₃	1	2	yes	complemented
126	#3271	C₂×C₃	1	2	yes	complemented
127	#3268	C₂×C₃	1	2	yes	complemented
128	#3266	C₂×C₃	1	2	yes	complemented
129	#3265	C₂×C₃	1	2	yes	complemented
130	#3219	C₂×C₃	1	1	yes	characteristic, complemented
131	#3214	C₂×C₃	1	1	yes	characteristic, complemented
132	#3203	C₂×C₃	1	2	yes	complemented
133	#3198	C₂×C₃	1	2	yes	complemented
134	#3117	C₂×C₃	1	1	yes	characteristic, complemented
135	#3112	C₂×C₃	1	1	yes	characteristic, complemented
136	#3013	C₂×C₃	1	2	yes	complemented
137	#3010	C₂×C₃	1	2	yes	complemented
138	#2980	C₂×C₃	1	1	yes	characteristic, complemented
139	C₃×2₋¹⁺⁴	—	4	4	no	—
140	C₃×2₋¹⁺⁴	—	4	4	no	—
141	C₂×C₃×#41	—	2	2	no	—
142	C₂×C₃×#41	—	2	2	no	—
143	C₂×C₃×#41	—	2	2	no	—
144	C₂×C₃×#41	—	2	1	no	—
145	C₂×C₃×#41	—	2	1	no	—
146	C₂×C₃×#41	C₂³	1	2	yes	—
147	C₂×C₃×#41	C₂³	1	2	yes	—
148	C₂×C₃×#41	C₂³	1	2	yes	—
149	C₂×C₃×#41	C₂³	1	2	yes	—
150	C₂×C₃×#41	C₂³	1	2	yes	—
151	C₂²×C₃×Q₈	—	2	2	no	—
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×Q₈	C₂³	1	2	yes	—
154	C₂²×C₃×Q₈	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	—	2	1	no	—
156	C₂²×C₃×D₄	C₂³	1	2	yes	—
157	C₃×#137	—	4	4	no	—
158	C₃×AGL(1,ℤ/8)	—	4	4	no	—
159	C₃×#135	—	4	4	no	—
160	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
162	C₂×C₃×SD₁₆	—	4	4	no	—
163	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
170	C₂×C₃×D₈	C₂³	1	2	yes	—
171	C₂×C₃×D₈	C₂³	1	2	yes	—
172	C₂×C₃×D₈	C₂³	1	2	yes	—
173	C₂×C₃×M₁₆	C₂³	1	2	yes	—
174	C₂×C₃×M₁₆	C₂³	1	2	yes	—
175	C₂²×C₃×C₈	C₂³	1	2	yes	—
176	C₂²×C₃×C₈	C₂³	1	2	yes	—
177	C₃×C₄⋊Q₈	—	2	2	no	—
178	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
179	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₃×#127	—	2	2	no	—
182	C₃×#127	—	2	2	no	—
183	C₃×#127	—	2	1	no	—
184	C₃×#127	D₄	1	1	yes	characteristic
185	C₃×#127	C₂³	1	1	yes	characteristic
186	C₃×#127	C₂³	1	1	yes	characteristic
187	C₃×#126	—	2	2	no	—
188	C₃×#126	—	2	2	no	—
189	C₃×#126	—	2	1	no	—
190	C₃×#125	C₂³	1	1	yes	characteristic
191	C₃×#124	—	2	2	no	—
192	C₃×#124	—	2	1	no	—
193	C₃×#124	—	2	2	no	—
194	C₃×#124	—	2	2	no	—
195	C₃×#124	—	2	1	no	—
196	C₃×#124	D₄	1	2	yes	—
197	C₃×#124	C₂³	1	2	yes	—
198	C₃×#124	C₂³	1	1	yes	characteristic
199	C₃×#123	—	2	1	no	—
200	C₃×#123	—	2	2	no	—
201	C₃×#123	—	2	2	no	—
202	C₃×#123	—	2	2	no	—
203	C₃×C₂²⋊Q₈	—	2	2	no	—
204	C₃×C₂²⋊Q₈	—	2	2	no	—
205	C₃×C₂²⋊Q₈	—	2	2	no	—
206	C₃×C₂²⋊Q₈	—	2	2	no	—
207	C₃×C₂²⋊Q₈	—	2	1	no	—
208	C₃×C₂²⋊Q₈	—	2	2	no	—
209	C₃×C₂²⋊Q₈	—	2	2	no	—
210	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃×#121	—	2	2	no	—
215	C₃×#121	—	2	2	no	—
216	C₃×#121	—	2	2	no	—
217	C₃×#121	—	2	2	no	—
218	C₃×#121	—	2	2	no	—
219	C₃×#121	—	2	2	no	—
220	C₃×#121	—	2	2	no	—
221	C₃×#121	—	2	2	no	—
222	C₃×#121	—	2	2	no	—
223	C₃×#121	—	2	1	no	—
224	C₃×#121	—	2	1	no	—
225	C₃×#121	—	2	1	no	—
226	C₃×#121	—	2	1	no	—
227	C₃×#121	—	2	2	no	—
228	C₃×#121	—	2	2	no	—
229	C₃×#121	—	2	2	no	—
230	C₃×#121	—	2	2	no	—
231	C₃×#121	D₄	1	2	yes	—
232	C₃×#121	D₄	1	1	yes	characteristic
233	C₃×#121	D₄	1	1	yes	characteristic
234	C₃×#121	C₂³	1	2	yes	—
235	C₃×#121	C₂³	1	1	yes	characteristic
236	C₃×#121	C₂³	1	2	yes	—
237	C₃×#121	C₂³	1	2	yes	—
238	C₃×#121	C₂³	1	2	yes	—
239	C₃×#121	C₂³	1	2	yes	—
240	C₃×#121	C₂³	1	2	yes	—
241	C₃×#120	—	2	2	no	—
242	C₃×#120	—	2	2	no	—
243	C₃×#120	—	2	2	no	—
244	C₃×#120	—	2	2	no	—
245	C₃×C₄×Q₈	—	2	1	no	—
246	C₃×C₄×Q₈	—	2	1	no	—
247	C₃×C₄×Q₈	—	2	1	no	—
248	C₃×C₄×Q₈	C₂³	1	2	yes	—
249	C₃×C₄×Q₈	C₂³	1	2	yes	—
250	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₃×C₄×D₄	—	2	2	no	—
252	C₃×C₄×D₄	—	2	1	no	—
253	C₃×C₄×D₄	—	2	2	no	—
254	C₃×C₄×D₄	—	2	1	no	—
255	C₃×C₄×D₄	—	2	2	no	—
256	C₃×C₄×D₄	—	2	2	no	—
257	C₃×C₄×D₄	—	2	2	no	—
258	C₃×C₄×D₄	—	2	1	no	—
259	C₃×C₄×D₄	—	2	1	no	—
260	C₃×C₄×D₄	—	2	1	no	—
261	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
262	C₃×C₄×D₄	C₂³	1	2	yes	—
263	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
264	C₃×C₄×D₄	C₂³	1	2	yes	—
265	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
266	C₃×#117	—	2	1	no	—
267	C₃×#117	C₂³	1	2	yes	—
268	C₂×C₃×C₄⋊C₄	—	2	1	no	—
269	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₃×C₄²	—	2	1	no	—
273	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
274	C₃×#107	C₂³	1	2	yes	—
275	C₃×#107	C₂³	1	2	yes	—
276	C₃×#107	C₂³	1	2	yes	—
277	C₃×#106	C₂³	1	2	yes	—
278	C₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃×#103	C₂³	1	2	yes	—
281	C₃×#103	C₂³	1	2	yes	—
282	C₃×#103	C₂³	1	2	yes	—
283	C₃×#103	C₂³	1	2	yes	—
284	C₃×#103	C₂³	1	2	yes	—
285	C₃×#103	C₂³	1	2	yes	—
286	C₃×#103	C₂³	1	2	yes	—
287	C₃×#103	C₂³	1	2	yes	—
288	C₃×#103	C₂³	1	2	yes	—
289	C₃×#102	C₂³	1	2	yes	—
290	C₃×#102	C₂³	1	2	yes	—
291	C₃×#102	C₂³	1	2	yes	—
292	C₃×#102	C₂³	1	2	yes	—
293	C₃×#102	C₂³	1	2	yes	—
294	C₃×#102	C₂³	1	2	yes	—
295	C₃×#102	C₂³	1	2	yes	—
296	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
297	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
298	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
299	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
300	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
301	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
302	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃×#97	C₂³	1	2	yes	—
304	C₃×#97	C₂³	1	1	yes	characteristic
305	C₃×#97	C₂³	1	1	yes	characteristic
306	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
307	C₂×#137	C₂²×C₃	1	2	yes	complemented
308	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
309	C₂×#135	C₂²×C₃	1	2	yes	complemented
310	C₂²×SD₁₆	C₂²×C₃	1	2	yes	—
311	#560	—	2	2	no	—
312	#556	C₂²×C₃	1	1	yes	characteristic
313	#553	C₂²×C₃	1	2	yes	—
314	#550	—	2	1	no	—
315	#550	—	2	1	no	—
316	#550	C₂²×C₃	1	1	yes	characteristic
317	#550	C₂²×C₃	1	2	yes	complemented
318	D₄×Q₈	—	2	1	no	—
319	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
320	#548	—	2	2	no	—
321	#548	C₂²×C₃	1	2	yes	—
322	#548	C₂²×C₃	1	2	yes	complemented
323	#547	C₂²×C₃	1	1	yes	characteristic
324	#546	—	2	1	no	—
325	#546	C₂²×C₃	1	2	yes	—
326	D₄²	C₂²×C₃	1	1	yes	characteristic
327	#542	—	2	1	no	—
328	#538	—	2	2	no	—
329	#537	—	2	1	no	—
330	#537	—	2	1	no	—
331	#537	C₂²×C₃	1	2	yes	—
332	#537	C₂²×C₃	1	2	yes	complemented
333	#535	—	2	1	no	—
334	#535	C₂²×C₃	1	2	yes	—
335	#532	—	2	2	no	—
336	#532	C₂²×C₃	1	1	yes	characteristic
337	#532	C₂²×C₃	1	1	yes	characteristic
338	#532	C₂²×C₃	1	1	yes	characteristic, complemented
339	#529	C₂²×C₃	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
341	#497	C₂²×C₃	1	1	yes	characteristic
342	#496	C₂²×C₃	1	2	yes	—
343	#496	C₂²×C₃	1	1	yes	characteristic
344	#491	C₂²×C₃	1	1	yes	characteristic, complemented
345	#490	C₂²×C₃	1	1	yes	characteristic, complemented
346	#489	C₂²×C₃	1	2	yes	complemented
347	#485	C₂²×C₃	1	2	yes	complemented
348	#484	C₂²×C₃	1	1	yes	characteristic, complemented
349	#484	C₂²×C₃	1	2	yes	complemented
350	#482	C₂²×C₃	1	2	yes	complemented
351	#481	C₂²×C₃	1	1	yes	characteristic
352	#480	C₂²×C₃	1	2	yes	complemented
353	#480	C₂²×C₃	1	2	yes	complemented
354	#479	C₂²×C₃	1	2	yes	complemented
355	#477	C₂²×C₃	1	2	yes	complemented
356	#469	C₂²×C₃	1	2	yes	complemented
357	#468	C₂²×C₃	1	2	yes	—
358	#468	C₂²×C₃	1	2	yes	—
359	#468	C₂²×C₃	1	2	yes	complemented
360	#467	C₂²×C₃	1	2	yes	complemented
361	#466	C₂²×C₃	1	2	yes	—
362	#466	C₂²×C₃	1	2	yes	—
363	#465	C₂²×C₃	1	2	yes	complemented
364	#464	C₂²×C₃	1	2	yes	—
365	#464	C₂²×C₃	1	2	yes	complemented
366	#463	C₂²×C₃	1	2	yes	—
367	#461	C₂²×C₃	1	2	yes	complemented
368	#460	C₂²×C₃	1	2	yes	—
369	#459	C₂²×C₃	1	2	yes	complemented
370	#452	C₂²×C₃	1	2	yes	complemented
371	#452	C₂²×C₃	1	2	yes	complemented
372	#452	C₂²×C₃	1	2	yes	complemented
373	#451	C₂²×C₃	1	1	yes	characteristic, complemented
374	#451	C₂²×C₃	1	2	yes	complemented
375	#450	C₂²×C₃	1	2	yes	—
376	#449	C₂²×C₃	1	2	yes	—
377	#449	C₂²×C₃	1	2	yes	—
378	#449	C₂²×C₃	1	2	yes	—
379	#449	C₂²×C₃	1	2	yes	complemented
380	#449	C₂²×C₃	1	2	yes	complemented
381	#449	C₂²×C₃	1	2	yes	complemented
382	#449	C₂²×C₃	1	2	yes	complemented
383	#448	C₂²×C₃	1	1	yes	characteristic
384	#448	C₂²×C₃	1	2	yes	—
385	#448	C₂²×C₃	1	2	yes	—
386	#448	C₂²×C₃	1	2	yes	complemented
387	#448	C₂²×C₃	1	2	yes	complemented
388	#447	C₂²×C₃	1	2	yes	—
389	#441	C₂²×C₃	1	2	yes	complemented
390	#440	C₂²×C₃	1	2	yes	—
391	#440	C₂²×C₃	1	2	yes	complemented
392	#440	C₂²×C₃	1	2	yes	complemented
393	#435	C₂²×C₃	1	2	yes	—
394	#435	C₂²×C₃	1	2	yes	complemented
395	#435	C₂²×C₃	1	2	yes	complemented
396	#435	C₂²×C₃	1	2	yes	complemented
397	#432	C₂²×C₃	1	1	yes	characteristic, complemented
398	#432	C₂²×C₃	1	1	yes	characteristic, complemented
399	#419	C₂²×C₃	1	2	yes	complemented
400	#417	C₂²×C₃	1	2	yes	complemented
401	#416	C₂²×C₃	1	2	yes	complemented
402	C₂×#103	C₂²×C₃	1	2	yes	complemented
403	#408	C₂²×C₃	1	2	yes	complemented
404	#408	C₂²×C₃	1	2	yes	complemented
405	C₂⁴×C₃	—	2	2	no	—
406	C₃×#41	—	2	4	no	—
407	C₃×#41	—	2	4	no	—
408	C₃×#41	—	4	2	no	—
409	C₃×#41	—	4	2	no	—
410	C₃×#41	—	4	2	no	—
411	C₃×#41	—	4	2	no	—
412	C₃×#41	—	4	2	no	—
413	C₃×#41	—	4	2	no	—
414	C₃×#41	—	4	8	no	—
415	C₃×#41	—	4	8	no	—
416	C₃×#41	—	4	2	no	—
417	C₃×#41	—	4	2	no	—
418	C₃×#41	—	4	8	no	—
419	C₃×#41	—	8	2	no	—
420	C₃×#41	—	8	2	no	—
421	C₂×C₃×Q₈	—	2	4	no	—
422	C₂×C₃×Q₈	—	2	1	no	—
423	C₂×C₃×Q₈	—	2	1	no	—
424	C₂×C₃×Q₈	—	2	2	no	—
425	C₂×C₃×Q₈	—	2	2	no	—
426	C₂×C₃×Q₈	—	2	4	no	—
427	C₂×C₃×Q₈	—	2	4	no	—
428	C₂×C₃×Q₈	—	4	2	no	—
429	C₂×C₃×Q₈	—	4	2	no	—
430	C₂×C₃×Q₈	—	4	8	no	—
431	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
432	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
433	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
435	C₂×C₃×D₄	—	2	2	no	—
436	C₂×C₃×D₄	—	2	2	no	—
437	C₂×C₃×D₄	—	2	2	no	—
438	C₂×C₃×D₄	—	2	1	no	—
439	C₂×C₃×D₄	—	2	2	no	—
440	C₂×C₃×D₄	—	2	2	no	—
441	C₂×C₃×D₄	—	2	2	no	—
442	C₂×C₃×D₄	—	2	2	no	—
443	C₂×C₃×D₄	—	2	2	no	—
444	C₂×C₃×D₄	—	2	2	no	—
445	C₂×C₃×D₄	—	2	2	no	—
446	C₂×C₃×D₄	—	2	1	no	—
447	C₂×C₃×D₄	—	2	1	no	—
448	C₂×C₃×D₄	—	2	1	no	—
449	C₂×C₃×D₄	—	2	1	no	—
450	C₂×C₃×D₄	—	2	2	no	—
451	C₂×C₃×D₄	—	4	2	no	—
452	C₂×C₃×D₄	—	4	2	no	—
453	C₂×C₃×D₄	—	8	2	no	—
454	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
455	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
456	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
457	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
458	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
459	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
460	C₂×C₃×D₄	C₂⁴	1	2	yes	—
461	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
462	C₂×C₃×D₄	C₂⁴	1	2	yes	—
463	C₂²×C₃×C₄	—	2	1	no	—
464	C₂²×C₃×C₄	—	2	2	no	—
465	C₂²×C₃×C₄	—	2	2	no	—
466	C₂²×C₃×C₄	—	2	1	no	—
467	C₂²×C₃×C₄	—	2	2	no	—
468	C₂²×C₃×C₄	—	2	1	no	—
469	C₂²×C₃×C₄	—	2	2	no	—
470	C₂²×C₃×C₄	—	2	2	no	—
471	C₂²×C₃×C₄	—	2	2	no	—
472	C₂²×C₃×C₄	—	2	2	no	—
473	C₂²×C₃×C₄	—	2	2	no	—
474	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
475	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
478	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
479	C₃×Q₁₆	—	2	4	no	—
480	C₃×Q₁₆	—	4	2	no	—
481	C₃×SD₁₆	—	2	4	no	—
482	C₃×SD₁₆	—	2	4	no	—
483	C₃×SD₁₆	—	2	4	no	—
484	C₃×SD₁₆	—	4	2	no	—
485	C₃×SD₁₆	—	4	2	no	—
486	C₃×SD₁₆	—	4	2	no	—
487	C₃×SD₁₆	—	4	2	no	—
488	C₃×D₈	—	4	2	no	—
489	C₃×D₈	—	4	2	no	—
490	C₃×D₈	—	4	2	no	—
491	C₃×M₁₆	—	4	2	no	—
492	C₃×M₁₆	—	4	2	no	—
493	C₂×C₃×C₈	—	4	2	no	—
494	C₂×C₃×C₈	—	4	2	no	—
495	C₂×C₃×C₈	C₂⁴	1	2	yes	—
496	C₂×C₃×C₈	C₂⁴	1	2	yes	—
497	C₂×C₃×C₈	C₂⁴	1	2	yes	—
498	C₂×C₃×C₈	C₂⁴	1	2	yes	—
499	C₃×C₄⋊C₄	—	2	2	no	—
500	C₃×C₄⋊C₄	—	2	2	no	—
501	C₃×C₄⋊C₄	—	2	1	no	—
502	C₃×C₄⋊C₄	—	2	2	no	—
503	C₃×C₄⋊C₄	—	2	1	no	—
504	C₃×C₄⋊C₄	—	2	1	no	—
505	C₃×C₄⋊C₄	—	2	1	no	—
506	C₃×C₄⋊C₄	—	2	1	no	—
507	C₃×C₄⋊C₄	—	2	1	no	—
508	C₃×C₄⋊C₄	—	2	2	no	—
509	C₃×C₄⋊C₄	—	2	2	no	—
510	C₃×C₄⋊C₄	—	2	1	no	—
511	C₃×C₄⋊C₄	—	2	2	no	—
512	C₃×C₄⋊C₄	—	2	1	no	—
513	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
514	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
515	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
516	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
517	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
518	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
519	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
520	C₃×C₂²⋊C₄	—	2	2	no	—
521	C₃×C₂²⋊C₄	—	2	2	no	—
522	C₃×C₂²⋊C₄	—	2	1	no	—
523	C₃×C₂²⋊C₄	—	2	2	no	—
524	C₃×C₂²⋊C₄	—	2	2	no	—
525	C₃×C₂²⋊C₄	—	2	1	no	—
526	C₃×C₂²⋊C₄	—	2	2	no	—
527	C₃×C₂²⋊C₄	—	2	1	no	—
528	C₃×C₂²⋊C₄	—	2	1	no	—
529	C₃×C₂²⋊C₄	—	2	2	no	—
530	C₃×C₂²⋊C₄	—	2	2	no	—
531	C₃×C₂²⋊C₄	—	2	2	no	—
532	C₃×C₂²⋊C₄	—	2	2	no	—
533	C₃×C₂²⋊C₄	—	2	2	no	—
534	C₃×C₂²⋊C₄	—	2	2	no	—
535	C₃×C₂²⋊C₄	—	2	2	no	—
536	C₃×C₂²⋊C₄	—	2	1	no	—
537	C₃×C₂²⋊C₄	—	2	2	no	—
538	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
539	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
540	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
541	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
542	C₃×C₄²	—	2	2	no	—
543	C₃×C₄²	—	2	2	no	—
544	C₃×C₄²	—	2	1	no	—
545	C₃×C₄²	—	2	2	no	—
546	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
547	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
548	C₃×C₄²	C₂⁴	1	1	yes	characteristic
549	C₃×C₄²	C₂⁴	1	1	yes	characteristic
550	2₋¹⁺⁴	—	4	4	no	—
551	2₋¹⁺⁴	—	4	4	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	2	no	—
555	C₂×#41	—	2	1	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	C₂³×C₃	1	2	yes	—
558	C₂×#41	C₂³×C₃	1	2	yes	—
559	C₂×#41	C₂³×C₃	1	2	yes	—
560	C₂×#41	C₂³×C₃	1	2	yes	—
561	C₂×#41	C₂³×C₃	1	2	yes	—
562	C₂²×Q₈	—	2	2	no	—
563	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
564	C₂²×Q₈	C₂³×C₃	1	2	yes	—
565	C₂²×Q₈	C₂³×C₃	1	2	yes	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₃	1	2	yes	—
568	#137	—	4	4	no	—
569	AGL(1,ℤ/8)	—	4	4	no	—
570	#135	—	4	4	no	—
571	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
572	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
573	C₂×SD₁₆	—	4	4	no	—
574	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
575	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
576	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
577	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
578	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
581	C₂×D₈	C₂³×C₃	1	2	yes	—
582	C₂×D₈	C₂³×C₃	1	2	yes	—
583	C₂×D₈	C₂³×C₃	1	2	yes	—
584	C₂×M₁₆	C₂³×C₃	1	2	yes	—
585	C₂×M₁₆	C₂³×C₃	1	2	yes	—
586	C₂²×C₈	C₂³×C₃	1	2	yes	—
587	C₂²×C₈	C₂³×C₃	1	2	yes	—
588	C₄⋊Q₈	—	2	2	no	—
589	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
590	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
591	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
592	#127	—	2	2	no	—
593	#127	—	2	1	no	—
594	#127	—	2	2	no	—
595	#127	C₃×D₄	1	1	yes	characteristic
596	#127	C₂³×C₃	1	1	yes	characteristic
597	#127	C₂³×C₃	1	1	yes	characteristic
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	1	no	—
601	#125	C₂³×C₃	1	1	yes	characteristic
602	#124	—	2	2	no	—
603	#124	—	2	1	no	—
604	#124	—	2	2	no	—
605	#124	—	2	2	no	—
606	#124	—	2	1	no	—
607	#124	C₃×D₄	1	2	yes	—
608	#124	C₂³×C₃	1	1	yes	characteristic
609	#124	C₂³×C₃	1	2	yes	—
610	#123	—	2	1	no	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
622	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
625	#121	—	2	2	no	—
626	#121	—	2	2	no	—
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	—	2	2	no	—
631	#121	—	2	2	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	1	no	—
635	#121	—	2	1	no	—
636	#121	—	2	1	no	—
637	#121	—	2	1	no	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	C₃×D₄	1	2	yes	—
643	#121	C₃×D₄	1	1	yes	characteristic
644	#121	C₃×D₄	1	1	yes	characteristic
645	#121	C₂³×C₃	1	1	yes	characteristic
646	#121	C₂³×C₃	1	2	yes	—
647	#121	C₂³×C₃	1	2	yes	—
648	#121	C₂³×C₃	1	2	yes	—
649	#121	C₂³×C₃	1	2	yes	—
650	#121	C₂³×C₃	1	2	yes	—
651	#121	C₂³×C₃	1	2	yes	—
652	#120	—	2	2	no	—
653	#120	—	2	2	no	—
654	#120	—	2	2	no	—
655	#120	—	2	2	no	—
656	C₄×Q₈	—	2	1	no	—
657	C₄×Q₈	—	2	1	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	C₂³×C₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₃	1	2	yes	—
661	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	1	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
673	C₄×D₄	C₂³×C₃	1	2	yes	—
674	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₃	1	2	yes	—
676	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
677	#117	—	2	1	no	—
678	#117	C₂³×C₃	1	2	yes	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
682	C₂×C₂²⋊C₄	—	2	2	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
685	#107	C₂³×C₃	1	2	yes	—
686	#107	C₂³×C₃	1	2	yes	—
687	#107	C₂³×C₃	1	2	yes	—
688	#106	C₂³×C₃	1	2	yes	—
689	C₄⋊C₈	C₂³×C₃	1	2	yes	—
690	C₄⋊C₈	C₂³×C₃	1	2	yes	—
691	#103	C₂³×C₃	1	2	yes	—
692	#103	C₂³×C₃	1	2	yes	—
693	#103	C₂³×C₃	1	2	yes	—
694	#103	C₂³×C₃	1	2	yes	—
695	#103	C₂³×C₃	1	2	yes	—
696	#103	C₂³×C₃	1	2	yes	—
697	#103	C₂³×C₃	1	2	yes	—
698	#103	C₂³×C₃	1	2	yes	—
699	#103	C₂³×C₃	1	2	yes	—
700	#102	C₂³×C₃	1	2	yes	—
701	#102	C₂³×C₃	1	2	yes	—
702	#102	C₂³×C₃	1	2	yes	—
703	#102	C₂³×C₃	1	2	yes	—
704	#102	C₂³×C₃	1	2	yes	—
705	#102	C₂³×C₃	1	2	yes	—
706	#102	C₂³×C₃	1	2	yes	—
707	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
708	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
710	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
714	#97	C₂³×C₃	1	2	yes	—
715	#97	C₂³×C₃	1	1	yes	characteristic
716	#97	C₂³×C₃	1	1	yes	characteristic
717	C₂³×C₃	—	2	1	no	—
718	C₂³×C₃	—	2	2	no	—
719	C₂³×C₃	—	2	2	no	—
720	C₂³×C₃	—	8	2	no	—
721	C₂³×C₃	—	8	2	no	—
722	C₂³×C₃	—	8	2	no	—
723	C₂³×C₃	C₂²×D₄	1	2	yes	—
724	C₂³×C₃	C₂²×D₄	1	2	yes	—
725	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
726	C₃×Q₈	—	2	4	no	—
727	C₃×Q₈	—	2	2	no	—
728	C₃×Q₈	—	2	2	no	—
729	C₃×Q₈	—	2	2	no	—
730	C₃×Q₈	—	2	2	no	—
731	C₃×Q₈	—	4	2	no	—
732	C₃×Q₈	—	4	4	no	—
733	C₃×Q₈	—	4	4	no	—
734	C₃×Q₈	—	4	2	no	—
735	C₃×Q₈	H(5,𝔽₂)	1	4	yes	—
736	C₃×D₄	—	2	2	no	—
737	C₃×D₄	—	2	2	no	—
738	C₃×D₄	—	2	2	no	—
739	C₃×D₄	—	2	2	no	—
740	C₃×D₄	—	2	2	no	—
741	C₃×D₄	—	4	1	no	—
742	C₃×D₄	—	4	2	no	—
743	C₃×D₄	—	4	2	no	—
744	C₃×D₄	—	4	2	no	—
745	C₃×D₄	—	4	2	no	—
746	C₃×D₄	—	4	1	no	—
747	C₃×D₄	—	4	4	no	—
748	C₃×D₄	—	4	4	no	—
749	C₃×D₄	—	4	2	no	—
750	C₃×D₄	—	4	2	no	—
751	C₃×D₄	—	4	4	no	—
752	C₃×D₄	—	8	1	no	—
753	C₃×D₄	—	8	1	no	—
754	C₃×D₄	—	8	2	no	—
755	C₃×D₄	—	8	2	no	—
756	C₃×D₄	—	8	2	no	—
757	C₃×D₄	—	8	1	no	—
758	C₃×D₄	—	8	2	no	—
759	C₃×D₄	—	8	2	no	—
760	C₃×D₄	—	8	2	no	—
761	C₃×D₄	—	8	2	no	—
762	C₃×D₄	—	8	2	no	—
763	C₂×C₃×C₄	—	2	4	no	—
764	C₂×C₃×C₄	—	2	2	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	2	2	no	—
767	C₂×C₃×C₄	—	2	2	no	—
768	C₂×C₃×C₄	—	2	2	no	—
769	C₂×C₃×C₄	—	2	2	no	—
770	C₂×C₃×C₄	—	2	1	no	—
771	C₂×C₃×C₄	—	2	2	no	—
772	C₂×C₃×C₄	—	2	1	no	—
773	C₂×C₃×C₄	—	2	2	no	—
774	C₂×C₃×C₄	—	2	1	no	—
775	C₂×C₃×C₄	—	2	2	no	—
776	C₂×C₃×C₄	—	4	1	no	—
777	C₂×C₃×C₄	—	4	1	no	—
778	C₂×C₃×C₄	—	4	4	no	—
779	C₂×C₃×C₄	—	4	4	no	—
780	C₂×C₃×C₄	—	4	4	no	—
781	C₂×C₃×C₄	—	4	4	no	—
782	C₂×C₃×C₄	—	4	2	no	—
783	C₂×C₃×C₄	—	4	4	no	—
784	C₂×C₃×C₄	—	8	2	no	—
785	C₂×C₃×C₄	—	8	2	no	—
786	C₂×C₃×C₄	—	8	1	no	—
787	C₂×C₃×C₄	—	8	2	no	—
788	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
790	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
791	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
792	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
793	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
794	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
795	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
796	C₃×C₈	—	2	2	no	—
797	C₃×C₈	—	2	2	no	—
798	C₃×C₈	—	2	2	no	—
799	C₃×C₈	—	2	2	no	—
800	C₂⁴	—	2	2	no	—
801	#41	—	2	4	no	—
802	#41	—	2	4	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	2	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	8	no	—
810	#41	—	4	8	no	—
811	#41	—	4	2	no	—
812	#41	—	4	2	no	—
813	#41	—	4	8	no	—
814	#41	—	8	2	no	—
815	#41	—	8	2	no	—
816	C₂×Q₈	—	2	4	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	4	no	—
822	C₂×Q₈	—	2	4	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	—	4	2	no	—
825	C₂×Q₈	—	4	8	no	—
826	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
827	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
828	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
829	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	8	2	no	—
849	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
850	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
851	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
852	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
853	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
854	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
855	C₂×D₄	C₂⁴×C₃	1	2	yes	—
856	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
857	C₂×D₄	C₂⁴×C₃	1	2	yes	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
874	Q₁₆	—	2	4	no	—
875	Q₁₆	—	4	2	no	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	2	4	no	—
878	SD₁₆	—	2	4	no	—
879	SD₁₆	—	4	2	no	—
880	SD₁₆	—	4	2	no	—
881	SD₁₆	—	4	2	no	—
882	SD₁₆	—	4	2	no	—
883	D₈	—	4	2	no	—
884	D₈	—	4	2	no	—
885	D₈	—	4	2	no	—
886	M₁₆	—	4	2	no	—
887	M₁₆	—	4	2	no	—
888	C₂×C₈	—	4	2	no	—
889	C₂×C₈	—	4	2	no	—
890	C₂×C₈	C₂⁴×C₃	1	2	yes	—
891	C₂×C₈	C₂⁴×C₃	1	2	yes	—
892	C₂×C₈	C₂⁴×C₃	1	2	yes	—
893	C₂×C₈	C₂⁴×C₃	1	2	yes	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
909	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
910	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
911	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
912	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
914	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	1	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	1	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	1	no	—
923	C₂²⋊C₄	—	2	1	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
934	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
935	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
936	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	2	no	—
941	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
942	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
943	C₄²	C₂⁴×C₃	1	1	yes	characteristic
944	C₄²	C₂⁴×C₃	1	1	yes	characteristic
945	C₂²×C₃	—	2	1	no	—
946	C₂²×C₃	—	2	2	no	—
947	C₂²×C₃	—	2	2	no	—
948	C₂²×C₃	—	2	1	no	—
949	C₂²×C₃	—	2	2	no	—
950	C₂²×C₃	—	2	2	no	—
951	C₂²×C₃	—	2	1	no	—
952	C₂²×C₃	—	2	2	no	—
953	C₂²×C₃	—	2	2	no	—
954	C₂²×C₃	—	4	1	no	—
955	C₂²×C₃	—	4	2	no	—
956	C₂²×C₃	—	4	2	no	—
957	C₂²×C₃	—	4	2	no	—
958	C₂²×C₃	—	4	2	no	—
959	C₂²×C₃	—	4	1	no	—
960	C₂²×C₃	—	4	2	no	—
961	C₂²×C₃	—	4	2	no	—
962	C₂²×C₃	—	4	1	no	—
963	C₂²×C₃	—	16	4	no	—
964	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
965	C₃×C₄	—	2	1	no	—
966	C₃×C₄	—	2	1	no	—
967	C₃×C₄	—	2	1	no	—
968	C₃×C₄	—	2	1	no	—
969	C₃×C₄	—	2	4	no	—
970	C₃×C₄	—	2	1	no	—
971	C₃×C₄	—	2	2	no	—
972	C₃×C₄	—	2	2	no	—
973	C₃×C₄	—	4	1	no	—
974	C₃×C₄	—	4	2	no	—
975	C₃×C₄	—	4	2	no	—
976	C₃×C₄	—	4	1	no	—
977	C₃×C₄	—	4	2	no	—
978	C₃×C₄	—	4	1	no	—
979	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	8	2	no	—
984	C₂³	—	8	2	no	—
985	C₂³	—	8	2	no	—
986	C₂³	C₂²×C₃×D₄	1	2	yes	—
987	C₂³	C₂²×C₃×D₄	1	2	yes	—
988	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
989	Q₈	—	2	4	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	4	2	no	—
995	Q₈	—	4	4	no	—
996	Q₈	—	4	4	no	—
997	Q₈	—	4	2	no	—
998	Q₈	C₃×H(5,𝔽₂)	1	4	yes	—
999	D₄	—	2	2	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	4	1	no	—
1005	D₄	—	4	2	no	—
1006	D₄	—	4	2	no	—
1007	D₄	—	4	2	no	—
1008	D₄	—	4	1	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	4	4	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	4	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	—	8	1	no	—
1018	D₄	—	8	2	no	—
1019	D₄	—	8	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	1	no	—
1025	D₄	—	8	2	no	—
1026	C₂×C₄	—	2	4	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	4	1	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1052	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1053	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1054	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1055	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1056	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1057	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1058	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1059	C₈	—	2	2	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	2	no	—
1062	C₈	—	2	2	no	—
1063	C₂×C₃	—	4	1	no	—
1064	C₂×C₃	—	4	2	no	—
1065	C₂×C₃	—	4	2	no	—
1066	C₂×C₃	—	8	2	no	—
1067	C₂×C₃	—	8	2	no	—
1068	C₂×C₃	—	8	1	no	—
1069	C₂×C₃	#3484	1	1	yes	characteristic
1070	C₂×C₃	#3585	1	1	yes	characteristic
1071	C₂×C₃	#3586	1	1	yes	characteristic
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	16	4	no	—
1091	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1092	C₄	—	2	4	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1107	C₃	#61671	1	1	yes	characteristic, direct product factor, Sylow
1108	C₂	—	4	2	no	—
1109	C₂	—	4	1	no	—
1110	C₂	—	4	2	no	—
1111	C₂	—	8	1	no	—
1112	C₂	—	8	2	no	—
1113	C₂	—	8	2	no	—
1114	C₂	C₃×#3484	1	1	yes	characteristic
1115	C₂	C₃×#3585	1	1	yes	characteristic
1116	C₂	C₃×#3586	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×#3320	C₂	semidirect
4. C₃×#3313	C₂	semidirect
5. C₃×#3309	C₂	semidirect
6. C₃×#3308	C₂	semidirect
7. C₃×#3271	C₂	semidirect
8. C₃×#3268	C₂	semidirect
9. C₃×#3266	C₂	semidirect
10. C₃×#3265	C₂	semidirect
11. C₃×#3219	C₂	semidirect
12. C₃×#3214	C₂	semidirect
13. C₃×#3203	C₂	semidirect
14. C₃×#3198	C₂	semidirect
15. C₃×#3117	C₂	semidirect
16. C₃×#3112	C₂	semidirect
17. C₃×#3013	C₂	semidirect
18. C₃×#3010	C₂	semidirect
19. C₃×#2980	C₂	semidirect
20. #61671	C₃	direct (N × H)
21. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₃×#137	C₂²	semidirect
24. C₂×C₃×#135	C₂²	semidirect
32. C₃×#550	C₂²	semidirect
34. C₃×D₄×Q₈	C₂²	semidirect
37. C₃×#548	C₂²	semidirect
47. C₃×#537	C₂²	semidirect
53. C₃×#532	C₂²	semidirect
55. C₂×C₃×C₄×Q₈	C₂²	semidirect
59. C₃×#491	C₂²	semidirect
60. C₃×#490	C₂²	semidirect
61. C₃×#489	C₂²	semidirect
62. C₃×#485	C₂²	semidirect
63. C₃×#484	C₂²	semidirect
64. C₃×#484	C₂²	semidirect
65. C₃×#482	C₂²	semidirect
67. C₃×#480	C₂²	semidirect
68. C₃×#480	C₂²	semidirect
69. C₃×#479	C₂²	semidirect
70. C₃×#477	C₂²	semidirect
71. C₃×#469	C₂²	semidirect
74. C₃×#468	C₂²	semidirect
75. C₃×#467	C₂²	semidirect
78. C₃×#465	C₂²	semidirect
80. C₃×#464	C₂²	semidirect
82. C₃×#461	C₂²	semidirect
84. C₃×#459	C₂²	semidirect
85. C₃×#452	C₂²	semidirect
86. C₃×#452	C₂²	semidirect
87. C₃×#452	C₂²	semidirect
88. C₃×#451	C₂²	semidirect
89. C₃×#451	C₂²	semidirect
94. C₃×#449	C₂²	semidirect
95. C₃×#449	C₂²	semidirect
96. C₃×#449	C₂²	semidirect
97. C₃×#449	C₂²	semidirect
101. C₃×#448	C₂²	semidirect
102. C₃×#448	C₂²	semidirect
104. C₃×#441	C₂²	semidirect
106. C₃×#440	C₂²	semidirect
107. C₃×#440	C₂²	semidirect
109. C₃×#435	C₂²	semidirect
110. C₃×#435	C₂²	semidirect
111. C₃×#435	C₂²	semidirect
112. C₃×#432	C₂²	semidirect
113. C₃×#432	C₂²	semidirect
114. C₃×#419	C₂²	semidirect
115. C₃×#417	C₂²	semidirect
116. C₃×#416	C₂²	semidirect
117. C₂×C₃×#103	C₂²	semidirect
118. C₃×#408	C₂²	semidirect
119. C₃×#408	C₂²	semidirect
120. #3546	C₂×C₃	semidirect
121. #3497	C₂×C₃	semidirect
122. #3320	C₂×C₃	semidirect
123. #3313	C₂×C₃	semidirect
124. #3309	C₂×C₃	semidirect
125. #3308	C₂×C₃	semidirect
126. #3271	C₂×C₃	semidirect
127. #3268	C₂×C₃	semidirect
128. #3266	C₂×C₃	semidirect
129. #3265	C₂×C₃	semidirect
130. #3219	C₂×C₃	semidirect
131. #3214	C₂×C₃	semidirect
132. #3203	C₂×C₃	semidirect
133. #3198	C₂×C₃	semidirect
134. #3117	C₂×C₃	semidirect
135. #3112	C₂×C₃	semidirect
136. #3013	C₂×C₃	semidirect
137. #3010	C₂×C₃	semidirect
138. #2980	C₂×C₃	semidirect
306. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
307. C₂×#137	C₂²×C₃	semidirect
309. C₂×#135	C₂²×C₃	semidirect
317. #550	C₂²×C₃	semidirect
319. D₄×Q₈	C₂²×C₃	semidirect
322. #548	C₂²×C₃	semidirect
332. #537	C₂²×C₃	semidirect
338. #532	C₂²×C₃	semidirect
340. C₂×C₄×Q₈	C₂²×C₃	semidirect
344. #491	C₂²×C₃	semidirect
345. #490	C₂²×C₃	semidirect
346. #489	C₂²×C₃	semidirect
347. #485	C₂²×C₃	semidirect
348. #484	C₂²×C₃	semidirect
349. #484	C₂²×C₃	semidirect
350. #482	C₂²×C₃	semidirect
352. #480	C₂²×C₃	semidirect
353. #480	C₂²×C₃	semidirect
354. #479	C₂²×C₃	semidirect
355. #477	C₂²×C₃	semidirect
356. #469	C₂²×C₃	semidirect
359. #468	C₂²×C₃	semidirect
360. #467	C₂²×C₃	semidirect
363. #465	C₂²×C₃	semidirect
365. #464	C₂²×C₃	semidirect
367. #461	C₂²×C₃	semidirect
369. #459	C₂²×C₃	semidirect
370. #452	C₂²×C₃	semidirect
371. #452	C₂²×C₃	semidirect
372. #452	C₂²×C₃	semidirect
373. #451	C₂²×C₃	semidirect
374. #451	C₂²×C₃	semidirect
379. #449	C₂²×C₃	semidirect
380. #449	C₂²×C₃	semidirect
381. #449	C₂²×C₃	semidirect
382. #449	C₂²×C₃	semidirect
386. #448	C₂²×C₃	semidirect
387. #448	C₂²×C₃	semidirect
389. #441	C₂²×C₃	semidirect
391. #440	C₂²×C₃	semidirect
392. #440	C₂²×C₃	semidirect
394. #435	C₂²×C₃	semidirect
395. #435	C₂²×C₃	semidirect
396. #435	C₂²×C₃	semidirect
397. #432	C₂²×C₃	semidirect
398. #432	C₂²×C₃	semidirect
399. #419	C₂²×C₃	semidirect
400. #417	C₂²×C₃	semidirect
401. #416	C₂²×C₃	semidirect
402. C₂×#103	C₂²×C₃	semidirect
403. #408	C₂²×C₃	semidirect
404. #408	C₂²×C₃	semidirect
1107. C₃	#61671	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×#3320	2
C₃×#3313	2
C₃×#3309	2
C₃×#3308	2
C₃×#3271	2
C₃×#3268	2
C₃×#3266	2
C₃×#3265	2
C₃×#3219	2
C₃×#3214	2
C₃×#3203	2
C₃×#3198	2
C₃×#3117	2
C₃×#3112	2
C₃×#3013	2
C₃×#3010	2
C₃×#2980	2
#61671	3

Subgroups — C3×#61671 #10680278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61671 #10680278