Subgroups — C₃×#60598 #10679205

Order 768.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3127	C₂	1	2	yes	maximal, complemented
4	C₃×#3126	C₂	1	2	yes	maximal, complemented
5	C₃×#3120	C₂	1	2	yes	maximal, complemented
6	C₃×#3119	C₂	1	2	yes	maximal, complemented
7	C₃×#3117	C₂	1	2	yes	maximal, complemented
8	C₃×#3111	C₂	1	2	yes	maximal, complemented
9	C₃×#3108	C₂	1	2	yes	maximal, complemented
10	C₃×#3102	C₂	1	2	yes	maximal, complemented
11	C₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#60598	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
26	C₂×C₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃×#137	C₂²	1	1	yes	characteristic
28	C₂×C₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₃×#135	C₂²	1	1	yes	characteristic
30	C₃×#553	—	2	2	no	—
31	C₃×#553	—	2	2	no	—
32	C₃×#553	—	2	1	no	—
33	C₃×#553	—	2	1	no	—
34	C₃×#552	—	2	1	no	—
35	C₃×#552	—	2	1	no	—
36	C₃×#541	C₂²	1	2	yes	—
37	C₃×#540	C₂²	1	2	yes	—
38	C₃×#537	C₂²	1	1	yes	characteristic
39	C₃×#537	C₂²	1	1	yes	characteristic
40	C₃×#532	C₂²	1	1	yes	characteristic
41	C₃×#529	C₂²	1	2	yes	—
42	C₃×#529	C₂²	1	2	yes	—
43	C₂×C₃×#125	C₂²	1	1	yes	characteristic
44	C₃×#520	—	2	2	no	—
45	C₃×#520	—	2	1	no	—
46	C₃×#520	C₂²	1	1	yes	characteristic
47	C₃×#520	C₂²	1	2	yes	—
48	C₃×#520	C₂²	1	1	yes	characteristic
49	C₃×#520	C₂²	1	1	yes	characteristic
50	C₃×#520	C₂²	1	1	yes	characteristic
51	C₃×#519	—	2	1	no	—
52	C₃×#519	C₂²	1	1	yes	characteristic
53	C₃×#519	C₂²	1	2	yes	—
54	C₃×C₄×#41	—	2	2	no	—
55	C₃×C₄×#41	—	2	1	no	—
56	C₃×C₄×#41	C₂²	1	1	yes	characteristic
57	C₃×C₄×#41	C₂²	1	2	yes	—
58	C₃×C₄×#41	C₂²	1	1	yes	characteristic
59	C₂×C₃×C₄×Q₈	—	2	1	no	—
60	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
62	C₃×#485	C₂²	1	2	yes	—
63	C₃×#485	C₂²	1	2	yes	—
64	C₃×#484	C₂²	1	2	yes	—
65	C₃×#483	C₂²	1	2	yes	—
66	C₃×#482	C₂²	1	2	yes	—
67	C₃×#482	C₂²	1	2	yes	—
68	C₃×#481	C₂²	1	2	yes	—
69	C₃×#480	C₂²	1	2	yes	—
70	C₃×#479	C₂²	1	2	yes	—
71	C₃×#479	C₂²	1	2	yes	—
72	C₃×#479	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×#478	C₂²	1	2	yes	—
77	C₃×#478	C₂²	1	2	yes	—
78	C₃×#464	C₂²	1	1	yes	characteristic
79	C₃×#464	C₂²	1	1	yes	characteristic
80	C₃×#464	C₂²	1	2	yes	—
81	C₃×#464	C₂²	1	2	yes	—
82	C₃×#463	C₂²	1	1	yes	characteristic
83	C₃×#463	C₂²	1	1	yes	characteristic
84	C₃×#462	C₂²	1	1	yes	characteristic
85	C₃×#462	C₂²	1	2	yes	—
86	C₃×#461	C₂²	1	1	yes	characteristic
87	C₃×#460	C₂²	1	1	yes	characteristic
88	C₃×#460	C₂²	1	2	yes	—
89	C₃×#459	C₂²	1	1	yes	characteristic
90	C₃×#452	C₂²	1	2	yes	—
91	C₃×#452	C₂²	1	2	yes	—
92	C₃×#451	C₂²	1	2	yes	—
93	C₃×#451	C₂²	1	2	yes	—
94	C₃×#449	C₂²	1	2	yes	—
95	C₃×#449	C₂²	1	2	yes	—
96	C₃×#448	C₂²	1	2	yes	—
97	C₃×#448	C₂²	1	2	yes	—
98	C₃×#442	C₂²	1	2	yes	—
99	C₃×#441	C₂²	1	2	yes	—
100	C₃×#441	C₂²	1	2	yes	—
101	C₃×#441	C₂²	1	2	yes	—
102	C₃×#440	C₂²	1	2	yes	—
103	C₃×#440	C₂²	1	2	yes	—
104	C₃×#440	C₂²	1	2	yes	—
105	C₃×#440	C₂²	1	2	yes	—
106	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
107	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
108	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
109	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
110	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
111	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
112	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
113	C₃×C₄×D₈	C₂²	1	2	yes	—
114	C₃×#433	C₂²	1	2	yes	—
115	C₃×#433	C₂²	1	2	yes	—
116	C₃×#432	C₂²	1	2	yes	—
117	C₃×#431	C₂²	1	2	yes	—
118	C₃×#428	C₂²	1	1	yes	characteristic
119	C₃×#428	C₂²	1	1	yes	characteristic
120	C₂×C₃×#107	C₂²	1	1	yes	characteristic
121	C₂×C₃×#106	C₂²	1	1	yes	characteristic
122	C₃×#423	C₂²	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
124	C₃×#417	C₂²	1	1	yes	characteristic
125	C₃×#417	C₂²	1	1	yes	characteristic
126	C₃×#417	C₂²	1	1	yes	characteristic
127	C₃×#417	C₂²	1	1	yes	characteristic
128	C₃×#416	C₂²	1	1	yes	characteristic
129	C₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₃×#103	C₂²	1	1	yes	characteristic
132	C₃×#408	C₂²	1	1	yes	characteristic
133	C₃×#408	C₂²	1	1	yes	characteristic
134	C₃×#405	C₂²	1	1	yes	characteristic
135	C₃×#405	C₂²	1	1	yes	characteristic
136	#3512	C₂×C₃	1	1	yes	characteristic, complemented
137	C₄×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
138	#3127	C₂×C₃	1	2	yes	complemented
139	#3126	C₂×C₃	1	2	yes	complemented
140	#3120	C₂×C₃	1	2	yes	complemented
141	#3119	C₂×C₃	1	2	yes	complemented
142	#3117	C₂×C₃	1	2	yes	complemented
143	#3111	C₂×C₃	1	2	yes	complemented
144	#3108	C₂×C₃	1	2	yes	complemented
145	#3102	C₂×C₃	1	2	yes	complemented
146	#3099	C₂×C₃	1	1	yes	characteristic, complemented
147	#3098	C₂×C₃	1	1	yes	characteristic, complemented
148	#3080	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂×#479	C₂×C₃	1	1	yes	characteristic, complemented
150	#3037	C₂×C₃	1	1	yes	characteristic, complemented
151	#3035	C₂×C₃	1	1	yes	characteristic, complemented
152	#3013	C₂×C₃	1	1	yes	characteristic, complemented
153	#3013	C₂×C₃	1	1	yes	characteristic, complemented
154	#2952	C₂×C₃	1	1	yes	characteristic, complemented
155	#2951	C₂×C₃	1	1	yes	characteristic, complemented
156	#2947	C₂×C₃	1	1	yes	characteristic, complemented
157	#2947	C₂×C₃	1	1	yes	characteristic, complemented
158	#2925	C₂×C₃	1	1	yes	characteristic, complemented
159	C₃×2₋¹⁺⁴	—	2	4	no	—
160	C₃×2₋¹⁺⁴	—	2	4	no	—
161	C₂×C₃×#41	—	2	1	no	—
162	C₂×C₃×#41	—	2	2	no	—
163	C₂×C₃×#41	C₂³	1	1	yes	characteristic
164	C₂×C₃×#41	C₂³	1	1	yes	characteristic
165	C₂×C₃×#41	C₂³	1	2	yes	—
166	C₂×C₃×#41	C₂³	1	1	yes	characteristic
167	C₂×C₃×#41	C₂³	1	1	yes	characteristic
168	C₂²×C₃×Q₈	—	2	1	no	—
169	C₂²×C₃×Q₈	C₂³	1	2	yes	—
170	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
171	C₃×#137	—	2	4	no	—
172	C₃×#137	—	2	4	no	—
173	C₃×#135	—	2	4	no	—
174	C₃×#135	—	2	4	no	—
175	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
177	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
178	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
179	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
180	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
181	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
182	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
183	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
184	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
185	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
186	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
187	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
188	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
189	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
190	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
192	C₃×#127	C₂³	1	1	yes	characteristic
193	C₃×#126	—	2	2	no	—
194	C₃×#126	—	2	2	no	—
195	C₃×#126	—	2	2	no	—
196	C₃×#126	—	2	2	no	—
197	C₃×#125	—	2	2	no	—
198	C₃×#125	—	2	2	no	—
199	C₃×#125	—	2	1	no	—
200	C₃×#125	—	2	1	no	—
201	C₃×#125	C₂³	1	2	yes	—
202	C₃×#125	C₂³	1	2	yes	—
203	C₃×#124	C₂³	1	1	yes	characteristic
204	C₃×#124	C₂³	1	1	yes	characteristic
205	C₃×#123	—	2	2	no	—
206	C₃×#123	—	2	2	no	—
207	C₃×#123	—	2	2	no	—
208	C₃×#123	—	2	2	no	—
209	C₃×C₂²⋊Q₈	—	2	1	no	—
210	C₃×C₂²⋊Q₈	—	2	1	no	—
211	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃×#121	—	2	1	no	—
214	C₃×#121	—	2	1	no	—
215	C₃×#121	—	2	2	no	—
216	C₃×#121	—	2	2	no	—
217	C₃×#121	—	2	1	no	—
218	C₃×#121	—	2	1	no	—
219	C₃×#121	—	2	2	no	—
220	C₃×#121	—	2	2	no	—
221	C₃×#121	C₂³	1	2	yes	—
222	C₃×#121	C₂³	1	2	yes	—
223	C₃×C₄×Q₈	—	2	1	no	—
224	C₃×C₄×Q₈	—	2	1	no	—
225	C₃×C₄×Q₈	—	2	2	no	—
226	C₃×C₄×Q₈	—	2	1	no	—
227	C₃×C₄×Q₈	—	2	2	no	—
228	C₃×C₄×Q₈	—	2	2	no	—
229	C₃×C₄×Q₈	—	2	1	no	—
230	C₃×C₄×Q₈	—	2	2	no	—
231	C₃×C₄×Q₈	—	2	1	no	—
232	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
233	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
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	2	yes	—
239	C₃×C₄×Q₈	C₂³	1	2	yes	—
240	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₃×C₄×Q₈	C₂³	1	2	yes	—
242	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₃×C₄×D₄	—	2	2	no	—
244	C₃×C₄×D₄	—	2	1	no	—
245	C₃×C₄×D₄	—	2	1	no	—
246	C₃×C₄×D₄	—	2	2	no	—
247	C₃×C₄×D₄	—	2	1	no	—
248	C₃×C₄×D₄	—	2	2	no	—
249	C₃×C₄×D₄	—	2	2	no	—
250	C₃×C₄×D₄	—	2	2	no	—
251	C₃×C₄×D₄	—	2	2	no	—
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	2	no	—
256	C₃×C₄×D₄	—	2	1	no	—
257	C₃×C₄×D₄	—	2	1	no	—
258	C₃×C₄×D₄	D₄	1	2	yes	—
259	C₃×C₄×D₄	D₄	1	1	yes	characteristic
260	C₃×C₄×D₄	D₄	1	2	yes	—
261	C₃×C₄×D₄	D₄	1	1	yes	characteristic
262	C₃×C₄×D₄	C₂³	1	2	yes	—
263	C₃×C₄×D₄	C₂³	1	2	yes	—
264	C₃×C₄×D₄	C₂³	1	2	yes	—
265	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
266	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
267	C₃×#117	—	2	1	no	—
268	C₃×#117	—	2	2	no	—
269	C₃×#117	—	2	1	no	—
270	C₃×#117	—	2	1	no	—
271	C₃×#117	—	2	2	no	—
272	C₃×#117	—	2	2	no	—
273	C₃×#117	—	2	2	no	—
274	C₃×#117	—	2	2	no	—
275	C₃×#117	—	2	1	no	—
276	C₃×#117	—	2	2	no	—
277	C₃×#117	—	2	2	no	—
278	C₃×#117	C₂³	1	1	yes	characteristic
279	C₃×#117	C₂³	1	2	yes	—
280	C₃×#117	C₂³	1	1	yes	characteristic
281	C₃×#117	C₂³	1	2	yes	—
282	C₂×C₃×C₄⋊C₄	—	2	1	no	—
283	C₂×C₃×C₄⋊C₄	—	2	2	no	—
284	C₂×C₃×C₄⋊C₄	—	2	1	no	—
285	C₂×C₃×C₄⋊C₄	—	2	1	no	—
286	C₂×C₃×C₄⋊C₄	—	2	1	no	—
287	C₂×C₃×C₄⋊C₄	—	2	2	no	—
288	C₂×C₃×C₄⋊C₄	—	2	1	no	—
289	C₂×C₃×C₄⋊C₄	—	2	1	no	—
290	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
294	C₂×C₃×C₄²	—	2	1	no	—
295	C₂×C₃×C₄²	—	2	2	no	—
296	C₂×C₃×C₄²	—	2	2	no	—
297	C₂×C₃×C₄²	—	2	1	no	—
298	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
299	C₂×C₃×C₄²	C₂³	1	2	yes	—
300	C₃×#107	C₂³	1	2	yes	—
301	C₃×#107	C₂³	1	2	yes	—
302	C₃×#107	C₂³	1	2	yes	—
303	C₃×#107	C₂³	1	2	yes	—
304	C₃×#106	C₂³	1	2	yes	—
305	C₃×#106	C₂³	1	2	yes	—
306	C₃×#106	C₂³	1	2	yes	—
307	C₃×#106	C₂³	1	2	yes	—
308	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
309	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
310	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
311	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
312	C₃×C₄⋊C₈	C₂³	1	2	yes	—
313	C₃×C₄⋊C₈	C₂³	1	2	yes	—
314	C₃×#103	C₂³	1	2	yes	—
315	C₃×#103	C₂³	1	2	yes	—
316	C₃×#103	C₂³	1	2	yes	—
317	C₃×#103	C₂³	1	2	yes	—
318	C₃×#103	C₂³	1	1	yes	characteristic
319	C₃×#103	C₂³	1	1	yes	characteristic
320	C₃×#103	C₂³	1	1	yes	characteristic
321	C₃×#103	C₂³	1	1	yes	characteristic
322	C₃×#103	C₂³	1	2	yes	—
323	C₃×#103	C₂³	1	2	yes	—
324	C₃×#103	C₂³	1	2	yes	—
325	C₃×#103	C₂³	1	2	yes	—
326	C₃×#102	C₂³	1	1	yes	characteristic
327	C₃×#102	C₂³	1	1	yes	characteristic
328	C₃×#102	C₂³	1	1	yes	characteristic
329	C₃×#102	C₂³	1	1	yes	characteristic
330	C₃×#102	C₂³	1	2	yes	—
331	C₃×#102	C₂³	1	2	yes	—
332	C₃×#102	C₂³	1	2	yes	—
333	C₃×#102	C₂³	1	2	yes	—
334	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃×#97	C₂³	1	2	yes	—
339	C₃×#97	C₂³	1	2	yes	—
340	C₃×C₄×C₈	C₂³	1	2	yes	—
341	C₃×C₄×C₈	C₂³	1	2	yes	—
342	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic
343	C₂×#137	C₂²×C₃	1	1	yes	characteristic
344	C₂×#137	C₂²×C₃	1	1	yes	characteristic
345	C₂×#135	C₂²×C₃	1	1	yes	characteristic
346	C₂×#135	C₂²×C₃	1	1	yes	characteristic
347	#553	—	2	2	no	—
348	#553	—	2	2	no	—
349	#553	—	2	1	no	—
350	#553	—	2	1	no	—
351	#552	—	2	1	no	—
352	#552	—	2	1	no	—
353	#541	C₂²×C₃	1	2	yes	—
354	#540	C₂²×C₃	1	2	yes	—
355	#537	C₂²×C₃	1	1	yes	characteristic
356	#537	C₂²×C₃	1	1	yes	characteristic
357	#532	C₂²×C₃	1	1	yes	characteristic
358	#529	C₂²×C₃	1	2	yes	—
359	#529	C₂²×C₃	1	2	yes	—
360	C₂×#125	C₂²×C₃	1	1	yes	characteristic
361	#520	—	2	2	no	—
362	#520	—	2	1	no	—
363	#520	C₂²×C₃	1	2	yes	—
364	#520	C₂²×C₃	1	1	yes	characteristic
365	#520	C₂²×C₃	1	1	yes	characteristic
366	#520	C₂²×C₃	1	1	yes	characteristic
367	#520	C₂²×C₃	1	1	yes	characteristic
368	#519	—	2	1	no	—
369	#519	C₂²×C₃	1	2	yes	—
370	#519	C₂²×C₃	1	1	yes	characteristic
371	C₄×#41	—	2	2	no	—
372	C₄×#41	—	2	1	no	—
373	C₄×#41	C₂²×C₃	1	1	yes	characteristic
374	C₄×#41	C₂²×C₃	1	2	yes	—
375	C₄×#41	C₂²×C₃	1	1	yes	characteristic
376	C₂×C₄×Q₈	—	2	1	no	—
377	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
379	#485	C₂²×C₃	1	2	yes	—
380	#485	C₂²×C₃	1	2	yes	—
381	#484	C₂²×C₃	1	2	yes	—
382	#483	C₂²×C₃	1	2	yes	—
383	#482	C₂²×C₃	1	2	yes	—
384	#482	C₂²×C₃	1	2	yes	—
385	#481	C₂²×C₃	1	2	yes	—
386	#480	C₂²×C₃	1	2	yes	—
387	#479	C₂²×C₃	1	2	yes	—
388	#479	C₂²×C₃	1	2	yes	—
389	#479	C₂²×C₃	1	2	yes	—
390	#479	C₂²×C₃	1	2	yes	—
391	#479	C₂²×C₃	1	2	yes	—
392	#479	C₂²×C₃	1	2	yes	—
393	#478	C₂²×C₃	1	2	yes	—
394	#478	C₂²×C₃	1	2	yes	—
395	#464	C₂²×C₃	1	2	yes	—
396	#464	C₂²×C₃	1	1	yes	characteristic
397	#464	C₂²×C₃	1	2	yes	—
398	#464	C₂²×C₃	1	1	yes	characteristic
399	#463	C₂²×C₃	1	1	yes	characteristic
400	#463	C₂²×C₃	1	1	yes	characteristic
401	#462	C₂²×C₃	1	2	yes	—
402	#462	C₂²×C₃	1	1	yes	characteristic
403	#461	C₂²×C₃	1	1	yes	characteristic
404	#460	C₂²×C₃	1	2	yes	—
405	#460	C₂²×C₃	1	1	yes	characteristic
406	#459	C₂²×C₃	1	1	yes	characteristic
407	#452	C₂²×C₃	1	2	yes	—
408	#452	C₂²×C₃	1	2	yes	—
409	#451	C₂²×C₃	1	2	yes	—
410	#451	C₂²×C₃	1	2	yes	—
411	#449	C₂²×C₃	1	2	yes	—
412	#449	C₂²×C₃	1	2	yes	—
413	#448	C₂²×C₃	1	2	yes	—
414	#448	C₂²×C₃	1	2	yes	—
415	#442	C₂²×C₃	1	2	yes	—
416	#441	C₂²×C₃	1	2	yes	—
417	#441	C₂²×C₃	1	2	yes	—
418	#441	C₂²×C₃	1	2	yes	—
419	#440	C₂²×C₃	1	2	yes	—
420	#440	C₂²×C₃	1	2	yes	—
421	#440	C₂²×C₃	1	2	yes	—
422	#440	C₂²×C₃	1	2	yes	—
423	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
424	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
426	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
427	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
428	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
429	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
430	C₄×D₈	C₂²×C₃	1	2	yes	—
431	#433	C₂²×C₃	1	2	yes	—
432	#433	C₂²×C₃	1	2	yes	—
433	#432	C₂²×C₃	1	2	yes	—
434	#431	C₂²×C₃	1	2	yes	—
435	#428	C₂²×C₃	1	1	yes	characteristic
436	#428	C₂²×C₃	1	1	yes	characteristic
437	C₂×#107	C₂²×C₃	1	1	yes	characteristic
438	C₂×#106	C₂²×C₃	1	1	yes	characteristic
439	#423	C₂²×C₃	1	1	yes	characteristic
440	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
441	#417	C₂²×C₃	1	1	yes	characteristic
442	#417	C₂²×C₃	1	1	yes	characteristic
443	#417	C₂²×C₃	1	1	yes	characteristic
444	#417	C₂²×C₃	1	1	yes	characteristic
445	#416	C₂²×C₃	1	1	yes	characteristic
446	#416	C₂²×C₃	1	1	yes	characteristic
447	C₂×#103	C₂²×C₃	1	1	yes	characteristic
448	C₂×#103	C₂²×C₃	1	1	yes	characteristic
449	#408	C₂²×C₃	1	1	yes	characteristic
450	#408	C₂²×C₃	1	1	yes	characteristic
451	#405	C₂²×C₃	1	1	yes	characteristic
452	#405	C₂²×C₃	1	1	yes	characteristic
453	C₃×#41	—	2	16	no	—
454	C₃×#41	—	2	8	no	—
455	C₃×#41	—	2	4	no	—
456	C₃×#41	—	2	4	no	—
457	C₃×#41	—	2	2	no	—
458	C₃×#41	—	2	2	no	—
459	C₃×#41	—	2	2	no	—
460	C₃×#41	—	2	2	no	—
461	C₃×#41	—	2	2	no	—
462	C₃×#41	—	2	2	no	—
463	C₃×#41	—	2	2	no	—
464	C₃×#41	#41	1	4	yes	—
465	C₂×C₃×Q₈	—	2	8	no	—
466	C₂×C₃×Q₈	—	2	4	no	—
467	C₂×C₃×Q₈	—	2	4	no	—
468	C₂×C₃×Q₈	—	2	2	no	—
469	C₂×C₃×Q₈	—	2	1	no	—
470	C₂×C₃×Q₈	—	2	2	no	—
471	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
472	C₂×C₃×Q₈	#41	1	4	yes	—
473	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
474	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
475	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
476	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
477	C₂×C₃×D₄	—	2	2	no	—
478	C₂×C₃×D₄	—	2	1	no	—
479	C₂×C₃×D₄	—	2	1	no	—
480	C₂×C₃×D₄	—	2	1	no	—
481	C₂×C₃×D₄	—	2	2	no	—
482	C₂×C₃×D₄	—	2	2	no	—
483	C₂×C₃×D₄	—	2	1	no	—
484	C₂×C₃×D₄	—	2	1	no	—
485	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
486	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
487	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
488	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
489	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
490	C₂²×C₃×C₄	—	2	2	no	—
491	C₂²×C₃×C₄	—	2	1	no	—
492	C₂²×C₃×C₄	—	2	2	no	—
493	C₂²×C₃×C₄	—	2	1	no	—
494	C₂²×C₃×C₄	—	2	2	no	—
495	C₂²×C₃×C₄	—	2	1	no	—
496	C₂²×C₃×C₄	—	2	1	no	—
497	C₂²×C₃×C₄	—	2	1	no	—
498	C₂²×C₃×C₄	—	2	1	no	—
499	C₂²×C₃×C₄	—	2	1	no	—
500	C₂²×C₃×C₄	—	2	1	no	—
501	C₂²×C₃×C₄	—	2	2	no	—
502	C₂²×C₃×C₄	—	2	1	no	—
503	C₂²×C₃×C₄	—	2	2	no	—
504	C₂²×C₃×C₄	—	2	2	no	—
505	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
506	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
507	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
509	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
510	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
511	C₃×Q₁₆	—	2	2	no	—
512	C₃×Q₁₆	—	2	2	no	—
513	C₃×Q₁₆	—	2	4	no	—
514	C₃×Q₁₆	—	2	4	no	—
515	C₃×SD₁₆	—	2	2	no	—
516	C₃×SD₁₆	—	2	2	no	—
517	C₃×SD₁₆	—	2	4	no	—
518	C₃×SD₁₆	—	2	4	no	—
519	C₃×SD₁₆	—	2	2	no	—
520	C₃×SD₁₆	—	2	2	no	—
521	C₃×D₈	—	2	2	no	—
522	C₃×D₈	—	2	2	no	—
523	C₃×M₁₆	—	2	2	no	—
524	C₃×M₁₆	—	2	2	no	—
525	C₂×C₃×C₈	—	2	2	no	—
526	C₂×C₃×C₈	—	2	2	no	—
527	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
528	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
529	C₂×C₃×C₈	C₂⁴	1	2	yes	—
530	C₂×C₃×C₈	C₂⁴	1	2	yes	—
531	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
532	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
533	C₃×C₄⋊C₄	—	2	2	no	—
534	C₃×C₄⋊C₄	—	2	2	no	—
535	C₃×C₄⋊C₄	—	2	2	no	—
536	C₃×C₄⋊C₄	—	2	2	no	—
537	C₃×C₄⋊C₄	—	2	1	no	—
538	C₃×C₄⋊C₄	—	2	2	no	—
539	C₃×C₄⋊C₄	—	2	1	no	—
540	C₃×C₄⋊C₄	—	2	1	no	—
541	C₃×C₄⋊C₄	—	2	1	no	—
542	C₃×C₄⋊C₄	—	2	2	no	—
543	C₃×C₄⋊C₄	—	2	2	no	—
544	C₃×C₄⋊C₄	—	2	2	no	—
545	C₃×C₄⋊C₄	—	2	2	no	—
546	C₃×C₄⋊C₄	—	2	2	no	—
547	C₃×C₄⋊C₄	—	2	2	no	—
548	C₃×C₄⋊C₄	—	2	2	no	—
549	C₃×C₄⋊C₄	—	2	1	no	—
550	C₃×C₄⋊C₄	—	2	2	no	—
551	C₃×C₄⋊C₄	—	2	2	no	—
552	C₃×C₄⋊C₄	—	2	1	no	—
553	C₃×C₄⋊C₄	—	2	1	no	—
554	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
555	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
556	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
557	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
558	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
559	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
560	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
561	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
562	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
563	C₃×C₂²⋊C₄	—	2	2	no	—
564	C₃×C₂²⋊C₄	—	2	1	no	—
565	C₃×C₂²⋊C₄	—	2	2	no	—
566	C₃×C₂²⋊C₄	—	2	2	no	—
567	C₃×C₂²⋊C₄	—	2	1	no	—
568	C₃×C₂²⋊C₄	—	2	2	no	—
569	C₃×C₂²⋊C₄	—	2	1	no	—
570	C₃×C₂²⋊C₄	—	2	1	no	—
571	C₃×C₂²⋊C₄	—	2	1	no	—
572	C₃×C₂²⋊C₄	—	2	2	no	—
573	C₃×C₂²⋊C₄	—	2	2	no	—
574	C₃×C₂²⋊C₄	—	2	2	no	—
575	C₃×C₂²⋊C₄	—	2	2	no	—
576	C₃×C₂²⋊C₄	—	2	1	no	—
577	C₃×C₂²⋊C₄	—	2	1	no	—
578	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
579	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
580	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
581	C₃×C₄²	—	2	2	no	—
582	C₃×C₄²	—	2	1	no	—
583	C₃×C₄²	—	2	2	no	—
584	C₃×C₄²	—	2	1	no	—
585	C₃×C₄²	—	2	2	no	—
586	C₃×C₄²	—	2	2	no	—
587	C₃×C₄²	—	2	2	no	—
588	C₃×C₄²	—	2	2	no	—
589	C₃×C₄²	—	2	1	no	—
590	C₃×C₄²	—	2	2	no	—
591	C₃×C₄²	—	2	2	no	—
592	C₃×C₄²	C₂×D₄	1	2	yes	—
593	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
594	C₃×C₄²	C₂×D₄	1	2	yes	—
595	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
596	C₃×C₄²	C₂⁴	1	2	yes	—
597	C₃×C₄²	C₂⁴	1	1	yes	characteristic
598	C₃×C₄²	C₂⁴	1	1	yes	characteristic
599	2₋¹⁺⁴	—	2	4	no	—
600	2₋¹⁺⁴	—	2	4	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	2	no	—
603	C₂×#41	C₂³×C₃	1	2	yes	—
604	C₂×#41	C₂³×C₃	1	1	yes	characteristic
605	C₂×#41	C₂³×C₃	1	1	yes	characteristic
606	C₂×#41	C₂³×C₃	1	1	yes	characteristic
607	C₂×#41	C₂³×C₃	1	1	yes	characteristic
608	C₂²×Q₈	—	2	1	no	—
609	C₂²×Q₈	C₂³×C₃	1	2	yes	—
610	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
611	#137	—	2	4	no	—
612	#137	—	2	4	no	—
613	#135	—	2	4	no	—
614	#135	—	2	4	no	—
615	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
616	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
617	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
618	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
620	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
621	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
622	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
623	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
624	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
625	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
626	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
627	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
628	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
629	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
630	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
632	#127	C₂³×C₃	1	1	yes	characteristic
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	1	no	—
640	#125	—	2	1	no	—
641	#125	C₂³×C₃	1	2	yes	—
642	#125	C₂³×C₃	1	2	yes	—
643	#124	C₂³×C₃	1	1	yes	characteristic
644	#124	C₂³×C₃	1	1	yes	characteristic
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	1	no	—
658	#121	—	2	1	no	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	C₂³×C₃	1	2	yes	—
662	#121	C₂³×C₃	1	2	yes	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	2	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	2	no	—
668	C₄×Q₈	—	2	2	no	—
669	C₄×Q₈	—	2	1	no	—
670	C₄×Q₈	—	2	2	no	—
671	C₄×Q₈	—	2	1	no	—
672	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
673	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
674	C₄×Q₈	C₂³×C₃	1	2	yes	—
675	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
676	C₄×Q₈	C₂³×C₃	1	2	yes	—
677	C₄×Q₈	C₂³×C₃	1	2	yes	—
678	C₄×Q₈	C₂³×C₃	1	2	yes	—
679	C₄×Q₈	C₂³×C₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
681	C₄×Q₈	C₂³×C₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₃	1	2	yes	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	C₃×D₄	1	2	yes	—
699	C₄×D₄	C₃×D₄	1	1	yes	characteristic
700	C₄×D₄	C₃×D₄	1	2	yes	—
701	C₄×D₄	C₃×D₄	1	1	yes	characteristic
702	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
703	C₄×D₄	C₂³×C₃	1	2	yes	—
704	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
705	C₄×D₄	C₂³×C₃	1	2	yes	—
706	C₄×D₄	C₂³×C₃	1	2	yes	—
707	#117	—	2	1	no	—
708	#117	—	2	2	no	—
709	#117	—	2	1	no	—
710	#117	—	2	1	no	—
711	#117	—	2	2	no	—
712	#117	—	2	2	no	—
713	#117	—	2	2	no	—
714	#117	—	2	2	no	—
715	#117	—	2	1	no	—
716	#117	—	2	2	no	—
717	#117	—	2	2	no	—
718	#117	C₂³×C₃	1	1	yes	characteristic
719	#117	C₂³×C₃	1	2	yes	—
720	#117	C₂³×C₃	1	1	yes	characteristic
721	#117	C₂³×C₃	1	2	yes	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	2	no	—
724	C₂×C₄⋊C₄	—	2	1	no	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	—	2	2	no	—
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	1	no	—
730	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
734	C₂×C₄²	—	2	1	no	—
735	C₂×C₄²	—	2	2	no	—
736	C₂×C₄²	—	2	2	no	—
737	C₂×C₄²	—	2	1	no	—
738	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₃	1	2	yes	—
740	#107	C₂³×C₃	1	2	yes	—
741	#107	C₂³×C₃	1	2	yes	—
742	#107	C₂³×C₃	1	2	yes	—
743	#107	C₂³×C₃	1	2	yes	—
744	#106	C₂³×C₃	1	2	yes	—
745	#106	C₂³×C₃	1	2	yes	—
746	#106	C₂³×C₃	1	2	yes	—
747	#106	C₂³×C₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
749	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
750	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
752	C₄⋊C₈	C₂³×C₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₃	1	2	yes	—
754	#103	C₂³×C₃	1	2	yes	—
755	#103	C₂³×C₃	1	2	yes	—
756	#103	C₂³×C₃	1	2	yes	—
757	#103	C₂³×C₃	1	2	yes	—
758	#103	C₂³×C₃	1	1	yes	characteristic
759	#103	C₂³×C₃	1	1	yes	characteristic
760	#103	C₂³×C₃	1	1	yes	characteristic
761	#103	C₂³×C₃	1	1	yes	characteristic
762	#103	C₂³×C₃	1	2	yes	—
763	#103	C₂³×C₃	1	2	yes	—
764	#103	C₂³×C₃	1	2	yes	—
765	#103	C₂³×C₃	1	2	yes	—
766	#102	C₂³×C₃	1	1	yes	characteristic
767	#102	C₂³×C₃	1	1	yes	characteristic
768	#102	C₂³×C₃	1	1	yes	characteristic
769	#102	C₂³×C₃	1	1	yes	characteristic
770	#102	C₂³×C₃	1	2	yes	—
771	#102	C₂³×C₃	1	2	yes	—
772	#102	C₂³×C₃	1	2	yes	—
773	#102	C₂³×C₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
778	#97	C₂³×C₃	1	2	yes	—
779	#97	C₂³×C₃	1	2	yes	—
780	C₄×C₈	C₂³×C₃	1	2	yes	—
781	C₄×C₈	C₂³×C₃	1	2	yes	—
782	C₂³×C₃	—	2	1	no	—
783	C₂³×C₃	—	2	1	no	—
784	C₂³×C₃	—	2	1	no	—
785	C₂³×C₃	C₂²×D₄	1	2	yes	—
786	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
787	C₃×Q₈	—	2	8	no	—
788	C₃×Q₈	—	2	2	no	—
789	C₃×Q₈	—	2	4	no	—
790	C₃×Q₈	—	2	1	no	—
791	C₃×Q₈	—	2	2	no	—
792	C₃×Q₈	—	2	1	no	—
793	C₃×Q₈	—	2	1	no	—
794	C₃×Q₈	—	2	1	no	—
795	C₃×Q₈	—	2	1	no	—
796	C₃×Q₈	C₂×#41	1	2	yes	—
797	C₃×Q₈	C₂×#41	1	4	yes	—
798	C₃×D₄	—	2	8	no	—
799	C₃×D₄	—	2	4	no	—
800	C₃×D₄	—	2	4	no	—
801	C₃×D₄	—	2	2	no	—
802	C₃×D₄	—	2	1	no	—
803	C₃×D₄	—	2	1	no	—
804	C₃×D₄	—	2	1	no	—
805	C₃×D₄	—	2	1	no	—
806	C₃×D₄	—	2	1	no	—
807	C₃×D₄	—	4	2	no	—
808	C₃×D₄	—	4	2	no	—
809	C₃×D₄	—	8	1	no	—
810	C₃×D₄	—	8	1	no	—
811	C₃×D₄	—	8	2	no	—
812	C₃×D₄	—	8	2	no	—
813	C₃×D₄	C₂×#41	1	2	yes	—
814	C₂×C₃×C₄	—	2	8	no	—
815	C₂×C₃×C₄	—	2	8	no	—
816	C₂×C₃×C₄	—	2	4	no	—
817	C₂×C₃×C₄	—	2	2	no	—
818	C₂×C₃×C₄	—	2	1	no	—
819	C₂×C₃×C₄	—	2	4	no	—
820	C₂×C₃×C₄	—	2	2	no	—
821	C₂×C₃×C₄	—	2	2	no	—
822	C₂×C₃×C₄	—	2	1	no	—
823	C₂×C₃×C₄	—	2	1	no	—
824	C₂×C₃×C₄	—	2	2	no	—
825	C₂×C₃×C₄	—	2	1	no	—
826	C₂×C₃×C₄	—	2	1	no	—
827	C₂×C₃×C₄	—	2	2	no	—
828	C₂×C₃×C₄	—	2	2	no	—
829	C₂×C₃×C₄	—	4	2	no	—
830	C₂×C₃×C₄	—	4	1	no	—
831	C₂×C₃×C₄	—	4	2	no	—
832	C₂×C₃×C₄	—	4	1	no	—
833	C₂×C₃×C₄	—	4	2	no	—
834	C₂×C₃×C₄	—	4	2	no	—
835	C₂×C₃×C₄	—	4	2	no	—
836	C₂×C₃×C₄	—	8	2	no	—
837	C₂×C₃×C₄	—	8	2	no	—
838	C₂×C₃×C₄	—	8	1	no	—
839	C₂×C₃×C₄	—	8	2	no	—
840	C₂×C₃×C₄	—	8	1	no	—
841	C₂×C₃×C₄	—	8	2	no	—
842	C₂×C₃×C₄	—	8	1	no	—
843	C₂×C₃×C₄	—	8	1	no	—
844	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
845	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
846	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
847	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
848	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
849	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂×C₃×C₄	C₂×#41	1	2	yes	—
853	C₂×C₃×C₄	C₂×#41	1	2	yes	—
854	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
855	C₃×C₈	—	2	1	no	—
856	C₃×C₈	—	2	1	no	—
857	C₃×C₈	—	2	1	no	—
858	C₃×C₈	—	2	1	no	—
859	C₃×C₈	—	2	2	no	—
860	C₃×C₈	—	2	2	no	—
861	#41	—	2	16	no	—
862	#41	—	2	8	no	—
863	#41	—	2	4	no	—
864	#41	—	2	4	no	—
865	#41	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	2	2	no	—
868	#41	—	2	2	no	—
869	#41	—	2	2	no	—
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	C₃×#41	1	4	yes	—
873	C₂×Q₈	—	2	8	no	—
874	C₂×Q₈	—	2	4	no	—
875	C₂×Q₈	—	2	4	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
880	C₂×Q₈	C₃×#41	1	4	yes	—
881	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
884	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
894	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
895	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
896	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
897	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
914	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
915	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
916	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	2	2	no	—
921	Q₁₆	—	2	4	no	—
922	Q₁₆	—	2	4	no	—
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	2	2	no	—
925	SD₁₆	—	2	4	no	—
926	SD₁₆	—	2	4	no	—
927	SD₁₆	—	2	2	no	—
928	SD₁₆	—	2	2	no	—
929	D₈	—	2	2	no	—
930	D₈	—	2	2	no	—
931	M₁₆	—	2	2	no	—
932	M₁₆	—	2	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₃	1	2	yes	—
938	C₂×C₈	C₂⁴×C₃	1	2	yes	—
939	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
963	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
964	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
965	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
987	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
988	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	C₂×C₃×D₄	1	2	yes	—
1001	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1002	C₄²	C₂×C₃×D₄	1	2	yes	—
1003	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₃	1	2	yes	—
1005	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1007	C₂²×C₃	—	2	1	no	—
1008	C₂²×C₃	—	2	1	no	—
1009	C₂²×C₃	—	2	2	no	—
1010	C₂²×C₃	—	2	2	no	—
1011	C₂²×C₃	—	2	2	no	—
1012	C₂²×C₃	—	2	2	no	—
1013	C₂²×C₃	—	4	1	no	—
1014	C₂²×C₃	—	4	1	no	—
1015	C₂²×C₃	—	4	1	no	—
1016	C₂²×C₃	—	4	1	no	—
1017	C₂²×C₃	—	4	1	no	—
1018	C₂²×C₃	—	4	1	no	—
1019	C₂²×C₃	—	4	1	no	—
1020	C₂²×C₃	—	4	1	no	—
1021	C₂²×C₃	#525	1	2	yes	—
1022	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1023	C₃×C₄	—	2	1	no	—
1024	C₃×C₄	—	2	2	no	—
1025	C₃×C₄	—	2	1	no	—
1026	C₃×C₄	—	2	1	no	—
1027	C₃×C₄	—	2	2	no	—
1028	C₃×C₄	—	2	1	no	—
1029	C₃×C₄	—	2	4	no	—
1030	C₃×C₄	—	2	2	no	—
1031	C₃×C₄	—	2	2	no	—
1032	C₃×C₄	—	4	2	no	—
1033	C₃×C₄	—	4	1	no	—
1034	C₃×C₄	—	4	2	no	—
1035	C₃×C₄	—	4	1	no	—
1036	C₃×C₄	—	4	2	no	—
1037	C₃×C₄	—	4	1	no	—
1038	C₃×C₄	—	4	1	no	—
1039	C₃×C₄	#525	1	2	yes	—
1040	C₃×C₄	C₂²×#41	1	1	yes	characteristic
1041	C₃×C₄	C₂²×#41	1	1	yes	characteristic
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	C₂²×C₃×D₄	1	2	yes	—
1046	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1047	Q₈	—	2	8	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	4	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	C₂×C₃×#41	1	2	yes	—
1057	Q₈	C₂×C₃×#41	1	4	yes	—
1058	D₄	—	2	8	no	—
1059	D₄	—	2	4	no	—
1060	D₄	—	2	4	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	C₂×C₃×#41	1	2	yes	—
1074	C₂×C₄	—	2	8	no	—
1075	C₂×C₄	—	2	8	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	4	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	4	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	1	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1106	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1108	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1109	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1112	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1113	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1114	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	2	no	—
1121	C₂×C₃	—	2	2	no	—
1122	C₂×C₃	—	4	2	no	—
1123	C₂×C₃	—	4	2	no	—
1124	C₂×C₃	—	8	1	no	—
1125	C₂×C₃	—	8	1	no	—
1126	C₂×C₃	C₂×#525	1	1	yes	characteristic
1127	C₂×C₃	#3584	1	1	yes	characteristic
1128	C₂×C₃	#3586	1	1	yes	characteristic
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	C₃×#525	1	2	yes	—
1144	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1145	C₄	—	2	4	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	C₃×#525	1	2	yes	—
1162	C₄	C₂²×C₃×#41	1	1	yes	characteristic
1163	C₄	C₂²×C₃×#41	1	1	yes	characteristic
1164	C₃	#60598	1	1	yes	characteristic, direct product factor, Sylow
1165	C₂	—	2	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	1	no	—
1170	C₂	C₂×C₃×#525	1	1	yes	characteristic
1171	C₂	C₃×#3584	1	1	yes	characteristic
1172	C₂	C₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3512	C₂	semidirect
2. C₃×C₄×2₋¹⁺⁴	C₂	semidirect
3. C₃×#3127	C₂	semidirect
4. C₃×#3126	C₂	semidirect
5. C₃×#3120	C₂	semidirect
6. C₃×#3119	C₂	semidirect
7. C₃×#3117	C₂	semidirect
8. C₃×#3111	C₂	semidirect
9. C₃×#3108	C₂	semidirect
10. C₃×#3102	C₂	semidirect
11. C₃×#3099	C₂	semidirect
12. C₃×#3098	C₂	semidirect
13. C₃×#3080	C₂	semidirect
14. C₂×C₃×#479	C₂	semidirect
15. C₃×#3037	C₂	semidirect
16. C₃×#3035	C₂	semidirect
17. C₃×#3013	C₂	semidirect
18. C₃×#3013	C₂	semidirect
19. C₃×#2952	C₂	semidirect
20. C₃×#2951	C₂	semidirect
21. C₃×#2947	C₂	semidirect
22. C₃×#2947	C₂	semidirect
23. C₃×#2925	C₂	semidirect
24. #60598	C₃	direct (N × H)
136. #3512	C₂×C₃	semidirect
137. C₄×2₋¹⁺⁴	C₂×C₃	semidirect
138. #3127	C₂×C₃	semidirect
139. #3126	C₂×C₃	semidirect
140. #3120	C₂×C₃	semidirect
141. #3119	C₂×C₃	semidirect
142. #3117	C₂×C₃	semidirect
143. #3111	C₂×C₃	semidirect
144. #3108	C₂×C₃	semidirect
145. #3102	C₂×C₃	semidirect
146. #3099	C₂×C₃	semidirect
147. #3098	C₂×C₃	semidirect
148. #3080	C₂×C₃	semidirect
149. C₂×#479	C₂×C₃	semidirect
150. #3037	C₂×C₃	semidirect
151. #3035	C₂×C₃	semidirect
152. #3013	C₂×C₃	semidirect
153. #3013	C₂×C₃	semidirect
154. #2952	C₂×C₃	semidirect
155. #2951	C₂×C₃	semidirect
156. #2947	C₂×C₃	semidirect
157. #2947	C₂×C₃	semidirect
158. #2925	C₂×C₃	semidirect
1164. C₃	#60598	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×#3512	2
C₃×C₄×2₋¹⁺⁴	2
C₃×#3127	2
C₃×#3126	2
C₃×#3120	2
C₃×#3119	2
C₃×#3117	2
C₃×#3111	2
C₃×#3108	2
C₃×#3102	2
C₃×#3099	2
C₃×#3098	2
C₃×#3080	2
C₂×C₃×#479	2
C₃×#3037	2
C₃×#3035	2
C₃×#3013	2
C₃×#2952	2
C₃×#2951	2
C₃×#2947	2
C₃×#2925	2
#60598	3

Subgroups — C3×#60598 #10679205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60598 #10679205