Subgroups — C₃×#61873 #10680480

Order 768.

1666 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₃×#3386	C₂	1	2	yes	maximal, complemented
6	C₃×#3385	C₂	1	2	yes	maximal, complemented
7	C₃×#3376	C₂	1	2	yes	maximal, complemented
8	C₃×#3376	C₂	1	2	yes	maximal, complemented
9	C₃×#3372	C₂	1	2	yes	maximal, complemented
10	C₃×#3367	C₂	1	2	yes	maximal, complemented
11	C₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₃×#3242	C₂	1	2	yes	maximal, complemented
13	C₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3123	C₂	1	2	yes	maximal, complemented
16	C₃×#3118	C₂	1	2	yes	maximal
17	C₃×#3114	C₂	1	1	yes	maximal, characteristic
18	C₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#61873	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#563	—	2	2	no	—
22	C₃×Q₈²	C₂²	1	1	yes	characteristic, complemented
23	C₃×#557	C₂²	1	1	yes	characteristic, complemented
24	C₃×#557	C₂²	1	2	yes	complemented
25	C₃×#556	—	2	1	no	—
26	C₃×#556	C₂²	1	2	yes	complemented
27	C₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃×#554	—	2	1	no	—
29	C₃×#554	—	2	2	no	—
30	C₃×#554	C₂²	1	2	yes	—
31	C₃×#554	C₂²	1	2	yes	—
32	C₃×#554	C₂²	1	2	yes	—
33	C₃×#554	C₂²	1	1	yes	characteristic, complemented
34	C₃×#552	—	2	1	no	—
35	C₃×D₄×Q₈	—	2	1	no	—
36	C₃×D₄×Q₈	C₂²	1	2	yes	—
37	C₃×#544	—	2	1	no	—
38	C₃×#544	C₂²	1	2	yes	—
39	C₃×#543	—	2	1	no	—
40	C₃×#543	—	2	1	no	—
41	C₃×#542	C₂²	1	2	yes	—
42	C₃×#541	—	2	1	no	—
43	C₃×#541	—	2	2	no	—
44	C₃×#541	C₂²	1	2	yes	—
45	C₃×#533	C₂²	1	1	yes	characteristic
46	C₃×#533	C₂²	1	1	yes	characteristic
47	C₃×#533	C₂²	1	1	yes	characteristic
48	C₃×#529	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
50	C₃×#518	C₂²	1	2	yes	—
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₃×#501	C₂²	1	2	yes	complemented
53	C₃×#501	C₂²	1	2	yes	complemented
54	C₃×#501	C₂²	1	1	yes	characteristic, complemented
55	C₃×#501	C₂²	1	2	yes	complemented
56	C₃×#501	C₂²	1	1	yes	characteristic, complemented
57	C₃×#500	C₂²	1	2	yes	complemented
58	C₃×#499	C₂²	1	2	yes	complemented
59	C₃×#491	C₂²	1	2	yes	complemented
60	C₃×#491	C₂²	1	2	yes	complemented
61	C₃×#489	C₂²	1	1	yes	characteristic, complemented
62	C₃×#489	C₂²	1	1	yes	characteristic, complemented
63	C₃×#489	C₂²	1	2	yes	complemented
64	C₃×#488	C₂²	1	2	yes	complemented
65	C₃×#487	C₂²	1	2	yes	complemented
66	C₃×#485	C₂²	1	2	yes	—
67	C₃×#485	C₂²	1	2	yes	—
68	C₃×#485	C₂²	1	2	yes	—
69	C₃×#484	C₂²	1	2	yes	—
70	C₃×#483	C₂²	1	1	yes	characteristic
71	C₃×#482	C₂²	1	2	yes	—
72	C₃×#480	C₂²	1	1	yes	characteristic
73	C₃×#479	C₂²	1	2	yes	complemented
74	C₃×#479	C₂²	1	2	yes	complemented
75	C₃×#479	C₂²	1	2	yes	complemented
76	C₃×#479	C₂²	1	2	yes	complemented
77	C₃×#478	C₂²	1	2	yes	—
78	C₃×#478	C₂²	1	2	yes	—
79	C₃×#478	C₂²	1	2	yes	—
80	C₃×#478	C₂²	1	2	yes	complemented
81	C₃×#478	C₂²	1	2	yes	complemented
82	C₃×#477	C₂²	1	2	yes	complemented
83	C₃×#477	C₂²	1	2	yes	complemented
84	C₃×#477	C₂²	1	2	yes	complemented
85	C₃×#476	C₂²	1	2	yes	—
86	C₃×#475	C₂²	1	2	yes	complemented
87	C₃×#475	C₂²	1	2	yes	complemented
88	C₃×#474	C₂²	1	2	yes	—
89	C₃×#474	C₂²	1	2	yes	—
90	C₃×#474	C₂²	1	2	yes	complemented
91	C₃×#463	C₂²	1	2	yes	—
92	C₃×#463	C₂²	1	2	yes	—
93	C₃×#463	C₂²	1	2	yes	—
94	C₃×#461	C₂²	1	2	yes	—
95	C₃×#461	C₂²	1	2	yes	—
96	C₃×#461	C₂²	1	2	yes	—
97	C₃×#450	C₂²	1	2	yes	—
98	C₃×#450	C₂²	1	1	yes	characteristic
99	C₃×#447	C₂²	1	1	yes	characteristic
100	C₃×#446	C₂²	1	2	yes	complemented
101	C₃×#446	C₂²	1	2	yes	complemented
102	C₃×#446	C₂²	1	2	yes	complemented
103	C₃×#446	C₂²	1	2	yes	complemented
104	C₃×#442	C₂²	1	2	yes	—
105	C₃×#442	C₂²	1	2	yes	—
106	C₃×#440	C₂²	1	2	yes	—
107	C₃×#440	C₂²	1	2	yes	—
108	C₃×#440	C₂²	1	2	yes	—
109	C₃×#440	C₂²	1	2	yes	—
110	C₃×#440	C₂²	1	2	yes	—
111	C₃×#440	C₂²	1	2	yes	—
112	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
113	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
114	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
115	C₃×C₄×D₈	C₂²	1	2	yes	—
116	C₃×#433	C₂²	1	2	yes	—
117	C₃×#433	C₂²	1	2	yes	—
118	C₃×#432	C₂²	1	1	yes	characteristic
119	C₃×#432	C₂²	1	1	yes	characteristic
120	#3555	C₂×C₃	1	1	yes	characteristic, complemented
121	#3501	C₂×C₃	1	1	yes	characteristic, complemented
122	#3389	C₂×C₃	1	2	yes	complemented
123	#3388	C₂×C₃	1	2	yes	complemented
124	#3386	C₂×C₃	1	2	yes	complemented
125	#3385	C₂×C₃	1	2	yes	complemented
126	#3376	C₂×C₃	1	2	yes	complemented
127	#3376	C₂×C₃	1	2	yes	complemented
128	#3372	C₂×C₃	1	2	yes	complemented
129	#3367	C₂×C₃	1	2	yes	complemented
130	#3243	C₂×C₃	1	2	yes	complemented
131	#3242	C₂×C₃	1	2	yes	complemented
132	#3240	C₂×C₃	1	1	yes	characteristic, complemented
133	#3237	C₂×C₃	1	1	yes	characteristic, complemented
134	#3123	C₂×C₃	1	2	yes	complemented
135	#3118	C₂×C₃	1	2	yes	—
136	#3114	C₂×C₃	1	1	yes	characteristic
137	#3110	C₂×C₃	1	1	yes	characteristic, complemented
138	#2987	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂²×C₃×Q₈	—	2	2	no	—
140	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	—	2	1	no	—
142	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
143	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
144	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₃×D₈	C₂³	1	2	yes	—
146	C₃×C₄⋊Q₈	—	2	2	no	—
147	C₃×C₄⋊Q₈	—	2	2	no	—
148	C₃×C₄⋊Q₈	—	2	1	no	—
149	C₃×C₄⋊Q₈	—	2	2	no	—
150	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
151	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
152	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃×#126	—	2	2	no	—
161	C₃×#126	—	2	2	no	—
162	C₃×#126	—	2	2	no	—
163	C₃×#126	—	2	2	no	—
164	C₃×#126	—	2	2	no	—
165	C₃×#126	—	2	2	no	—
166	C₃×#126	—	2	1	no	—
167	C₃×#125	—	2	2	no	—
168	C₃×#125	—	2	2	no	—
169	C₃×#125	—	2	2	no	—
170	C₃×#125	—	2	2	no	—
171	C₃×#125	—	2	2	no	—
172	C₃×#125	—	2	1	no	—
173	C₃×#125	—	2	2	no	—
174	C₃×#125	—	2	1	no	—
175	C₃×#125	D₄	1	2	yes	—
176	C₃×#125	C₂³	1	1	yes	characteristic
177	C₃×#125	C₂³	1	2	yes	—
178	C₃×#125	C₂³	1	2	yes	—
179	C₃×#125	C₂³	1	2	yes	—
180	C₃×#125	C₂³	1	2	yes	—
181	C₃×#124	—	2	2	no	—
182	C₃×#124	C₂³	1	1	yes	characteristic
183	C₃×#124	C₂³	1	2	yes	—
184	C₃×#123	—	2	1	no	—
185	C₃×#123	—	2	2	no	—
186	C₃×C₂²⋊Q₈	—	2	2	no	—
187	C₃×C₂²⋊Q₈	—	2	2	no	—
188	C₃×C₂²⋊Q₈	—	2	1	no	—
189	C₃×C₂²⋊Q₈	—	2	1	no	—
190	C₃×C₂²⋊Q₈	—	2	2	no	—
191	C₃×C₂²⋊Q₈	—	2	2	no	—
192	C₃×C₂²⋊Q₈	—	2	1	no	—
193	C₃×C₂²⋊Q₈	—	2	1	no	—
194	C₃×C₂²⋊Q₈	—	2	1	no	—
195	C₃×C₂²⋊Q₈	—	2	2	no	—
196	C₃×C₂²⋊Q₈	—	2	2	no	—
197	C₃×C₂²⋊Q₈	—	2	2	no	—
198	C₃×C₂²⋊Q₈	—	2	2	no	—
199	C₃×C₂²⋊Q₈	—	2	2	no	—
200	C₃×C₂²⋊Q₈	—	2	2	no	—
201	C₃×C₂²⋊Q₈	—	2	2	no	—
202	C₃×C₂²⋊Q₈	—	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	2	no	—
208	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃×#121	C₂³	1	1	yes	characteristic
214	C₃×C₄×Q₈	—	2	1	no	—
215	C₃×C₄×Q₈	—	2	1	no	—
216	C₃×C₄×Q₈	—	2	2	no	—
217	C₃×C₄×Q₈	—	2	1	no	—
218	C₃×C₄×Q₈	—	2	1	no	—
219	C₃×C₄×Q₈	—	2	1	no	—
220	C₃×C₄×Q₈	C₂³	1	2	yes	—
221	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₃×C₄×Q₈	C₂³	1	2	yes	—
223	C₃×C₄×Q₈	C₂³	1	2	yes	—
224	C₃×C₄×Q₈	C₂³	1	2	yes	—
225	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₃×C₄×Q₈	C₂³	1	2	yes	—
227	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₃×C₄×D₄	—	2	1	no	—
229	C₃×C₄×D₄	—	2	2	no	—
230	C₃×C₄×D₄	—	2	2	no	—
231	C₃×C₄×D₄	—	2	1	no	—
232	C₃×C₄×D₄	—	2	1	no	—
233	C₃×C₄×D₄	C₂³	1	2	yes	—
234	C₃×C₄×D₄	C₂³	1	2	yes	—
235	C₃×C₄×D₄	C₂³	1	2	yes	—
236	C₃×C₄×D₄	C₂³	1	2	yes	—
237	C₃×C₄×D₄	C₂³	1	2	yes	—
238	C₃×C₄×D₄	C₂³	1	2	yes	—
239	C₃×C₄×D₄	C₂³	1	2	yes	—
240	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₃×#117	—	2	1	no	—
242	C₃×#117	—	2	2	no	—
243	C₃×#117	—	2	1	no	—
244	C₃×#117	—	2	1	no	—
245	C₃×#117	C₂³	1	2	yes	—
246	C₃×#117	C₂³	1	2	yes	—
247	C₂×C₃×C₄⋊C₄	—	2	2	no	—
248	C₂×C₃×C₄⋊C₄	—	2	2	no	—
249	C₂×C₃×C₄⋊C₄	—	2	2	no	—
250	C₂×C₃×C₄⋊C₄	—	2	1	no	—
251	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₃×#107	C₂³	1	2	yes	—
257	C₃×#107	C₂³	1	2	yes	—
258	C₃×#107	C₂³	1	2	yes	—
259	C₃×#107	C₂³	1	2	yes	—
260	C₃×#107	C₂³	1	2	yes	—
261	C₃×#107	C₂³	1	2	yes	—
262	C₃×#107	C₂³	1	2	yes	—
263	C₃×#106	C₂³	1	2	yes	—
264	C₃×#106	C₂³	1	2	yes	—
265	C₃×#106	C₂³	1	2	yes	—
266	C₃×#106	C₂³	1	2	yes	—
267	C₃×#106	C₂³	1	2	yes	—
268	C₃×C₄⋊C₈	C₂³	1	2	yes	—
269	C₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₃×C₄⋊C₈	C₂³	1	2	yes	—
271	C₃×C₄⋊C₈	C₂³	1	2	yes	—
272	C₃×C₄⋊C₈	C₂³	1	2	yes	—
273	C₃×C₄⋊C₈	C₂³	1	2	yes	—
274	C₃×#103	C₂³	1	2	yes	—
275	C₃×#103	C₂³	1	2	yes	—
276	C₃×#103	C₂³	1	2	yes	—
277	C₃×#103	C₂³	1	2	yes	—
278	C₃×#103	C₂³	1	2	yes	—
279	C₃×#103	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×#102	C₂³	1	2	yes	—
284	C₃×#102	C₂³	1	2	yes	—
285	C₃×#102	C₂³	1	2	yes	—
286	C₃×#102	C₂³	1	2	yes	—
287	C₃×#102	C₂³	1	2	yes	—
288	C₃×#102	C₂³	1	2	yes	—
289	C₃×#102	C₂³	1	2	yes	—
290	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
293	C₃×#97	C₂³	1	1	yes	characteristic
294	C₃×#97	C₂³	1	1	yes	characteristic
295	C₃×#97	C₂³	1	2	yes	—
296	C₃×#97	C₂³	1	2	yes	—
297	C₃×#97	C₂³	1	2	yes	—
298	C₃×C₄×C₈	C₂³	1	2	yes	—
299	C₃×C₄×C₈	C₂³	1	2	yes	—
300	#563	—	2	2	no	—
301	Q₈²	C₂²×C₃	1	1	yes	characteristic, complemented
302	#557	C₂²×C₃	1	1	yes	characteristic, complemented
303	#557	C₂²×C₃	1	2	yes	complemented
304	#556	—	2	1	no	—
305	#556	C₂²×C₃	1	2	yes	complemented
306	#556	C₂²×C₃	1	1	yes	characteristic, complemented
307	#554	—	2	1	no	—
308	#554	—	2	2	no	—
309	#554	C₂²×C₃	1	2	yes	—
310	#554	C₂²×C₃	1	2	yes	—
311	#554	C₂²×C₃	1	2	yes	—
312	#554	C₂²×C₃	1	1	yes	characteristic, complemented
313	#552	—	2	1	no	—
314	D₄×Q₈	—	2	1	no	—
315	D₄×Q₈	C₂²×C₃	1	2	yes	—
316	#544	—	2	1	no	—
317	#544	C₂²×C₃	1	2	yes	—
318	#543	—	2	1	no	—
319	#543	—	2	1	no	—
320	#542	C₂²×C₃	1	2	yes	—
321	#541	—	2	1	no	—
322	#541	—	2	2	no	—
323	#541	C₂²×C₃	1	2	yes	—
324	#533	C₂²×C₃	1	1	yes	characteristic
325	#533	C₂²×C₃	1	1	yes	characteristic
326	#533	C₂²×C₃	1	1	yes	characteristic
327	#529	C₂²×C₃	1	1	yes	characteristic
328	C₂×C₂²⋊Q₈	—	2	2	no	—
329	#518	C₂²×C₃	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
331	#501	C₂²×C₃	1	2	yes	complemented
332	#501	C₂²×C₃	1	2	yes	complemented
333	#501	C₂²×C₃	1	1	yes	characteristic, complemented
334	#501	C₂²×C₃	1	2	yes	complemented
335	#501	C₂²×C₃	1	1	yes	characteristic, complemented
336	#500	C₂²×C₃	1	2	yes	complemented
337	#499	C₂²×C₃	1	2	yes	complemented
338	#491	C₂²×C₃	1	2	yes	complemented
339	#491	C₂²×C₃	1	2	yes	complemented
340	#489	C₂²×C₃	1	1	yes	characteristic, complemented
341	#489	C₂²×C₃	1	2	yes	complemented
342	#489	C₂²×C₃	1	1	yes	characteristic, complemented
343	#488	C₂²×C₃	1	2	yes	complemented
344	#487	C₂²×C₃	1	2	yes	complemented
345	#485	C₂²×C₃	1	2	yes	—
346	#485	C₂²×C₃	1	2	yes	—
347	#485	C₂²×C₃	1	2	yes	—
348	#484	C₂²×C₃	1	2	yes	—
349	#483	C₂²×C₃	1	1	yes	characteristic
350	#482	C₂²×C₃	1	2	yes	—
351	#480	C₂²×C₃	1	1	yes	characteristic
352	#479	C₂²×C₃	1	2	yes	complemented
353	#479	C₂²×C₃	1	2	yes	complemented
354	#479	C₂²×C₃	1	2	yes	complemented
355	#479	C₂²×C₃	1	2	yes	complemented
356	#478	C₂²×C₃	1	2	yes	—
357	#478	C₂²×C₃	1	2	yes	—
358	#478	C₂²×C₃	1	2	yes	—
359	#478	C₂²×C₃	1	2	yes	complemented
360	#478	C₂²×C₃	1	2	yes	complemented
361	#477	C₂²×C₃	1	2	yes	complemented
362	#477	C₂²×C₃	1	2	yes	complemented
363	#477	C₂²×C₃	1	2	yes	complemented
364	#476	C₂²×C₃	1	2	yes	—
365	#475	C₂²×C₃	1	2	yes	complemented
366	#475	C₂²×C₃	1	2	yes	complemented
367	#474	C₂²×C₃	1	2	yes	—
368	#474	C₂²×C₃	1	2	yes	—
369	#474	C₂²×C₃	1	2	yes	complemented
370	#463	C₂²×C₃	1	2	yes	—
371	#463	C₂²×C₃	1	2	yes	—
372	#463	C₂²×C₃	1	2	yes	—
373	#461	C₂²×C₃	1	2	yes	—
374	#461	C₂²×C₃	1	2	yes	—
375	#461	C₂²×C₃	1	2	yes	—
376	#450	C₂²×C₃	1	2	yes	—
377	#450	C₂²×C₃	1	1	yes	characteristic
378	#447	C₂²×C₃	1	1	yes	characteristic
379	#446	C₂²×C₃	1	2	yes	complemented
380	#446	C₂²×C₃	1	2	yes	complemented
381	#446	C₂²×C₃	1	2	yes	complemented
382	#446	C₂²×C₃	1	2	yes	complemented
383	#442	C₂²×C₃	1	2	yes	—
384	#442	C₂²×C₃	1	2	yes	—
385	#440	C₂²×C₃	1	2	yes	—
386	#440	C₂²×C₃	1	2	yes	—
387	#440	C₂²×C₃	1	2	yes	—
388	#440	C₂²×C₃	1	2	yes	—
389	#440	C₂²×C₃	1	2	yes	—
390	#440	C₂²×C₃	1	2	yes	—
391	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
392	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
393	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
394	C₄×D₈	C₂²×C₃	1	2	yes	—
395	#433	C₂²×C₃	1	2	yes	—
396	#433	C₂²×C₃	1	2	yes	—
397	#432	C₂²×C₃	1	1	yes	characteristic
398	#432	C₂²×C₃	1	1	yes	characteristic
399	C₂⁴×C₃	—	2	1	no	—
400	C₂×C₃×Q₈	—	2	1	no	—
401	C₂×C₃×Q₈	—	2	1	no	—
402	C₂×C₃×Q₈	—	2	1	no	—
403	C₂×C₃×Q₈	—	2	2	no	—
404	C₂×C₃×Q₈	—	2	2	no	—
405	C₂×C₃×Q₈	—	2	2	no	—
406	C₂×C₃×Q₈	—	8	4	no	—
407	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
408	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
409	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
410	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
411	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×D₄	—	2	4	no	—
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	—	2	1	no	—
415	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
416	C₂×C₃×D₄	C₂⁴	1	2	yes	—
417	C₂²×C₃×C₄	—	2	1	no	—
418	C₂²×C₃×C₄	—	2	1	no	—
419	C₂²×C₃×C₄	—	2	2	no	—
420	C₂²×C₃×C₄	—	2	2	no	—
421	C₂²×C₃×C₄	—	2	2	no	—
422	C₂²×C₃×C₄	—	2	2	no	—
423	C₂²×C₃×C₄	—	2	2	no	—
424	C₂²×C₃×C₄	—	2	2	no	—
425	C₂²×C₃×C₄	—	2	2	no	—
426	C₂²×C₃×C₄	—	8	2	no	—
427	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₃×SD₁₆	—	2	4	no	—
431	C₃×SD₁₆	—	2	4	no	—
432	C₃×SD₁₆	—	2	4	no	—
433	C₃×D₈	—	2	4	no	—
434	C₂×C₃×C₈	C₂⁴	1	2	yes	—
435	C₂×C₃×C₈	C₂⁴	1	2	yes	—
436	C₂×C₃×C₈	C₂⁴	1	2	yes	—
437	C₂×C₃×C₈	C₂⁴	1	2	yes	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	2	1	no	—
440	C₃×C₄⋊C₄	—	2	1	no	—
441	C₃×C₄⋊C₄	—	2	2	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	2	2	no	—
446	C₃×C₄⋊C₄	—	2	2	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	1	no	—
449	C₃×C₄⋊C₄	—	2	1	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	1	no	—
452	C₃×C₄⋊C₄	—	2	1	no	—
453	C₃×C₄⋊C₄	—	2	1	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	2	1	no	—
456	C₃×C₄⋊C₄	—	2	2	no	—
457	C₃×C₄⋊C₄	—	2	2	no	—
458	C₃×C₄⋊C₄	—	2	1	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	2	no	—
461	C₃×C₄⋊C₄	—	2	2	no	—
462	C₃×C₄⋊C₄	—	2	2	no	—
463	C₃×C₄⋊C₄	—	2	2	no	—
464	C₃×C₄⋊C₄	—	2	2	no	—
465	C₃×C₄⋊C₄	—	2	1	no	—
466	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
467	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
468	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
469	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
470	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
471	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
472	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
473	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
474	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
475	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
478	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
479	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
480	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
481	C₃×C₂²⋊C₄	—	2	2	no	—
482	C₃×C₂²⋊C₄	—	2	2	no	—
483	C₃×C₂²⋊C₄	—	2	1	no	—
484	C₃×C₂²⋊C₄	—	2	2	no	—
485	C₃×C₂²⋊C₄	—	2	2	no	—
486	C₃×C₂²⋊C₄	—	2	2	no	—
487	C₃×C₂²⋊C₄	—	2	2	no	—
488	C₃×C₂²⋊C₄	—	2	2	no	—
489	C₃×C₂²⋊C₄	—	2	2	no	—
490	C₃×C₂²⋊C₄	—	2	1	no	—
491	C₃×C₂²⋊C₄	—	2	1	no	—
492	C₃×C₂²⋊C₄	—	2	1	no	—
493	C₃×C₂²⋊C₄	—	2	2	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	2	1	no	—
496	C₃×C₂²⋊C₄	—	2	2	no	—
497	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
498	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
499	C₃×C₄²	—	2	2	no	—
500	C₃×C₄²	—	2	1	no	—
501	C₃×C₄²	—	2	2	no	—
502	C₃×C₄²	—	2	2	no	—
503	C₃×C₄²	—	2	2	no	—
504	C₃×C₄²	—	2	2	no	—
505	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
506	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
507	C₃×C₄²	C₂⁴	1	2	yes	—
508	C₃×C₄²	C₂⁴	1	2	yes	—
509	C₃×C₄²	C₂⁴	1	1	yes	characteristic
510	C₃×C₄²	C₂⁴	1	1	yes	characteristic
511	C₂²×Q₈	—	2	2	no	—
512	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
515	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
516	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
517	C₂×D₈	C₂³×C₃	1	2	yes	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	—	2	2	no	—
522	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
523	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#126	—	2	1	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	—	2	1	no	—
545	#125	—	2	2	no	—
546	#125	—	2	1	no	—
547	#125	C₃×D₄	1	2	yes	—
548	#125	C₂³×C₃	1	1	yes	characteristic
549	#125	C₂³×C₃	1	2	yes	—
550	#125	C₂³×C₃	1	2	yes	—
551	#125	C₂³×C₃	1	2	yes	—
552	#125	C₂³×C₃	1	2	yes	—
553	#124	—	2	2	no	—
554	#124	C₂³×C₃	1	1	yes	characteristic
555	#124	C₂³×C₃	1	2	yes	—
556	#123	—	2	1	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
581	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
582	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
583	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
584	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
585	#121	C₂³×C₃	1	1	yes	characteristic
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₃	1	2	yes	—
596	C₄×Q₈	C₂³×C₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	C₂³×C₃	1	2	yes	—
606	C₄×D₄	C₂³×C₃	1	2	yes	—
607	C₄×D₄	C₂³×C₃	1	2	yes	—
608	C₄×D₄	C₂³×C₃	1	2	yes	—
609	C₄×D₄	C₂³×C₃	1	2	yes	—
610	C₄×D₄	C₂³×C₃	1	2	yes	—
611	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₃	1	2	yes	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	—	2	1	no	—
616	#117	—	2	1	no	—
617	#117	C₂³×C₃	1	2	yes	—
618	#117	C₂³×C₃	1	2	yes	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
628	#107	C₂³×C₃	1	2	yes	—
629	#107	C₂³×C₃	1	2	yes	—
630	#107	C₂³×C₃	1	2	yes	—
631	#107	C₂³×C₃	1	2	yes	—
632	#107	C₂³×C₃	1	2	yes	—
633	#107	C₂³×C₃	1	2	yes	—
634	#107	C₂³×C₃	1	2	yes	—
635	#106	C₂³×C₃	1	2	yes	—
636	#106	C₂³×C₃	1	2	yes	—
637	#106	C₂³×C₃	1	2	yes	—
638	#106	C₂³×C₃	1	2	yes	—
639	#106	C₂³×C₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₃	1	2	yes	—
642	C₄⋊C₈	C₂³×C₃	1	2	yes	—
643	C₄⋊C₈	C₂³×C₃	1	2	yes	—
644	C₄⋊C₈	C₂³×C₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₃	1	2	yes	—
646	#103	C₂³×C₃	1	2	yes	—
647	#103	C₂³×C₃	1	2	yes	—
648	#103	C₂³×C₃	1	2	yes	—
649	#103	C₂³×C₃	1	2	yes	—
650	#103	C₂³×C₃	1	2	yes	—
651	#103	C₂³×C₃	1	2	yes	—
652	#103	C₂³×C₃	1	2	yes	—
653	#103	C₂³×C₃	1	2	yes	—
654	#103	C₂³×C₃	1	2	yes	—
655	#102	C₂³×C₃	1	2	yes	—
656	#102	C₂³×C₃	1	2	yes	—
657	#102	C₂³×C₃	1	2	yes	—
658	#102	C₂³×C₃	1	2	yes	—
659	#102	C₂³×C₃	1	2	yes	—
660	#102	C₂³×C₃	1	2	yes	—
661	#102	C₂³×C₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
663	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
664	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
665	#97	C₂³×C₃	1	1	yes	characteristic
666	#97	C₂³×C₃	1	1	yes	characteristic
667	#97	C₂³×C₃	1	2	yes	—
668	#97	C₂³×C₃	1	2	yes	—
669	#97	C₂³×C₃	1	2	yes	—
670	C₄×C₈	C₂³×C₃	1	2	yes	—
671	C₄×C₈	C₂³×C₃	1	2	yes	—
672	C₂³×C₃	—	2	4	no	—
673	C₂³×C₃	—	2	2	no	—
674	C₂³×C₃	—	2	1	no	—
675	C₂³×C₃	—	8	1	no	—
676	C₂³×C₃	—	8	1	no	—
677	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
678	C₃×Q₈	—	2	2	no	—
679	C₃×Q₈	—	2	2	no	—
680	C₃×Q₈	—	2	2	no	—
681	C₃×Q₈	—	4	2	no	—
682	C₃×Q₈	—	4	1	no	—
683	C₃×Q₈	—	4	1	no	—
684	C₃×Q₈	—	4	2	no	—
685	C₃×Q₈	—	8	1	no	—
686	C₃×Q₈	—	8	2	no	—
687	C₃×Q₈	—	8	1	no	—
688	C₃×Q₈	—	8	2	no	—
689	C₃×Q₈	—	8	2	no	—
690	C₃×D₄	—	2	4	no	—
691	C₃×D₄	—	2	2	no	—
692	C₃×D₄	—	2	2	no	—
693	C₃×D₄	—	8	1	no	—
694	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	2	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	2	no	—
701	C₂×C₃×C₄	—	2	2	no	—
702	C₂×C₃×C₄	—	2	2	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	4	1	no	—
705	C₂×C₃×C₄	—	4	1	no	—
706	C₂×C₃×C₄	—	4	2	no	—
707	C₂×C₃×C₄	—	4	4	no	—
708	C₂×C₃×C₄	—	8	2	no	—
709	C₂×C₃×C₄	—	8	2	no	—
710	C₂×C₃×C₄	—	8	2	no	—
711	C₂×C₃×C₄	—	8	2	no	—
712	C₂×C₃×C₄	—	8	2	no	—
713	C₂×C₃×C₄	—	8	2	no	—
714	C₂×C₃×C₄	—	8	1	no	—
715	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
717	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
719	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
720	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
721	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
722	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
723	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
724	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
725	C₃×C₈	—	2	2	no	—
726	C₃×C₈	—	2	2	no	—
727	C₃×C₈	—	2	2	no	—
728	C₃×C₈	—	2	2	no	—
729	C₂⁴	—	2	1	no	—
730	C₂×Q₈	—	2	1	no	—
731	C₂×Q₈	—	2	1	no	—
732	C₂×Q₈	—	2	1	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	8	4	no	—
737	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
738	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
739	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
740	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
741	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
746	C₂×D₄	C₂⁴×C₃	1	2	yes	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	8	2	no	—
757	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
758	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
760	SD₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	4	no	—
763	D₈	—	2	4	no	—
764	C₂×C₈	C₂⁴×C₃	1	2	yes	—
765	C₂×C₈	C₂⁴×C₃	1	2	yes	—
766	C₂×C₈	C₂⁴×C₃	1	2	yes	—
767	C₂×C₈	C₂⁴×C₃	1	2	yes	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
797	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
798	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
799	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
800	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
801	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
802	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
803	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
804	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
805	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
806	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
808	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	1	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	1	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
828	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	1	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
836	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
837	C₄²	C₂⁴×C₃	1	2	yes	—
838	C₄²	C₂⁴×C₃	1	2	yes	—
839	C₄²	C₂⁴×C₃	1	1	yes	characteristic
840	C₄²	C₂⁴×C₃	1	1	yes	characteristic
841	C₂²×C₃	—	2	1	no	—
842	C₂²×C₃	—	2	1	no	—
843	C₂²×C₃	—	2	1	no	—
844	C₂²×C₃	—	2	4	no	—
845	C₂²×C₃	—	4	2	no	—
846	C₂²×C₃	—	4	2	no	—
847	C₂²×C₃	—	4	1	no	—
848	C₂²×C₃	—	4	1	no	—
849	C₂²×C₃	—	4	1	no	—
850	C₂²×C₃	—	8	4	no	—
851	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
852	C₃×C₄	—	2	1	no	—
853	C₃×C₄	—	2	1	no	—
854	C₃×C₄	—	2	2	no	—
855	C₃×C₄	—	2	2	no	—
856	C₃×C₄	—	2	1	no	—
857	C₃×C₄	—	2	1	no	—
858	C₃×C₄	—	2	2	no	—
859	C₃×C₄	—	2	2	no	—
860	C₃×C₄	—	2	1	no	—
861	C₃×C₄	—	4	2	no	—
862	C₃×C₄	—	4	2	no	—
863	C₃×C₄	—	4	2	no	—
864	C₃×C₄	—	4	1	no	—
865	C₃×C₄	—	4	1	no	—
866	C₃×C₄	—	4	2	no	—
867	C₃×C₄	—	4	2	no	—
868	C₃×C₄	—	4	1	no	—
869	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	8	1	no	—
874	C₂³	—	8	1	no	—
875	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
876	Q₈	—	2	2	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	4	2	no	—
880	Q₈	—	4	1	no	—
881	Q₈	—	4	1	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	8	2	no	—
884	Q₈	—	8	2	no	—
885	Q₈	—	8	1	no	—
886	Q₈	—	8	2	no	—
887	Q₈	—	8	1	no	—
888	D₄	—	2	4	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	8	1	no	—
892	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	2	no	—
911	C₂×C₄	—	8	2	no	—
912	C₂×C₄	—	8	1	no	—
913	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
914	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
915	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
916	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
917	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
918	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
919	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
920	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
921	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
922	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
923	C₈	—	2	2	no	—
924	C₈	—	2	2	no	—
925	C₈	—	2	2	no	—
926	C₈	—	2	2	no	—
927	C₂×C₃	—	4	1	no	—
928	C₂×C₃	—	4	4	no	—
929	C₂×C₃	—	8	1	no	—
930	C₂×C₃	#3486	1	1	yes	characteristic
931	C₂×C₃	#3585	1	1	yes	characteristic
932	C₂×C₃	#3586	1	1	yes	characteristic
933	C₂²	—	2	1	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	8	4	no	—
943	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
962	C₃	#61873	1	1	yes	characteristic, direct product factor, Sylow
963	C₂	—	4	1	no	—
964	C₂	—	4	4	no	—
965	C₂	—	8	1	no	—
966	C₂	C₃×#3486	1	1	yes	characteristic
967	C₂	C₃×#3585	1	1	yes	characteristic
968	C₂	C₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3555	C₂	semidirect
2. C₃×#3501	C₂	semidirect
3. C₃×#3389	C₂	semidirect
4. C₃×#3388	C₂	semidirect
5. C₃×#3386	C₂	semidirect
6. C₃×#3385	C₂	semidirect
7. C₃×#3376	C₂	semidirect
8. C₃×#3376	C₂	semidirect
9. C₃×#3372	C₂	semidirect
10. C₃×#3367	C₂	semidirect
11. C₃×#3243	C₂	semidirect
12. C₃×#3242	C₂	semidirect
13. C₃×#3240	C₂	semidirect
14. C₃×#3237	C₂	semidirect
15. C₃×#3123	C₂	semidirect
18. C₃×#3110	C₂	semidirect
19. C₃×#2987	C₂	semidirect
20. #61873	C₃	direct (N × H)
22. C₃×Q₈²	C₂²	semidirect
23. C₃×#557	C₂²	semidirect
24. C₃×#557	C₂²	semidirect
26. C₃×#556	C₂²	semidirect
27. C₃×#556	C₂²	semidirect
33. C₃×#554	C₂²	semidirect
52. C₃×#501	C₂²	semidirect
53. C₃×#501	C₂²	semidirect
54. C₃×#501	C₂²	semidirect
55. C₃×#501	C₂²	semidirect
56. C₃×#501	C₂²	semidirect
57. C₃×#500	C₂²	semidirect
58. C₃×#499	C₂²	semidirect
59. C₃×#491	C₂²	semidirect
60. C₃×#491	C₂²	semidirect
61. C₃×#489	C₂²	semidirect
62. C₃×#489	C₂²	semidirect
63. C₃×#489	C₂²	semidirect
64. C₃×#488	C₂²	semidirect
65. C₃×#487	C₂²	semidirect
73. C₃×#479	C₂²	semidirect
74. C₃×#479	C₂²	semidirect
75. C₃×#479	C₂²	semidirect
76. C₃×#479	C₂²	semidirect
80. C₃×#478	C₂²	semidirect
81. C₃×#478	C₂²	semidirect
82. C₃×#477	C₂²	semidirect
83. C₃×#477	C₂²	semidirect
84. C₃×#477	C₂²	semidirect
86. C₃×#475	C₂²	semidirect
87. C₃×#475	C₂²	semidirect
90. C₃×#474	C₂²	semidirect
100. C₃×#446	C₂²	semidirect
101. C₃×#446	C₂²	semidirect
102. C₃×#446	C₂²	semidirect
103. C₃×#446	C₂²	semidirect
120. #3555	C₂×C₃	semidirect
121. #3501	C₂×C₃	semidirect
122. #3389	C₂×C₃	semidirect
123. #3388	C₂×C₃	semidirect
124. #3386	C₂×C₃	semidirect
125. #3385	C₂×C₃	semidirect
126. #3376	C₂×C₃	semidirect
127. #3376	C₂×C₃	semidirect
128. #3372	C₂×C₃	semidirect
129. #3367	C₂×C₃	semidirect
130. #3243	C₂×C₃	semidirect
131. #3242	C₂×C₃	semidirect
132. #3240	C₂×C₃	semidirect
133. #3237	C₂×C₃	semidirect
134. #3123	C₂×C₃	semidirect
137. #3110	C₂×C₃	semidirect
138. #2987	C₂×C₃	semidirect
301. Q₈²	C₂²×C₃	semidirect
302. #557	C₂²×C₃	semidirect
303. #557	C₂²×C₃	semidirect
305. #556	C₂²×C₃	semidirect
306. #556	C₂²×C₃	semidirect
312. #554	C₂²×C₃	semidirect
331. #501	C₂²×C₃	semidirect
332. #501	C₂²×C₃	semidirect
333. #501	C₂²×C₃	semidirect
334. #501	C₂²×C₃	semidirect
335. #501	C₂²×C₃	semidirect
336. #500	C₂²×C₃	semidirect
337. #499	C₂²×C₃	semidirect
338. #491	C₂²×C₃	semidirect
339. #491	C₂²×C₃	semidirect
340. #489	C₂²×C₃	semidirect
341. #489	C₂²×C₃	semidirect
342. #489	C₂²×C₃	semidirect
343. #488	C₂²×C₃	semidirect
344. #487	C₂²×C₃	semidirect
352. #479	C₂²×C₃	semidirect
353. #479	C₂²×C₃	semidirect
354. #479	C₂²×C₃	semidirect
355. #479	C₂²×C₃	semidirect
359. #478	C₂²×C₃	semidirect
360. #478	C₂²×C₃	semidirect
361. #477	C₂²×C₃	semidirect
362. #477	C₂²×C₃	semidirect
363. #477	C₂²×C₃	semidirect
365. #475	C₂²×C₃	semidirect
366. #475	C₂²×C₃	semidirect
369. #474	C₂²×C₃	semidirect
379. #446	C₂²×C₃	semidirect
380. #446	C₂²×C₃	semidirect
381. #446	C₂²×C₃	semidirect
382. #446	C₂²×C₃	semidirect
962. C₃	#61873	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×#3555	2
C₃×#3501	2
C₃×#3389	2
C₃×#3388	2
C₃×#3386	2
C₃×#3385	2
C₃×#3376	2
C₃×#3372	2
C₃×#3367	2
C₃×#3243	2
C₃×#3242	2
C₃×#3240	2
C₃×#3237	2
C₃×#3123	2
C₃×#3118	2
C₃×#3114	2
C₃×#3110	2
C₃×#2987	2
#61873	3

Subgroups — C3×#61873 #10680480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61873 #10680480