Subgroups — C₃×#61875 #10680482

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 942 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
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×#3387	C₂	1	2	yes	maximal, complemented
6	C₃×#3387	C₂	1	2	yes	maximal, complemented
7	C₃×#3377	C₂	1	2	yes	maximal, complemented
8	C₃×#3377	C₂	1	2	yes	maximal, complemented
9	C₃×#3374	C₂	1	2	yes	maximal, complemented
10	C₃×#3369	C₂	1	2	yes	maximal, complemented
11	C₃×#3244	C₂	1	2	yes	maximal
12	C₃×#3242	C₂	1	2	yes	maximal, complemented
13	C₃×#3240	C₂	1	1	yes	maximal, characteristic
14	C₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₃×#3121	C₂	1	2	yes	maximal
17	C₃×#3117	C₂	1	1	yes	maximal, characteristic
18	C₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#61875	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#563	—	2	2	no	—
22	C₃×Q₈²	—	2	1	no	—
23	C₃×Q₈²	C₂²	1	1	yes	characteristic
24	C₃×Q₈²	C₂²	1	2	yes	—
25	C₃×#557	—	2	1	no	—
26	C₃×#557	—	2	2	no	—
27	C₃×#557	C₂²	1	1	yes	characteristic
28	C₃×#557	C₂²	1	2	yes	—
29	C₃×#557	C₂²	1	2	yes	—
30	C₃×#557	C₂²	1	2	yes	—
31	C₃×#557	C₂²	1	2	yes	—
32	C₃×#556	—	2	1	no	—
33	C₃×#556	C₂²	1	2	yes	—
34	C₃×#556	C₂²	1	1	yes	characteristic
35	C₃×#554	C₂²	1	1	yes	characteristic
36	C₃×#552	—	2	1	no	—
37	C₃×#544	—	2	1	no	—
38	C₃×#544	—	2	1	no	—
39	C₃×#544	—	2	1	no	—
40	C₃×#544	C₂²	1	2	yes	—
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	—	2	2	no	—
46	C₃×#533	C₂²	1	1	yes	characteristic
47	C₃×#533	C₂²	1	1	yes	characteristic
48	C₃×#533	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×#499	C₂²	1	2	yes	—
58	C₃×#498	C₂²	1	2	yes	—
59	C₃×#491	C₂²	1	2	yes	—
60	C₃×#491	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×#487	C₂²	1	2	yes	—
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	1	yes	characteristic
70	C₃×#483	C₂²	1	2	yes	—
71	C₃×#482	C₂²	1	2	yes	—
72	C₃×#481	C₂²	1	1	yes	characteristic
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×#479	C₂²	1	2	yes	—
79	C₃×#479	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×#475	C₂²	1	2	yes	—
87	C₃×#475	C₂²	1	2	yes	—
88	C₃×#475	C₂²	1	2	yes	—
89	C₃×#475	C₂²	1	2	yes	—
90	C₃×#475	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×#462	C₂²	1	2	yes	—
95	C₃×#462	C₂²	1	2	yes	—
96	C₃×#462	C₂²	1	2	yes	—
97	C₃×#451	C₂²	1	2	yes	—
98	C₃×#451	C₂²	1	1	yes	characteristic
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×#441	C₂²	1	2	yes	—
107	C₃×#441	C₂²	1	2	yes	—
108	C₃×#441	C₂²	1	2	yes	—
109	C₃×#441	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×Q₁₆	C₂²	1	2	yes	—
114	C₃×C₄×Q₁₆	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	#3555	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	#3387	C₂×C₃	1	2	yes	complemented
125	#3387	C₂×C₃	1	2	yes	complemented
126	#3377	C₂×C₃	1	2	yes	complemented
127	#3377	C₂×C₃	1	2	yes	complemented
128	#3374	C₂×C₃	1	2	yes	complemented
129	#3369	C₂×C₃	1	2	yes	complemented
130	#3244	C₂×C₃	1	2	yes	—
131	#3242	C₂×C₃	1	2	yes	complemented
132	#3240	C₂×C₃	1	1	yes	characteristic
133	#3237	C₂×C₃	1	1	yes	characteristic, complemented
134	#3127	C₂×C₃	1	2	yes	complemented
135	#3121	C₂×C₃	1	2	yes	—
136	#3117	C₂×C₃	1	1	yes	characteristic
137	#3113	C₂×C₃	1	1	yes	characteristic, complemented
138	#2987	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
140	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
144	C₃×C₄⋊Q₈	—	2	2	no	—
145	C₃×C₄⋊Q₈	—	2	2	no	—
146	C₃×C₄⋊Q₈	—	2	2	no	—
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	2	no	—
151	C₃×C₄⋊Q₈	—	2	1	no	—
152	C₃×C₄⋊Q₈	—	2	2	no	—
153	C₃×C₄⋊Q₈	—	2	2	no	—
154	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃×#126	—	2	2	no	—
165	C₃×#126	—	2	2	no	—
166	C₃×#126	—	2	2	no	—
167	C₃×#126	—	2	2	no	—
168	C₃×#126	—	2	2	no	—
169	C₃×#126	—	2	2	no	—
170	C₃×#126	—	2	1	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	—	2	2	no	—
176	C₃×#125	—	2	2	no	—
177	C₃×#125	—	2	2	no	—
178	C₃×#125	—	2	1	no	—
179	C₃×#125	—	2	2	no	—
180	C₃×#125	—	2	2	no	—
181	C₃×#125	—	2	2	no	—
182	C₃×#125	—	2	2	no	—
183	C₃×#125	—	2	2	no	—
184	C₃×#125	—	2	1	no	—
185	C₃×#125	D₄	1	2	yes	—
186	C₃×#125	C₂³	1	1	yes	characteristic
187	C₃×#125	C₂³	1	2	yes	—
188	C₃×#125	C₂³	1	2	yes	—
189	C₃×#125	C₂³	1	2	yes	—
190	C₃×#125	C₂³	1	2	yes	—
191	C₃×#124	—	2	2	no	—
192	C₃×#124	C₂³	1	1	yes	characteristic
193	C₃×#124	C₂³	1	2	yes	—
194	C₃×#123	—	2	1	no	—
195	C₃×#123	—	2	2	no	—
196	C₃×C₂²⋊Q₈	—	2	2	no	—
197	C₃×C₂²⋊Q₈	—	2	1	no	—
198	C₃×C₂²⋊Q₈	—	2	1	no	—
199	C₃×C₂²⋊Q₈	—	2	1	no	—
200	C₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
205	C₃×C₂²⋊Q₈	—	2	2	no	—
206	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
207	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃×#121	C₂³	1	1	yes	characteristic
212	C₃×C₄×Q₈	—	2	2	no	—
213	C₃×C₄×Q₈	—	2	1	no	—
214	C₃×C₄×Q₈	—	2	1	no	—
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	2	yes	—
236	C₃×C₄×Q₈	C₂³	1	2	yes	—
237	C₃×C₄×Q₈	C₂³	1	2	yes	—
238	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₃×C₄×D₄	—	2	1	no	—
241	C₃×C₄×D₄	C₂³	1	2	yes	—
242	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
243	C₃×#117	—	2	1	no	—
244	C₃×#117	—	2	2	no	—
245	C₃×#117	—	2	1	no	—
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	1	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×#106	C₂³	1	2	yes	—
262	C₃×#106	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×#103	C₂³	1	2	yes	—
284	C₃×#103	C₂³	1	2	yes	—
285	C₃×#103	C₂³	1	2	yes	—
286	C₃×#103	C₂³	1	2	yes	—
287	C₃×#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	2	yes	—
294	C₃×#97	C₂³	1	1	yes	characteristic
295	C₃×#97	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
302	Q₈²	C₂²×C₃	1	2	yes	—
303	Q₈²	C₂²×C₃	1	1	yes	characteristic
304	#557	—	2	1	no	—
305	#557	—	2	2	no	—
306	#557	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
311	#556	—	2	1	no	—
312	#556	C₂²×C₃	1	2	yes	—
313	#556	C₂²×C₃	1	1	yes	characteristic
314	#554	C₂²×C₃	1	1	yes	characteristic
315	#552	—	2	1	no	—
316	#544	—	2	1	no	—
317	#544	—	2	1	no	—
318	#544	—	2	1	no	—
319	#544	C₂²×C₃	1	2	yes	—
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	—	2	2	no	—
325	#533	C₂²×C₃	1	1	yes	characteristic
326	#533	C₂²×C₃	1	1	yes	characteristic
327	#533	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	#499	C₂²×C₃	1	2	yes	—
337	#498	C₂²×C₃	1	2	yes	—
338	#491	C₂²×C₃	1	2	yes	—
339	#491	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	#487	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
349	#483	C₂²×C₃	1	2	yes	—
350	#482	C₂²×C₃	1	2	yes	—
351	#481	C₂²×C₃	1	1	yes	characteristic
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	#479	C₂²×C₃	1	2	yes	—
358	#479	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	#475	C₂²×C₃	1	2	yes	—
366	#475	C₂²×C₃	1	2	yes	—
367	#475	C₂²×C₃	1	2	yes	—
368	#475	C₂²×C₃	1	2	yes	—
369	#475	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	#462	C₂²×C₃	1	2	yes	—
374	#462	C₂²×C₃	1	2	yes	—
375	#462	C₂²×C₃	1	2	yes	—
376	#451	C₂²×C₃	1	2	yes	—
377	#451	C₂²×C₃	1	1	yes	characteristic
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	#441	C₂²×C₃	1	2	yes	—
386	#441	C₂²×C₃	1	2	yes	—
387	#441	C₂²×C₃	1	2	yes	—
388	#441	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×Q₁₆	C₂²×C₃	1	2	yes	—
393	C₄×Q₁₆	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	C₂×C₃×Q₈	—	2	4	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	1	no	—
405	C₂×C₃×Q₈	—	2	2	no	—
406	C₂×C₃×Q₈	—	2	2	no	—
407	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
408	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
409	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
410	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
411	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	—	2	1	no	—
416	C₂²×C₃×C₄	—	2	1	no	—
417	C₂²×C₃×C₄	—	2	1	no	—
418	C₂²×C₃×C₄	—	2	2	no	—
419	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₃×Q₁₆	—	2	4	no	—
423	C₃×Q₁₆	—	2	4	no	—
424	C₃×Q₁₆	—	2	4	no	—
425	C₃×SD₁₆	—	2	4	no	—
426	C₂×C₃×C₈	C₂⁴	1	2	yes	—
427	C₂×C₃×C₈	C₂⁴	1	2	yes	—
428	C₂×C₃×C₈	C₂⁴	1	2	yes	—
429	C₂×C₃×C₈	C₂⁴	1	2	yes	—
430	C₃×C₄⋊C₄	—	2	1	no	—
431	C₃×C₄⋊C₄	—	2	2	no	—
432	C₃×C₄⋊C₄	—	2	2	no	—
433	C₃×C₄⋊C₄	—	2	2	no	—
434	C₃×C₄⋊C₄	—	2	1	no	—
435	C₃×C₄⋊C₄	—	2	1	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	2	2	no	—
440	C₃×C₄⋊C₄	—	2	2	no	—
441	C₃×C₄⋊C₄	—	2	1	no	—
442	C₃×C₄⋊C₄	—	2	1	no	—
443	C₃×C₄⋊C₄	—	2	1	no	—
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	2	1	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	2	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	2	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	2	2	no	—
456	C₃×C₄⋊C₄	—	2	1	no	—
457	C₃×C₄⋊C₄	—	2	2	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	1	no	—
464	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
465	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
466	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
471	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
472	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
473	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
474	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
475	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
476	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
478	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
479	C₃×C₂²⋊C₄	—	2	2	no	—
480	C₃×C₂²⋊C₄	—	2	2	no	—
481	C₃×C₂²⋊C₄	—	2	1	no	—
482	C₃×C₂²⋊C₄	—	2	1	no	—
483	C₃×C₂²⋊C₄	—	2	1	no	—
484	C₃×C₂²⋊C₄	—	2	1	no	—
485	C₃×C₂²⋊C₄	—	2	2	no	—
486	C₃×C₂²⋊C₄	—	2	2	no	—
487	C₃×C₂²⋊C₄	—	2	1	no	—
488	C₃×C₂²⋊C₄	—	2	2	no	—
489	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
490	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
491	C₃×C₄²	—	2	2	no	—
492	C₃×C₄²	—	2	2	no	—
493	C₃×C₄²	—	2	2	no	—
494	C₃×C₄²	—	2	1	no	—
495	C₃×C₄²	—	2	2	no	—
496	C₃×C₄²	—	2	2	no	—
497	C₃×C₄²	—	2	2	no	—
498	C₃×C₄²	—	2	2	no	—
499	C₃×C₄²	—	2	2	no	—
500	C₃×C₄²	—	2	2	no	—
501	C₃×C₄²	—	2	2	no	—
502	C₃×C₄²	—	2	2	no	—
503	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
504	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
505	C₃×C₄²	C₂⁴	1	2	yes	—
506	C₃×C₄²	C₂⁴	1	2	yes	—
507	C₃×C₄²	C₂⁴	1	1	yes	characteristic
508	C₃×C₄²	C₂⁴	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
510	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
511	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
512	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
513	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
514	C₄⋊Q₈	—	2	2	no	—
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	—	2	2	no	—
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	—	2	2	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
525	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	1	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	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	2	no	—
553	#125	—	2	2	no	—
554	#125	—	2	1	no	—
555	#125	C₃×D₄	1	2	yes	—
556	#125	C₂³×C₃	1	1	yes	characteristic
557	#125	C₂³×C₃	1	2	yes	—
558	#125	C₂³×C₃	1	2	yes	—
559	#125	C₂³×C₃	1	2	yes	—
560	#125	C₂³×C₃	1	2	yes	—
561	#124	—	2	2	no	—
562	#124	C₂³×C₃	1	1	yes	characteristic
563	#124	C₂³×C₃	1	2	yes	—
564	#123	—	2	1	no	—
565	#123	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	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	C₃×D₄	1	2	yes	—
577	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
578	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
579	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
580	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
581	#121	C₂³×C₃	1	1	yes	characteristic
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	C₂³×C₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
603	C₄×Q₈	C₂³×C₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₃	1	2	yes	—
607	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₃	1	2	yes	—
609	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
610	C₄×D₄	—	2	1	no	—
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	2	no	—
617	#117	—	2	2	no	—
618	#117	—	2	1	no	—
619	#117	C₂³×C₃	1	2	yes	—
620	#117	C₂³×C₃	1	2	yes	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₄²	—	2	1	no	—
625	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
626	#107	C₂³×C₃	1	2	yes	—
627	#107	C₂³×C₃	1	2	yes	—
628	#107	C₂³×C₃	1	2	yes	—
629	#107	C₂³×C₃	1	2	yes	—
630	#107	C₂³×C₃	1	2	yes	—
631	#106	C₂³×C₃	1	2	yes	—
632	#106	C₂³×C₃	1	2	yes	—
633	#106	C₂³×C₃	1	2	yes	—
634	#106	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	C₄⋊C₈	C₂³×C₃	1	2	yes	—
639	C₄⋊C₈	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	#103	C₂³×C₃	1	2	yes	—
645	#103	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	#103	C₂³×C₃	1	2	yes	—
656	#103	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	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
661	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
662	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
663	#97	C₂³×C₃	1	2	yes	—
664	#97	C₂³×C₃	1	1	yes	characteristic
665	#97	C₂³×C₃	1	1	yes	characteristic
666	#97	C₂³×C₃	1	2	yes	—
667	#97	C₂³×C₃	1	2	yes	—
668	C₄×C₈	C₂³×C₃	1	2	yes	—
669	C₄×C₈	C₂³×C₃	1	2	yes	—
670	C₂³×C₃	—	2	1	no	—
671	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
672	C₃×Q₈	—	2	4	no	—
673	C₃×Q₈	—	2	2	no	—
674	C₃×Q₈	—	2	2	no	—
675	C₃×Q₈	—	2	2	no	—
676	C₃×Q₈	—	2	2	no	—
677	C₃×Q₈	—	4	1	no	—
678	C₃×Q₈	—	4	1	no	—
679	C₃×Q₈	—	4	2	no	—
680	C₃×Q₈	—	4	2	no	—
681	C₃×Q₈	—	8	1	no	—
682	C₃×Q₈	—	8	1	no	—
683	C₃×Q₈	—	8	2	no	—
684	C₃×Q₈	—	8	2	no	—
685	C₃×Q₈	—	8	2	no	—
686	C₃×Q₈	2₋¹⁺⁴	1	4	yes	—
687	C₃×D₄	—	2	2	no	—
688	C₃×D₄	—	8	1	no	—
689	C₂×C₃×C₄	—	2	4	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	2	no	—
692	C₂×C₃×C₄	—	2	2	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	2	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	2	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	4	1	no	—
701	C₂×C₃×C₄	—	4	1	no	—
702	C₂×C₃×C₄	—	4	2	no	—
703	C₂×C₃×C₄	—	8	2	no	—
704	C₂×C₃×C₄	—	8	1	no	—
705	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
706	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
707	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
708	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
709	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
710	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
711	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
712	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
713	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
714	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
715	C₃×C₈	—	2	2	no	—
716	C₃×C₈	—	2	2	no	—
717	C₃×C₈	—	2	2	no	—
718	C₃×C₈	—	2	2	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	1	no	—
721	C₂×Q₈	—	2	1	no	—
722	C₂×Q₈	—	2	1	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	1	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
728	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
729	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
730	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
732	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
740	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
742	Q₁₆	—	2	4	no	—
743	Q₁₆	—	2	4	no	—
744	Q₁₆	—	2	4	no	—
745	SD₁₆	—	2	4	no	—
746	C₂×C₈	C₂⁴×C₃	1	2	yes	—
747	C₂×C₈	C₂⁴×C₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₃	1	2	yes	—
749	C₂×C₈	C₂⁴×C₃	1	2	yes	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	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	1	no	—
777	C₄⋊C₄	—	2	2	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	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
785	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
786	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
787	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
788	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
789	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
790	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
791	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
792	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
797	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	1	no	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
810	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	1	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
824	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
825	C₄²	C₂⁴×C₃	1	2	yes	—
826	C₄²	C₂⁴×C₃	1	2	yes	—
827	C₄²	C₂⁴×C₃	1	1	yes	characteristic
828	C₄²	C₂⁴×C₃	1	1	yes	characteristic
829	C₂²×C₃	—	2	1	no	—
830	C₂²×C₃	—	2	1	no	—
831	C₂²×C₃	—	2	1	no	—
832	C₂²×C₃	—	4	1	no	—
833	C₂²×C₃	—	4	1	no	—
834	C₂²×C₃	—	4	1	no	—
835	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
836	C₃×C₄	—	2	1	no	—
837	C₃×C₄	—	2	1	no	—
838	C₃×C₄	—	2	1	no	—
839	C₃×C₄	—	2	1	no	—
840	C₃×C₄	—	2	2	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	2	2	no	—
843	C₃×C₄	—	2	2	no	—
844	C₃×C₄	—	2	4	no	—
845	C₃×C₄	—	2	1	no	—
846	C₃×C₄	—	4	1	no	—
847	C₃×C₄	—	4	2	no	—
848	C₃×C₄	—	4	2	no	—
849	C₃×C₄	—	4	1	no	—
850	C₃×C₄	—	4	2	no	—
851	C₃×C₄	—	4	2	no	—
852	C₃×C₄	—	4	2	no	—
853	C₃×C₄	—	4	1	no	—
854	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
855	C₂³	—	2	1	no	—
856	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
857	Q₈	—	2	4	no	—
858	Q₈	—	2	2	no	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	2	2	no	—
862	Q₈	—	4	1	no	—
863	Q₈	—	4	1	no	—
864	Q₈	—	4	2	no	—
865	Q₈	—	4	2	no	—
866	Q₈	—	8	1	no	—
867	Q₈	—	8	1	no	—
868	Q₈	—	8	2	no	—
869	Q₈	—	8	2	no	—
870	Q₈	—	8	2	no	—
871	Q₈	C₃×2₋¹⁺⁴	1	4	yes	—
872	D₄	—	2	2	no	—
873	D₄	—	8	1	no	—
874	C₂×C₄	—	2	4	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	1	no	—
890	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
891	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
892	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
893	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
894	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
895	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
896	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
897	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
898	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
899	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
900	C₈	—	2	2	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₂×C₃	—	4	1	no	—
905	C₂×C₃	—	8	1	no	—
906	C₂×C₃	#3486	1	1	yes	characteristic
907	C₂×C₃	#3586	1	1	yes	characteristic
908	C₂×C₃	#3586	1	1	yes	characteristic
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
916	C₄	—	2	4	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
935	C₃	#61875	1	1	yes	characteristic, direct product factor, Sylow
936	C₂	—	4	1	no	—
937	C₂	—	8	1	no	—
938	C₂	C₃×#3486	1	1	yes	characteristic
939	C₂	C₃×#3586	1	1	yes	characteristic
940	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×#121	C₂³
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×#3387	C₂	semidirect
6. C₃×#3387	C₂	semidirect
7. C₃×#3377	C₂	semidirect
8. C₃×#3377	C₂	semidirect
9. C₃×#3374	C₂	semidirect
10. C₃×#3369	C₂	semidirect
12. C₃×#3242	C₂	semidirect
14. C₃×#3237	C₂	semidirect
15. C₃×#3127	C₂	semidirect
18. C₃×#3113	C₂	semidirect
19. C₃×#2987	C₂	semidirect
20. #61875	C₃	direct (N × H)
121. #3502	C₂×C₃	semidirect
122. #3390	C₂×C₃	semidirect
123. #3388	C₂×C₃	semidirect
124. #3387	C₂×C₃	semidirect
125. #3387	C₂×C₃	semidirect
126. #3377	C₂×C₃	semidirect
127. #3377	C₂×C₃	semidirect
128. #3374	C₂×C₃	semidirect
129. #3369	C₂×C₃	semidirect
131. #3242	C₂×C₃	semidirect
133. #3237	C₂×C₃	semidirect
134. #3127	C₂×C₃	semidirect
137. #3113	C₂×C₃	semidirect
138. #2987	C₂×C₃	semidirect
935. C₃	#61875	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×#3502	2
C₃×#3390	2
C₃×#3388	2
C₃×#3387	2
C₃×#3377	2
C₃×#3374	2
C₃×#3369	2
C₃×#3244	2
C₃×#3242	2
C₃×#3240	2
C₃×#3237	2
C₃×#3127	2
C₃×#3121	2
C₃×#3117	2
C₃×#3113	2
C₃×#2987	2
#61875	3

Subgroups — C3×#61875 #10680482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61875 #10680482