Subgroups — C₃×#61874 #10680481

Order 768.

1654 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×#3554	C₂	1	1	yes	maximal, characteristic
2	C₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3390	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×#3375	C₂	1	2	yes	maximal, complemented
8	C₃×#3371	C₂	1	2	yes	maximal, complemented
9	C₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₃×#3368	C₂	1	2	yes	maximal, complemented
11	C₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₃×#3241	C₂	1	2	yes	maximal, complemented
13	C₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3126	C₂	1	2	yes	maximal, complemented
16	C₃×#3121	C₂	1	2	yes	maximal, complemented
17	C₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#61874	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#562	—	2	2	no	—
22	C₃×#559	C₂²	1	1	yes	characteristic
23	C₃×#559	C₂²	1	2	yes	—
24	C₃×Q₈²	—	2	1	no	—
25	C₃×Q₈²	C₂²	1	2	yes	—
26	C₃×#557	—	2	1	no	—
27	C₃×#557	—	2	2	no	—
28	C₃×#557	C₂²	1	2	yes	—
29	C₃×#557	C₂²	1	2	yes	—
30	C₃×#557	C₂²	1	1	yes	characteristic
31	C₃×#557	C₂²	1	2	yes	—
32	C₃×#554	C₂²	1	2	yes	—
33	C₃×#550	C₂²	1	1	yes	characteristic
34	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
35	C₃×#548	—	2	1	no	—
36	C₃×#547	—	2	1	no	—
37	C₃×#544	—	2	1	no	—
38	C₃×#544	—	2	1	no	—
39	C₃×#544	C₂²	1	2	yes	—
40	C₃×#542	—	2	1	no	—
41	C₃×#542	C₂²	1	2	yes	—
42	C₃×#540	C₂²	1	2	yes	—
43	C₃×#539	—	2	2	no	—
44	C₃×#536	—	2	1	no	—
45	C₃×#533	—	2	2	no	—
46	C₃×#533	C₂²	1	1	yes	characteristic
47	C₃×#533	C₂²	1	1	yes	characteristic
48	C₃×#532	C₂²	1	1	yes	characteristic
49	C₃×#529	C₂²	1	1	yes	characteristic
50	C₃×#519	C₂²	1	2	yes	—
51	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
52	C₃×#501	C₂²	1	1	yes	characteristic
53	C₃×#501	C₂²	1	2	yes	—
54	C₃×#501	C₂²	1	2	yes	—
55	C₃×#501	C₂²	1	2	yes	—
56	C₃×#501	C₂²	1	1	yes	characteristic
57	C₃×#500	C₂²	1	2	yes	—
58	C₃×#499	C₂²	1	2	yes	—
59	C₃×#490	C₂²	1	2	yes	—
60	C₃×#490	C₂²	1	2	yes	—
61	C₃×#489	C₂²	1	1	yes	characteristic
62	C₃×#489	C₂²	1	1	yes	characteristic
63	C₃×#489	C₂²	1	2	yes	—
64	C₃×#488	C₂²	1	2	yes	—
65	C₃×#486	C₂²	1	2	yes	—
66	C₃×#485	C₂²	1	2	yes	—
67	C₃×#484	C₂²	1	1	yes	characteristic
68	C₃×#482	C₂²	1	2	yes	—
69	C₃×#482	C₂²	1	2	yes	—
70	C₃×#482	C₂²	1	2	yes	—
71	C₃×#481	C₂²	1	1	yes	characteristic
72	C₃×#480	C₂²	1	2	yes	—
73	C₃×#479	C₂²	1	2	yes	—
74	C₃×#479	C₂²	1	2	yes	—
75	C₃×#479	C₂²	1	2	yes	—
76	C₃×#479	C₂²	1	2	yes	—
77	C₃×#479	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	—
81	C₃×#478	C₂²	1	2	yes	—
82	C₃×#477	C₂²	1	2	yes	—
83	C₃×#477	C₂²	1	2	yes	—
84	C₃×#477	C₂²	1	2	yes	—
85	C₃×#476	C₂²	1	2	yes	—
86	C₃×#476	C₂²	1	2	yes	—
87	C₃×#475	C₂²	1	2	yes	—
88	C₃×#474	C₂²	1	2	yes	—
89	C₃×#474	C₂²	1	2	yes	—
90	C₃×#474	C₂²	1	2	yes	—
91	C₃×#464	C₂²	1	2	yes	—
92	C₃×#464	C₂²	1	2	yes	—
93	C₃×#464	C₂²	1	2	yes	—
94	C₃×#460	C₂²	1	2	yes	—
95	C₃×#460	C₂²	1	2	yes	—
96	C₃×#460	C₂²	1	2	yes	—
97	C₃×#451	C₂²	1	1	yes	characteristic
98	C₃×#448	C₂²	1	2	yes	—
99	C₃×#448	C₂²	1	1	yes	characteristic
100	C₃×#446	C₂²	1	2	yes	—
101	C₃×#446	C₂²	1	2	yes	—
102	C₃×#446	C₂²	1	2	yes	—
103	C₃×#446	C₂²	1	2	yes	—
104	C₃×#441	C₂²	1	2	yes	—
105	C₃×#441	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×Q₁₆	C₂²	1	2	yes	—
113	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
114	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
115	C₃×C₄×SD₁₆	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	#3554	C₂×C₃	1	1	yes	characteristic
121	#3502	C₂×C₃	1	1	yes	characteristic, complemented
122	#3390	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	#3375	C₂×C₃	1	2	yes	complemented
127	#3371	C₂×C₃	1	2	yes	complemented
128	#3371	C₂×C₃	1	2	yes	complemented
129	#3368	C₂×C₃	1	2	yes	complemented
130	#3243	C₂×C₃	1	2	yes	complemented
131	#3241	C₂×C₃	1	2	yes	complemented
132	#3240	C₂×C₃	1	1	yes	characteristic, complemented
133	#3235	C₂×C₃	1	1	yes	characteristic, complemented
134	#3126	C₂×C₃	1	2	yes	complemented
135	#3121	C₂×C₃	1	2	yes	complemented
136	#3117	C₂×C₃	1	1	yes	characteristic, complemented
137	#3112	C₂×C₃	1	1	yes	characteristic, complemented
138	#2987	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂×C₃×#41	—	2	1	no	—
140	C₂×C₃×#41	—	2	1	no	—
141	C₂²×C₃×Q₈	—	2	1	no	—
142	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
143	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
147	C₃×C₄⋊Q₈	—	2	2	no	—
148	C₃×C₄⋊Q₈	—	2	2	no	—
149	C₃×C₄⋊Q₈	—	2	2	no	—
150	C₃×C₄⋊Q₈	—	2	1	no	—
151	C₃×C₄⋊Q₈	—	2	2	no	—
152	C₃×C₄⋊Q₈	—	2	2	no	—
153	C₃×C₄⋊Q₈	—	2	2	no	—
154	C₃×C₄⋊Q₈	—	2	2	no	—
155	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃×#127	C₂³	1	1	yes	characteristic
164	C₃×#127	C₂³	1	2	yes	—
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	2	no	—
173	C₃×#125	—	2	2	no	—
174	C₃×#125	—	2	2	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	—	2	1	no	—
183	C₃×#124	—	2	2	no	—
184	C₃×#124	—	2	1	no	—
185	C₃×#124	C₂³	1	1	yes	characteristic
186	C₃×#124	C₂³	1	2	yes	—
187	C₃×#123	—	2	1	no	—
188	C₃×#123	—	2	2	no	—
189	C₃×#123	—	2	2	no	—
190	C₃×#123	—	2	2	no	—
191	C₃×#123	—	2	2	no	—
192	C₃×#123	—	2	2	no	—
193	C₃×#123	—	2	2	no	—
194	C₃×C₂²⋊Q₈	—	2	2	no	—
195	C₃×C₂²⋊Q₈	—	2	1	no	—
196	C₃×C₂²⋊Q₈	—	2	1	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	1	no	—
202	C₃×C₂²⋊Q₈	—	2	2	no	—
203	C₃×C₂²⋊Q₈	—	2	2	no	—
204	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
205	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
206	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₃×#121	—	2	1	no	—
209	C₃×#121	—	2	2	no	—
210	C₃×#121	—	2	1	no	—
211	C₃×#121	—	2	2	no	—
212	C₃×#121	—	2	2	no	—
213	C₃×#121	C₂³	1	1	yes	characteristic
214	C₃×#121	C₂³	1	2	yes	—
215	C₃×C₄×Q₈	—	2	2	no	—
216	C₃×C₄×Q₈	—	2	2	no	—
217	C₃×C₄×Q₈	—	2	2	no	—
218	C₃×C₄×Q₈	—	2	2	no	—
219	C₃×C₄×Q₈	—	2	2	no	—
220	C₃×C₄×Q₈	—	2	2	no	—
221	C₃×C₄×Q₈	—	2	1	no	—
222	C₃×C₄×Q₈	—	2	1	no	—
223	C₃×C₄×Q₈	—	2	1	no	—
224	C₃×C₄×Q₈	—	2	1	no	—
225	C₃×C₄×Q₈	—	2	1	no	—
226	C₃×C₄×Q₈	C₂³	1	2	yes	—
227	C₃×C₄×Q₈	C₂³	1	2	yes	—
228	C₃×C₄×Q₈	C₂³	1	2	yes	—
229	C₃×C₄×Q₈	C₂³	1	2	yes	—
230	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₃×C₄×Q₈	C₂³	1	2	yes	—
232	C₃×C₄×Q₈	C₂³	1	2	yes	—
233	C₃×C₄×Q₈	C₂³	1	2	yes	—
234	C₃×C₄×Q₈	C₂³	1	2	yes	—
235	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₃×C₄×D₄	—	2	1	no	—
238	C₃×C₄×D₄	—	2	2	no	—
239	C₃×C₄×D₄	—	2	1	no	—
240	C₃×C₄×D₄	—	2	1	no	—
241	C₃×C₄×D₄	C₂³	1	2	yes	—
242	C₃×C₄×D₄	C₂³	1	2	yes	—
243	C₃×C₄×D₄	C₂³	1	2	yes	—
244	C₃×C₄×D₄	C₂³	1	2	yes	—
245	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
246	C₃×#117	—	2	2	no	—
247	C₃×#117	—	2	2	no	—
248	C₃×#117	—	2	1	no	—
249	C₃×#117	C₂³	1	2	yes	—
250	C₃×#117	C₂³	1	2	yes	—
251	C₂×C₃×C₄⋊C₄	—	2	1	no	—
252	C₂×C₃×C₄⋊C₄	—	2	2	no	—
253	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	—	2	1	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×#102	C₂³	1	2	yes	—
282	C₃×#102	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	2	yes	—
291	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	#562	—	2	2	no	—
301	#559	C₂²×C₃	1	1	yes	characteristic
302	#559	C₂²×C₃	1	2	yes	—
303	Q₈²	—	2	1	no	—
304	Q₈²	C₂²×C₃	1	2	yes	—
305	#557	—	2	1	no	—
306	#557	—	2	2	no	—
307	#557	C₂²×C₃	1	2	yes	—
308	#557	C₂²×C₃	1	2	yes	—
309	#557	C₂²×C₃	1	2	yes	—
310	#557	C₂²×C₃	1	1	yes	characteristic
311	#554	C₂²×C₃	1	2	yes	—
312	#550	C₂²×C₃	1	1	yes	characteristic
313	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
314	#548	—	2	1	no	—
315	#547	—	2	1	no	—
316	#544	—	2	1	no	—
317	#544	—	2	1	no	—
318	#544	C₂²×C₃	1	2	yes	—
319	#542	—	2	1	no	—
320	#542	C₂²×C₃	1	2	yes	—
321	#540	C₂²×C₃	1	2	yes	—
322	#539	—	2	2	no	—
323	#536	—	2	1	no	—
324	#533	—	2	2	no	—
325	#533	C₂²×C₃	1	1	yes	characteristic
326	#533	C₂²×C₃	1	1	yes	characteristic
327	#532	C₂²×C₃	1	1	yes	characteristic
328	#529	C₂²×C₃	1	1	yes	characteristic
329	#519	C₂²×C₃	1	2	yes	—
330	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
331	#501	C₂²×C₃	1	1	yes	characteristic
332	#501	C₂²×C₃	1	2	yes	—
333	#501	C₂²×C₃	1	2	yes	—
334	#501	C₂²×C₃	1	2	yes	—
335	#501	C₂²×C₃	1	1	yes	characteristic
336	#500	C₂²×C₃	1	2	yes	—
337	#499	C₂²×C₃	1	2	yes	—
338	#490	C₂²×C₃	1	2	yes	—
339	#490	C₂²×C₃	1	2	yes	—
340	#489	C₂²×C₃	1	1	yes	characteristic
341	#489	C₂²×C₃	1	2	yes	—
342	#489	C₂²×C₃	1	1	yes	characteristic
343	#488	C₂²×C₃	1	2	yes	—
344	#486	C₂²×C₃	1	2	yes	—
345	#485	C₂²×C₃	1	2	yes	—
346	#484	C₂²×C₃	1	1	yes	characteristic
347	#482	C₂²×C₃	1	2	yes	—
348	#482	C₂²×C₃	1	2	yes	—
349	#482	C₂²×C₃	1	2	yes	—
350	#481	C₂²×C₃	1	1	yes	characteristic
351	#480	C₂²×C₃	1	2	yes	—
352	#479	C₂²×C₃	1	2	yes	—
353	#479	C₂²×C₃	1	2	yes	—
354	#479	C₂²×C₃	1	2	yes	—
355	#479	C₂²×C₃	1	2	yes	—
356	#479	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	—
360	#478	C₂²×C₃	1	2	yes	—
361	#477	C₂²×C₃	1	2	yes	—
362	#477	C₂²×C₃	1	2	yes	—
363	#477	C₂²×C₃	1	2	yes	—
364	#476	C₂²×C₃	1	2	yes	—
365	#476	C₂²×C₃	1	2	yes	—
366	#475	C₂²×C₃	1	2	yes	—
367	#474	C₂²×C₃	1	2	yes	—
368	#474	C₂²×C₃	1	2	yes	—
369	#474	C₂²×C₃	1	2	yes	—
370	#464	C₂²×C₃	1	2	yes	—
371	#464	C₂²×C₃	1	2	yes	—
372	#464	C₂²×C₃	1	2	yes	—
373	#460	C₂²×C₃	1	2	yes	—
374	#460	C₂²×C₃	1	2	yes	—
375	#460	C₂²×C₃	1	2	yes	—
376	#451	C₂²×C₃	1	1	yes	characteristic
377	#448	C₂²×C₃	1	2	yes	—
378	#448	C₂²×C₃	1	1	yes	characteristic
379	#446	C₂²×C₃	1	2	yes	—
380	#446	C₂²×C₃	1	2	yes	—
381	#446	C₂²×C₃	1	2	yes	—
382	#446	C₂²×C₃	1	2	yes	—
383	#441	C₂²×C₃	1	2	yes	—
384	#441	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×Q₁₆	C₂²×C₃	1	2	yes	—
392	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
393	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
394	C₄×SD₁₆	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	C₃×#41	—	8	2	no	—
400	C₃×#41	—	8	2	no	—
401	C₂×C₃×Q₈	—	2	4	no	—
402	C₂×C₃×Q₈	—	2	1	no	—
403	C₂×C₃×Q₈	—	2	1	no	—
404	C₂×C₃×Q₈	—	2	1	no	—
405	C₂×C₃×Q₈	—	2	1	no	—
406	C₂×C₃×Q₈	—	2	2	no	—
407	C₂×C₃×Q₈	—	2	2	no	—
408	C₂×C₃×Q₈	—	2	2	no	—
409	C₂×C₃×Q₈	—	8	2	no	—
410	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
411	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
412	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
413	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
415	C₂×C₃×D₄	—	2	1	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	1	no	—
418	C₂×C₃×D₄	—	2	1	no	—
419	C₂×C₃×D₄	—	2	2	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	C₂⁴	1	2	yes	—
422	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×C₄	—	2	1	no	—
424	C₂²×C₃×C₄	—	2	1	no	—
425	C₂²×C₃×C₄	—	2	1	no	—
426	C₂²×C₃×C₄	—	2	2	no	—
427	C₂²×C₃×C₄	—	2	2	no	—
428	C₂²×C₃×C₄	—	2	2	no	—
429	C₂²×C₃×C₄	—	2	2	no	—
430	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₃×Q₁₆	—	2	4	no	—
434	C₃×SD₁₆	—	2	4	no	—
435	C₃×SD₁₆	—	2	4	no	—
436	C₃×SD₁₆	—	2	4	no	—
437	C₂×C₃×C₈	C₂⁴	1	2	yes	—
438	C₂×C₃×C₈	C₂⁴	1	2	yes	—
439	C₂×C₃×C₈	C₂⁴	1	2	yes	—
440	C₂×C₃×C₈	C₂⁴	1	2	yes	—
441	C₃×C₄⋊C₄	—	2	1	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	1	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	2	no	—
449	C₃×C₄⋊C₄	—	2	2	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	1	no	—
458	C₃×C₄⋊C₄	—	2	2	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	2	no	—
466	C₃×C₄⋊C₄	—	2	1	no	—
467	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
471	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
472	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
473	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
474	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
475	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
476	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
478	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
479	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
480	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
481	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
482	C₃×C₂²⋊C₄	—	2	2	no	—
483	C₃×C₂²⋊C₄	—	2	1	no	—
484	C₃×C₂²⋊C₄	—	2	1	no	—
485	C₃×C₂²⋊C₄	—	2	1	no	—
486	C₃×C₂²⋊C₄	—	2	1	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	2	no	—
492	C₃×C₂²⋊C₄	—	2	2	no	—
493	C₃×C₂²⋊C₄	—	2	2	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
496	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
497	C₃×C₄²	—	2	2	no	—
498	C₃×C₄²	—	2	2	no	—
499	C₃×C₄²	—	2	1	no	—
500	C₃×C₄²	—	2	2	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	—	2	2	no	—
506	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
507	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
508	C₃×C₄²	C₂⁴	1	2	yes	—
509	C₃×C₄²	C₂⁴	1	2	yes	—
510	C₃×C₄²	C₂⁴	1	1	yes	characteristic
511	C₃×C₄²	C₂⁴	1	1	yes	characteristic
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	2	1	no	—
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
516	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
517	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
518	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
519	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
520	C₄⋊Q₈	—	2	2	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
529	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
533	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
536	#127	C₂³×C₃	1	1	yes	characteristic
537	#127	C₂³×C₃	1	2	yes	—
538	#126	—	2	2	no	—
539	#126	—	2	1	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	C₃×D₄	1	2	yes	—
549	#125	C₂³×C₃	1	1	yes	characteristic
550	#125	C₂³×C₃	1	2	yes	—
551	#125	C₂³×C₃	1	2	yes	—
552	#125	C₂³×C₃	1	2	yes	—
553	#125	C₂³×C₃	1	2	yes	—
554	#124	—	2	1	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	1	no	—
558	#124	C₂³×C₃	1	1	yes	characteristic
559	#124	C₂³×C₃	1	2	yes	—
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	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	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
578	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
579	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
580	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
581	#121	—	2	1	no	—
582	#121	—	2	2	no	—
583	#121	—	2	1	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	C₂³×C₃	1	1	yes	characteristic
587	#121	C₂³×C₃	1	2	yes	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	C₂³×C₃	1	2	yes	—
600	C₄×Q₈	C₂³×C₃	1	2	yes	—
601	C₄×Q₈	C₂³×C₃	1	2	yes	—
602	C₄×Q₈	C₂³×C₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₃	1	2	yes	—
607	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₃	1	2	yes	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₃	1	2	yes	—
616	C₄×D₄	C₂³×C₃	1	2	yes	—
617	C₄×D₄	C₂³×C₃	1	2	yes	—
618	C₄×D₄	C₂³×C₃	1	2	yes	—
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	—	2	1	no	—
622	#117	C₂³×C₃	1	2	yes	—
623	#117	C₂³×C₃	1	2	yes	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	#107	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	#106	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	C₄⋊C₈	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	#102	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	#102	C₂³×C₃	1	2	yes	—
663	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
665	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
666	#97	C₂³×C₃	1	1	yes	characteristic
667	#97	C₂³×C₃	1	1	yes	characteristic
668	#97	C₂³×C₃	1	2	yes	—
669	#97	C₂³×C₃	1	2	yes	—
670	#97	C₂³×C₃	1	2	yes	—
671	C₄×C₈	C₂³×C₃	1	2	yes	—
672	C₄×C₈	C₂³×C₃	1	2	yes	—
673	C₂³×C₃	—	2	1	no	—
674	C₂³×C₃	—	2	2	no	—
675	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
676	C₃×Q₈	—	2	4	no	—
677	C₃×Q₈	—	2	2	no	—
678	C₃×Q₈	—	2	2	no	—
679	C₃×Q₈	—	4	1	no	—
680	C₃×Q₈	—	4	2	no	—
681	C₃×Q₈	—	4	1	no	—
682	C₃×Q₈	—	4	2	no	—
683	C₃×Q₈	—	4	2	no	—
684	C₃×Q₈	—	8	1	no	—
685	C₃×Q₈	—	8	2	no	—
686	C₃×Q₈	—	8	2	no	—
687	C₃×Q₈	—	8	2	no	—
688	C₃×Q₈	2₋¹⁺⁴	1	4	yes	—
689	C₃×D₄	—	2	2	no	—
690	C₃×D₄	—	2	2	no	—
691	C₃×D₄	—	2	2	no	—
692	C₃×D₄	—	4	2	no	—
693	C₃×D₄	—	8	1	no	—
694	C₃×D₄	—	8	2	no	—
695	C₃×D₄	—	8	2	no	—
696	C₃×D₄	—	8	1	no	—
697	C₃×D₄	—	8	2	no	—
698	C₂×C₃×C₄	—	2	4	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	2	2	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	2	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	2	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	2	1	no	—
708	C₂×C₃×C₄	—	4	1	no	—
709	C₂×C₃×C₄	—	4	1	no	—
710	C₂×C₃×C₄	—	4	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	2	no	—
715	C₂×C₃×C₄	—	8	1	no	—
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	1	yes	characteristic
719	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
720	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
721	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
722	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
723	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
724	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
725	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
726	C₃×C₈	—	2	2	no	—
727	C₃×C₈	—	2	2	no	—
728	C₃×C₈	—	2	2	no	—
729	C₃×C₈	—	2	2	no	—
730	#41	—	8	2	no	—
731	#41	—	8	2	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	2	1	no	—
734	C₂×Q₈	—	2	1	no	—
735	C₂×Q₈	—	2	1	no	—
736	C₂×Q₈	—	2	1	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	8	2	no	—
741	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
742	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
743	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
744	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
745	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	C₂⁴×C₃	1	2	yes	—
753	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
762	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
764	Q₁₆	—	2	4	no	—
765	SD₁₆	—	2	4	no	—
766	SD₁₆	—	2	4	no	—
767	SD₁₆	—	2	4	no	—
768	C₂×C₈	C₂⁴×C₃	1	2	yes	—
769	C₂×C₈	C₂⁴×C₃	1	2	yes	—
770	C₂×C₈	C₂⁴×C₃	1	2	yes	—
771	C₂×C₈	C₂⁴×C₃	1	2	yes	—
772	C₄⋊C₄	—	2	1	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	1	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	1	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	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
805	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
806	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
811	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
812	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	2	1	no	—
817	C₂²⋊C₄	—	2	1	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
827	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
828	C₄²	—	2	2	no	—
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	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
838	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
839	C₄²	C₂⁴×C₃	1	2	yes	—
840	C₄²	C₂⁴×C₃	1	2	yes	—
841	C₄²	C₂⁴×C₃	1	1	yes	characteristic
842	C₄²	C₂⁴×C₃	1	1	yes	characteristic
843	C₂²×C₃	—	2	1	no	—
844	C₂²×C₃	—	2	1	no	—
845	C₂²×C₃	—	2	1	no	—
846	C₂²×C₃	—	4	1	no	—
847	C₂²×C₃	—	4	2	no	—
848	C₂²×C₃	—	4	2	no	—
849	C₂²×C₃	—	4	1	no	—
850	C₂²×C₃	—	4	1	no	—
851	C₂²×C₃	—	4	2	no	—
852	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
853	C₃×C₄	—	2	1	no	—
854	C₃×C₄	—	2	1	no	—
855	C₃×C₄	—	2	2	no	—
856	C₃×C₄	—	2	2	no	—
857	C₃×C₄	—	2	1	no	—
858	C₃×C₄	—	2	1	no	—
859	C₃×C₄	—	2	2	no	—
860	C₃×C₄	—	2	2	no	—
861	C₃×C₄	—	2	4	no	—
862	C₃×C₄	—	2	1	no	—
863	C₃×C₄	—	4	1	no	—
864	C₃×C₄	—	4	2	no	—
865	C₃×C₄	—	4	2	no	—
866	C₃×C₄	—	4	2	no	—
867	C₃×C₄	—	4	1	no	—
868	C₃×C₄	—	4	2	no	—
869	C₃×C₄	—	4	1	no	—
870	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	2	no	—
873	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
874	Q₈	—	2	4	no	—
875	Q₈	—	2	2	no	—
876	Q₈	—	2	2	no	—
877	Q₈	—	4	1	no	—
878	Q₈	—	4	1	no	—
879	Q₈	—	4	2	no	—
880	Q₈	—	4	2	no	—
881	Q₈	—	4	2	no	—
882	Q₈	—	8	2	no	—
883	Q₈	—	8	1	no	—
884	Q₈	—	8	2	no	—
885	Q₈	—	8	2	no	—
886	Q₈	C₃×2₋¹⁺⁴	1	4	yes	—
887	D₄	—	2	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	2	no	—
890	D₄	—	4	2	no	—
891	D₄	—	8	2	no	—
892	D₄	—	8	1	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	1	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	2	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	2	no	—
911	C₂×C₄	—	8	2	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	—	8	1	no	—
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	1	yes	characteristic
917	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
918	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
919	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
920	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
921	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
922	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
923	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
924	C₈	—	2	2	no	—
925	C₈	—	2	2	no	—
926	C₈	—	2	2	no	—
927	C₈	—	2	2	no	—
928	C₂×C₃	—	4	1	no	—
929	C₂×C₃	—	8	1	no	—
930	C₂×C₃	—	8	2	no	—
931	C₂×C₃	#3486	1	1	yes	characteristic
932	C₂×C₃	#3585	1	1	yes	characteristic
933	C₂×C₃	#3586	1	1	yes	characteristic
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	1	no	—
943	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
944	C₄	—	2	4	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
962	C₃	#61874	1	1	yes	characteristic, direct product factor, Sylow
963	C₂	—	4	1	no	—
964	C₂	—	8	1	no	—
965	C₂	—	8	2	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×#3554	C₂
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
2. C₃×#3502	C₂	semidirect
3. C₃×#3390	C₂	semidirect
4. C₃×#3388	C₂	semidirect
5. C₃×#3386	C₂	semidirect
6. C₃×#3385	C₂	semidirect
7. C₃×#3375	C₂	semidirect
8. C₃×#3371	C₂	semidirect
9. C₃×#3371	C₂	semidirect
10. C₃×#3368	C₂	semidirect
11. C₃×#3243	C₂	semidirect
12. C₃×#3241	C₂	semidirect
13. C₃×#3240	C₂	semidirect
14. C₃×#3235	C₂	semidirect
15. C₃×#3126	C₂	semidirect
16. C₃×#3121	C₂	semidirect
17. C₃×#3117	C₂	semidirect
18. C₃×#3112	C₂	semidirect
19. C₃×#2987	C₂	semidirect
20. #61874	C₃	direct (N × H)
121. #3502	C₂×C₃	semidirect
122. #3390	C₂×C₃	semidirect
123. #3388	C₂×C₃	semidirect
124. #3386	C₂×C₃	semidirect
125. #3385	C₂×C₃	semidirect
126. #3375	C₂×C₃	semidirect
127. #3371	C₂×C₃	semidirect
128. #3371	C₂×C₃	semidirect
129. #3368	C₂×C₃	semidirect
130. #3243	C₂×C₃	semidirect
131. #3241	C₂×C₃	semidirect
132. #3240	C₂×C₃	semidirect
133. #3235	C₂×C₃	semidirect
134. #3126	C₂×C₃	semidirect
135. #3121	C₂×C₃	semidirect
136. #3117	C₂×C₃	semidirect
137. #3112	C₂×C₃	semidirect
138. #2987	C₂×C₃	semidirect
962. C₃	#61874	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×#3554	2
C₃×#3502	2
C₃×#3390	2
C₃×#3388	2
C₃×#3386	2
C₃×#3385	2
C₃×#3375	2
C₃×#3371	2
C₃×#3368	2
C₃×#3243	2
C₃×#3241	2
C₃×#3240	2
C₃×#3235	2
C₃×#3126	2
C₃×#3121	2
C₃×#3117	2
C₃×#3112	2
C₃×#2987	2
#61874	3

Subgroups — C3×#61874 #10680481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61874 #10680481