Subgroups — C₃×#61645 #10680252

Order 768.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3327	C₂	1	2	yes	maximal, complemented
4	C₃×#3326	C₂	1	2	yes	maximal, complemented
5	C₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₃×#3276	C₂	1	2	yes	maximal, complemented
9	C₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₃×#3269	C₂	1	2	yes	maximal, complemented
11	C₃×#3223	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3221	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3201	C₂	1	2	yes	maximal, complemented
14	C₃×#3197	C₂	1	2	yes	maximal, complemented
15	C₃×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3013	C₂	1	2	yes	maximal, complemented
18	C₃×#3004	C₂	1	2	yes	maximal, complemented
19	C₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	#61645	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
22	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×#137	C₂²	1	2	yes	—
24	C₂×C₃×#137	C₂²	1	2	yes	—
25	C₂×C₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₃×#135	C₂²	1	2	yes	complemented
27	C₃×#560	—	2	2	no	—
28	C₃×#553	—	2	2	no	—
29	C₃×#553	C₂²	1	2	yes	—
30	C₃×#552	C₂²	1	2	yes	—
31	C₃×#550	C₂²	1	2	yes	—
32	C₃×D₄×Q₈	—	2	2	no	—
33	C₃×D₄×Q₈	C₂²	1	2	yes	—
34	C₃×D₄×Q₈	C₂²	1	2	yes	—
35	C₃×#548	—	2	2	no	—
36	C₃×#548	C₂²	1	2	yes	—
37	C₃×#548	C₂²	1	2	yes	—
38	C₃×#547	C₂²	1	2	yes	—
39	C₃×#541	C₂²	1	1	yes	characteristic
40	C₃×#540	—	2	2	no	—
41	C₃×#540	C₂²	1	1	yes	characteristic
42	C₃×#539	—	2	2	no	—
43	C₃×#537	C₂²	1	2	yes	—
44	C₃×#536	—	2	2	no	—
45	C₃×#536	C₂²	1	1	yes	characteristic
46	C₃×#536	C₂²	1	1	yes	characteristic
47	C₃×#525	—	2	2	no	—
48	C₃×#525	C₂²	1	1	yes	characteristic
49	C₃×#525	C₂²	1	2	yes	—
50	C₃×#525	C₂²	1	1	yes	characteristic
51	C₃×#519	C₂²	1	1	yes	characteristic
52	C₃×#497	C₂²	1	1	yes	characteristic, complemented
53	C₃×#496	C₂²	1	1	yes	characteristic, complemented
54	C₃×#494	C₂²	1	1	yes	characteristic, complemented
55	C₃×#492	C₂²	1	1	yes	characteristic, complemented
56	C₃×#491	C₂²	1	1	yes	characteristic, complemented
57	C₃×#491	C₂²	1	1	yes	characteristic, complemented
58	C₃×#488	C₂²	1	1	yes	characteristic, complemented
59	C₃×#488	C₂²	1	1	yes	characteristic, complemented
60	C₃×#485	C₂²	1	2	yes	—
61	C₃×#485	C₂²	1	2	yes	—
62	C₃×#484	C₂²	1	2	yes	complemented
63	C₃×#483	C₂²	1	2	yes	complemented
64	C₃×#482	C₂²	1	2	yes	—
65	C₃×#482	C₂²	1	2	yes	—
66	C₃×#479	C₂²	1	2	yes	complemented
67	C₃×#479	C₂²	1	2	yes	complemented
68	C₃×#470	C₂²	1	2	yes	—
69	C₃×#470	C₂²	1	2	yes	complemented
70	C₃×#469	C₂²	1	2	yes	—
71	C₃×#468	C₂²	1	2	yes	—
72	C₃×#468	C₂²	1	2	yes	—
73	C₃×#468	C₂²	1	2	yes	complemented
74	C₃×#467	C₂²	1	2	yes	complemented
75	C₃×#465	C₂²	1	2	yes	complemented
76	C₃×#464	C₂²	1	2	yes	complemented
77	C₃×#463	C₂²	1	2	yes	complemented
78	C₃×#462	C₂²	1	2	yes	complemented
79	C₃×#462	C₂²	1	2	yes	complemented
80	C₃×#461	C₂²	1	2	yes	complemented
81	C₃×#460	C₂²	1	2	yes	complemented
82	C₃×#452	C₂²	1	2	yes	—
83	C₃×#452	C₂²	1	2	yes	—
84	C₃×#452	C₂²	1	2	yes	complemented
85	C₃×#452	C₂²	1	2	yes	complemented
86	C₃×#452	C₂²	1	2	yes	complemented
87	C₃×#451	C₂²	1	2	yes	—
88	C₃×#451	C₂²	1	2	yes	—
89	C₃×#451	C₂²	1	2	yes	—
90	C₃×#451	C₂²	1	2	yes	—
91	C₃×#451	C₂²	1	2	yes	complemented
92	C₃×#449	C₂²	1	2	yes	—
93	C₃×#449	C₂²	1	2	yes	—
94	C₃×#449	C₂²	1	2	yes	complemented
95	C₃×#448	C₂²	1	2	yes	—
96	C₃×#448	C₂²	1	2	yes	—
97	C₃×#448	C₂²	1	2	yes	—
98	C₃×#448	C₂²	1	2	yes	—
99	C₃×#448	C₂²	1	2	yes	complemented
100	C₃×#441	C₂²	1	2	yes	complemented
101	C₃×#440	C₂²	1	2	yes	complemented
102	C₃×C₄×Q₁₆	C₂²	1	2	yes	complemented
103	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
104	C₃×#436	C₂²	1	2	yes	—
105	C₃×#436	C₂²	1	2	yes	—
106	C₃×#435	C₂²	1	2	yes	—
107	C₃×#435	C₂²	1	2	yes	—
108	C₃×#433	C₂²	1	1	yes	characteristic
109	C₃×#433	C₂²	1	1	yes	characteristic
110	C₃×#419	C₂²	1	2	yes	—
111	C₃×#419	C₂²	1	2	yes	—
112	C₃×#417	C₂²	1	2	yes	complemented
113	C₂×C₃×#103	C₂²	1	2	yes	complemented
114	C₃×#408	C₂²	1	2	yes	—
115	C₃×#407	C₂²	1	2	yes	—
116	#3539	C₂×C₃	1	1	yes	characteristic, complemented
117	#3486	C₂×C₃	1	1	yes	characteristic, complemented
118	#3327	C₂×C₃	1	2	yes	complemented
119	#3326	C₂×C₃	1	2	yes	complemented
120	#3320	C₂×C₃	1	2	yes	complemented
121	#3312	C₂×C₃	1	2	yes	complemented
122	#3278	C₂×C₃	1	2	yes	complemented
123	#3276	C₂×C₃	1	2	yes	complemented
124	#3271	C₂×C₃	1	2	yes	complemented
125	#3269	C₂×C₃	1	2	yes	complemented
126	#3223	C₂×C₃	1	1	yes	characteristic, complemented
127	#3221	C₂×C₃	1	1	yes	characteristic, complemented
128	#3201	C₂×C₃	1	2	yes	complemented
129	#3197	C₂×C₃	1	2	yes	complemented
130	#3127	C₂×C₃	1	1	yes	characteristic, complemented
131	#3126	C₂×C₃	1	1	yes	characteristic, complemented
132	#3013	C₂×C₃	1	2	yes	complemented
133	#3004	C₂×C₃	1	2	yes	complemented
134	#2978	C₂×C₃	1	1	yes	characteristic, complemented
135	C₃×2₋¹⁺⁴	—	4	4	no	—
136	C₂×C₃×#41	—	2	2	no	—
137	C₂×C₃×#41	—	2	1	no	—
138	C₂×C₃×#41	C₂³	1	2	yes	—
139	C₂×C₃×#41	C₂³	1	2	yes	—
140	C₂×C₃×#41	C₂³	1	2	yes	—
141	C₂×C₃×#41	C₂³	1	1	yes	characteristic
142	C₂×C₃×#41	C₂³	1	1	yes	characteristic
143	C₂²×C₃×Q₈	—	2	1	no	—
144	C₂²×C₃×Q₈	—	2	1	no	—
145	C₂²×C₃×Q₈	—	2	2	no	—
146	C₂²×C₃×Q₈	—	4	4	no	—
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	2	yes	—
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×Q₈	C₂³	1	2	yes	—
151	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	—	2	1	no	—
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₃×#137	—	4	4	no	—
155	C₃×#137	—	4	4	no	—
156	C₃×#137	—	4	4	no	—
157	C₃×#135	—	4	4	no	—
158	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
159	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
162	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
163	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₃×D₈	C₂³	1	2	yes	—
170	C₂×C₃×M₁₆	C₂³	1	2	yes	—
171	C₂×C₃×M₁₆	C₂³	1	2	yes	—
172	C₂×C₃×M₁₆	C₂³	1	2	yes	—
173	C₂²×C₃×C₈	C₂³	1	2	yes	—
174	C₃×C₄⋊Q₈	—	2	1	no	—
175	C₃×C₄⋊Q₈	—	2	2	no	—
176	C₃×C₄⋊Q₈	—	2	2	no	—
177	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₃×#127	—	2	2	no	—
181	C₃×#127	C₂³	1	1	yes	characteristic
182	C₃×#126	—	2	2	no	—
183	C₃×#126	—	2	2	no	—
184	C₃×#126	—	2	2	no	—
185	C₃×#125	—	2	2	no	—
186	C₃×#125	—	2	2	no	—
187	C₃×#125	C₂³	1	1	yes	characteristic
188	C₃×#125	C₂³	1	1	yes	characteristic
189	C₃×#124	—	2	1	no	—
190	C₃×#124	—	2	2	no	—
191	C₃×#124	—	2	2	no	—
192	C₃×#124	C₂³	1	1	yes	characteristic
193	C₃×#124	C₂³	1	1	yes	characteristic
194	C₃×#123	—	2	2	no	—
195	C₃×#123	—	2	2	no	—
196	C₃×#123	—	2	1	no	—
197	C₃×#123	—	2	2	no	—
198	C₃×#123	—	2	2	no	—
199	C₃×#123	—	2	2	no	—
200	C₃×#123	—	2	2	no	—
201	C₃×#123	—	2	2	no	—
202	C₃×#123	—	2	2	no	—
203	C₃×#123	D₄	1	2	yes	—
204	C₃×C₂²⋊Q₈	—	2	2	no	—
205	C₃×C₂²⋊Q₈	—	2	2	no	—
206	C₃×C₂²⋊Q₈	—	2	2	no	—
207	C₃×C₂²⋊Q₈	—	2	2	no	—
208	C₃×C₂²⋊Q₈	—	2	2	no	—
209	C₃×C₂²⋊Q₈	—	2	2	no	—
210	C₃×C₂²⋊Q₈	—	2	2	no	—
211	C₃×C₂²⋊Q₈	—	2	2	no	—
212	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
213	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃×#121	—	2	2	no	—
220	C₃×#121	—	2	2	no	—
221	C₃×#121	—	2	2	no	—
222	C₃×#121	—	2	2	no	—
223	C₃×#121	—	2	2	no	—
224	C₃×#121	—	2	2	no	—
225	C₃×#121	—	2	2	no	—
226	C₃×#121	—	2	2	no	—
227	C₃×#121	—	2	2	no	—
228	C₃×#121	—	2	2	no	—
229	C₃×#121	D₄	1	2	yes	—
230	C₃×#121	C₂³	1	2	yes	—
231	C₃×#121	C₂³	1	2	yes	—
232	C₃×#121	C₂³	1	2	yes	—
233	C₃×#121	C₂³	1	2	yes	—
234	C₃×#120	—	2	2	no	—
235	C₃×#120	—	2	1	no	—
236	C₃×#120	D₄	1	2	yes	—
237	C₃×C₄×Q₈	—	2	2	no	—
238	C₃×C₄×Q₈	C₂³	1	2	yes	—
239	C₃×C₄×Q₈	C₂³	1	2	yes	—
240	C₃×C₄×Q₈	C₂³	1	2	yes	—
241	C₃×C₄×D₄	—	2	2	no	—
242	C₃×C₄×D₄	—	2	2	no	—
243	C₃×C₄×D₄	—	2	2	no	—
244	C₃×C₄×D₄	—	2	2	no	—
245	C₃×C₄×D₄	—	2	2	no	—
246	C₃×C₄×D₄	—	2	2	no	—
247	C₃×C₄×D₄	—	2	2	no	—
248	C₃×C₄×D₄	—	2	2	no	—
249	C₃×C₄×D₄	—	2	2	no	—
250	C₃×C₄×D₄	C₂³	1	2	yes	—
251	C₃×C₄×D₄	C₂³	1	2	yes	—
252	C₃×C₄×D₄	C₂³	1	2	yes	—
253	C₃×#117	—	2	2	no	—
254	C₃×#117	—	2	2	no	—
255	C₃×#117	C₂³	1	2	yes	—
256	C₃×#117	C₂³	1	1	yes	characteristic
257	C₃×#117	C₂³	1	1	yes	characteristic
258	C₂×C₃×C₄⋊C₄	—	2	2	no	—
259	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
260	C₃×#107	C₂³	1	2	yes	—
261	C₃×#107	C₂³	1	2	yes	—
262	C₃×#106	C₂³	1	2	yes	—
263	C₃×#106	C₂³	1	2	yes	—
264	C₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₃×#103	C₂³	1	2	yes	—
267	C₃×#103	C₂³	1	2	yes	—
268	C₃×#103	C₂³	1	2	yes	—
269	C₃×#103	C₂³	1	2	yes	—
270	C₃×#103	C₂³	1	2	yes	—
271	C₃×#103	C₂³	1	2	yes	—
272	C₃×#103	C₂³	1	2	yes	—
273	C₃×#103	C₂³	1	2	yes	—
274	C₃×#103	C₂³	1	2	yes	—
275	C₃×#103	C₂³	1	2	yes	—
276	C₃×#103	C₂³	1	2	yes	—
277	C₃×#103	C₂³	1	2	yes	—
278	C₃×#102	C₂³	1	2	yes	—
279	C₃×#102	C₂³	1	2	yes	—
280	C₃×#102	C₂³	1	2	yes	—
281	C₃×#102	C₂³	1	2	yes	—
282	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₃×#97	C₂³	1	1	yes	characteristic
289	C₃×#97	C₂³	1	1	yes	characteristic
290	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
291	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
292	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic
293	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
294	C₂×#137	C₂²×C₃	1	2	yes	—
295	C₂×#137	C₂²×C₃	1	2	yes	—
296	C₂×#137	C₂²×C₃	1	2	yes	complemented
297	C₂×#135	C₂²×C₃	1	2	yes	complemented
298	#560	—	2	2	no	—
299	#553	—	2	2	no	—
300	#553	C₂²×C₃	1	2	yes	—
301	#552	C₂²×C₃	1	2	yes	—
302	#550	C₂²×C₃	1	2	yes	—
303	D₄×Q₈	—	2	2	no	—
304	D₄×Q₈	C₂²×C₃	1	2	yes	—
305	D₄×Q₈	C₂²×C₃	1	2	yes	—
306	#548	—	2	2	no	—
307	#548	C₂²×C₃	1	2	yes	—
308	#548	C₂²×C₃	1	2	yes	—
309	#547	C₂²×C₃	1	2	yes	—
310	#541	C₂²×C₃	1	1	yes	characteristic
311	#540	—	2	2	no	—
312	#540	C₂²×C₃	1	1	yes	characteristic
313	#539	—	2	2	no	—
314	#537	C₂²×C₃	1	2	yes	—
315	#536	—	2	2	no	—
316	#536	C₂²×C₃	1	1	yes	characteristic
317	#536	C₂²×C₃	1	1	yes	characteristic
318	#525	—	2	2	no	—
319	#525	C₂²×C₃	1	1	yes	characteristic
320	#525	C₂²×C₃	1	2	yes	—
321	#525	C₂²×C₃	1	1	yes	characteristic
322	#519	C₂²×C₃	1	1	yes	characteristic
323	#497	C₂²×C₃	1	1	yes	characteristic, complemented
324	#496	C₂²×C₃	1	1	yes	characteristic, complemented
325	#494	C₂²×C₃	1	1	yes	characteristic, complemented
326	#492	C₂²×C₃	1	1	yes	characteristic, complemented
327	#491	C₂²×C₃	1	1	yes	characteristic, complemented
328	#491	C₂²×C₃	1	1	yes	characteristic, complemented
329	#488	C₂²×C₃	1	1	yes	characteristic, complemented
330	#488	C₂²×C₃	1	1	yes	characteristic, complemented
331	#485	C₂²×C₃	1	2	yes	—
332	#485	C₂²×C₃	1	2	yes	—
333	#484	C₂²×C₃	1	2	yes	complemented
334	#483	C₂²×C₃	1	2	yes	complemented
335	#482	C₂²×C₃	1	2	yes	—
336	#482	C₂²×C₃	1	2	yes	—
337	#479	C₂²×C₃	1	2	yes	complemented
338	#479	C₂²×C₃	1	2	yes	complemented
339	#470	C₂²×C₃	1	2	yes	—
340	#470	C₂²×C₃	1	2	yes	complemented
341	#469	C₂²×C₃	1	2	yes	—
342	#468	C₂²×C₃	1	2	yes	—
343	#468	C₂²×C₃	1	2	yes	—
344	#468	C₂²×C₃	1	2	yes	complemented
345	#467	C₂²×C₃	1	2	yes	complemented
346	#465	C₂²×C₃	1	2	yes	complemented
347	#464	C₂²×C₃	1	2	yes	complemented
348	#463	C₂²×C₃	1	2	yes	complemented
349	#462	C₂²×C₃	1	2	yes	complemented
350	#462	C₂²×C₃	1	2	yes	complemented
351	#461	C₂²×C₃	1	2	yes	complemented
352	#460	C₂²×C₃	1	2	yes	complemented
353	#452	C₂²×C₃	1	2	yes	—
354	#452	C₂²×C₃	1	2	yes	—
355	#452	C₂²×C₃	1	2	yes	complemented
356	#452	C₂²×C₃	1	2	yes	complemented
357	#452	C₂²×C₃	1	2	yes	complemented
358	#451	C₂²×C₃	1	2	yes	—
359	#451	C₂²×C₃	1	2	yes	—
360	#451	C₂²×C₃	1	2	yes	—
361	#451	C₂²×C₃	1	2	yes	—
362	#451	C₂²×C₃	1	2	yes	complemented
363	#449	C₂²×C₃	1	2	yes	—
364	#449	C₂²×C₃	1	2	yes	—
365	#449	C₂²×C₃	1	2	yes	complemented
366	#448	C₂²×C₃	1	2	yes	—
367	#448	C₂²×C₃	1	2	yes	—
368	#448	C₂²×C₃	1	2	yes	—
369	#448	C₂²×C₃	1	2	yes	—
370	#448	C₂²×C₃	1	2	yes	complemented
371	#441	C₂²×C₃	1	2	yes	complemented
372	#440	C₂²×C₃	1	2	yes	complemented
373	C₄×Q₁₆	C₂²×C₃	1	2	yes	complemented
374	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
375	#436	C₂²×C₃	1	2	yes	—
376	#436	C₂²×C₃	1	2	yes	—
377	#435	C₂²×C₃	1	2	yes	—
378	#435	C₂²×C₃	1	2	yes	—
379	#433	C₂²×C₃	1	1	yes	characteristic
380	#433	C₂²×C₃	1	1	yes	characteristic
381	#419	C₂²×C₃	1	2	yes	—
382	#419	C₂²×C₃	1	2	yes	—
383	#417	C₂²×C₃	1	2	yes	complemented
384	C₂×#103	C₂²×C₃	1	2	yes	complemented
385	#408	C₂²×C₃	1	2	yes	—
386	#407	C₂²×C₃	1	2	yes	—
387	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
388	C₃×#41	—	2	4	no	—
389	C₃×#41	—	4	2	no	—
390	C₃×#41	—	4	2	no	—
391	C₃×#41	—	4	2	no	—
392	C₃×#41	—	4	8	no	—
393	C₃×#41	—	4	2	no	—
394	C₃×#41	—	4	2	no	—
395	C₃×#41	—	4	2	no	—
396	C₃×#41	—	4	2	no	—
397	C₃×#41	—	4	4	no	—
398	C₂×C₃×Q₈	—	2	4	no	—
399	C₂×C₃×Q₈	—	2	1	no	—
400	C₂×C₃×Q₈	—	2	2	no	—
401	C₂×C₃×Q₈	—	2	2	no	—
402	C₂×C₃×Q₈	—	2	1	no	—
403	C₂×C₃×Q₈	—	2	2	no	—
404	C₂×C₃×Q₈	—	2	4	no	—
405	C₂×C₃×Q₈	—	2	4	no	—
406	C₂×C₃×Q₈	—	2	4	no	—
407	C₂×C₃×Q₈	—	4	2	no	—
408	C₂×C₃×Q₈	—	4	2	no	—
409	C₂×C₃×Q₈	—	4	2	no	—
410	C₂×C₃×Q₈	—	4	2	no	—
411	C₂×C₃×Q₈	—	4	4	no	—
412	C₂×C₃×Q₈	—	4	8	no	—
413	C₂×C₃×Q₈	—	4	4	no	—
414	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
415	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
419	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	2	1	no	—
422	C₂×C₃×D₄	—	2	2	no	—
423	C₂×C₃×D₄	—	2	2	no	—
424	C₂×C₃×D₄	—	2	2	no	—
425	C₂×C₃×D₄	—	2	2	no	—
426	C₂×C₃×D₄	—	2	2	no	—
427	C₂×C₃×D₄	—	2	2	no	—
428	C₂×C₃×D₄	—	2	2	no	—
429	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
430	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
431	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
432	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
433	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
434	C₂×C₃×D₄	C₂⁴	1	2	yes	—
435	C₂²×C₃×C₄	—	2	1	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	1	no	—
440	C₂²×C₃×C₄	—	2	2	no	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	1	no	—
443	C₂²×C₃×C₄	—	2	2	no	—
444	C₂²×C₃×C₄	—	2	2	no	—
445	C₂²×C₃×C₄	—	2	2	no	—
446	C₂²×C₃×C₄	—	4	2	no	—
447	C₂²×C₃×C₄	—	4	4	no	—
448	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
449	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
450	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
452	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
453	C₃×Q₁₆	—	2	4	no	—
454	C₃×Q₁₆	—	2	4	no	—
455	C₃×Q₁₆	—	4	2	no	—
456	C₃×Q₁₆	—	4	2	no	—
457	C₃×Q₁₆	—	4	2	no	—
458	C₃×SD₁₆	—	2	4	no	—
459	C₃×SD₁₆	—	2	4	no	—
460	C₃×SD₁₆	—	4	2	no	—
461	C₃×SD₁₆	—	4	2	no	—
462	C₃×SD₁₆	—	4	2	no	—
463	C₃×SD₁₆	—	4	2	no	—
464	C₃×D₈	—	4	2	no	—
465	C₃×M₁₆	—	4	2	no	—
466	C₃×M₁₆	—	4	2	no	—
467	C₃×M₁₆	—	4	2	no	—
468	C₂×C₃×C₈	—	4	2	no	—
469	C₂×C₃×C₈	C₂⁴	1	2	yes	—
470	C₂×C₃×C₈	C₂⁴	1	2	yes	—
471	C₂×C₃×C₈	C₂⁴	1	2	yes	—
472	C₂×C₃×C₈	C₂⁴	1	2	yes	—
473	C₃×C₄⋊C₄	—	2	2	no	—
474	C₃×C₄⋊C₄	—	2	2	no	—
475	C₃×C₄⋊C₄	—	2	2	no	—
476	C₃×C₄⋊C₄	—	2	2	no	—
477	C₃×C₄⋊C₄	—	2	2	no	—
478	C₃×C₄⋊C₄	—	2	2	no	—
479	C₃×C₄⋊C₄	—	2	2	no	—
480	C₃×C₄⋊C₄	—	2	2	no	—
481	C₃×C₄⋊C₄	—	2	2	no	—
482	C₃×C₄⋊C₄	—	2	2	no	—
483	C₃×C₄⋊C₄	—	2	2	no	—
484	C₃×C₄⋊C₄	—	2	2	no	—
485	C₃×C₄⋊C₄	—	2	2	no	—
486	C₃×C₄⋊C₄	—	2	2	no	—
487	C₃×C₄⋊C₄	—	2	2	no	—
488	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
489	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
490	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
491	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
492	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
493	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
494	C₃×C₂²⋊C₄	—	2	1	no	—
495	C₃×C₂²⋊C₄	—	2	2	no	—
496	C₃×C₂²⋊C₄	—	2	2	no	—
497	C₃×C₂²⋊C₄	—	2	2	no	—
498	C₃×C₂²⋊C₄	—	2	2	no	—
499	C₃×C₂²⋊C₄	—	2	2	no	—
500	C₃×C₂²⋊C₄	—	2	2	no	—
501	C₃×C₂²⋊C₄	—	2	2	no	—
502	C₃×C₂²⋊C₄	—	2	2	no	—
503	C₃×C₂²⋊C₄	—	2	2	no	—
504	C₃×C₂²⋊C₄	—	2	2	no	—
505	C₃×C₂²⋊C₄	—	2	2	no	—
506	C₃×C₂²⋊C₄	—	2	2	no	—
507	C₃×C₂²⋊C₄	—	2	2	no	—
508	C₃×C₂²⋊C₄	—	2	2	no	—
509	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
510	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
511	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
512	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
513	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
514	C₃×C₄²	—	2	2	no	—
515	C₃×C₄²	—	2	2	no	—
516	C₃×C₄²	—	2	2	no	—
517	C₃×C₄²	—	2	2	no	—
518	C₃×C₄²	—	2	1	no	—
519	C₃×C₄²	C₂⁴	1	1	yes	characteristic
520	C₃×C₄²	C₂⁴	1	1	yes	characteristic
521	2₋¹⁺⁴	—	4	4	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	C₂³×C₃	1	2	yes	—
525	C₂×#41	C₂³×C₃	1	1	yes	characteristic
526	C₂×#41	C₂³×C₃	1	2	yes	—
527	C₂×#41	C₂³×C₃	1	2	yes	—
528	C₂×#41	C₂³×C₃	1	1	yes	characteristic
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	—	2	1	no	—
531	C₂²×Q₈	—	2	2	no	—
532	C₂²×Q₈	—	4	4	no	—
533	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₃	1	2	yes	—
535	C₂²×Q₈	C₂³×C₃	1	2	yes	—
536	C₂²×Q₈	C₂³×C₃	1	2	yes	—
537	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
538	C₂³×C₄	—	2	1	no	—
539	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
540	#137	—	4	4	no	—
541	#137	—	4	4	no	—
542	#137	—	4	4	no	—
543	#135	—	4	4	no	—
544	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
545	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
546	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
547	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
548	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
549	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
554	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
555	C₂×D₈	C₂³×C₃	1	2	yes	—
556	C₂×M₁₆	C₂³×C₃	1	2	yes	—
557	C₂×M₁₆	C₂³×C₃	1	2	yes	—
558	C₂×M₁₆	C₂³×C₃	1	2	yes	—
559	C₂²×C₈	C₂³×C₃	1	2	yes	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
566	#127	—	2	2	no	—
567	#127	C₂³×C₃	1	1	yes	characteristic
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#125	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	C₂³×C₃	1	1	yes	characteristic
574	#125	C₂³×C₃	1	1	yes	characteristic
575	#124	—	2	1	no	—
576	#124	—	2	2	no	—
577	#124	—	2	2	no	—
578	#124	C₂³×C₃	1	1	yes	characteristic
579	#124	C₂³×C₃	1	1	yes	characteristic
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	1	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	C₃×D₄	1	2	yes	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	C₃×D₄	1	2	yes	—
616	#121	C₂³×C₃	1	2	yes	—
617	#121	C₂³×C₃	1	2	yes	—
618	#121	C₂³×C₃	1	2	yes	—
619	#121	C₂³×C₃	1	2	yes	—
620	#120	—	2	1	no	—
621	#120	—	2	2	no	—
622	#120	C₃×D₄	1	2	yes	—
623	C₄×Q₈	—	2	2	no	—
624	C₄×Q₈	C₂³×C₃	1	2	yes	—
625	C₄×Q₈	C₂³×C₃	1	2	yes	—
626	C₄×Q₈	C₂³×C₃	1	2	yes	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	C₂³×C₃	1	2	yes	—
637	C₄×D₄	C₂³×C₃	1	2	yes	—
638	C₄×D₄	C₂³×C₃	1	2	yes	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	C₂³×C₃	1	1	yes	characteristic
642	#117	C₂³×C₃	1	2	yes	—
643	#117	C₂³×C₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
646	#107	C₂³×C₃	1	2	yes	—
647	#107	C₂³×C₃	1	2	yes	—
648	#106	C₂³×C₃	1	2	yes	—
649	#106	C₂³×C₃	1	2	yes	—
650	C₄⋊C₈	C₂³×C₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₃	1	2	yes	—
652	#103	C₂³×C₃	1	2	yes	—
653	#103	C₂³×C₃	1	2	yes	—
654	#103	C₂³×C₃	1	2	yes	—
655	#103	C₂³×C₃	1	2	yes	—
656	#103	C₂³×C₃	1	2	yes	—
657	#103	C₂³×C₃	1	2	yes	—
658	#103	C₂³×C₃	1	2	yes	—
659	#103	C₂³×C₃	1	2	yes	—
660	#103	C₂³×C₃	1	2	yes	—
661	#103	C₂³×C₃	1	2	yes	—
662	#103	C₂³×C₃	1	2	yes	—
663	#103	C₂³×C₃	1	2	yes	—
664	#102	C₂³×C₃	1	2	yes	—
665	#102	C₂³×C₃	1	2	yes	—
666	#102	C₂³×C₃	1	2	yes	—
667	#102	C₂³×C₃	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
674	#97	C₂³×C₃	1	1	yes	characteristic
675	#97	C₂³×C₃	1	1	yes	characteristic
676	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
677	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
678	C₂³×C₃	—	2	1	no	—
679	C₂³×C₃	—	2	2	no	—
680	C₂³×C₃	—	4	1	no	—
681	C₂³×C₃	—	4	2	no	—
682	C₂³×C₃	C₂²×D₄	1	2	yes	—
683	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
684	C₂³×C₃	C₂²×D₄	1	2	yes	—
685	C₃×Q₈	—	2	4	no	—
686	C₃×Q₈	—	2	2	no	—
687	C₃×Q₈	—	2	2	no	—
688	C₃×Q₈	—	2	2	no	—
689	C₃×Q₈	—	2	2	no	—
690	C₃×Q₈	—	2	2	no	—
691	C₃×Q₈	—	2	2	no	—
692	C₃×Q₈	—	4	1	no	—
693	C₃×Q₈	—	4	4	no	—
694	C₃×Q₈	—	4	4	no	—
695	C₃×Q₈	—	4	4	no	—
696	C₃×Q₈	—	4	2	no	—
697	C₃×Q₈	H(5,𝔽₂)	1	4	yes	—
698	C₃×D₄	—	2	2	no	—
699	C₃×D₄	—	2	2	no	—
700	C₃×D₄	—	2	2	no	—
701	C₃×D₄	—	4	2	no	—
702	C₃×D₄	—	4	2	no	—
703	C₃×D₄	—	4	1	no	—
704	C₃×D₄	—	4	2	no	—
705	C₃×D₄	—	4	4	no	—
706	C₃×D₄	—	4	4	no	—
707	C₃×D₄	—	4	2	no	—
708	C₃×D₄	—	8	2	no	—
709	C₃×D₄	—	8	2	no	—
710	C₃×D₄	—	8	2	no	—
711	C₃×D₄	—	8	2	no	—
712	C₃×D₄	—	8	2	no	—
713	C₃×D₄	—	8	2	no	—
714	C₂×C₃×C₄	—	2	4	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	2	no	—
718	C₂×C₃×C₄	—	2	2	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	2	no	—
721	C₂×C₃×C₄	—	2	2	no	—
722	C₂×C₃×C₄	—	2	2	no	—
723	C₂×C₃×C₄	—	2	2	no	—
724	C₂×C₃×C₄	—	2	2	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	1	no	—
728	C₂×C₃×C₄	—	4	2	no	—
729	C₂×C₃×C₄	—	4	1	no	—
730	C₂×C₃×C₄	—	4	4	no	—
731	C₂×C₃×C₄	—	4	4	no	—
732	C₂×C₃×C₄	—	4	4	no	—
733	C₂×C₃×C₄	—	4	4	no	—
734	C₂×C₃×C₄	—	4	2	no	—
735	C₂×C₃×C₄	—	4	2	no	—
736	C₂×C₃×C₄	—	8	2	no	—
737	C₂×C₃×C₄	—	8	2	no	—
738	C₂×C₃×C₄	—	8	2	no	—
739	C₂×C₃×C₄	—	8	2	no	—
740	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
741	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
742	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
743	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
745	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
746	C₃×C₈	—	2	2	no	—
747	C₃×C₈	—	2	2	no	—
748	C₃×C₈	—	2	2	no	—
749	C₃×C₈	—	2	2	no	—
750	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
751	#41	—	2	4	no	—
752	#41	—	4	2	no	—
753	#41	—	4	2	no	—
754	#41	—	4	2	no	—
755	#41	—	4	8	no	—
756	#41	—	4	2	no	—
757	#41	—	4	2	no	—
758	#41	—	4	2	no	—
759	#41	—	4	2	no	—
760	#41	—	4	4	no	—
761	C₂×Q₈	—	2	4	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	4	no	—
768	C₂×Q₈	—	2	4	no	—
769	C₂×Q₈	—	2	4	no	—
770	C₂×Q₈	—	4	2	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	—	4	2	no	—
773	C₂×Q₈	—	4	2	no	—
774	C₂×Q₈	—	4	4	no	—
775	C₂×Q₈	—	4	8	no	—
776	C₂×Q₈	—	4	4	no	—
777	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
778	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
780	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
781	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
782	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
793	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
794	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
795	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
796	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
797	C₂×D₄	C₂⁴×C₃	1	2	yes	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	4	no	—
811	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
812	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
816	Q₁₆	—	2	4	no	—
817	Q₁₆	—	2	4	no	—
818	Q₁₆	—	4	2	no	—
819	Q₁₆	—	4	2	no	—
820	Q₁₆	—	4	2	no	—
821	SD₁₆	—	2	4	no	—
822	SD₁₆	—	2	4	no	—
823	SD₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	D₈	—	4	2	no	—
828	M₁₆	—	4	2	no	—
829	M₁₆	—	4	2	no	—
830	M₁₆	—	4	2	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	C₂⁴×C₃	1	2	yes	—
833	C₂×C₈	C₂⁴×C₃	1	2	yes	—
834	C₂×C₈	C₂⁴×C₃	1	2	yes	—
835	C₂×C₈	C₂⁴×C₃	1	2	yes	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
852	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
853	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
856	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
873	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
874	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
875	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
876	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	1	no	—
882	C₄²	C₂⁴×C₃	1	1	yes	characteristic
883	C₄²	C₂⁴×C₃	1	1	yes	characteristic
884	C₂²×C₃	—	2	2	no	—
885	C₂²×C₃	—	2	2	no	—
886	C₂²×C₃	—	2	2	no	—
887	C₂²×C₃	—	2	2	no	—
888	C₂²×C₃	—	2	2	no	—
889	C₂²×C₃	—	2	1	no	—
890	C₂²×C₃	—	2	2	no	—
891	C₂²×C₃	—	2	2	no	—
892	C₂²×C₃	—	4	4	no	—
893	C₂²×C₃	—	4	2	no	—
894	C₂²×C₃	—	4	2	no	—
895	C₂²×C₃	—	4	2	no	—
896	C₂²×C₃	—	4	1	no	—
897	C₂²×C₃	—	4	2	no	—
898	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
899	C₃×C₄	—	2	2	no	—
900	C₃×C₄	—	2	2	no	—
901	C₃×C₄	—	2	4	no	—
902	C₃×C₄	—	2	1	no	—
903	C₃×C₄	—	2	2	no	—
904	C₃×C₄	—	2	2	no	—
905	C₃×C₄	—	4	2	no	—
906	C₃×C₄	—	4	2	no	—
907	C₃×C₄	—	4	2	no	—
908	C₃×C₄	—	4	1	no	—
909	C₃×C₄	—	4	1	no	—
910	C₃×C₄	—	4	1	no	—
911	C₃×C₄	—	4	2	no	—
912	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	4	1	no	—
916	C₂³	—	4	2	no	—
917	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
918	C₂³	C₂²×C₃×D₄	1	2	yes	—
919	C₂³	C₂²×C₃×D₄	1	2	yes	—
920	Q₈	—	2	4	no	—
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	4	1	no	—
928	Q₈	—	4	4	no	—
929	Q₈	—	4	4	no	—
930	Q₈	—	4	4	no	—
931	Q₈	—	4	2	no	—
932	Q₈	C₃×H(5,𝔽₂)	1	4	yes	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	4	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	C₂×C₄	—	2	4	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	2	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
976	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
977	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
978	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
979	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
980	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
981	C₈	—	2	2	no	—
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₈	—	2	2	no	—
985	C₂×C₃	—	4	2	no	—
986	C₂×C₃	—	4	2	no	—
987	C₂×C₃	—	4	1	no	—
988	C₂×C₃	—	8	2	no	—
989	C₂×C₃	—	8	1	no	—
990	C₂×C₃	#3484	1	1	yes	characteristic
991	C₂×C₃	#3586	1	2	yes	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	4	4	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1007	C₄	—	2	4	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1021	C₃	#61645	1	1	yes	characteristic, direct product factor, Sylow
1022	C₂	—	4	1	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	1	no	—
1026	C₂	—	8	2	no	—
1027	C₂	C₃×#3484	1	1	yes	characteristic
1028	C₂	C₃×#3586	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3539	C₂	semidirect
2. C₃×#3486	C₂	semidirect
3. C₃×#3327	C₂	semidirect
4. C₃×#3326	C₂	semidirect
5. C₃×#3320	C₂	semidirect
6. C₃×#3312	C₂	semidirect
7. C₃×#3278	C₂	semidirect
8. C₃×#3276	C₂	semidirect
9. C₃×#3271	C₂	semidirect
10. C₃×#3269	C₂	semidirect
11. C₃×#3223	C₂	semidirect
12. C₃×#3221	C₂	semidirect
13. C₃×#3201	C₂	semidirect
14. C₃×#3197	C₂	semidirect
15. C₃×#3127	C₂	semidirect
16. C₃×#3126	C₂	semidirect
17. C₃×#3013	C₂	semidirect
18. C₃×#3004	C₂	semidirect
19. C₃×#2978	C₂	semidirect
20. #61645	C₃	direct (N × H)
25. C₂×C₃×#137	C₂²	semidirect
26. C₂×C₃×#135	C₂²	semidirect
52. C₃×#497	C₂²	semidirect
53. C₃×#496	C₂²	semidirect
54. C₃×#494	C₂²	semidirect
55. C₃×#492	C₂²	semidirect
56. C₃×#491	C₂²	semidirect
57. C₃×#491	C₂²	semidirect
58. C₃×#488	C₂²	semidirect
59. C₃×#488	C₂²	semidirect
62. C₃×#484	C₂²	semidirect
63. C₃×#483	C₂²	semidirect
66. C₃×#479	C₂²	semidirect
67. C₃×#479	C₂²	semidirect
69. C₃×#470	C₂²	semidirect
73. C₃×#468	C₂²	semidirect
74. C₃×#467	C₂²	semidirect
75. C₃×#465	C₂²	semidirect
76. C₃×#464	C₂²	semidirect
77. C₃×#463	C₂²	semidirect
78. C₃×#462	C₂²	semidirect
79. C₃×#462	C₂²	semidirect
80. C₃×#461	C₂²	semidirect
81. C₃×#460	C₂²	semidirect
84. C₃×#452	C₂²	semidirect
85. C₃×#452	C₂²	semidirect
86. C₃×#452	C₂²	semidirect
91. C₃×#451	C₂²	semidirect
94. C₃×#449	C₂²	semidirect
99. C₃×#448	C₂²	semidirect
100. C₃×#441	C₂²	semidirect
101. C₃×#440	C₂²	semidirect
102. C₃×C₄×Q₁₆	C₂²	semidirect
103. C₃×C₄×SD₁₆	C₂²	semidirect
112. C₃×#417	C₂²	semidirect
113. C₂×C₃×#103	C₂²	semidirect
116. #3539	C₂×C₃	semidirect
117. #3486	C₂×C₃	semidirect
118. #3327	C₂×C₃	semidirect
119. #3326	C₂×C₃	semidirect
120. #3320	C₂×C₃	semidirect
121. #3312	C₂×C₃	semidirect
122. #3278	C₂×C₃	semidirect
123. #3276	C₂×C₃	semidirect
124. #3271	C₂×C₃	semidirect
125. #3269	C₂×C₃	semidirect
126. #3223	C₂×C₃	semidirect
127. #3221	C₂×C₃	semidirect
128. #3201	C₂×C₃	semidirect
129. #3197	C₂×C₃	semidirect
130. #3127	C₂×C₃	semidirect
131. #3126	C₂×C₃	semidirect
132. #3013	C₂×C₃	semidirect
133. #3004	C₂×C₃	semidirect
134. #2978	C₂×C₃	semidirect
296. C₂×#137	C₂²×C₃	semidirect
297. C₂×#135	C₂²×C₃	semidirect
323. #497	C₂²×C₃	semidirect
324. #496	C₂²×C₃	semidirect
325. #494	C₂²×C₃	semidirect
326. #492	C₂²×C₃	semidirect
327. #491	C₂²×C₃	semidirect
328. #491	C₂²×C₃	semidirect
329. #488	C₂²×C₃	semidirect
330. #488	C₂²×C₃	semidirect
333. #484	C₂²×C₃	semidirect
334. #483	C₂²×C₃	semidirect
337. #479	C₂²×C₃	semidirect
338. #479	C₂²×C₃	semidirect
340. #470	C₂²×C₃	semidirect
344. #468	C₂²×C₃	semidirect
345. #467	C₂²×C₃	semidirect
346. #465	C₂²×C₃	semidirect
347. #464	C₂²×C₃	semidirect
348. #463	C₂²×C₃	semidirect
349. #462	C₂²×C₃	semidirect
350. #462	C₂²×C₃	semidirect
351. #461	C₂²×C₃	semidirect
352. #460	C₂²×C₃	semidirect
355. #452	C₂²×C₃	semidirect
356. #452	C₂²×C₃	semidirect
357. #452	C₂²×C₃	semidirect
362. #451	C₂²×C₃	semidirect
365. #449	C₂²×C₃	semidirect
370. #448	C₂²×C₃	semidirect
371. #441	C₂²×C₃	semidirect
372. #440	C₂²×C₃	semidirect
373. C₄×Q₁₆	C₂²×C₃	semidirect
374. C₄×SD₁₆	C₂²×C₃	semidirect
383. #417	C₂²×C₃	semidirect
384. C₂×#103	C₂²×C₃	semidirect
1021. C₃	#61645	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×#3539	2
C₃×#3486	2
C₃×#3327	2
C₃×#3326	2
C₃×#3320	2
C₃×#3312	2
C₃×#3278	2
C₃×#3276	2
C₃×#3271	2
C₃×#3269	2
C₃×#3223	2
C₃×#3221	2
C₃×#3201	2
C₃×#3197	2
C₃×#3127	2
C₃×#3126	2
C₃×#3013	2
C₃×#3004	2
C₃×#2978	2
#61645	3

Subgroups — C3×#61645 #10680252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61645 #10680252