Subgroups — C₃×#61816 #10680423

Order 768.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3349	C₂	1	2	yes	maximal, complemented
6	C₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3313	C₂	1	2	yes	maximal, complemented
12	C₃×#3308	C₂	1	2	yes	maximal, complemented
13	C₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3203	C₂	1	2	yes	maximal, complemented
18	C₃×#3201	C₂	1	2	yes	maximal, complemented
19	C₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#3098	C₂	1	2	yes	maximal, complemented
22	C₃×#3097	C₂	1	2	yes	maximal, complemented
23	C₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	#61816	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#562	—	2	2	no	—
26	C₃×#556	C₂²	1	2	yes	—
27	C₃×#555	—	2	1	no	—
28	C₃×#555	C₂²	1	1	yes	characteristic
29	C₃×#555	C₂²	1	1	yes	characteristic
30	C₃×#555	C₂²	1	1	yes	characteristic
31	C₃×#554	C₂²	1	1	yes	characteristic
32	C₃×#554	C₂²	1	1	yes	characteristic
33	C₃×#554	C₂²	1	1	yes	characteristic
34	C₃×#553	—	2	1	no	—
35	C₃×#553	—	2	1	no	—
36	C₃×#553	—	2	1	no	—
37	C₃×#552	C₂²	1	2	yes	—
38	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
39	C₃×#548	—	2	2	no	—
40	C₃×#548	C₂²	1	2	yes	—
41	C₃×#547	C₂²	1	1	yes	characteristic
42	C₃×#547	C₂²	1	2	yes	—
43	C₃×#544	—	2	1	no	—
44	C₃×#542	—	2	2	no	—
45	C₃×#542	—	2	2	no	—
46	C₃×#540	—	2	1	no	—
47	C₃×#537	C₂²	1	2	yes	—
48	C₃×#537	C₂²	1	2	yes	—
49	C₃×#536	C₂²	1	2	yes	—
50	C₃×#533	—	2	1	no	—
51	C₃×#533	C₂²	1	1	yes	characteristic
52	C₃×#532	—	2	1	no	—
53	C₃×#532	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃×#529	C₂²	1	1	yes	characteristic
56	C₃×#520	C₂²	1	2	yes	—
57	C₃×C₄×#41	C₂²	1	1	yes	characteristic
58	C₃×#501	C₂²	1	2	yes	—
59	C₃×#500	C₂²	1	1	yes	characteristic
60	C₃×#500	C₂²	1	1	yes	characteristic
61	C₃×#489	C₂²	1	2	yes	—
62	C₃×#487	C₂²	1	1	yes	characteristic
63	C₃×#487	C₂²	1	1	yes	characteristic
64	C₃×#485	C₂²	1	2	yes	—
65	C₃×#485	C₂²	1	2	yes	—
66	C₃×#485	C₂²	1	2	yes	—
67	C₃×#485	C₂²	1	2	yes	—
68	C₃×#485	C₂²	1	1	yes	characteristic
69	C₃×#485	C₂²	1	2	yes	—
70	C₃×#484	C₂²	1	2	yes	—
71	C₃×#484	C₂²	1	2	yes	—
72	C₃×#484	C₂²	1	2	yes	—
73	C₃×#484	C₂²	1	2	yes	—
74	C₃×#484	C₂²	1	2	yes	—
75	C₃×#483	C₂²	1	2	yes	—
76	C₃×#483	C₂²	1	2	yes	—
77	C₃×#482	C₂²	1	2	yes	—
78	C₃×#482	C₂²	1	2	yes	—
79	C₃×#482	C₂²	1	1	yes	characteristic
80	C₃×#480	C₂²	1	2	yes	—
81	C₃×#480	C₂²	1	2	yes	—
82	C₃×#480	C₂²	1	2	yes	—
83	C₃×#479	C₂²	1	1	yes	characteristic
84	C₃×#478	C₂²	1	1	yes	characteristic
85	C₃×#477	C₂²	1	2	yes	—
86	C₃×#477	C₂²	1	2	yes	—
87	C₃×#477	C₂²	1	1	yes	characteristic
88	C₃×#477	C₂²	1	1	yes	characteristic
89	C₃×#477	C₂²	1	1	yes	characteristic
90	C₃×#476	C₂²	1	1	yes	characteristic
91	C₃×#476	C₂²	1	1	yes	characteristic
92	C₃×#476	C₂²	1	1	yes	characteristic
93	C₃×#470	C₂²	1	2	yes	—
94	C₃×#468	C₂²	1	2	yes	—
95	C₃×#468	C₂²	1	2	yes	—
96	C₃×#468	C₂²	1	2	yes	—
97	C₃×#467	C₂²	1	2	yes	—
98	C₃×#467	C₂²	1	2	yes	—
99	C₃×#466	C₂²	1	2	yes	—
100	C₃×#465	C₂²	1	2	yes	—
101	C₃×#464	C₂²	1	1	yes	characteristic
102	C₃×#463	C₂²	1	1	yes	characteristic
103	C₃×#462	C₂²	1	1	yes	characteristic
104	C₃×#461	C₂²	1	1	yes	characteristic
105	C₃×#452	C₂²	1	1	yes	characteristic
106	C₃×#452	C₂²	1	2	yes	—
107	C₃×#452	C₂²	1	2	yes	—
108	C₃×#451	C₂²	1	2	yes	—
109	C₃×#449	C₂²	1	1	yes	characteristic
110	C₃×#449	C₂²	1	2	yes	—
111	C₃×#448	C₂²	1	2	yes	—
112	C₃×#441	C₂²	1	2	yes	—
113	C₃×#440	C₂²	1	2	yes	—
114	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
115	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
116	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
118	C₃×#436	C₂²	1	1	yes	characteristic
119	C₃×#436	C₂²	1	1	yes	characteristic
120	C₃×#435	C₂²	1	2	yes	—
121	C₃×#435	C₂²	1	2	yes	—
122	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
123	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
124	C₃×#432	C₂²	1	1	yes	characteristic
125	C₃×#431	C₂²	1	1	yes	characteristic
126	C₃×#428	C₂²	1	2	yes	—
127	C₃×#428	C₂²	1	2	yes	—
128	C₃×#427	C₂²	1	2	yes	—
129	C₂×C₃×#107	C₂²	1	2	yes	—
130	C₃×#419	C₂²	1	2	yes	—
131	C₃×#417	C₂²	1	2	yes	—
132	C₃×#416	C₂²	1	2	yes	—
133	C₂×C₃×#103	C₂²	1	2	yes	—
134	C₃×#408	C₂²	1	2	yes	—
135	C₃×#408	C₂²	1	2	yes	—
136	#3547	C₂×C₃	1	1	yes	characteristic, complemented
137	#3511	C₂×C₃	1	1	yes	characteristic, complemented
138	#3357	C₂×C₃	1	1	yes	characteristic, complemented
139	#3357	C₂×C₃	1	1	yes	characteristic, complemented
140	#3349	C₂×C₃	1	2	yes	complemented
141	#3343	C₂×C₃	1	2	yes	complemented
142	#3341	C₂×C₃	1	1	yes	characteristic, complemented
143	#3338	C₂×C₃	1	1	yes	characteristic, complemented
144	#3331	C₂×C₃	1	1	yes	characteristic, complemented
145	#3329	C₂×C₃	1	1	yes	characteristic, complemented
146	#3313	C₂×C₃	1	2	yes	complemented
147	#3308	C₂×C₃	1	2	yes	complemented
148	#3303	C₂×C₃	1	1	yes	characteristic, complemented
149	#3299	C₂×C₃	1	1	yes	characteristic, complemented
150	#3238	C₂×C₃	1	1	yes	characteristic, complemented
151	#3230	C₂×C₃	1	1	yes	characteristic, complemented
152	#3203	C₂×C₃	1	2	yes	complemented
153	#3201	C₂×C₃	1	2	yes	complemented
154	#3116	C₂×C₃	1	1	yes	characteristic, complemented
155	#3102	C₂×C₃	1	1	yes	characteristic, complemented
156	#3098	C₂×C₃	1	2	yes	complemented
157	#3097	C₂×C₃	1	2	yes	complemented
158	#2981	C₂×C₃	1	1	yes	characteristic, complemented
159	C₂×C₃×#41	—	2	2	no	—
160	C₂×C₃×#41	C₂³	1	2	yes	—
161	C₂×C₃×#41	C₂³	1	1	yes	characteristic
162	C₂×C₃×#41	C₂³	1	2	yes	—
163	C₂²×C₃×Q₈	—	2	1	no	—
164	C₂²×C₃×Q₈	C₂³	1	2	yes	—
165	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
170	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
171	C₂×C₃×M₁₆	C₂³	1	2	yes	—
172	C₂×C₃×M₁₆	C₂³	1	2	yes	—
173	C₂²×C₃×C₈	C₂³	1	2	yes	—
174	C₂²×C₃×C₈	C₂³	1	2	yes	—
175	C₃×C₄⋊Q₈	—	2	2	no	—
176	C₃×C₄⋊Q₈	—	2	1	no	—
177	C₃×C₄⋊Q₈	—	2	1	no	—
178	C₃×C₄⋊Q₈	—	2	1	no	—
179	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
180	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
185	C₃×#127	D₄	1	1	yes	characteristic
186	C₃×#126	—	2	2	no	—
187	C₃×#126	—	2	2	no	—
188	C₃×#126	—	2	2	no	—
189	C₃×#126	—	2	1	no	—
190	C₃×#125	—	2	2	no	—
191	C₃×#125	—	2	1	no	—
192	C₃×#125	—	2	1	no	—
193	C₃×#125	—	2	1	no	—
194	C₃×#125	—	2	1	no	—
195	C₃×#125	C₂³	1	1	yes	characteristic
196	C₃×#124	—	2	2	no	—
197	C₃×#124	—	2	2	no	—
198	C₃×#124	—	2	2	no	—
199	C₃×#124	—	2	2	no	—
200	C₃×#124	—	2	2	no	—
201	C₃×#124	—	2	2	no	—
202	C₃×#124	D₄	1	2	yes	—
203	C₃×#124	C₂³	1	1	yes	characteristic
204	C₃×#123	—	2	2	no	—
205	C₃×#123	—	2	2	no	—
206	C₃×#123	—	2	2	no	—
207	C₃×#123	—	2	1	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	—	2	1	no	—
214	C₃×C₂²⋊Q₈	—	2	2	no	—
215	C₃×C₂²⋊Q₈	—	2	2	no	—
216	C₃×C₂²⋊Q₈	—	2	2	no	—
217	C₃×C₂²⋊Q₈	—	2	2	no	—
218	C₃×C₂²⋊Q₈	—	2	2	no	—
219	C₃×C₂²⋊Q₈	—	2	2	no	—
220	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
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	—	2	1	no	—
232	C₃×#121	—	2	1	no	—
233	C₃×#121	—	2	2	no	—
234	C₃×#121	—	2	2	no	—
235	C₃×#121	—	2	2	no	—
236	C₃×#121	—	2	1	no	—
237	C₃×#121	—	2	1	no	—
238	C₃×#121	D₄	1	2	yes	—
239	C₃×#121	D₄	1	1	yes	characteristic
240	C₃×#121	D₄	1	1	yes	characteristic
241	C₃×#121	C₂³	1	2	yes	—
242	C₃×#121	C₂³	1	2	yes	—
243	C₃×#121	C₂³	1	1	yes	characteristic
244	C₃×#121	C₂³	1	2	yes	—
245	C₃×C₄×Q₈	—	2	2	no	—
246	C₃×C₄×Q₈	—	2	2	no	—
247	C₃×C₄×Q₈	—	2	1	no	—
248	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₃×C₄×Q₈	C₂³	1	2	yes	—
251	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₃×C₄×D₄	—	2	2	no	—
253	C₃×C₄×D₄	—	2	2	no	—
254	C₃×C₄×D₄	—	2	2	no	—
255	C₃×C₄×D₄	—	2	1	no	—
256	C₃×C₄×D₄	—	2	1	no	—
257	C₃×C₄×D₄	—	2	1	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	—	2	1	no	—
262	C₃×C₄×D₄	—	2	2	no	—
263	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
264	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
265	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
266	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
267	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
268	C₃×C₄×D₄	C₂³	1	2	yes	—
269	C₃×#117	—	2	1	no	—
270	C₃×#117	—	2	1	no	—
271	C₃×#117	—	2	1	no	—
272	C₃×#117	—	2	1	no	—
273	C₃×#117	—	2	2	no	—
274	C₃×#117	—	2	1	no	—
275	C₃×#117	—	2	1	no	—
276	C₃×#117	C₂³	1	2	yes	—
277	C₃×#117	C₂³	1	2	yes	—
278	C₃×#117	C₂³	1	2	yes	—
279	C₃×#117	C₂³	1	1	yes	characteristic
280	C₂×C₃×C₄⋊C₄	—	2	1	no	—
281	C₂×C₃×C₄⋊C₄	—	2	1	no	—
282	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
283	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
284	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
285	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
286	C₂×C₃×C₄²	—	2	1	no	—
287	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
288	C₃×#107	C₂³	1	1	yes	characteristic
289	C₃×#107	C₂³	1	2	yes	—
290	C₃×#107	C₂³	1	2	yes	—
291	C₃×#107	C₂³	1	2	yes	—
292	C₃×#107	C₂³	1	1	yes	characteristic
293	C₃×#107	C₂³	1	2	yes	—
294	C₃×#107	C₂³	1	2	yes	—
295	C₃×#107	C₂³	1	2	yes	—
296	C₃×#107	C₂³	1	2	yes	—
297	C₃×#106	C₂³	1	2	yes	—
298	C₃×#106	C₂³	1	2	yes	—
299	C₃×#106	C₂³	1	1	yes	characteristic
300	C₃×#106	C₂³	1	1	yes	characteristic
301	C₃×#106	C₂³	1	2	yes	—
302	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
303	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
304	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
305	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
306	C₃×#103	C₂³	1	1	yes	characteristic
307	C₃×#103	C₂³	1	2	yes	—
308	C₃×#103	C₂³	1	2	yes	—
309	C₃×#103	C₂³	1	2	yes	—
310	C₃×#103	C₂³	1	2	yes	—
311	C₃×#103	C₂³	1	2	yes	—
312	C₃×#103	C₂³	1	2	yes	—
313	C₃×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
320	C₃×#102	C₂³	1	2	yes	—
321	C₃×#102	C₂³	1	1	yes	characteristic
322	C₃×#102	C₂³	1	2	yes	—
323	C₃×#102	C₂³	1	1	yes	characteristic
324	C₃×#102	C₂³	1	1	yes	characteristic
325	C₃×#102	C₂³	1	2	yes	—
326	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
327	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
328	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
329	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
330	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
331	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
332	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
333	C₃×#97	C₂³	1	2	yes	—
334	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
335	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
336	#562	—	2	2	no	—
337	#556	C₂²×C₃	1	2	yes	—
338	#555	—	2	1	no	—
339	#555	C₂²×C₃	1	1	yes	characteristic
340	#555	C₂²×C₃	1	1	yes	characteristic
341	#555	C₂²×C₃	1	1	yes	characteristic
342	#554	C₂²×C₃	1	1	yes	characteristic
343	#554	C₂²×C₃	1	1	yes	characteristic
344	#554	C₂²×C₃	1	1	yes	characteristic
345	#553	—	2	1	no	—
346	#553	—	2	1	no	—
347	#553	—	2	1	no	—
348	#552	C₂²×C₃	1	2	yes	—
349	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
350	#548	—	2	2	no	—
351	#548	C₂²×C₃	1	2	yes	—
352	#547	C₂²×C₃	1	1	yes	characteristic
353	#547	C₂²×C₃	1	2	yes	—
354	#544	—	2	1	no	—
355	#542	—	2	2	no	—
356	#542	—	2	2	no	—
357	#540	—	2	1	no	—
358	#537	C₂²×C₃	1	2	yes	—
359	#537	C₂²×C₃	1	2	yes	—
360	#536	C₂²×C₃	1	2	yes	—
361	#533	—	2	1	no	—
362	#533	C₂²×C₃	1	1	yes	characteristic
363	#532	—	2	1	no	—
364	#532	C₂²×C₃	1	1	yes	characteristic
365	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
366	#529	C₂²×C₃	1	1	yes	characteristic
367	#520	C₂²×C₃	1	2	yes	—
368	C₄×#41	C₂²×C₃	1	1	yes	characteristic
369	#501	C₂²×C₃	1	2	yes	—
370	#500	C₂²×C₃	1	1	yes	characteristic
371	#500	C₂²×C₃	1	1	yes	characteristic
372	#489	C₂²×C₃	1	2	yes	—
373	#487	C₂²×C₃	1	1	yes	characteristic
374	#487	C₂²×C₃	1	1	yes	characteristic
375	#485	C₂²×C₃	1	2	yes	—
376	#485	C₂²×C₃	1	2	yes	—
377	#485	C₂²×C₃	1	2	yes	—
378	#485	C₂²×C₃	1	1	yes	characteristic
379	#485	C₂²×C₃	1	2	yes	—
380	#485	C₂²×C₃	1	2	yes	—
381	#484	C₂²×C₃	1	2	yes	—
382	#484	C₂²×C₃	1	2	yes	—
383	#484	C₂²×C₃	1	2	yes	—
384	#484	C₂²×C₃	1	2	yes	—
385	#484	C₂²×C₃	1	2	yes	—
386	#483	C₂²×C₃	1	2	yes	—
387	#483	C₂²×C₃	1	2	yes	—
388	#482	C₂²×C₃	1	2	yes	—
389	#482	C₂²×C₃	1	2	yes	—
390	#482	C₂²×C₃	1	1	yes	characteristic
391	#480	C₂²×C₃	1	2	yes	—
392	#480	C₂²×C₃	1	2	yes	—
393	#480	C₂²×C₃	1	2	yes	—
394	#479	C₂²×C₃	1	1	yes	characteristic
395	#478	C₂²×C₃	1	1	yes	characteristic
396	#477	C₂²×C₃	1	1	yes	characteristic
397	#477	C₂²×C₃	1	1	yes	characteristic
398	#477	C₂²×C₃	1	2	yes	—
399	#477	C₂²×C₃	1	2	yes	—
400	#477	C₂²×C₃	1	1	yes	characteristic
401	#476	C₂²×C₃	1	1	yes	characteristic
402	#476	C₂²×C₃	1	1	yes	characteristic
403	#476	C₂²×C₃	1	1	yes	characteristic
404	#470	C₂²×C₃	1	2	yes	—
405	#468	C₂²×C₃	1	2	yes	—
406	#468	C₂²×C₃	1	2	yes	—
407	#468	C₂²×C₃	1	2	yes	—
408	#467	C₂²×C₃	1	2	yes	—
409	#467	C₂²×C₃	1	2	yes	—
410	#466	C₂²×C₃	1	2	yes	—
411	#465	C₂²×C₃	1	2	yes	—
412	#464	C₂²×C₃	1	1	yes	characteristic
413	#463	C₂²×C₃	1	1	yes	characteristic
414	#462	C₂²×C₃	1	1	yes	characteristic
415	#461	C₂²×C₃	1	1	yes	characteristic
416	#452	C₂²×C₃	1	2	yes	—
417	#452	C₂²×C₃	1	1	yes	characteristic
418	#452	C₂²×C₃	1	2	yes	—
419	#451	C₂²×C₃	1	2	yes	—
420	#449	C₂²×C₃	1	1	yes	characteristic
421	#449	C₂²×C₃	1	2	yes	—
422	#448	C₂²×C₃	1	2	yes	—
423	#441	C₂²×C₃	1	2	yes	—
424	#440	C₂²×C₃	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
426	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
427	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
428	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
429	#436	C₂²×C₃	1	1	yes	characteristic
430	#436	C₂²×C₃	1	1	yes	characteristic
431	#435	C₂²×C₃	1	2	yes	—
432	#435	C₂²×C₃	1	2	yes	—
433	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
434	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
435	#432	C₂²×C₃	1	1	yes	characteristic
436	#431	C₂²×C₃	1	1	yes	characteristic
437	#428	C₂²×C₃	1	2	yes	—
438	#428	C₂²×C₃	1	2	yes	—
439	#427	C₂²×C₃	1	2	yes	—
440	C₂×#107	C₂²×C₃	1	2	yes	—
441	#419	C₂²×C₃	1	2	yes	—
442	#417	C₂²×C₃	1	2	yes	—
443	#416	C₂²×C₃	1	2	yes	—
444	C₂×#103	C₂²×C₃	1	2	yes	—
445	#408	C₂²×C₃	1	2	yes	—
446	#408	C₂²×C₃	1	2	yes	—
447	C₃×#41	—	4	2	no	—
448	C₃×#41	—	4	2	no	—
449	C₃×#41	—	4	1	no	—
450	C₃×#41	—	4	1	no	—
451	C₃×#41	—	4	2	no	—
452	C₃×#41	—	4	2	no	—
453	C₃×#41	—	8	4	no	—
454	C₂×C₃×Q₈	—	2	2	no	—
455	C₂×C₃×Q₈	—	2	1	no	—
456	C₂×C₃×Q₈	—	2	2	no	—
457	C₂×C₃×Q₈	—	2	1	no	—
458	C₂×C₃×Q₈	—	2	1	no	—
459	C₂×C₃×Q₈	—	4	2	no	—
460	C₂×C₃×Q₈	—	4	2	no	—
461	C₂×C₃×Q₈	—	8	2	no	—
462	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
463	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
464	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
465	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
466	C₂×C₃×D₄	—	2	1	no	—
467	C₂×C₃×D₄	—	2	1	no	—
468	C₂×C₃×D₄	—	2	2	no	—
469	C₂×C₃×D₄	—	2	2	no	—
470	C₂×C₃×D₄	—	2	2	no	—
471	C₂×C₃×D₄	—	2	2	no	—
472	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
473	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
474	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
475	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
476	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
477	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
478	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
479	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
480	C₂²×C₃×C₄	—	2	2	no	—
481	C₂²×C₃×C₄	—	2	2	no	—
482	C₂²×C₃×C₄	—	2	2	no	—
483	C₂²×C₃×C₄	—	2	2	no	—
484	C₂²×C₃×C₄	—	2	2	no	—
485	C₂²×C₃×C₄	—	2	1	no	—
486	C₂²×C₃×C₄	—	2	1	no	—
487	C₂²×C₃×C₄	—	2	1	no	—
488	C₂²×C₃×C₄	—	2	1	no	—
489	C₂²×C₃×C₄	—	2	2	no	—
490	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
491	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
492	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
493	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
494	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
495	C₃×Q₁₆	—	4	1	no	—
496	C₃×Q₁₆	—	4	2	no	—
497	C₃×SD₁₆	—	4	2	no	—
498	C₃×SD₁₆	—	4	1	no	—
499	C₃×SD₁₆	—	4	1	no	—
500	C₃×D₈	—	4	1	no	—
501	C₃×M₁₆	—	4	2	no	—
502	C₃×M₁₆	—	4	2	no	—
503	C₂×C₃×C₈	—	4	2	no	—
504	C₂×C₃×C₈	—	4	2	no	—
505	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
506	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
507	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
508	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
509	C₂×C₃×C₈	C₂⁴	1	2	yes	—
510	C₂×C₃×C₈	C₂⁴	1	2	yes	—
511	C₃×C₄⋊C₄	—	2	1	no	—
512	C₃×C₄⋊C₄	—	2	1	no	—
513	C₃×C₄⋊C₄	—	2	1	no	—
514	C₃×C₄⋊C₄	—	2	2	no	—
515	C₃×C₄⋊C₄	—	2	2	no	—
516	C₃×C₄⋊C₄	—	2	2	no	—
517	C₃×C₄⋊C₄	—	2	2	no	—
518	C₃×C₄⋊C₄	—	2	2	no	—
519	C₃×C₄⋊C₄	—	2	2	no	—
520	C₃×C₄⋊C₄	—	2	1	no	—
521	C₃×C₄⋊C₄	—	2	1	no	—
522	C₃×C₄⋊C₄	—	2	1	no	—
523	C₃×C₄⋊C₄	—	2	1	no	—
524	C₃×C₄⋊C₄	—	2	2	no	—
525	C₃×C₄⋊C₄	—	2	1	no	—
526	C₃×C₄⋊C₄	—	2	1	no	—
527	C₃×C₄⋊C₄	—	2	2	no	—
528	C₃×C₄⋊C₄	—	2	2	no	—
529	C₃×C₄⋊C₄	—	2	2	no	—
530	C₃×C₄⋊C₄	—	2	2	no	—
531	C₃×C₄⋊C₄	—	2	1	no	—
532	C₃×C₄⋊C₄	—	2	2	no	—
533	C₃×C₄⋊C₄	—	2	1	no	—
534	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
535	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
536	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
537	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
538	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
539	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
540	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
541	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
542	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
543	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
544	C₃×C₂²⋊C₄	—	2	2	no	—
545	C₃×C₂²⋊C₄	—	2	2	no	—
546	C₃×C₂²⋊C₄	—	2	1	no	—
547	C₃×C₂²⋊C₄	—	2	2	no	—
548	C₃×C₂²⋊C₄	—	2	2	no	—
549	C₃×C₂²⋊C₄	—	2	2	no	—
550	C₃×C₂²⋊C₄	—	2	2	no	—
551	C₃×C₂²⋊C₄	—	2	2	no	—
552	C₃×C₂²⋊C₄	—	2	2	no	—
553	C₃×C₂²⋊C₄	—	2	2	no	—
554	C₃×C₂²⋊C₄	—	2	1	no	—
555	C₃×C₂²⋊C₄	—	2	1	no	—
556	C₃×C₂²⋊C₄	—	2	1	no	—
557	C₃×C₂²⋊C₄	—	2	1	no	—
558	C₃×C₂²⋊C₄	—	2	1	no	—
559	C₃×C₂²⋊C₄	—	2	2	no	—
560	C₃×C₂²⋊C₄	—	2	2	no	—
561	C₃×C₂²⋊C₄	—	2	2	no	—
562	C₃×C₂²⋊C₄	—	2	1	no	—
563	C₃×C₂²⋊C₄	—	2	1	no	—
564	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
565	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
566	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
567	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
568	C₃×C₄²	—	2	1	no	—
569	C₃×C₄²	—	2	1	no	—
570	C₃×C₄²	—	2	1	no	—
571	C₃×C₄²	—	2	2	no	—
572	C₃×C₄²	—	2	2	no	—
573	C₃×C₄²	—	2	2	no	—
574	C₃×C₄²	—	2	2	no	—
575	C₃×C₄²	—	2	1	no	—
576	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
577	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
578	C₃×C₄²	C₂⁴	1	1	yes	characteristic
579	C₃×C₄²	C₂⁴	1	1	yes	characteristic
580	C₂×#41	—	2	2	no	—
581	C₂×#41	C₂³×C₃	1	1	yes	characteristic
582	C₂×#41	C₂³×C₃	1	2	yes	—
583	C₂×#41	C₂³×C₃	1	2	yes	—
584	C₂²×Q₈	—	2	1	no	—
585	C₂²×Q₈	C₂³×C₃	1	2	yes	—
586	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
587	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
589	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
590	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
591	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
592	C₂×M₁₆	C₂³×C₃	1	2	yes	—
593	C₂×M₁₆	C₂³×C₃	1	2	yes	—
594	C₂²×C₈	C₂³×C₃	1	2	yes	—
595	C₂²×C₈	C₂³×C₃	1	2	yes	—
596	C₄⋊Q₈	—	2	2	no	—
597	C₄⋊Q₈	—	2	1	no	—
598	C₄⋊Q₈	—	2	1	no	—
599	C₄⋊Q₈	—	2	1	no	—
600	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
604	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
605	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
606	#127	C₃×D₄	1	1	yes	characteristic
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	1	no	—
611	#125	—	2	1	no	—
612	#125	—	2	1	no	—
613	#125	—	2	2	no	—
614	#125	—	2	1	no	—
615	#125	—	2	1	no	—
616	#125	C₂³×C₃	1	1	yes	characteristic
617	#124	—	2	2	no	—
618	#124	—	2	2	no	—
619	#124	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	—	2	2	no	—
623	#124	C₃×D₄	1	2	yes	—
624	#124	C₂³×C₃	1	1	yes	characteristic
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	1	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	1	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
642	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
648	#121	—	2	2	no	—
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	1	no	—
657	#121	—	2	2	no	—
658	#121	—	2	1	no	—
659	#121	C₃×D₄	1	2	yes	—
660	#121	C₃×D₄	1	1	yes	characteristic
661	#121	C₃×D₄	1	1	yes	characteristic
662	#121	C₂³×C₃	1	1	yes	characteristic
663	#121	C₂³×C₃	1	2	yes	—
664	#121	C₂³×C₃	1	2	yes	—
665	#121	C₂³×C₃	1	2	yes	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	—	2	2	no	—
668	C₄×Q₈	—	2	1	no	—
669	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
670	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
671	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
672	C₄×Q₈	C₂³×C₃	1	2	yes	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
685	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
687	C₄×D₄	C₂³×C₃	1	2	yes	—
688	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
689	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
690	#117	—	2	1	no	—
691	#117	—	2	1	no	—
692	#117	—	2	1	no	—
693	#117	—	2	1	no	—
694	#117	—	2	2	no	—
695	#117	—	2	1	no	—
696	#117	—	2	1	no	—
697	#117	C₂³×C₃	1	1	yes	characteristic
698	#117	C₂³×C₃	1	2	yes	—
699	#117	C₂³×C₃	1	2	yes	—
700	#117	C₂³×C₃	1	2	yes	—
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	—	2	1	no	—
703	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
709	#107	C₂³×C₃	1	1	yes	characteristic
710	#107	C₂³×C₃	1	2	yes	—
711	#107	C₂³×C₃	1	2	yes	—
712	#107	C₂³×C₃	1	2	yes	—
713	#107	C₂³×C₃	1	1	yes	characteristic
714	#107	C₂³×C₃	1	2	yes	—
715	#107	C₂³×C₃	1	2	yes	—
716	#107	C₂³×C₃	1	2	yes	—
717	#107	C₂³×C₃	1	2	yes	—
718	#106	C₂³×C₃	1	2	yes	—
719	#106	C₂³×C₃	1	2	yes	—
720	#106	C₂³×C₃	1	1	yes	characteristic
721	#106	C₂³×C₃	1	1	yes	characteristic
722	#106	C₂³×C₃	1	2	yes	—
723	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
724	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
725	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
726	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
727	#103	C₂³×C₃	1	1	yes	characteristic
728	#103	C₂³×C₃	1	2	yes	—
729	#103	C₂³×C₃	1	2	yes	—
730	#103	C₂³×C₃	1	2	yes	—
731	#103	C₂³×C₃	1	2	yes	—
732	#103	C₂³×C₃	1	2	yes	—
733	#103	C₂³×C₃	1	2	yes	—
734	#103	C₂³×C₃	1	1	yes	characteristic
735	#103	C₂³×C₃	1	2	yes	—
736	#103	C₂³×C₃	1	2	yes	—
737	#103	C₂³×C₃	1	1	yes	characteristic
738	#103	C₂³×C₃	1	1	yes	characteristic
739	#103	C₂³×C₃	1	2	yes	—
740	#102	C₂³×C₃	1	1	yes	characteristic
741	#102	C₂³×C₃	1	2	yes	—
742	#102	C₂³×C₃	1	1	yes	characteristic
743	#102	C₂³×C₃	1	2	yes	—
744	#102	C₂³×C₃	1	1	yes	characteristic
745	#102	C₂³×C₃	1	1	yes	characteristic
746	#102	C₂³×C₃	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
748	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
749	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
751	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
752	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
753	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
754	#97	C₂³×C₃	1	2	yes	—
755	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
756	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
757	C₂³×C₃	—	2	1	no	—
758	C₂³×C₃	—	2	1	no	—
759	C₂³×C₃	C₂²×D₄	1	2	yes	—
760	C₂³×C₃	C₂²×D₄	1	2	yes	—
761	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
762	C₃×Q₈	—	2	1	no	—
763	C₃×Q₈	—	2	1	no	—
764	C₃×Q₈	—	2	2	no	—
765	C₃×Q₈	—	2	1	no	—
766	C₃×Q₈	—	2	1	no	—
767	C₃×Q₈	—	2	2	no	—
768	C₃×Q₈	—	4	2	no	—
769	C₃×Q₈	—	4	4	no	—
770	C₃×Q₈	—	8	1	no	—
771	C₃×Q₈	—	8	2	no	—
772	C₃×Q₈	—	8	1	no	—
773	C₃×Q₈	—	8	1	no	—
774	C₃×D₄	—	2	2	no	—
775	C₃×D₄	—	2	2	no	—
776	C₃×D₄	—	2	1	no	—
777	C₃×D₄	—	2	1	no	—
778	C₃×D₄	—	2	1	no	—
779	C₃×D₄	—	2	1	no	—
780	C₃×D₄	—	4	2	no	—
781	C₃×D₄	—	4	2	no	—
782	C₃×D₄	—	4	2	no	—
783	C₃×D₄	—	4	2	no	—
784	C₃×D₄	—	4	2	no	—
785	C₃×D₄	—	8	1	no	—
786	C₃×D₄	—	8	2	no	—
787	C₃×D₄	—	8	2	no	—
788	C₃×D₄	—	8	2	no	—
789	C₃×D₄	—	8	2	no	—
790	C₂×C₃×C₄	—	2	2	no	—
791	C₂×C₃×C₄	—	2	2	no	—
792	C₂×C₃×C₄	—	2	2	no	—
793	C₂×C₃×C₄	—	2	2	no	—
794	C₂×C₃×C₄	—	2	2	no	—
795	C₂×C₃×C₄	—	2	1	no	—
796	C₂×C₃×C₄	—	2	1	no	—
797	C₂×C₃×C₄	—	2	1	no	—
798	C₂×C₃×C₄	—	2	1	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	2	no	—
801	C₂×C₃×C₄	—	2	1	no	—
802	C₂×C₃×C₄	—	2	1	no	—
803	C₂×C₃×C₄	—	2	1	no	—
804	C₂×C₃×C₄	—	2	2	no	—
805	C₂×C₃×C₄	—	2	2	no	—
806	C₂×C₃×C₄	—	2	2	no	—
807	C₂×C₃×C₄	—	4	1	no	—
808	C₂×C₃×C₄	—	4	2	no	—
809	C₂×C₃×C₄	—	4	2	no	—
810	C₂×C₃×C₄	—	4	2	no	—
811	C₂×C₃×C₄	—	4	2	no	—
812	C₂×C₃×C₄	—	8	2	no	—
813	C₂×C₃×C₄	—	8	2	no	—
814	C₂×C₃×C₄	—	8	2	no	—
815	C₂×C₃×C₄	—	8	2	no	—
816	C₂×C₃×C₄	—	8	2	no	—
817	C₂×C₃×C₄	—	8	2	no	—
818	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
819	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
820	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
821	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
822	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
823	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
824	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
825	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
826	C₃×C₈	—	2	1	no	—
827	C₃×C₈	—	2	1	no	—
828	C₃×C₈	—	2	2	no	—
829	C₃×C₈	—	2	2	no	—
830	C₃×C₈	—	2	1	no	—
831	C₃×C₈	—	2	1	no	—
832	#41	—	4	2	no	—
833	#41	—	4	2	no	—
834	#41	—	4	1	no	—
835	#41	—	4	1	no	—
836	#41	—	4	2	no	—
837	#41	—	4	2	no	—
838	#41	—	8	4	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	2	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	4	2	no	—
845	C₂×Q₈	—	4	2	no	—
846	C₂×Q₈	—	8	2	no	—
847	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
848	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
849	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
858	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
859	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
860	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
861	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
862	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
863	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
864	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
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	—	2	2	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
880	Q₁₆	—	4	1	no	—
881	Q₁₆	—	4	2	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	1	no	—
884	SD₁₆	—	4	1	no	—
885	D₈	—	4	1	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	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₃	1	2	yes	—
895	C₂×C₈	C₂⁴×C₃	1	2	yes	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
920	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
921	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
922	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
926	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
927	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
928	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
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	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
950	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
951	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
952	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
953	C₄²	—	2	1	no	—
954	C₄²	—	2	1	no	—
955	C₄²	—	2	1	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
962	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
963	C₄²	C₂⁴×C₃	1	1	yes	characteristic
964	C₄²	C₂⁴×C₃	1	1	yes	characteristic
965	C₂²×C₃	—	2	1	no	—
966	C₂²×C₃	—	2	2	no	—
967	C₂²×C₃	—	2	2	no	—
968	C₂²×C₃	—	2	2	no	—
969	C₂²×C₃	—	2	1	no	—
970	C₂²×C₃	—	2	2	no	—
971	C₂²×C₃	—	2	1	no	—
972	C₂²×C₃	—	2	2	no	—
973	C₂²×C₃	—	2	2	no	—
974	C₂²×C₃	—	4	1	no	—
975	C₂²×C₃	—	4	1	no	—
976	C₂²×C₃	—	4	1	no	—
977	C₂²×C₃	—	4	1	no	—
978	C₂²×C₃	—	4	1	no	—
979	C₂²×C₃	—	4	1	no	—
980	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
981	C₃×C₄	—	2	1	no	—
982	C₃×C₄	—	2	1	no	—
983	C₃×C₄	—	2	1	no	—
984	C₃×C₄	—	2	2	no	—
985	C₃×C₄	—	2	2	no	—
986	C₃×C₄	—	2	1	no	—
987	C₃×C₄	—	4	1	no	—
988	C₃×C₄	—	4	1	no	—
989	C₃×C₄	—	4	2	no	—
990	C₃×C₄	—	4	2	no	—
991	C₃×C₄	—	4	2	no	—
992	C₃×C₄	—	4	1	no	—
993	C₃×C₄	—	4	2	no	—
994	C₃×C₄	—	4	1	no	—
995	C₃×C₄	—	4	1	no	—
996	C₃×C₄	—	4	1	no	—
997	C₃×C₄	#578	1	2	yes	—
998	C₃×C₄	#585	1	1	yes	characteristic
999	C₃×C₄	#585	1	1	yes	characteristic
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	C₂²×C₃×D₄	1	2	yes	—
1003	C₂³	C₂²×C₃×D₄	1	2	yes	—
1004	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	4	no	—
1013	Q₈	—	8	2	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	1	no	—
1016	Q₈	—	8	1	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	2	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	2	no	—
1030	D₄	—	8	2	no	—
1031	D₄	—	8	1	no	—
1032	D₄	—	8	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1062	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1063	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1064	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1065	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1066	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1067	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1068	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	2	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₂×C₃	—	4	1	no	—
1076	C₂×C₃	—	4	2	no	—
1077	C₂×C₃	—	4	2	no	—
1078	C₂×C₃	—	8	1	no	—
1079	C₂×C₃	—	8	1	no	—
1080	C₂×C₃	#3485	1	1	yes	characteristic
1081	C₂×C₃	C₂×#578	1	1	yes	characteristic
1082	C₂×C₃	#3585	1	1	yes	characteristic
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	C₃×#578	1	2	yes	—
1116	C₄	C₃×#585	1	1	yes	characteristic
1117	C₄	C₃×#585	1	1	yes	characteristic
1118	C₃	#61816	1	1	yes	characteristic, direct product factor, Sylow
1119	C₂	—	4	2	no	—
1120	C₂	—	4	1	no	—
1121	C₂	—	4	2	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₃×#3485	1	1	yes	characteristic
1125	C₂	C₂×C₃×#578	1	1	yes	characteristic
1126	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 ◁ C₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3547	C₂	semidirect
2. C₃×#3511	C₂	semidirect
3. C₃×#3357	C₂	semidirect
4. C₃×#3357	C₂	semidirect
5. C₃×#3349	C₂	semidirect
6. C₃×#3343	C₂	semidirect
7. C₃×#3341	C₂	semidirect
8. C₃×#3338	C₂	semidirect
9. C₃×#3331	C₂	semidirect
10. C₃×#3329	C₂	semidirect
11. C₃×#3313	C₂	semidirect
12. C₃×#3308	C₂	semidirect
13. C₃×#3303	C₂	semidirect
14. C₃×#3299	C₂	semidirect
15. C₃×#3238	C₂	semidirect
16. C₃×#3230	C₂	semidirect
17. C₃×#3203	C₂	semidirect
18. C₃×#3201	C₂	semidirect
19. C₃×#3116	C₂	semidirect
20. C₃×#3102	C₂	semidirect
21. C₃×#3098	C₂	semidirect
22. C₃×#3097	C₂	semidirect
23. C₃×#2981	C₂	semidirect
24. #61816	C₃	direct (N × H)
136. #3547	C₂×C₃	semidirect
137. #3511	C₂×C₃	semidirect
138. #3357	C₂×C₃	semidirect
139. #3357	C₂×C₃	semidirect
140. #3349	C₂×C₃	semidirect
141. #3343	C₂×C₃	semidirect
142. #3341	C₂×C₃	semidirect
143. #3338	C₂×C₃	semidirect
144. #3331	C₂×C₃	semidirect
145. #3329	C₂×C₃	semidirect
146. #3313	C₂×C₃	semidirect
147. #3308	C₂×C₃	semidirect
148. #3303	C₂×C₃	semidirect
149. #3299	C₂×C₃	semidirect
150. #3238	C₂×C₃	semidirect
151. #3230	C₂×C₃	semidirect
152. #3203	C₂×C₃	semidirect
153. #3201	C₂×C₃	semidirect
154. #3116	C₂×C₃	semidirect
155. #3102	C₂×C₃	semidirect
156. #3098	C₂×C₃	semidirect
157. #3097	C₂×C₃	semidirect
158. #2981	C₂×C₃	semidirect
1118. C₃	#61816	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×#3547	2
C₃×#3511	2
C₃×#3357	2
C₃×#3349	2
C₃×#3343	2
C₃×#3341	2
C₃×#3338	2
C₃×#3331	2
C₃×#3329	2
C₃×#3313	2
C₃×#3308	2
C₃×#3303	2
C₃×#3299	2
C₃×#3238	2
C₃×#3230	2
C₃×#3203	2
C₃×#3201	2
C₃×#3116	2
C₃×#3102	2
C₃×#3098	2
C₃×#3097	2
C₃×#2981	2
#61816	3

Subgroups — C3×#61816 #10680423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61816 #10680423