Subgroups — C₃×#61668 #10680275

Order 768.

2200 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₃×#3332	C₂	1	2	yes	maximal, complemented
5	C₃×#3295	C₂	1	2	yes	maximal, complemented
6	C₃×#3294	C₂	1	2	yes	maximal, complemented
7	C₃×#3287	C₂	1	2	yes	maximal, complemented
8	C₃×#3284	C₂	1	2	yes	maximal, complemented
9	C₃×#3274	C₂	1	2	yes	maximal, complemented
10	C₃×#3272	C₂	1	2	yes	maximal, complemented
11	C₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3198	C₂	1	4	yes	maximal, complemented
14	C₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3012	C₂	1	4	yes	maximal, complemented
17	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	#61668	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	—
20	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₃×#135	C₂²	1	4	yes	complemented
22	C₃×#562	—	2	2	no	—
23	C₃×#554	—	2	1	no	—
24	C₃×#554	C₂²	1	2	yes	complemented
25	C₃×#550	—	2	1	no	—
26	C₃×#550	C₂²	1	2	yes	—
27	C₃×#550	C₂²	1	2	yes	—
28	C₃×#550	C₂²	1	2	yes	complemented
29	C₃×#547	C₂²	1	2	yes	complemented
30	C₃×#547	C₂²	1	2	yes	complemented
31	C₃×D₄²	—	2	2	no	—
32	C₃×D₄²	—	2	2	no	—
33	C₃×D₄²	C₂²	1	2	yes	—
34	C₃×D₄²	C₂²	1	2	yes	—
35	C₃×#540	—	2	2	no	—
36	C₃×#537	—	2	2	no	—
37	C₃×#537	C₂²	1	4	yes	complemented
38	C₃×#535	—	2	2	no	—
39	C₃×#535	C₂²	1	2	yes	—
40	C₃×#533	C₂²	1	1	yes	characteristic, complemented
41	C₃×#532	—	2	1	no	—
42	C₃×#532	C₂²	1	1	yes	characteristic
43	C₃×#532	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#127	—	2	1	no	—
45	C₂×C₃×#127	C₂²	1	1	yes	characteristic
46	C₃×C₄×#41	C₂²	1	1	yes	characteristic
47	C₃×#493	C₂²	1	2	yes	complemented
48	C₃×#492	C₂²	1	2	yes	complemented
49	C₃×#486	C₂²	1	2	yes	complemented
50	C₃×#486	C₂²	1	2	yes	complemented
51	C₃×#485	C₂²	1	2	yes	complemented
52	C₃×#482	C₂²	1	2	yes	complemented
53	C₃×#481	C₂²	1	4	yes	complemented
54	C₃×#480	C₂²	1	4	yes	complemented
55	C₃×#477	C₂²	1	1	yes	characteristic, complemented
56	C₃×#476	C₂²	1	1	yes	characteristic, complemented
57	C₃×#475	C₂²	1	1	yes	characteristic, complemented
58	C₃×#474	C₂²	1	1	yes	characteristic, complemented
59	C₃×#469	C₂²	1	4	yes	complemented
60	C₃×#468	C₂²	1	4	yes	complemented
61	C₃×#466	C₂²	1	4	yes	complemented
62	C₃×#465	C₂²	1	4	yes	complemented
63	C₃×#462	C₂²	1	1	yes	characteristic, complemented
64	C₃×#461	C₂²	1	1	yes	characteristic, complemented
65	C₃×#460	C₂²	1	2	yes	complemented
66	C₃×#460	C₂²	1	2	yes	complemented
67	C₃×#460	C₂²	1	1	yes	characteristic, complemented
68	C₃×#459	C₂²	1	2	yes	complemented
69	C₃×#459	C₂²	1	2	yes	complemented
70	C₃×#459	C₂²	1	1	yes	characteristic, complemented
71	C₃×#452	C₂²	1	2	yes	—
72	C₃×#452	C₂²	1	4	yes	complemented
73	C₃×#450	C₂²	1	4	yes	complemented
74	C₃×#450	C₂²	1	4	yes	complemented
75	C₃×#449	C₂²	1	2	yes	—
76	C₃×#449	C₂²	1	4	yes	complemented
77	C₃×#449	C₂²	1	4	yes	complemented
78	C₃×#449	C₂²	1	4	yes	complemented
79	C₃×#447	C₂²	1	4	yes	complemented
80	C₃×#447	C₂²	1	4	yes	complemented
81	C₃×C₄×Q₁₆	C₂²	1	2	yes	complemented
82	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
83	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
84	C₃×C₄×D₈	C₂²	1	2	yes	complemented
85	C₃×#436	C₂²	1	2	yes	complemented
86	C₃×#436	C₂²	1	2	yes	complemented
87	C₃×C₈×D₄	C₂²	1	2	yes	complemented
88	C₃×C₈×D₄	C₂²	1	2	yes	complemented
89	C₃×#431	C₂²	1	1	yes	characteristic, complemented
90	C₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃×#417	C₂²	1	4	yes	complemented
92	C₂×C₃×#102	C₂²	1	4	yes	complemented
93	C₃×#408	C₂²	1	4	yes	complemented
94	#3548	C₂×C₃	1	1	yes	characteristic, complemented
95	#3498	C₂×C₃	1	1	yes	characteristic, complemented
96	#3333	C₂×C₃	1	2	yes	complemented
97	#3332	C₂×C₃	1	2	yes	complemented
98	#3295	C₂×C₃	1	2	yes	complemented
99	#3294	C₂×C₃	1	2	yes	complemented
100	#3287	C₂×C₃	1	2	yes	complemented
101	#3284	C₂×C₃	1	2	yes	complemented
102	#3274	C₂×C₃	1	2	yes	complemented
103	#3272	C₂×C₃	1	2	yes	complemented
104	#3208	C₂×C₃	1	1	yes	characteristic, complemented
105	#3205	C₂×C₃	1	1	yes	characteristic, complemented
106	#3198	C₂×C₃	1	4	yes	complemented
107	#3107	C₂×C₃	1	1	yes	characteristic, complemented
108	#3106	C₂×C₃	1	1	yes	characteristic, complemented
109	#3012	C₂×C₃	1	4	yes	complemented
110	#2979	C₂×C₃	1	1	yes	characteristic, complemented
111	C₃×H(5,𝔽₂)	—	4	4	no	—
112	C₃×H(5,𝔽₂)	—	4	4	no	—
113	C₂×C₃×#41	—	2	2	no	—
114	C₂×C₃×#41	—	2	2	no	—
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	C₂³	1	1	yes	characteristic
117	C₂×C₃×#41	C₂³	1	4	yes	—
118	C₂×C₃×#41	C₂³	1	4	yes	—
119	C₂×C₃×#41	C₂³	1	2	yes	—
120	C₂²×C₃×D₄	—	2	2	no	—
121	C₂²×C₃×D₄	—	2	4	no	—
122	C₂²×C₃×D₄	—	2	2	no	—
123	C₂²×C₃×D₄	—	2	2	no	—
124	C₂²×C₃×D₄	—	2	1	no	—
125	C₂²×C₃×D₄	—	2	1	no	—
126	C₂²×C₃×D₄	C₂³	1	4	yes	—
127	C₂²×C₃×D₄	C₂³	1	2	yes	—
128	C₃×AGL(1,ℤ/8)	—	4	8	no	—
129	C₃×#135	—	4	8	no	—
130	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₃×SD₁₆	C₂³	1	4	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×D₈	C₂³	1	4	yes	—
138	C₂×C₃×M₁₆	C₂³	1	4	yes	—
139	C₂²×C₃×C₈	C₂³	1	4	yes	—
140	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
141	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃×#127	—	2	2	no	—
145	C₃×#127	—	2	2	no	—
146	C₃×#127	—	2	2	no	—
147	C₃×#127	—	2	2	no	—
148	C₃×#127	—	2	1	no	—
149	C₃×#127	—	2	1	no	—
150	C₃×#127	D₄	1	1	yes	characteristic
151	C₃×#127	C₂³	1	2	yes	—
152	C₃×#127	C₂³	1	1	yes	characteristic
153	C₃×#127	C₂³	1	2	yes	—
154	C₃×#125	—	2	2	no	—
155	C₃×#125	—	2	1	no	—
156	C₃×#124	—	2	2	no	—
157	C₃×#124	—	2	1	no	—
158	C₃×#124	D₄	1	2	yes	—
159	C₃×#123	—	2	4	no	—
160	C₃×#123	—	2	4	no	—
161	C₃×C₂²⋊Q₈	—	2	4	no	—
162	C₃×C₂²⋊Q₈	—	2	1	no	—
163	C₃×C₂²⋊Q₈	—	2	2	no	—
164	C₃×C₂²⋊Q₈	—	2	4	no	—
165	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
167	C₃×#121	—	2	4	no	—
168	C₃×#121	—	2	4	no	—
169	C₃×#121	—	2	4	no	—
170	C₃×#121	—	2	2	no	—
171	C₃×#121	—	2	1	no	—
172	C₃×#121	—	2	2	no	—
173	C₃×#121	—	2	2	no	—
174	C₃×#121	—	2	4	no	—
175	C₃×#121	—	2	4	no	—
176	C₃×#121	—	2	4	no	—
177	C₃×#121	D₄	1	2	yes	—
178	C₃×#121	D₄	1	2	yes	—
179	C₃×#121	C₂³	1	2	yes	—
180	C₃×#121	C₂³	1	4	yes	—
181	C₃×#121	C₂³	1	4	yes	—
182	C₃×#121	C₂³	1	4	yes	—
183	C₃×#120	—	2	4	no	—
184	C₃×#120	—	2	4	no	—
185	C₃×#120	—	2	4	no	—
186	C₃×C₄×Q₈	—	2	1	no	—
187	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
188	C₃×C₄×Q₈	C₂³	1	2	yes	—
189	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
190	C₃×C₄×D₄	—	2	2	no	—
191	C₃×C₄×D₄	—	2	1	no	—
192	C₃×C₄×D₄	—	2	1	no	—
193	C₃×C₄×D₄	—	2	2	no	—
194	C₃×C₄×D₄	—	2	2	no	—
195	C₃×C₄×D₄	—	2	2	no	—
196	C₃×C₄×D₄	—	2	1	no	—
197	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
198	C₃×C₄×D₄	C₂³	1	2	yes	—
199	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
200	C₃×C₄×D₄	C₂³	1	2	yes	—
201	C₃×C₄×D₄	C₂³	1	2	yes	—
202	C₃×#117	—	2	1	no	—
203	C₃×#117	—	2	1	no	—
204	C₃×#117	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	—	2	2	no	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₃×C₄²	—	2	1	no	—
208	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₃×#107	C₂³	1	2	yes	—
210	C₃×#107	C₂³	1	2	yes	—
211	C₃×#106	C₂³	1	2	yes	—
212	C₃×#106	C₂³	1	2	yes	—
213	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₃×#103	C₂³	1	2	yes	—
218	C₃×#103	C₂³	1	2	yes	—
219	C₃×#103	C₂³	1	2	yes	—
220	C₃×#103	C₂³	1	2	yes	—
221	C₃×#102	C₂³	1	2	yes	—
222	C₃×#102	C₂³	1	2	yes	—
223	C₃×#102	C₂³	1	4	yes	—
224	C₃×#102	C₂³	1	4	yes	—
225	C₃×#102	C₂³	1	4	yes	—
226	C₃×#102	C₂³	1	4	yes	—
227	C₃×#102	C₂³	1	2	yes	—
228	C₃×#102	C₂³	1	2	yes	—
229	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
233	C₃×C₄×C₈	C₂³	1	2	yes	—
234	C₃×C₄×C₈	C₂³	1	2	yes	—
235	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
236	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	complemented
237	C₂×#135	C₂²×C₃	1	4	yes	complemented
238	#562	—	2	2	no	—
239	#554	—	2	1	no	—
240	#554	C₂²×C₃	1	2	yes	complemented
241	#550	—	2	1	no	—
242	#550	C₂²×C₃	1	2	yes	—
243	#550	C₂²×C₃	1	2	yes	—
244	#550	C₂²×C₃	1	2	yes	complemented
245	#547	C₂²×C₃	1	2	yes	complemented
246	#547	C₂²×C₃	1	2	yes	complemented
247	D₄²	—	2	2	no	—
248	D₄²	—	2	2	no	—
249	D₄²	C₂²×C₃	1	2	yes	—
250	D₄²	C₂²×C₃	1	2	yes	—
251	#540	—	2	2	no	—
252	#537	—	2	2	no	—
253	#537	C₂²×C₃	1	4	yes	complemented
254	#535	—	2	2	no	—
255	#535	C₂²×C₃	1	2	yes	—
256	#533	C₂²×C₃	1	1	yes	characteristic, complemented
257	#532	—	2	1	no	—
258	#532	C₂²×C₃	1	1	yes	characteristic
259	#532	C₂²×C₃	1	1	yes	characteristic, complemented
260	C₂×#127	—	2	1	no	—
261	C₂×#127	C₂²×C₃	1	1	yes	characteristic
262	C₄×#41	C₂²×C₃	1	1	yes	characteristic
263	#493	C₂²×C₃	1	2	yes	complemented
264	#492	C₂²×C₃	1	2	yes	complemented
265	#486	C₂²×C₃	1	2	yes	complemented
266	#486	C₂²×C₃	1	2	yes	complemented
267	#485	C₂²×C₃	1	2	yes	complemented
268	#482	C₂²×C₃	1	2	yes	complemented
269	#481	C₂²×C₃	1	4	yes	complemented
270	#480	C₂²×C₃	1	4	yes	complemented
271	#477	C₂²×C₃	1	1	yes	characteristic, complemented
272	#476	C₂²×C₃	1	1	yes	characteristic, complemented
273	#475	C₂²×C₃	1	1	yes	characteristic, complemented
274	#474	C₂²×C₃	1	1	yes	characteristic, complemented
275	#469	C₂²×C₃	1	4	yes	complemented
276	#468	C₂²×C₃	1	4	yes	complemented
277	#466	C₂²×C₃	1	4	yes	complemented
278	#465	C₂²×C₃	1	4	yes	complemented
279	#462	C₂²×C₃	1	1	yes	characteristic, complemented
280	#461	C₂²×C₃	1	1	yes	characteristic, complemented
281	#460	C₂²×C₃	1	2	yes	complemented
282	#460	C₂²×C₃	1	1	yes	characteristic, complemented
283	#460	C₂²×C₃	1	2	yes	complemented
284	#459	C₂²×C₃	1	2	yes	complemented
285	#459	C₂²×C₃	1	1	yes	characteristic, complemented
286	#459	C₂²×C₃	1	2	yes	complemented
287	#452	C₂²×C₃	1	2	yes	—
288	#452	C₂²×C₃	1	4	yes	complemented
289	#450	C₂²×C₃	1	4	yes	complemented
290	#450	C₂²×C₃	1	4	yes	complemented
291	#449	C₂²×C₃	1	2	yes	—
292	#449	C₂²×C₃	1	4	yes	complemented
293	#449	C₂²×C₃	1	4	yes	complemented
294	#449	C₂²×C₃	1	4	yes	complemented
295	#447	C₂²×C₃	1	4	yes	complemented
296	#447	C₂²×C₃	1	4	yes	complemented
297	C₄×Q₁₆	C₂²×C₃	1	2	yes	complemented
298	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
299	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
300	C₄×D₈	C₂²×C₃	1	2	yes	complemented
301	#436	C₂²×C₃	1	2	yes	complemented
302	#436	C₂²×C₃	1	2	yes	complemented
303	C₈×D₄	C₂²×C₃	1	2	yes	complemented
304	C₈×D₄	C₂²×C₃	1	2	yes	complemented
305	#431	C₂²×C₃	1	1	yes	characteristic, complemented
306	#431	C₂²×C₃	1	1	yes	characteristic, complemented
307	#417	C₂²×C₃	1	4	yes	complemented
308	C₂×#102	C₂²×C₃	1	4	yes	complemented
309	#408	C₂²×C₃	1	4	yes	complemented
310	C₂⁴×C₃	—	2	4	no	—
311	C₂⁴×C₃	—	2	2	no	—
312	C₃×#41	—	2	2	no	—
313	C₃×#41	—	2	2	no	—
314	C₃×#41	—	2	8	no	—
315	C₃×#41	—	4	2	no	—
316	C₃×#41	—	4	2	no	—
317	C₃×#41	—	4	4	no	—
318	C₃×#41	—	4	8	no	—
319	C₃×#41	—	4	4	no	—
320	C₃×#41	—	4	4	no	—
321	C₃×#41	—	8	2	no	—
322	C₃×#41	—	8	4	no	—
323	C₂×C₃×Q₈	—	2	1	no	—
324	C₂×C₃×Q₈	—	2	1	no	—
325	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
326	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
327	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×C₃×D₄	—	2	1	no	—
329	C₂×C₃×D₄	—	2	8	no	—
330	C₂×C₃×D₄	—	2	4	no	—
331	C₂×C₃×D₄	—	2	4	no	—
332	C₂×C₃×D₄	—	2	4	no	—
333	C₂×C₃×D₄	—	2	2	no	—
334	C₂×C₃×D₄	—	2	4	no	—
335	C₂×C₃×D₄	—	2	4	no	—
336	C₂×C₃×D₄	—	2	1	no	—
337	C₂×C₃×D₄	—	2	2	no	—
338	C₂×C₃×D₄	—	2	2	no	—
339	C₂×C₃×D₄	—	2	4	no	—
340	C₂×C₃×D₄	—	2	2	no	—
341	C₂×C₃×D₄	—	2	2	no	—
342	C₂×C₃×D₄	—	2	2	no	—
343	C₂×C₃×D₄	—	2	1	no	—
344	C₂×C₃×D₄	—	4	4	no	—
345	C₂×C₃×D₄	—	4	2	no	—
346	C₂×C₃×D₄	—	4	2	no	—
347	C₂×C₃×D₄	—	4	8	no	—
348	C₂×C₃×D₄	—	4	16	no	—
349	C₂×C₃×D₄	—	8	2	no	—
350	C₂×C₃×D₄	—	8	2	no	—
351	C₂×C₃×D₄	—	8	4	no	—
352	C₂×C₃×D₄	—	8	4	no	—
353	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
354	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
355	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
356	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
357	C₂×C₃×D₄	C₂⁴	1	4	yes	—
358	C₂×C₃×D₄	C₂⁴	1	2	yes	—
359	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
360	C₂²×C₃×C₄	—	2	1	no	—
361	C₂²×C₃×C₄	—	2	4	no	—
362	C₂²×C₃×C₄	—	2	1	no	—
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	—	2	2	no	—
365	C₂²×C₃×C₄	—	2	4	no	—
366	C₂²×C₃×C₄	—	2	4	no	—
367	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
371	C₃×Q₁₆	—	2	4	no	—
372	C₃×SD₁₆	—	2	4	no	—
373	C₃×SD₁₆	—	2	4	no	—
374	C₃×SD₁₆	—	4	4	no	—
375	C₃×SD₁₆	—	4	4	no	—
376	C₃×D₈	—	2	4	no	—
377	C₃×D₈	—	4	4	no	—
378	C₃×D₈	—	4	4	no	—
379	C₃×M₁₆	—	4	4	no	—
380	C₂×C₃×C₈	—	4	4	no	—
381	C₂×C₃×C₈	C₂⁴	1	2	yes	—
382	C₂×C₃×C₈	C₂⁴	1	2	yes	—
383	C₂×C₃×C₈	C₂⁴	1	2	yes	—
384	C₂×C₃×C₈	C₂⁴	1	2	yes	—
385	C₃×C₄⋊C₄	—	2	1	no	—
386	C₃×C₄⋊C₄	—	2	4	no	—
387	C₃×C₄⋊C₄	—	2	4	no	—
388	C₃×C₄⋊C₄	—	2	1	no	—
389	C₃×C₄⋊C₄	—	2	1	no	—
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	—	2	1	no	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₃×C₂²⋊C₄	—	2	2	no	—
402	C₃×C₂²⋊C₄	—	2	1	no	—
403	C₃×C₂²⋊C₄	—	2	4	no	—
404	C₃×C₂²⋊C₄	—	2	1	no	—
405	C₃×C₂²⋊C₄	—	2	1	no	—
406	C₃×C₂²⋊C₄	—	2	4	no	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	2	2	no	—
410	C₃×C₂²⋊C₄	—	2	2	no	—
411	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
412	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
413	C₃×C₄²	—	2	1	no	—
414	C₃×C₄²	—	2	1	no	—
415	C₃×C₄²	—	2	1	no	—
416	C₃×C₄²	—	2	2	no	—
417	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
418	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
419	C₃×C₄²	C₂⁴	1	1	yes	characteristic
420	C₃×C₄²	C₂⁴	1	1	yes	characteristic
421	H(5,𝔽₂)	—	4	4	no	—
422	H(5,𝔽₂)	—	4	4	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	1	no	—
426	C₂×#41	C₂³×C₃	1	1	yes	characteristic
427	C₂×#41	C₂³×C₃	1	4	yes	—
428	C₂×#41	C₂³×C₃	1	4	yes	—
429	C₂×#41	C₂³×C₃	1	2	yes	—
430	C₂²×D₄	—	2	2	no	—
431	C₂²×D₄	—	2	4	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	2	2	no	—
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	—	2	1	no	—
436	C₂²×D₄	C₂³×C₃	1	4	yes	—
437	C₂²×D₄	C₂³×C₃	1	2	yes	—
438	AGL(1,ℤ/8)	—	4	8	no	—
439	#135	—	4	8	no	—
440	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
441	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
442	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
443	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
444	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
445	C₂×D₈	C₂³×C₃	1	2	yes	—
446	C₂×D₈	C₂³×C₃	1	4	yes	—
447	C₂×D₈	C₂³×C₃	1	4	yes	—
448	C₂×M₁₆	C₂³×C₃	1	4	yes	—
449	C₂²×C₈	C₂³×C₃	1	4	yes	—
450	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
451	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
452	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
453	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
454	#127	—	2	2	no	—
455	#127	—	2	2	no	—
456	#127	—	2	2	no	—
457	#127	—	2	2	no	—
458	#127	—	2	1	no	—
459	#127	—	2	1	no	—
460	#127	C₃×D₄	1	1	yes	characteristic
461	#127	C₂³×C₃	1	2	yes	—
462	#127	C₂³×C₃	1	2	yes	—
463	#127	C₂³×C₃	1	1	yes	characteristic
464	#125	—	2	2	no	—
465	#125	—	2	1	no	—
466	#124	—	2	2	no	—
467	#124	—	2	1	no	—
468	#124	C₃×D₄	1	2	yes	—
469	#123	—	2	4	no	—
470	#123	—	2	4	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
476	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
477	#121	—	2	4	no	—
478	#121	—	2	4	no	—
479	#121	—	2	2	no	—
480	#121	—	2	4	no	—
481	#121	—	2	1	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	2	4	no	—
485	#121	—	2	4	no	—
486	#121	—	2	4	no	—
487	#121	C₃×D₄	1	2	yes	—
488	#121	C₃×D₄	1	2	yes	—
489	#121	C₂³×C₃	1	2	yes	—
490	#121	C₂³×C₃	1	4	yes	—
491	#121	C₂³×C₃	1	4	yes	—
492	#121	C₂³×C₃	1	4	yes	—
493	#120	—	2	4	no	—
494	#120	—	2	4	no	—
495	#120	—	2	4	no	—
496	C₄×Q₈	—	2	1	no	—
497	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
498	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
499	C₄×Q₈	C₂³×C₃	1	2	yes	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
508	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
509	C₄×D₄	C₂³×C₃	1	2	yes	—
510	C₄×D₄	C₂³×C₃	1	2	yes	—
511	C₄×D₄	C₂³×C₃	1	2	yes	—
512	#117	—	2	1	no	—
513	#117	—	2	1	no	—
514	#117	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
519	#107	C₂³×C₃	1	2	yes	—
520	#107	C₂³×C₃	1	2	yes	—
521	#106	C₂³×C₃	1	2	yes	—
522	#106	C₂³×C₃	1	2	yes	—
523	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
524	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
525	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
526	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
527	#103	C₂³×C₃	1	2	yes	—
528	#103	C₂³×C₃	1	2	yes	—
529	#103	C₂³×C₃	1	2	yes	—
530	#103	C₂³×C₃	1	2	yes	—
531	#102	C₂³×C₃	1	2	yes	—
532	#102	C₂³×C₃	1	2	yes	—
533	#102	C₂³×C₃	1	4	yes	—
534	#102	C₂³×C₃	1	4	yes	—
535	#102	C₂³×C₃	1	4	yes	—
536	#102	C₂³×C₃	1	4	yes	—
537	#102	C₂³×C₃	1	2	yes	—
538	#102	C₂³×C₃	1	2	yes	—
539	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
540	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
541	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
542	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
543	C₄×C₈	C₂³×C₃	1	2	yes	—
544	C₄×C₈	C₂³×C₃	1	2	yes	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	2	4	no	—
548	C₂³×C₃	—	4	8	no	—
549	C₂³×C₃	—	4	4	no	—
550	C₂³×C₃	—	8	2	no	—
551	C₂³×C₃	—	8	4	no	—
552	C₂³×C₃	—	8	2	no	—
553	C₂³×C₃	—	8	4	no	—
554	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
555	C₂³×C₃	C₂²×D₄	1	4	yes	—
556	C₃×Q₈	—	2	1	no	—
557	C₃×Q₈	—	2	2	no	—
558	C₃×Q₈	—	2	2	no	—
559	C₃×Q₈	—	4	2	no	—
560	C₃×Q₈	—	4	2	no	—
561	C₃×Q₈	—	8	1	no	—
562	C₃×Q₈	H(5,𝔽₂)	1	2	yes	—
563	C₃×D₄	—	2	4	no	—
564	C₃×D₄	—	2	4	no	—
565	C₃×D₄	—	2	4	no	—
566	C₃×D₄	—	2	1	no	—
567	C₃×D₄	—	2	2	no	—
568	C₃×D₄	—	2	2	no	—
569	C₃×D₄	—	2	4	no	—
570	C₃×D₄	—	2	4	no	—
571	C₃×D₄	—	4	2	no	—
572	C₃×D₄	—	4	4	no	—
573	C₃×D₄	—	4	8	no	—
574	C₃×D₄	—	4	8	no	—
575	C₃×D₄	—	4	4	no	—
576	C₃×D₄	—	4	4	no	—
577	C₃×D₄	—	4	2	no	—
578	C₃×D₄	—	4	4	no	—
579	C₃×D₄	—	8	2	no	—
580	C₃×D₄	—	8	2	no	—
581	C₃×D₄	—	8	1	no	—
582	C₃×D₄	—	8	4	no	—
583	C₃×D₄	—	8	4	no	—
584	C₃×D₄	—	8	4	no	—
585	C₃×D₄	—	8	2	no	—
586	C₃×D₄	—	8	4	no	—
587	C₃×D₄	H(5,𝔽₂)	1	2	yes	—
588	C₂×C₃×C₄	—	2	4	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	4	no	—
593	C₂×C₃×C₄	—	2	4	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	4	8	no	—
602	C₂×C₃×C₄	—	4	2	no	—
603	C₂×C₃×C₄	—	4	4	no	—
604	C₂×C₃×C₄	—	4	2	no	—
605	C₂×C₃×C₄	—	8	4	no	—
606	C₂×C₃×C₄	—	8	4	no	—
607	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
611	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
614	C₃×C₈	—	2	2	no	—
615	C₃×C₈	—	2	2	no	—
616	C₃×C₈	—	2	2	no	—
617	C₃×C₈	—	2	2	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	2	no	—
620	#41	—	2	2	no	—
621	#41	—	2	2	no	—
622	#41	—	2	8	no	—
623	#41	—	4	2	no	—
624	#41	—	4	2	no	—
625	#41	—	4	4	no	—
626	#41	—	4	8	no	—
627	#41	—	4	4	no	—
628	#41	—	4	4	no	—
629	#41	—	8	2	no	—
630	#41	—	8	4	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
635	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	8	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	8	no	—
656	C₂×D₄	—	4	16	no	—
657	C₂×D₄	—	8	2	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	—	8	4	no	—
660	C₂×D₄	—	8	4	no	—
661	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
662	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
663	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
664	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
665	C₂×D₄	C₂⁴×C₃	1	4	yes	—
666	C₂×D₄	C₂⁴×C₃	1	2	yes	—
667	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
679	Q₁₆	—	2	4	no	—
680	SD₁₆	—	2	4	no	—
681	SD₁₆	—	2	4	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	4	no	—
684	D₈	—	2	4	no	—
685	D₈	—	4	4	no	—
686	D₈	—	4	4	no	—
687	M₁₆	—	4	4	no	—
688	C₂×C₈	—	4	4	no	—
689	C₂×C₈	C₂⁴×C₃	1	2	yes	—
690	C₂×C₈	C₂⁴×C₃	1	2	yes	—
691	C₂×C₈	C₂⁴×C₃	1	2	yes	—
692	C₂×C₈	C₂⁴×C₃	1	2	yes	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
704	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
720	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	2	no	—
725	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
726	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
727	C₄²	C₂⁴×C₃	1	1	yes	characteristic
728	C₄²	C₂⁴×C₃	1	1	yes	characteristic
729	C₂²×C₃	—	2	1	no	—
730	C₂²×C₃	—	2	2	no	—
731	C₂²×C₃	—	2	4	no	—
732	C₂²×C₃	—	2	1	no	—
733	C₂²×C₃	—	2	4	no	—
734	C₂²×C₃	—	2	1	no	—
735	C₂²×C₃	—	2	4	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	1	no	—
738	C₂²×C₃	—	4	4	no	—
739	C₂²×C₃	—	4	2	no	—
740	C₂²×C₃	—	4	2	no	—
741	C₂²×C₃	—	4	4	no	—
742	C₂²×C₃	—	4	4	no	—
743	C₂²×C₃	—	4	2	no	—
744	C₂²×C₃	—	16	8	no	—
745	C₂²×C₃	—	16	4	no	—
746	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
747	C₃×C₄	—	2	1	no	—
748	C₃×C₄	—	2	2	no	—
749	C₃×C₄	—	2	4	no	—
750	C₃×C₄	—	2	1	no	—
751	C₃×C₄	—	2	1	no	—
752	C₃×C₄	—	4	2	no	—
753	C₃×C₄	—	4	2	no	—
754	C₃×C₄	—	4	1	no	—
755	C₃×C₄	—	4	2	no	—
756	C₃×C₄	—	4	1	no	—
757	C₃×C₄	#576	1	2	yes	—
758	C₃×C₄	#577	1	2	yes	—
759	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
760	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂³	—	2	1	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	4	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	8	2	no	—
767	C₂³	—	8	4	no	—
768	C₂³	—	8	2	no	—
769	C₂³	—	8	4	no	—
770	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
771	C₂³	C₂²×C₃×D₄	1	4	yes	—
772	Q₈	—	2	1	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	8	1	no	—
778	Q₈	C₃×H(5,𝔽₂)	1	2	yes	—
779	D₄	—	2	4	no	—
780	D₄	—	2	4	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	1	no	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	4	2	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	8	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	2	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	1	no	—
798	D₄	—	8	4	no	—
799	D₄	—	8	4	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	4	no	—
803	D₄	C₃×H(5,𝔽₂)	1	2	yes	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	4	8	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
825	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
826	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
827	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
828	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₂×C₃	—	4	4	no	—
835	C₂×C₃	—	4	1	no	—
836	C₂×C₃	—	4	2	no	—
837	C₂×C₃	—	8	2	no	—
838	C₂×C₃	—	8	4	no	—
839	C₂×C₃	#3484	1	1	yes	characteristic
840	C₂×C₃	C₂×#576	1	1	yes	characteristic
841	C₂×C₃	C₂×#577	1	1	yes	characteristic
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	4	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	4	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	16	8	no	—
858	C₂²	—	16	4	no	—
859	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	C₃×#576	1	2	yes	—
871	C₄	C₃×#577	1	2	yes	—
872	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
873	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
874	C₃	#61668	1	1	yes	characteristic, direct product factor, Sylow
875	C₂	—	4	1	no	—
876	C₂	—	4	4	no	—
877	C₂	—	4	2	no	—
878	C₂	—	8	4	no	—
879	C₂	—	8	2	no	—
880	C₂	C₃×#3484	1	1	yes	characteristic
881	C₂	C₂×C₃×#576	1	1	yes	characteristic
882	C₂	C₂×C₃×#577	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3548	C₂	semidirect
2. C₃×#3498	C₂	semidirect
3. C₃×#3333	C₂	semidirect
4. C₃×#3332	C₂	semidirect
5. C₃×#3295	C₂	semidirect
6. C₃×#3294	C₂	semidirect
7. C₃×#3287	C₂	semidirect
8. C₃×#3284	C₂	semidirect
9. C₃×#3274	C₂	semidirect
10. C₃×#3272	C₂	semidirect
11. C₃×#3208	C₂	semidirect
12. C₃×#3205	C₂	semidirect
13. C₃×#3198	C₂	semidirect
14. C₃×#3107	C₂	semidirect
15. C₃×#3106	C₂	semidirect
16. C₃×#3012	C₂	semidirect
17. C₃×#2979	C₂	semidirect
18. #61668	C₃	direct (N × H)
20. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₃×#135	C₂²	semidirect
24. C₃×#554	C₂²	semidirect
28. C₃×#550	C₂²	semidirect
29. C₃×#547	C₂²	semidirect
30. C₃×#547	C₂²	semidirect
37. C₃×#537	C₂²	semidirect
40. C₃×#533	C₂²	semidirect
43. C₃×#532	C₂²	semidirect
47. C₃×#493	C₂²	semidirect
48. C₃×#492	C₂²	semidirect
49. C₃×#486	C₂²	semidirect
50. C₃×#486	C₂²	semidirect
51. C₃×#485	C₂²	semidirect
52. C₃×#482	C₂²	semidirect
53. C₃×#481	C₂²	semidirect
54. C₃×#480	C₂²	semidirect
55. C₃×#477	C₂²	semidirect
56. C₃×#476	C₂²	semidirect
57. C₃×#475	C₂²	semidirect
58. C₃×#474	C₂²	semidirect
59. C₃×#469	C₂²	semidirect
60. C₃×#468	C₂²	semidirect
61. C₃×#466	C₂²	semidirect
62. C₃×#465	C₂²	semidirect
63. C₃×#462	C₂²	semidirect
64. C₃×#461	C₂²	semidirect
65. C₃×#460	C₂²	semidirect
66. C₃×#460	C₂²	semidirect
67. C₃×#460	C₂²	semidirect
68. C₃×#459	C₂²	semidirect
69. C₃×#459	C₂²	semidirect
70. C₃×#459	C₂²	semidirect
72. C₃×#452	C₂²	semidirect
73. C₃×#450	C₂²	semidirect
74. C₃×#450	C₂²	semidirect
76. C₃×#449	C₂²	semidirect
77. C₃×#449	C₂²	semidirect
78. C₃×#449	C₂²	semidirect
79. C₃×#447	C₂²	semidirect
80. C₃×#447	C₂²	semidirect
81. C₃×C₄×Q₁₆	C₂²	semidirect
82. C₃×C₄×SD₁₆	C₂²	semidirect
83. C₃×C₄×SD₁₆	C₂²	semidirect
84. C₃×C₄×D₈	C₂²	semidirect
85. C₃×#436	C₂²	semidirect
86. C₃×#436	C₂²	semidirect
87. C₃×C₈×D₄	C₂²	semidirect
88. C₃×C₈×D₄	C₂²	semidirect
89. C₃×#431	C₂²	semidirect
90. C₃×#431	C₂²	semidirect
91. C₃×#417	C₂²	semidirect
92. C₂×C₃×#102	C₂²	semidirect
93. C₃×#408	C₂²	semidirect
94. #3548	C₂×C₃	semidirect
95. #3498	C₂×C₃	semidirect
96. #3333	C₂×C₃	semidirect
97. #3332	C₂×C₃	semidirect
98. #3295	C₂×C₃	semidirect
99. #3294	C₂×C₃	semidirect
100. #3287	C₂×C₃	semidirect
101. #3284	C₂×C₃	semidirect
102. #3274	C₂×C₃	semidirect
103. #3272	C₂×C₃	semidirect
104. #3208	C₂×C₃	semidirect
105. #3205	C₂×C₃	semidirect
106. #3198	C₂×C₃	semidirect
107. #3107	C₂×C₃	semidirect
108. #3106	C₂×C₃	semidirect
109. #3012	C₂×C₃	semidirect
110. #2979	C₂×C₃	semidirect
236. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
237. C₂×#135	C₂²×C₃	semidirect
240. #554	C₂²×C₃	semidirect
244. #550	C₂²×C₃	semidirect
245. #547	C₂²×C₃	semidirect
246. #547	C₂²×C₃	semidirect
253. #537	C₂²×C₃	semidirect
256. #533	C₂²×C₃	semidirect
259. #532	C₂²×C₃	semidirect
263. #493	C₂²×C₃	semidirect
264. #492	C₂²×C₃	semidirect
265. #486	C₂²×C₃	semidirect
266. #486	C₂²×C₃	semidirect
267. #485	C₂²×C₃	semidirect
268. #482	C₂²×C₃	semidirect
269. #481	C₂²×C₃	semidirect
270. #480	C₂²×C₃	semidirect
271. #477	C₂²×C₃	semidirect
272. #476	C₂²×C₃	semidirect
273. #475	C₂²×C₃	semidirect
274. #474	C₂²×C₃	semidirect
275. #469	C₂²×C₃	semidirect
276. #468	C₂²×C₃	semidirect
277. #466	C₂²×C₃	semidirect
278. #465	C₂²×C₃	semidirect
279. #462	C₂²×C₃	semidirect
280. #461	C₂²×C₃	semidirect
281. #460	C₂²×C₃	semidirect
282. #460	C₂²×C₃	semidirect
283. #460	C₂²×C₃	semidirect
284. #459	C₂²×C₃	semidirect
285. #459	C₂²×C₃	semidirect
286. #459	C₂²×C₃	semidirect
288. #452	C₂²×C₃	semidirect
289. #450	C₂²×C₃	semidirect
290. #450	C₂²×C₃	semidirect
292. #449	C₂²×C₃	semidirect
293. #449	C₂²×C₃	semidirect
294. #449	C₂²×C₃	semidirect
295. #447	C₂²×C₃	semidirect
296. #447	C₂²×C₃	semidirect
297. C₄×Q₁₆	C₂²×C₃	semidirect
298. C₄×SD₁₆	C₂²×C₃	semidirect
299. C₄×SD₁₆	C₂²×C₃	semidirect
300. C₄×D₈	C₂²×C₃	semidirect
301. #436	C₂²×C₃	semidirect
302. #436	C₂²×C₃	semidirect
303. C₈×D₄	C₂²×C₃	semidirect
304. C₈×D₄	C₂²×C₃	semidirect
305. #431	C₂²×C₃	semidirect
306. #431	C₂²×C₃	semidirect
307. #417	C₂²×C₃	semidirect
308. C₂×#102	C₂²×C₃	semidirect
309. #408	C₂²×C₃	semidirect
874. C₃	#61668	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×#3548	2
C₃×#3498	2
C₃×#3333	2
C₃×#3332	2
C₃×#3295	2
C₃×#3294	2
C₃×#3287	2
C₃×#3284	2
C₃×#3274	2
C₃×#3272	2
C₃×#3208	2
C₃×#3205	2
C₃×#3198	2
C₃×#3107	2
C₃×#3106	2
C₃×#3012	2
C₃×#2979	2
#61668	3

Subgroups — C3×#61668 #10680275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61668 #10680275