Subgroups — C₃×#60584 #10679191

Order 768.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3124	C₂	1	4	yes	maximal, complemented
4	C₃×#3119	C₂	1	4	yes	maximal, complemented
5	C₃×#3114	C₂	1	2	yes	maximal, complemented
6	C₃×#3112	C₂	1	2	yes	maximal, complemented
7	C₃×#3108	C₂	1	2	yes	maximal, complemented
8	C₃×#3100	C₂	1	2	yes	maximal, complemented
9	C₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3083	C₂	1	2	yes	maximal, complemented
12	C₃×#3045	C₂	1	2	yes	maximal, complemented
13	C₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2951	C₂	1	2	yes	maximal, complemented
16	C₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	#60584	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₃×#135	C₂²	1	2	yes	—
22	C₃×#555	—	2	1	no	—
23	C₃×#553	—	2	1	no	—
24	C₃×#553	—	2	1	no	—
25	C₃×#551	—	2	2	no	—
26	C₃×#547	—	2	1	no	—
27	C₃×#546	—	2	2	no	—
28	C₃×#544	C₂²	1	1	yes	characteristic, complemented
29	C₃×#542	C₂²	1	2	yes	complemented
30	C₃×#540	C₂²	1	2	yes	complemented
31	C₃×#535	C₂²	1	1	yes	characteristic, complemented
32	C₃×#532	C₂²	1	2	yes	—
33	C₃×#529	C₂²	1	2	yes	—
34	C₃×#525	C₂²	1	1	yes	characteristic
35	C₂×C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#520	—	2	1	no	—
37	C₃×#520	—	2	1	no	—
38	C₃×#520	—	2	2	no	—
39	C₃×#520	C₂²	1	2	yes	—
40	C₃×#520	C₂²	1	2	yes	—
41	C₃×#520	C₂²	1	4	yes	complemented
42	C₃×#520	C₂²	1	1	yes	characteristic, complemented
43	C₃×#518	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
45	C₂×C₃×C₄×D₄	—	2	2	no	—
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
47	C₂×C₃×#117	—	2	1	no	—
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
50	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×#484	C₂²	1	2	yes	complemented
52	C₃×#483	C₂²	1	2	yes	complemented
53	C₃×#481	C₂²	1	2	yes	complemented
54	C₃×#480	C₂²	1	2	yes	—
55	C₃×#480	C₂²	1	2	yes	—
56	C₃×#480	C₂²	1	4	yes	complemented
57	C₃×#480	C₂²	1	2	yes	complemented
58	C₃×#479	C₂²	1	4	yes	complemented
59	C₃×#478	C₂²	1	4	yes	complemented
60	C₃×#477	C₂²	1	4	yes	complemented
61	C₃×#474	C₂²	1	4	yes	complemented
62	C₃×#464	C₂²	1	4	yes	complemented
63	C₃×#463	C₂²	1	4	yes	complemented
64	C₃×#460	C₂²	1	4	yes	complemented
65	C₃×#459	C₂²	1	4	yes	complemented
66	C₃×#452	C₂²	1	2	yes	complemented
67	C₃×#451	C₂²	1	1	yes	characteristic, complemented
68	C₃×#450	C₂²	1	1	yes	characteristic, complemented
69	C₃×#449	C₂²	1	4	yes	—
70	C₃×#449	C₂²	1	2	yes	complemented
71	C₃×#448	C₂²	1	2	yes	—
72	C₃×#448	C₂²	1	1	yes	characteristic, complemented
73	C₃×#447	C₂²	1	2	yes	—
74	C₃×#447	C₂²	1	1	yes	characteristic, complemented
75	C₃×#442	C₂²	1	4	yes	complemented
76	C₃×#440	C₂²	1	4	yes	complemented
77	C₃×#440	C₂²	1	4	yes	complemented
78	C₃×#440	C₂²	1	4	yes	complemented
79	C₃×C₄×Q₁₆	C₂²	1	4	yes	complemented
80	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
81	C₃×C₄×D₈	C₂²	1	4	yes	complemented
82	C₃×C₄×D₈	C₂²	1	4	yes	complemented
83	C₃×#433	C₂²	1	4	yes	complemented
84	C₃×#432	C₂²	1	2	yes	complemented
85	C₃×#431	C₂²	1	2	yes	complemented
86	C₃×#428	C₂²	1	2	yes	complemented
87	C₂×C₃×#107	C₂²	1	2	yes	complemented
88	C₃×#424	C₂²	1	2	yes	complemented
89	C₃×#417	C₂²	1	2	yes	—
90	C₃×#417	C₂²	1	2	yes	complemented
91	C₃×#416	C₂²	1	2	yes	—
92	C₂×C₃×#102	C₂²	1	2	yes	complemented
93	C₃×#407	C₂²	1	1	yes	characteristic
94	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
95	C₃×#405	C₂²	1	2	yes	complemented
96	#3494	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#520	C₂×C₃	1	1	yes	characteristic, complemented
98	#3124	C₂×C₃	1	4	yes	complemented
99	#3119	C₂×C₃	1	4	yes	complemented
100	#3114	C₂×C₃	1	2	yes	complemented
101	#3112	C₂×C₃	1	2	yes	complemented
102	#3108	C₂×C₃	1	2	yes	complemented
103	#3100	C₂×C₃	1	2	yes	complemented
104	#3092	C₂×C₃	1	1	yes	characteristic, complemented
105	C₂×#480	C₂×C₃	1	1	yes	characteristic, complemented
106	#3083	C₂×C₃	1	2	yes	complemented
107	#3045	C₂×C₃	1	2	yes	complemented
108	#3006	C₂×C₃	1	1	yes	characteristic, complemented
109	#3002	C₂×C₃	1	1	yes	characteristic, complemented
110	#2951	C₂×C₃	1	2	yes	complemented
111	#2946	C₂×C₃	1	2	yes	complemented
112	#2924	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂×C₃×#41	—	2	8	no	—
114	C₂×C₃×#41	—	2	1	no	—
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	—	2	2	no	—
117	C₂×C₃×#41	C₂³	1	1	yes	characteristic
118	C₂×C₃×#41	C₂³	1	2	yes	—
119	C₂×C₃×#41	C₂³	1	2	yes	—
120	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
121	C₂²×C₃×D₄	—	2	1	no	—
122	C₂²×C₃×D₄	—	2	1	no	—
123	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
124	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
125	C₂³×C₃×C₄	—	2	1	no	—
126	C₂³×C₃×C₄	—	2	1	no	—
127	C₂³×C₃×C₄	—	2	2	no	—
128	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
129	C₃×AGL(1,ℤ/8)	—	2	8	no	—
130	C₃×#135	—	2	8	no	—
131	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
132	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
135	C₂×C₃×D₈	C₂³	1	2	yes	—
136	C₂×C₃×D₈	C₂³	1	4	yes	—
137	C₂×C₃×M₁₆	C₂³	1	2	yes	—
138	C₂²×C₃×C₈	C₂³	1	2	yes	—
139	C₃×C₄⋊Q₈	—	2	1	no	—
140	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃×#127	C₂³	1	2	yes	—
142	C₃×#126	—	2	2	no	—
143	C₃×#126	—	2	2	no	—
144	C₃×#125	—	2	1	no	—
145	C₃×#125	C₂³	1	2	yes	—
146	C₃×#124	—	2	2	no	—
147	C₃×#124	—	2	2	no	—
148	C₃×#124	C₂³	1	2	yes	—
149	C₃×#123	—	2	1	no	—
150	C₃×#123	—	2	2	no	—
151	C₃×#123	—	2	2	no	—
152	C₃×#123	—	2	2	no	—
153	C₃×#123	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	2	no	—
155	C₃×C₂²⋊Q₈	—	2	2	no	—
156	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃×#121	—	2	1	no	—
159	C₃×#121	—	2	1	no	—
160	C₃×#121	—	2	2	no	—
161	C₃×#121	—	2	1	no	—
162	C₃×#121	—	2	1	no	—
163	C₃×#121	—	2	2	no	—
164	C₃×#121	—	2	2	no	—
165	C₃×#121	C₂³	1	2	yes	—
166	C₃×#121	C₂³	1	1	yes	characteristic
167	C₃×#121	C₂³	1	2	yes	—
168	C₃×#121	C₂³	1	1	yes	characteristic
169	C₃×#120	—	2	1	no	—
170	C₃×#120	—	2	2	no	—
171	C₃×C₄×Q₈	—	2	2	no	—
172	C₃×C₄×Q₈	—	2	2	no	—
173	C₃×C₄×Q₈	C₂³	1	4	yes	—
174	C₃×C₄×Q₈	C₂³	1	2	yes	—
175	C₃×C₄×Q₈	C₂³	1	4	yes	—
176	C₃×C₄×D₄	—	2	1	no	—
177	C₃×C₄×D₄	—	2	1	no	—
178	C₃×C₄×D₄	—	2	2	no	—
179	C₃×C₄×D₄	—	2	1	no	—
180	C₃×C₄×D₄	—	2	1	no	—
181	C₃×C₄×D₄	—	2	4	no	—
182	C₃×C₄×D₄	—	2	4	no	—
183	C₃×C₄×D₄	—	2	4	no	—
184	C₃×C₄×D₄	—	2	4	no	—
185	C₃×C₄×D₄	—	2	2	no	—
186	C₃×C₄×D₄	—	2	2	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	—	2	2	no	—
189	C₃×C₄×D₄	C₂³	1	2	yes	—
190	C₃×C₄×D₄	C₂³	1	2	yes	—
191	C₃×C₄×D₄	C₂³	1	4	yes	—
192	C₃×C₄×D₄	C₂³	1	2	yes	—
193	C₃×C₄×D₄	C₂³	1	4	yes	—
194	C₃×#117	—	2	2	no	—
195	C₃×#117	—	2	2	no	—
196	C₃×#117	—	2	4	no	—
197	C₃×#117	—	2	1	no	—
198	C₃×#117	—	2	2	no	—
199	C₃×#117	D₄	1	2	yes	—
200	C₃×#117	D₄	1	1	yes	characteristic
201	C₃×#117	D₄	1	1	yes	characteristic
202	C₃×#117	C₂³	1	1	yes	characteristic
203	C₃×#117	C₂³	1	1	yes	characteristic
204	C₃×#117	C₂³	1	1	yes	characteristic
205	C₃×#117	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₃×C₄⋊C₄	—	2	2	no	—
208	C₂×C₃×C₄⋊C₄	—	2	1	no	—
209	C₂×C₃×C₄⋊C₄	—	2	1	no	—
210	C₂×C₃×C₄⋊C₄	—	2	2	no	—
211	C₂×C₃×C₄⋊C₄	—	2	2	no	—
212	C₂×C₃×C₄⋊C₄	—	2	4	no	—
213	C₂×C₃×C₄⋊C₄	—	2	1	no	—
214	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
224	C₂×C₃×C₄²	—	2	2	no	—
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₃×#107	C₂³	1	4	yes	—
227	C₃×#107	C₂³	1	4	yes	—
228	C₃×#107	C₂³	1	4	yes	—
229	C₃×#106	C₂³	1	4	yes	—
230	C₃×C₄⋊C₈	C₂³	1	4	yes	—
231	C₃×C₄⋊C₈	C₂³	1	4	yes	—
232	C₃×#103	C₂³	1	2	yes	—
233	C₃×#103	C₂³	1	2	yes	—
234	C₃×#103	C₂³	1	4	yes	—
235	C₃×#103	C₂³	1	4	yes	—
236	C₃×#102	C₂³	1	4	yes	—
237	C₃×#102	C₂³	1	4	yes	—
238	C₃×#102	C₂³	1	2	yes	—
239	C₃×#102	C₂³	1	2	yes	—
240	C₃×#102	C₂³	1	4	yes	—
241	C₃×#102	C₂³	1	4	yes	—
242	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
243	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
244	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₃×#97	C₂³	1	4	yes	—
248	C₃×C₄×C₈	C₂³	1	4	yes	—
249	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
250	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
251	C₂×#135	C₂²×C₃	1	2	yes	—
252	#555	—	2	1	no	—
253	#553	—	2	1	no	—
254	#553	—	2	1	no	—
255	#551	—	2	2	no	—
256	#547	—	2	1	no	—
257	#546	—	2	2	no	—
258	#544	C₂²×C₃	1	1	yes	characteristic, complemented
259	#542	C₂²×C₃	1	2	yes	complemented
260	#540	C₂²×C₃	1	2	yes	complemented
261	#535	C₂²×C₃	1	1	yes	characteristic, complemented
262	#532	C₂²×C₃	1	2	yes	—
263	#529	C₂²×C₃	1	2	yes	—
264	#525	C₂²×C₃	1	1	yes	characteristic
265	C₂×#121	C₂²×C₃	1	1	yes	characteristic
266	#520	—	2	1	no	—
267	#520	—	2	1	no	—
268	#520	—	2	2	no	—
269	#520	C₂²×C₃	1	2	yes	—
270	#520	C₂²×C₃	1	2	yes	—
271	#520	C₂²×C₃	1	4	yes	complemented
272	#520	C₂²×C₃	1	1	yes	characteristic, complemented
273	#518	C₂²×C₃	1	1	yes	characteristic, complemented
274	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
275	C₂×C₄×D₄	—	2	2	no	—
276	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
277	C₂×#117	—	2	1	no	—
278	C₂×#117	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	—	2	1	no	—
280	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
281	#484	C₂²×C₃	1	2	yes	complemented
282	#483	C₂²×C₃	1	2	yes	complemented
283	#481	C₂²×C₃	1	2	yes	complemented
284	#480	C₂²×C₃	1	2	yes	—
285	#480	C₂²×C₃	1	2	yes	—
286	#480	C₂²×C₃	1	4	yes	complemented
287	#480	C₂²×C₃	1	2	yes	complemented
288	#479	C₂²×C₃	1	4	yes	complemented
289	#478	C₂²×C₃	1	4	yes	complemented
290	#477	C₂²×C₃	1	4	yes	complemented
291	#474	C₂²×C₃	1	4	yes	complemented
292	#464	C₂²×C₃	1	4	yes	complemented
293	#463	C₂²×C₃	1	4	yes	complemented
294	#460	C₂²×C₃	1	4	yes	complemented
295	#459	C₂²×C₃	1	4	yes	complemented
296	#452	C₂²×C₃	1	2	yes	complemented
297	#451	C₂²×C₃	1	1	yes	characteristic, complemented
298	#450	C₂²×C₃	1	1	yes	characteristic, complemented
299	#449	C₂²×C₃	1	4	yes	—
300	#449	C₂²×C₃	1	2	yes	complemented
301	#448	C₂²×C₃	1	2	yes	—
302	#448	C₂²×C₃	1	1	yes	characteristic, complemented
303	#447	C₂²×C₃	1	2	yes	—
304	#447	C₂²×C₃	1	1	yes	characteristic, complemented
305	#442	C₂²×C₃	1	4	yes	complemented
306	#440	C₂²×C₃	1	4	yes	complemented
307	#440	C₂²×C₃	1	4	yes	complemented
308	#440	C₂²×C₃	1	4	yes	complemented
309	C₄×Q₁₆	C₂²×C₃	1	4	yes	complemented
310	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
311	C₄×D₈	C₂²×C₃	1	4	yes	complemented
312	C₄×D₈	C₂²×C₃	1	4	yes	complemented
313	#433	C₂²×C₃	1	4	yes	complemented
314	#432	C₂²×C₃	1	2	yes	complemented
315	#431	C₂²×C₃	1	2	yes	complemented
316	#428	C₂²×C₃	1	2	yes	complemented
317	C₂×#107	C₂²×C₃	1	2	yes	complemented
318	#424	C₂²×C₃	1	2	yes	complemented
319	#417	C₂²×C₃	1	2	yes	—
320	#417	C₂²×C₃	1	2	yes	complemented
321	#416	C₂²×C₃	1	2	yes	—
322	C₂×#102	C₂²×C₃	1	2	yes	complemented
323	#407	C₂²×C₃	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
325	#405	C₂²×C₃	1	2	yes	complemented
326	C₂⁴×C₃	—	2	1	no	—
327	C₂⁴×C₃	—	2	1	no	—
328	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
329	C₃×#41	—	2	8	no	—
330	C₃×#41	—	2	8	no	—
331	C₃×#41	—	2	4	no	—
332	C₃×#41	—	2	4	no	—
333	C₃×#41	—	2	4	no	—
334	C₃×#41	—	2	4	no	—
335	C₃×#41	—	8	4	no	—
336	C₃×#41	#41	1	8	yes	complemented
337	C₂×C₃×Q₈	—	2	4	no	—
338	C₂×C₃×Q₈	—	2	1	no	—
339	C₂×C₃×Q₈	—	2	2	no	—
340	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
341	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
342	C₂×C₃×D₄	—	2	8	no	—
343	C₂×C₃×D₄	—	2	2	no	—
344	C₂×C₃×D₄	—	2	2	no	—
345	C₂×C₃×D₄	—	2	4	no	—
346	C₂×C₃×D₄	—	2	1	no	—
347	C₂×C₃×D₄	—	2	1	no	—
348	C₂×C₃×D₄	—	2	2	no	—
349	C₂×C₃×D₄	—	2	1	no	—
350	C₂×C₃×D₄	—	2	2	no	—
351	C₂×C₃×D₄	—	2	1	no	—
352	C₂×C₃×D₄	—	2	1	no	—
353	C₂×C₃×D₄	—	2	2	no	—
354	C₂×C₃×D₄	—	2	2	no	—
355	C₂×C₃×D₄	—	2	4	no	—
356	C₂×C₃×D₄	—	8	2	no	—
357	C₂×C₃×D₄	C₂⁴	1	2	yes	—
358	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
359	C₂×C₃×D₄	C₂⁴	1	2	yes	—
360	C₂²×C₃×C₄	—	2	8	no	—
361	C₂²×C₃×C₄	—	2	1	no	—
362	C₂²×C₃×C₄	—	2	2	no	—
363	C₂²×C₃×C₄	—	2	2	no	—
364	C₂²×C₃×C₄	—	2	4	no	—
365	C₂²×C₃×C₄	—	2	2	no	—
366	C₂²×C₃×C₄	—	2	1	no	—
367	C₂²×C₃×C₄	—	2	2	no	—
368	C₂²×C₃×C₄	—	2	2	no	—
369	C₂²×C₃×C₄	—	2	1	no	—
370	C₂²×C₃×C₄	—	2	2	no	—
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	4	no	—
373	C₂²×C₃×C₄	—	2	4	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	8	4	no	—
376	C₂²×C₃×C₄	—	8	2	no	—
377	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
378	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₃×Q₁₆	—	2	4	no	—
386	C₃×SD₁₆	—	2	4	no	—
387	C₃×SD₁₆	—	2	8	no	—
388	C₃×SD₁₆	—	2	4	no	—
389	C₃×D₈	—	2	4	no	—
390	C₃×D₈	—	2	8	no	—
391	C₃×M₁₆	—	2	4	no	—
392	C₂×C₃×C₈	—	2	4	no	—
393	C₂×C₃×C₈	C₂⁴	1	2	yes	—
394	C₂×C₃×C₈	C₂⁴	1	4	yes	—
395	C₂×C₃×C₈	C₂⁴	1	2	yes	—
396	C₃×C₄⋊C₄	—	2	2	no	—
397	C₃×C₄⋊C₄	—	2	2	no	—
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	4	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	1	no	—
402	C₃×C₄⋊C₄	—	2	2	no	—
403	C₃×C₄⋊C₄	—	2	1	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	2	no	—
407	C₃×C₄⋊C₄	—	2	1	no	—
408	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
415	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	1	no	—
421	C₃×C₂²⋊C₄	—	2	4	no	—
422	C₃×C₂²⋊C₄	—	2	4	no	—
423	C₃×C₂²⋊C₄	—	2	2	no	—
424	C₃×C₂²⋊C₄	—	2	2	no	—
425	C₃×C₂²⋊C₄	—	2	2	no	—
426	C₃×C₂²⋊C₄	—	2	2	no	—
427	C₃×C₂²⋊C₄	—	2	2	no	—
428	C₃×C₂²⋊C₄	—	2	2	no	—
429	C₃×C₂²⋊C₄	—	2	1	no	—
430	C₃×C₂²⋊C₄	—	2	2	no	—
431	C₃×C₂²⋊C₄	—	2	1	no	—
432	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₃×C₄²	—	2	4	no	—
437	C₃×C₄²	—	2	4	no	—
438	C₃×C₄²	—	2	2	no	—
439	C₃×C₄²	—	2	1	no	—
440	C₃×C₄²	C₂×D₄	1	2	yes	—
441	C₃×C₄²	C₂×D₄	1	2	yes	—
442	C₃×C₄²	C₂⁴	1	2	yes	—
443	C₃×C₄²	C₂⁴	1	2	yes	—
444	C₂×#41	—	2	8	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	C₂³×C₃	1	2	yes	—
449	C₂×#41	C₂³×C₃	1	1	yes	characteristic
450	C₂×#41	C₂³×C₃	1	2	yes	—
451	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
455	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	—	2	2	no	—
459	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
460	AGL(1,ℤ/8)	—	2	8	no	—
461	#135	—	2	8	no	—
462	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
463	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
464	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
465	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
466	C₂×D₈	C₂³×C₃	1	2	yes	—
467	C₂×D₈	C₂³×C₃	1	4	yes	—
468	C₂×M₁₆	C₂³×C₃	1	2	yes	—
469	C₂²×C₈	C₂³×C₃	1	2	yes	—
470	C₄⋊Q₈	—	2	1	no	—
471	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
472	#127	C₂³×C₃	1	2	yes	—
473	#126	—	2	2	no	—
474	#126	—	2	2	no	—
475	#125	—	2	1	no	—
476	#125	C₂³×C₃	1	2	yes	—
477	#124	—	2	2	no	—
478	#124	—	2	2	no	—
479	#124	C₂³×C₃	1	2	yes	—
480	#123	—	2	1	no	—
481	#123	—	2	2	no	—
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
488	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
489	#121	—	2	1	no	—
490	#121	—	2	1	no	—
491	#121	—	2	2	no	—
492	#121	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	C₂³×C₃	1	2	yes	—
497	#121	C₂³×C₃	1	2	yes	—
498	#121	C₂³×C₃	1	1	yes	characteristic
499	#121	C₂³×C₃	1	1	yes	characteristic
500	#120	—	2	1	no	—
501	#120	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	C₂³×C₃	1	4	yes	—
505	C₄×Q₈	C₂³×C₃	1	4	yes	—
506	C₄×Q₈	C₂³×C₃	1	2	yes	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	C₂³×C₃	1	4	yes	—
521	C₄×D₄	C₂³×C₃	1	4	yes	—
522	C₄×D₄	C₂³×C₃	1	2	yes	—
523	C₄×D₄	C₂³×C₃	1	2	yes	—
524	C₄×D₄	C₂³×C₃	1	2	yes	—
525	#117	—	2	2	no	—
526	#117	—	2	2	no	—
527	#117	—	2	4	no	—
528	#117	—	2	1	no	—
529	#117	—	2	2	no	—
530	#117	C₃×D₄	1	2	yes	—
531	#117	C₃×D₄	1	1	yes	characteristic
532	#117	C₃×D₄	1	1	yes	characteristic
533	#117	C₂³×C₃	1	1	yes	characteristic
534	#117	C₂³×C₃	1	1	yes	characteristic
535	#117	C₂³×C₃	1	1	yes	characteristic
536	#117	C₂³×C₃	1	2	yes	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	2	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	4	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	2	no	—
554	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
555	C₂×C₄²	—	2	2	no	—
556	C₂×C₄²	C₂³×C₃	1	2	yes	—
557	#107	C₂³×C₃	1	4	yes	—
558	#107	C₂³×C₃	1	4	yes	—
559	#107	C₂³×C₃	1	4	yes	—
560	#106	C₂³×C₃	1	4	yes	—
561	C₄⋊C₈	C₂³×C₃	1	4	yes	—
562	C₄⋊C₈	C₂³×C₃	1	4	yes	—
563	#103	C₂³×C₃	1	2	yes	—
564	#103	C₂³×C₃	1	2	yes	—
565	#103	C₂³×C₃	1	4	yes	—
566	#103	C₂³×C₃	1	4	yes	—
567	#102	C₂³×C₃	1	4	yes	—
568	#102	C₂³×C₃	1	4	yes	—
569	#102	C₂³×C₃	1	2	yes	—
570	#102	C₂³×C₃	1	2	yes	—
571	#102	C₂³×C₃	1	4	yes	—
572	#102	C₂³×C₃	1	4	yes	—
573	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
574	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
575	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
576	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
578	#97	C₂³×C₃	1	4	yes	—
579	C₄×C₈	C₂³×C₃	1	4	yes	—
580	C₂³×C₃	—	2	4	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	2	no	—
584	C₂³×C₃	—	2	2	no	—
585	C₂³×C₃	—	2	1	no	—
586	C₂³×C₃	—	4	1	no	—
587	C₂³×C₃	—	4	2	no	—
588	C₂³×C₃	—	4	2	no	—
589	C₂³×C₃	—	4	2	no	—
590	C₂³×C₃	—	8	1	no	—
591	C₂³×C₃	—	8	1	no	—
592	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
593	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
594	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
595	C₃×Q₈	—	2	4	no	—
596	C₃×Q₈	—	2	2	no	—
597	C₃×Q₈	—	2	2	no	—
598	C₃×Q₈	—	8	2	no	—
599	C₃×Q₈	C₂×#41	1	4	yes	—
600	C₃×D₄	—	2	8	no	—
601	C₃×D₄	—	2	4	no	—
602	C₃×D₄	—	2	8	no	—
603	C₃×D₄	—	2	2	no	—
604	C₃×D₄	—	2	4	no	—
605	C₃×D₄	—	2	2	no	—
606	C₃×D₄	—	4	2	no	—
607	C₃×D₄	—	4	4	no	—
608	C₃×D₄	—	4	2	no	—
609	C₃×D₄	—	4	2	no	—
610	C₃×D₄	—	8	2	no	—
611	C₃×D₄	—	8	2	no	—
612	C₃×D₄	—	8	1	no	—
613	C₃×D₄	—	8	2	no	—
614	C₃×D₄	C₂×#41	1	4	yes	—
615	C₂×C₃×C₄	—	2	4	no	—
616	C₂×C₃×C₄	—	2	8	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	4	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	8	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	4	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	4	2	no	—
631	C₂×C₃×C₄	—	4	4	no	—
632	C₂×C₃×C₄	—	4	2	no	—
633	C₂×C₃×C₄	—	8	2	no	—
634	C₂×C₃×C₄	—	8	4	no	—
635	C₂×C₃×C₄	—	8	4	no	—
636	C₂×C₃×C₄	—	8	2	no	—
637	C₂×C₃×C₄	—	8	2	no	—
638	C₂×C₃×C₄	—	8	2	no	—
639	C₂×C₃×C₄	—	8	2	no	—
640	C₂×C₃×C₄	—	8	1	no	—
641	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
642	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
643	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
645	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
646	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₃×C₄	C₂×#41	1	4	yes	—
649	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
650	C₃×C₈	—	2	2	no	—
651	C₃×C₈	—	2	2	no	—
652	C₃×C₈	—	2	4	no	—
653	C₂⁴	—	2	1	no	—
654	C₂⁴	—	2	1	no	—
655	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
656	#41	—	2	8	no	—
657	#41	—	2	8	no	—
658	#41	—	2	4	no	—
659	#41	—	2	4	no	—
660	#41	—	2	4	no	—
661	#41	—	2	4	no	—
662	#41	—	8	4	no	—
663	#41	C₃×#41	1	8	yes	complemented
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
669	C₂×D₄	—	2	8	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	8	2	no	—
684	C₂×D₄	C₂⁴×C₃	1	2	yes	—
685	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
686	C₂×D₄	C₂⁴×C₃	1	2	yes	—
687	C₂²×C₄	—	2	8	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	8	4	no	—
703	C₂²×C₄	—	8	2	no	—
704	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
705	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	Q₁₆	—	2	4	no	—
713	SD₁₆	—	2	4	no	—
714	SD₁₆	—	2	8	no	—
715	SD₁₆	—	2	4	no	—
716	D₈	—	2	4	no	—
717	D₈	—	2	8	no	—
718	M₁₆	—	2	4	no	—
719	C₂×C₈	—	2	4	no	—
720	C₂×C₈	C₂⁴×C₃	1	2	yes	—
721	C₂×C₈	C₂⁴×C₃	1	4	yes	—
722	C₂×C₈	C₂⁴×C₃	1	2	yes	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
736	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
737	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
738	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
739	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
740	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
742	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	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	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
760	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
761	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
762	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	1	no	—
767	C₄²	C₂×C₃×D₄	1	2	yes	—
768	C₄²	C₂×C₃×D₄	1	2	yes	—
769	C₄²	C₂⁴×C₃	1	2	yes	—
770	C₄²	C₂⁴×C₃	1	2	yes	—
771	C₂²×C₃	—	2	1	no	—
772	C₂²×C₃	—	2	1	no	—
773	C₂²×C₃	—	2	1	no	—
774	C₂²×C₃	—	2	1	no	—
775	C₂²×C₃	—	2	1	no	—
776	C₂²×C₃	—	2	1	no	—
777	C₂²×C₃	—	2	4	no	—
778	C₂²×C₃	—	2	1	no	—
779	C₂²×C₃	—	4	4	no	—
780	C₂²×C₃	—	4	8	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	2	no	—
783	C₂²×C₃	—	4	2	no	—
784	C₂²×C₃	—	4	1	no	—
785	C₂²×C₃	—	4	1	no	—
786	C₂²×C₃	—	4	2	no	—
787	C₂²×C₃	—	4	1	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	16	2	no	—
790	C₂²×C₃	#525	1	2	yes	—
791	C₂²×C₃	#576	1	2	yes	—
792	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
793	C₃×C₄	—	2	2	no	—
794	C₃×C₄	—	2	2	no	—
795	C₃×C₄	—	2	1	no	—
796	C₃×C₄	—	2	4	no	—
797	C₃×C₄	—	2	1	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	4	1	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	—	4	4	no	—
803	C₃×C₄	—	4	2	no	—
804	C₃×C₄	—	4	1	no	—
805	C₃×C₄	#525	1	2	yes	—
806	C₃×C₄	C₂²×#41	1	2	yes	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	8	1	no	—
818	C₂³	—	8	1	no	—
819	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
820	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
821	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
822	Q₈	—	2	4	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	8	2	no	—
826	Q₈	C₂×C₃×#41	1	4	yes	—
827	D₄	—	2	8	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	8	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	2	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	2	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	—	8	1	no	—
841	D₄	C₂×C₃×#41	1	4	yes	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	8	4	no	—
861	C₂×C₄	—	8	4	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	1	no	—
868	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
869	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
870	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
871	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
872	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
873	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
874	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
875	C₂×C₄	C₂×C₃×#41	1	4	yes	—
876	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	4	no	—
880	C₂×C₃	—	2	2	no	—
881	C₂×C₃	—	2	2	no	—
882	C₂×C₃	—	4	1	no	—
883	C₂×C₃	—	4	4	no	—
884	C₂×C₃	—	8	1	no	—
885	C₂×C₃	—	8	2	no	—
886	C₂×C₃	C₂×#525	1	1	yes	characteristic
887	C₂×C₃	C₂×#576	1	1	yes	characteristic
888	C₂×C₃	#3586	1	1	yes	characteristic
889	C₂²	—	2	1	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	8	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	16	2	no	—
908	C₂²	C₃×#525	1	2	yes	—
909	C₂²	C₃×#576	1	2	yes	—
910	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
911	C₄	—	2	1	no	—
912	C₄	—	2	4	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	4	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	C₃×#525	1	2	yes	—
924	C₄	C₂²×C₃×#41	1	2	yes	—
925	C₃	#60584	1	1	yes	characteristic, direct product factor, Sylow
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	4	no	—
930	C₂	—	8	2	no	—
931	C₂	—	8	1	no	—
932	C₂	C₂×C₃×#525	1	1	yes	characteristic
933	C₂	C₂×C₃×#576	1	1	yes	characteristic
934	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 ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3494	C₂	semidirect
2. C₂×C₃×#520	C₂	semidirect
3. C₃×#3124	C₂	semidirect
4. C₃×#3119	C₂	semidirect
5. C₃×#3114	C₂	semidirect
6. C₃×#3112	C₂	semidirect
7. C₃×#3108	C₂	semidirect
8. C₃×#3100	C₂	semidirect
9. C₃×#3092	C₂	semidirect
10. C₂×C₃×#480	C₂	semidirect
11. C₃×#3083	C₂	semidirect
12. C₃×#3045	C₂	semidirect
13. C₃×#3006	C₂	semidirect
14. C₃×#3002	C₂	semidirect
15. C₃×#2951	C₂	semidirect
16. C₃×#2946	C₂	semidirect
17. C₃×#2924	C₂	semidirect
18. #60584	C₃	direct (N × H)
28. C₃×#544	C₂²	semidirect
29. C₃×#542	C₂²	semidirect
30. C₃×#540	C₂²	semidirect
31. C₃×#535	C₂²	semidirect
41. C₃×#520	C₂²	semidirect
42. C₃×#520	C₂²	semidirect
43. C₃×#518	C₂²	semidirect
44. C₂×C₃×C₄×Q₈	C₂²	semidirect
46. C₂×C₃×C₄×D₄	C₂²	semidirect
51. C₃×#484	C₂²	semidirect
52. C₃×#483	C₂²	semidirect
53. C₃×#481	C₂²	semidirect
56. C₃×#480	C₂²	semidirect
57. C₃×#480	C₂²	semidirect
58. C₃×#479	C₂²	semidirect
59. C₃×#478	C₂²	semidirect
60. C₃×#477	C₂²	semidirect
61. C₃×#474	C₂²	semidirect
62. C₃×#464	C₂²	semidirect
63. C₃×#463	C₂²	semidirect
64. C₃×#460	C₂²	semidirect
65. C₃×#459	C₂²	semidirect
66. C₃×#452	C₂²	semidirect
67. C₃×#451	C₂²	semidirect
68. C₃×#450	C₂²	semidirect
70. C₃×#449	C₂²	semidirect
72. C₃×#448	C₂²	semidirect
74. C₃×#447	C₂²	semidirect
75. C₃×#442	C₂²	semidirect
76. C₃×#440	C₂²	semidirect
77. C₃×#440	C₂²	semidirect
78. C₃×#440	C₂²	semidirect
79. C₃×C₄×Q₁₆	C₂²	semidirect
80. C₃×C₄×SD₁₆	C₂²	semidirect
81. C₃×C₄×D₈	C₂²	semidirect
82. C₃×C₄×D₈	C₂²	semidirect
83. C₃×#433	C₂²	semidirect
84. C₃×#432	C₂²	semidirect
85. C₃×#431	C₂²	semidirect
86. C₃×#428	C₂²	semidirect
87. C₂×C₃×#107	C₂²	semidirect
88. C₃×#424	C₂²	semidirect
90. C₃×#417	C₂²	semidirect
92. C₂×C₃×#102	C₂²	semidirect
95. C₃×#405	C₂²	semidirect
96. #3494	C₂×C₃	semidirect
97. C₂×#520	C₂×C₃	semidirect
98. #3124	C₂×C₃	semidirect
99. #3119	C₂×C₃	semidirect
100. #3114	C₂×C₃	semidirect
101. #3112	C₂×C₃	semidirect
102. #3108	C₂×C₃	semidirect
103. #3100	C₂×C₃	semidirect
104. #3092	C₂×C₃	semidirect
105. C₂×#480	C₂×C₃	semidirect
106. #3083	C₂×C₃	semidirect
107. #3045	C₂×C₃	semidirect
108. #3006	C₂×C₃	semidirect
109. #3002	C₂×C₃	semidirect
110. #2951	C₂×C₃	semidirect
111. #2946	C₂×C₃	semidirect
112. #2924	C₂×C₃	semidirect
258. #544	C₂²×C₃	semidirect
259. #542	C₂²×C₃	semidirect
260. #540	C₂²×C₃	semidirect
261. #535	C₂²×C₃	semidirect
271. #520	C₂²×C₃	semidirect
272. #520	C₂²×C₃	semidirect
273. #518	C₂²×C₃	semidirect
274. C₂×C₄×Q₈	C₂²×C₃	semidirect
276. C₂×C₄×D₄	C₂²×C₃	semidirect
281. #484	C₂²×C₃	semidirect
282. #483	C₂²×C₃	semidirect
283. #481	C₂²×C₃	semidirect
286. #480	C₂²×C₃	semidirect
287. #480	C₂²×C₃	semidirect
288. #479	C₂²×C₃	semidirect
289. #478	C₂²×C₃	semidirect
290. #477	C₂²×C₃	semidirect
291. #474	C₂²×C₃	semidirect
292. #464	C₂²×C₃	semidirect
293. #463	C₂²×C₃	semidirect
294. #460	C₂²×C₃	semidirect
295. #459	C₂²×C₃	semidirect
296. #452	C₂²×C₃	semidirect
297. #451	C₂²×C₃	semidirect
298. #450	C₂²×C₃	semidirect
300. #449	C₂²×C₃	semidirect
302. #448	C₂²×C₃	semidirect
304. #447	C₂²×C₃	semidirect
305. #442	C₂²×C₃	semidirect
306. #440	C₂²×C₃	semidirect
307. #440	C₂²×C₃	semidirect
308. #440	C₂²×C₃	semidirect
309. C₄×Q₁₆	C₂²×C₃	semidirect
310. C₄×SD₁₆	C₂²×C₃	semidirect
311. C₄×D₈	C₂²×C₃	semidirect
312. C₄×D₈	C₂²×C₃	semidirect
313. #433	C₂²×C₃	semidirect
314. #432	C₂²×C₃	semidirect
315. #431	C₂²×C₃	semidirect
316. #428	C₂²×C₃	semidirect
317. C₂×#107	C₂²×C₃	semidirect
318. #424	C₂²×C₃	semidirect
320. #417	C₂²×C₃	semidirect
322. C₂×#102	C₂²×C₃	semidirect
325. #405	C₂²×C₃	semidirect
336. C₃×#41	#41	semidirect
663. #41	C₃×#41	semidirect
925. C₃	#60584	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×#3494	2
C₂×C₃×#520	2
C₃×#3124	2
C₃×#3119	2
C₃×#3114	2
C₃×#3112	2
C₃×#3108	2
C₃×#3100	2
C₃×#3092	2
C₂×C₃×#480	2
C₃×#3083	2
C₃×#3045	2
C₃×#3006	2
C₃×#3002	2
C₃×#2951	2
C₃×#2946	2
C₃×#2924	2
#60584	3

Subgroups — C3×#60584 #10679191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60584 #10679191