Subgroups — C₃×#42463 #10661070

Order 768.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2825	C₂	1	2	yes	maximal, complemented
2	C₃×#2797	C₂	1	2	yes	maximal, complemented
3	C₃×#2759	C₂	1	2	yes	maximal, complemented
4	C₃×#2751	C₂	1	2	yes	maximal, complemented
5	C₃×#2733	C₂	1	2	yes	maximal, complemented
6	C₃×#2648	C₂	1	2	yes	maximal, complemented
7	C₃×#2631	C₂	1	2	yes	maximal, complemented
8	C₃×#2615	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2459	C₂	1	2	yes	maximal, complemented
16	C₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2388	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
24	#42463	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×#124	C₂²	1	2	yes	—
28	C₂×C₃×#124	C₂²	1	2	yes	—
29	C₂×C₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×#401	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#397	C₂²	1	2	yes	—
44	C₃×#397	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#396	C₂²	1	2	yes	—
51	C₃×#395	C₂²	1	1	yes	characteristic
52	C₃×#394	C₂²	1	1	yes	characteristic
53	C₃×#394	C₂²	1	1	yes	characteristic
54	C₃×#394	C₂²	1	1	yes	characteristic
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#394	C₂²	1	2	yes	—
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#394	C₂²	1	2	yes	—
60	C₃×#393	C₂²	1	2	yes	—
61	C₃×#393	C₂²	1	2	yes	—
62	C₃×#393	C₂²	1	1	yes	characteristic
63	C₃×#393	C₂²	1	2	yes	—
64	C₃×#392	C₂²	1	1	yes	characteristic
65	C₃×#392	C₂²	1	2	yes	—
66	C₃×#392	C₂²	1	2	yes	—
67	C₃×#392	C₂²	1	2	yes	—
68	C₃×#392	C₂²	1	1	yes	characteristic
69	C₃×#392	C₂²	1	1	yes	characteristic
70	C₃×#392	C₂²	1	2	yes	—
71	C₃×#392	C₂²	1	2	yes	—
72	C₃×#392	C₂²	1	2	yes	—
73	C₃×#391	C₂²	1	2	yes	—
74	C₃×#391	C₂²	1	2	yes	—
75	C₃×#391	C₂²	1	2	yes	—
76	C₃×#390	C₂²	1	1	yes	characteristic
77	C₃×#390	C₂²	1	2	yes	—
78	C₃×#390	C₂²	1	1	yes	characteristic
79	C₃×#390	C₂²	1	2	yes	—
80	C₃×#390	C₂²	1	2	yes	—
81	C₃×#389	C₂²	1	1	yes	characteristic
82	C₃×#389	C₂²	1	1	yes	characteristic
83	C₃×#389	C₂²	1	1	yes	characteristic
84	C₃×#389	C₂²	1	1	yes	characteristic
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#388	C₂²	1	2	yes	—
89	C₃×#388	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	2	yes	—
91	C₃×#388	C₂²	1	2	yes	—
92	C₃×#388	C₂²	1	2	yes	—
93	C₃×#387	C₂²	1	2	yes	—
94	C₃×#387	C₂²	1	2	yes	—
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#386	C₂²	1	2	yes	—
98	C₃×#386	C₂²	1	2	yes	—
99	C₃×#386	C₂²	1	2	yes	—
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#386	C₂²	1	2	yes	—
102	C₃×#386	C₂²	1	2	yes	—
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#385	C₂²	1	2	yes	—
105	C₃×#383	C₂²	1	2	yes	—
106	C₃×#382	C₂²	1	1	yes	characteristic
107	C₃×#382	C₂²	1	1	yes	characteristic
108	C₃×#381	C₂²	1	2	yes	—
109	C₃×#380	C₂²	1	1	yes	characteristic
110	C₃×#380	C₂²	1	1	yes	characteristic
111	C₃×#380	C₂²	1	1	yes	characteristic
112	C₃×#380	C₂²	1	1	yes	characteristic
113	C₃×#380	C₂²	1	1	yes	characteristic
114	C₃×#380	C₂²	1	1	yes	characteristic
115	C₃×#380	C₂²	1	1	yes	characteristic
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
124	#2825	C₂×C₃	1	2	yes	complemented
125	#2797	C₂×C₃	1	2	yes	complemented
126	#2759	C₂×C₃	1	2	yes	complemented
127	#2751	C₂×C₃	1	2	yes	complemented
128	#2733	C₂×C₃	1	2	yes	complemented
129	#2648	C₂×C₃	1	2	yes	complemented
130	#2631	C₂×C₃	1	2	yes	complemented
131	#2615	C₂×C₃	1	1	yes	characteristic, complemented
132	#2547	C₂×C₃	1	1	yes	characteristic, complemented
133	#2535	C₂×C₃	1	1	yes	characteristic, complemented
134	#2495	C₂×C₃	1	1	yes	characteristic, complemented
135	#2494	C₂×C₃	1	1	yes	characteristic, complemented
136	#2491	C₂×C₃	1	1	yes	characteristic, complemented
137	#2485	C₂×C₃	1	1	yes	characteristic, complemented
138	#2459	C₂×C₃	1	2	yes	complemented
139	#2439	C₂×C₃	1	1	yes	characteristic, complemented
140	#2420	C₂×C₃	1	1	yes	characteristic, complemented
141	#2414	C₂×C₃	1	1	yes	characteristic, complemented
142	#2414	C₂×C₃	1	1	yes	characteristic, complemented
143	#2388	C₂×C₃	1	1	yes	characteristic, complemented
144	#2361	C₂×C₃	1	1	yes	characteristic, complemented
145	#2352	C₂×C₃	1	1	yes	characteristic, complemented
146	#2311	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×C₃×#41	—	2	4	no	—
148	C₂×C₃×#41	—	4	2	no	—
149	C₂×C₃×#41	—	4	2	no	—
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	2	yes	—
152	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	2	yes	—
158	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
166	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
167	C₂³×C₃×C₄	C₂³	1	2	yes	—
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₃×C₄⋊Q₈	—	4	2	no	—
170	C₃×#124	—	4	4	no	—
171	C₃×#124	—	4	4	no	—
172	C₃×#121	—	2	4	no	—
173	C₃×#121	—	4	2	no	—
174	C₃×#121	—	4	2	no	—
175	C₃×#121	—	4	2	no	—
176	C₃×C₄×D₄	—	2	4	no	—
177	C₃×C₄×D₄	—	4	4	no	—
178	C₃×C₄×D₄	—	4	2	no	—
179	C₃×C₄×D₄	—	4	2	no	—
180	C₃×C₄×D₄	—	4	2	no	—
181	C₃×#117	—	4	2	no	—
182	C₃×#117	—	4	2	no	—
183	C₂×C₃×C₄⋊C₄	—	4	2	no	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₄²	C₂³	1	2	yes	—
236	C₂×C₃×C₄²	C₂³	1	2	yes	—
237	C₂×C₃×C₄²	C₂³	1	2	yes	—
238	C₂×C₃×C₄²	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	2	yes	—
264	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	C₂×#124	C₂²×C₃	1	2	yes	—
267	C₂×#124	C₂²×C₃	1	2	yes	—
268	C₂×#121	C₂²×C₃	1	1	yes	characteristic
269	C₂×#121	C₂²×C₃	1	1	yes	characteristic
270	C₂×#121	C₂²×C₃	1	1	yes	characteristic
271	C₂×#121	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
277	C₂×#117	C₂²×C₃	1	1	yes	characteristic
278	C₂×#117	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
280	#401	C₂²×C₃	1	2	yes	—
281	#400	C₂²×C₃	1	2	yes	—
282	#397	C₂²×C₃	1	2	yes	—
283	#397	C₂²×C₃	1	2	yes	—
284	#397	C₂²×C₃	1	2	yes	—
285	#397	C₂²×C₃	1	2	yes	—
286	#397	C₂²×C₃	1	2	yes	—
287	#397	C₂²×C₃	1	2	yes	—
288	#397	C₂²×C₃	1	2	yes	—
289	#396	C₂²×C₃	1	2	yes	—
290	#395	C₂²×C₃	1	1	yes	characteristic
291	#394	C₂²×C₃	1	2	yes	—
292	#394	C₂²×C₃	1	2	yes	—
293	#394	C₂²×C₃	1	2	yes	—
294	#394	C₂²×C₃	1	1	yes	characteristic
295	#394	C₂²×C₃	1	1	yes	characteristic
296	#394	C₂²×C₃	1	1	yes	characteristic
297	#394	C₂²×C₃	1	2	yes	—
298	#394	C₂²×C₃	1	2	yes	—
299	#393	C₂²×C₃	1	2	yes	—
300	#393	C₂²×C₃	1	2	yes	—
301	#393	C₂²×C₃	1	2	yes	—
302	#393	C₂²×C₃	1	1	yes	characteristic
303	#392	C₂²×C₃	1	1	yes	characteristic
304	#392	C₂²×C₃	1	2	yes	—
305	#392	C₂²×C₃	1	2	yes	—
306	#392	C₂²×C₃	1	2	yes	—
307	#392	C₂²×C₃	1	2	yes	—
308	#392	C₂²×C₃	1	2	yes	—
309	#392	C₂²×C₃	1	1	yes	characteristic
310	#392	C₂²×C₃	1	2	yes	—
311	#392	C₂²×C₃	1	1	yes	characteristic
312	#391	C₂²×C₃	1	2	yes	—
313	#391	C₂²×C₃	1	2	yes	—
314	#391	C₂²×C₃	1	2	yes	—
315	#390	C₂²×C₃	1	2	yes	—
316	#390	C₂²×C₃	1	1	yes	characteristic
317	#390	C₂²×C₃	1	2	yes	—
318	#390	C₂²×C₃	1	1	yes	characteristic
319	#390	C₂²×C₃	1	2	yes	—
320	#389	C₂²×C₃	1	1	yes	characteristic
321	#389	C₂²×C₃	1	1	yes	characteristic
322	#389	C₂²×C₃	1	1	yes	characteristic
323	#389	C₂²×C₃	1	1	yes	characteristic
324	#388	C₂²×C₃	1	2	yes	—
325	#388	C₂²×C₃	1	2	yes	—
326	#388	C₂²×C₃	1	2	yes	—
327	#388	C₂²×C₃	1	2	yes	—
328	#388	C₂²×C₃	1	2	yes	—
329	#388	C₂²×C₃	1	2	yes	—
330	#388	C₂²×C₃	1	2	yes	—
331	#388	C₂²×C₃	1	2	yes	—
332	#387	C₂²×C₃	1	2	yes	—
333	#387	C₂²×C₃	1	2	yes	—
334	#387	C₂²×C₃	1	2	yes	—
335	#387	C₂²×C₃	1	2	yes	—
336	#386	C₂²×C₃	1	2	yes	—
337	#386	C₂²×C₃	1	2	yes	—
338	#386	C₂²×C₃	1	2	yes	—
339	#386	C₂²×C₃	1	2	yes	—
340	#386	C₂²×C₃	1	2	yes	—
341	#386	C₂²×C₃	1	2	yes	—
342	#386	C₂²×C₃	1	2	yes	—
343	#385	C₂²×C₃	1	2	yes	—
344	#383	C₂²×C₃	1	2	yes	—
345	#382	C₂²×C₃	1	1	yes	characteristic
346	#382	C₂²×C₃	1	1	yes	characteristic
347	#381	C₂²×C₃	1	2	yes	—
348	#380	C₂²×C₃	1	1	yes	characteristic
349	#380	C₂²×C₃	1	1	yes	characteristic
350	#380	C₂²×C₃	1	1	yes	characteristic
351	#380	C₂²×C₃	1	1	yes	characteristic
352	#380	C₂²×C₃	1	1	yes	characteristic
353	#380	C₂²×C₃	1	1	yes	characteristic
354	#380	C₂²×C₃	1	1	yes	characteristic
355	#380	C₂²×C₃	1	1	yes	characteristic
356	#380	C₂²×C₃	1	1	yes	characteristic
357	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
361	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
362	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
363	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
364	C₂⁴×C₃	C₂⁴	1	2	yes	—
365	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
367	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
368	C₃×#41	—	4	16	no	—
369	C₂×C₃×Q₈	—	2	2	no	—
370	C₂×C₃×Q₈	—	2	4	no	—
371	C₂×C₃×Q₈	—	4	1	no	—
372	C₂×C₃×Q₈	—	4	1	no	—
373	C₂×C₃×Q₈	—	4	2	no	—
374	C₂×C₃×Q₈	—	4	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	—	2	4	no	—
377	C₂×C₃×D₄	—	2	2	no	—
378	C₂×C₃×D₄	—	2	2	no	—
379	C₂×C₃×D₄	—	2	2	no	—
380	C₂×C₃×D₄	—	2	2	no	—
381	C₂×C₃×D₄	—	2	2	no	—
382	C₂×C₃×D₄	—	2	2	no	—
383	C₂×C₃×D₄	—	2	2	no	—
384	C₂×C₃×D₄	—	4	1	no	—
385	C₂×C₃×D₄	—	4	2	no	—
386	C₂×C₃×D₄	—	4	1	no	—
387	C₂×C₃×D₄	—	4	1	no	—
388	C₂×C₃×D₄	—	4	1	no	—
389	C₂×C₃×D₄	—	4	1	no	—
390	C₂×C₃×D₄	—	4	1	no	—
391	C₂×C₃×D₄	—	4	2	no	—
392	C₂×C₃×D₄	—	4	1	no	—
393	C₂×C₃×D₄	—	4	1	no	—
394	C₂×C₃×D₄	—	4	1	no	—
395	C₂×C₃×D₄	—	4	1	no	—
396	C₂×C₃×D₄	—	4	1	no	—
397	C₂×C₃×D₄	—	4	1	no	—
398	C₂×C₃×D₄	—	4	1	no	—
399	C₂×C₃×D₄	—	4	2	no	—
400	C₂×C₃×D₄	—	4	2	no	—
401	C₂×C₃×D₄	—	4	2	no	—
402	C₂×C₃×D₄	—	4	2	no	—
403	C₂×C₃×D₄	—	4	2	no	—
404	C₂×C₃×D₄	—	4	2	no	—
405	C₂×C₃×D₄	—	4	2	no	—
406	C₂×C₃×D₄	—	4	2	no	—
407	C₂×C₃×D₄	—	4	2	no	—
408	C₂²×C₃×C₄	—	2	2	no	—
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	2	no	—
412	C₂²×C₃×C₄	—	2	2	no	—
413	C₂²×C₃×C₄	—	2	2	no	—
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	2	no	—
416	C₂²×C₃×C₄	—	2	2	no	—
417	C₂²×C₃×C₄	—	2	2	no	—
418	C₂²×C₃×C₄	—	2	2	no	—
419	C₂²×C₃×C₄	—	4	2	no	—
420	C₂²×C₃×C₄	—	4	2	no	—
421	C₂²×C₃×C₄	—	4	2	no	—
422	C₂²×C₃×C₄	—	4	2	no	—
423	C₂²×C₃×C₄	—	4	2	no	—
424	C₂²×C₃×C₄	—	4	2	no	—
425	C₂²×C₃×C₄	#41	1	4	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
430	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
432	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
435	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
436	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
439	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	2	2	no	—
446	C₃×C₄⋊C₄	—	2	2	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	2	no	—
449	C₃×C₄⋊C₄	—	2	2	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	4	2	no	—
453	C₃×C₄⋊C₄	—	4	2	no	—
454	C₃×C₄⋊C₄	—	4	2	no	—
455	C₃×C₄⋊C₄	—	4	2	no	—
456	C₃×C₄⋊C₄	—	4	1	no	—
457	C₃×C₄⋊C₄	—	4	1	no	—
458	C₃×C₄⋊C₄	—	4	2	no	—
459	C₃×C₄⋊C₄	—	4	2	no	—
460	C₃×C₂²⋊C₄	—	2	2	no	—
461	C₃×C₂²⋊C₄	—	2	2	no	—
462	C₃×C₂²⋊C₄	—	2	4	no	—
463	C₃×C₂²⋊C₄	—	2	2	no	—
464	C₃×C₂²⋊C₄	—	2	4	no	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	4	2	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	C₃×C₂²⋊C₄	—	4	2	no	—
469	C₃×C₂²⋊C₄	—	4	1	no	—
470	C₃×C₂²⋊C₄	—	4	1	no	—
471	C₃×C₂²⋊C₄	—	4	2	no	—
472	C₃×C₂²⋊C₄	—	4	1	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₂²⋊C₄	—	4	2	no	—
475	C₃×C₂²⋊C₄	—	4	2	no	—
476	C₃×C₂²⋊C₄	—	4	2	no	—
477	C₃×C₂²⋊C₄	—	4	2	no	—
478	C₃×C₂²⋊C₄	—	4	1	no	—
479	C₃×C₂²⋊C₄	—	4	1	no	—
480	C₃×C₂²⋊C₄	—	4	2	no	—
481	C₃×C₂²⋊C₄	—	4	1	no	—
482	C₃×C₂²⋊C₄	—	4	1	no	—
483	C₃×C₂²⋊C₄	—	4	2	no	—
484	C₃×C₂²⋊C₄	—	4	2	no	—
485	C₃×C₂²⋊C₄	—	4	2	no	—
486	C₃×C₂²⋊C₄	—	4	2	no	—
487	C₃×C₂²⋊C₄	—	4	2	no	—
488	C₃×C₂²⋊C₄	—	4	2	no	—
489	C₃×C₂²⋊C₄	—	4	2	no	—
490	C₃×C₂²⋊C₄	—	4	2	no	—
491	C₃×C₂²⋊C₄	—	4	2	no	—
492	C₃×C₄²	—	2	2	no	—
493	C₃×C₄²	—	2	2	no	—
494	C₃×C₄²	—	2	4	no	—
495	C₃×C₄²	—	2	2	no	—
496	C₃×C₄²	—	4	2	no	—
497	C₃×C₄²	—	4	2	no	—
498	C₃×C₄²	—	4	2	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	4	2	no	—
501	C₂×#41	—	4	2	no	—
502	C₂²×Q₈	C₂³×C₃	1	2	yes	—
503	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₃	1	2	yes	—
506	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
507	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
508	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₃	1	2	yes	—
513	C₂²×D₄	C₂³×C₃	1	2	yes	—
514	C₂²×D₄	C₂³×C₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₃	1	2	yes	—
520	C₂³×C₄	C₂³×C₃	1	2	yes	—
521	C₄⋊Q₈	—	4	2	no	—
522	#124	—	4	4	no	—
523	#124	—	4	4	no	—
524	#121	—	2	4	no	—
525	#121	—	4	2	no	—
526	#121	—	4	2	no	—
527	#121	—	4	2	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	4	4	no	—
530	C₄×D₄	—	4	2	no	—
531	C₄×D₄	—	4	2	no	—
532	C₄×D₄	—	4	2	no	—
533	#117	—	4	2	no	—
534	#117	—	4	2	no	—
535	C₂×C₄⋊C₄	—	4	2	no	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₃	1	2	yes	—
589	C₂×C₄²	C₂³×C₃	1	2	yes	—
590	C₂×C₄²	C₂³×C₃	1	2	yes	—
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	1	yes	characteristic
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	1	yes	characteristic
595	#95	C₂³×C₃	1	1	yes	characteristic
596	#95	C₂³×C₃	1	1	yes	characteristic
597	#95	C₂³×C₃	1	1	yes	characteristic
598	#95	C₂³×C₃	1	1	yes	characteristic
599	#95	C₂³×C₃	1	2	yes	—
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	2	yes	—
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	2	yes	—
606	#95	C₂³×C₃	1	2	yes	—
607	#95	C₂³×C₃	1	2	yes	—
608	#95	C₂³×C₃	1	2	yes	—
609	#95	C₂³×C₃	1	2	yes	—
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	2	yes	—
612	#95	C₂³×C₃	1	2	yes	—
613	#95	C₂³×C₃	1	2	yes	—
614	#95	C₂³×C₃	1	2	yes	—
615	#95	C₂³×C₃	1	2	yes	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	2	1	no	—
621	C₂³×C₃	—	2	1	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	2	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	—	2	1	no	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	2	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	—	2	1	no	—
631	C₂³×C₃	—	2	2	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	2	1	no	—
634	C₂³×C₃	—	2	1	no	—
635	C₂³×C₃	—	2	1	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	2	1	no	—
638	C₂³×C₃	—	2	1	no	—
639	C₂³×C₃	—	2	1	no	—
640	C₂³×C₃	—	2	1	no	—
641	C₂³×C₃	—	2	2	no	—
642	C₂³×C₃	—	2	2	no	—
643	C₂³×C₃	—	2	1	no	—
644	C₂³×C₃	—	2	1	no	—
645	C₂³×C₃	—	2	1	no	—
646	C₂³×C₃	—	2	1	no	—
647	C₂³×C₃	—	2	1	no	—
648	C₂³×C₃	—	2	2	no	—
649	C₂³×C₃	—	2	1	no	—
650	C₂³×C₃	C₂×#41	1	2	yes	—
651	C₂³×C₃	C₂⁵	1	1	yes	characteristic
652	C₃×Q₈	—	4	4	no	—
653	C₃×Q₈	—	8	4	no	—
654	C₃×D₄	—	4	4	no	—
655	C₃×D₄	—	4	4	no	—
656	C₃×D₄	—	4	4	no	—
657	C₃×D₄	—	4	8	no	—
658	C₃×D₄	—	4	4	no	—
659	C₃×D₄	—	4	4	no	—
660	C₃×D₄	—	4	4	no	—
661	C₃×D₄	—	4	4	no	—
662	C₃×D₄	—	8	4	no	—
663	C₃×D₄	—	8	4	no	—
664	C₃×D₄	—	8	4	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	8	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	1	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	2	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	1	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	2	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	2	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	2	no	—
712	C₂×C₃×C₄	—	2	2	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	2	no	—
715	C₂×C₃×C₄	—	4	4	no	—
716	C₂×C₃×C₄	—	4	4	no	—
717	C₂×C₃×C₄	—	4	4	no	—
718	C₂×C₃×C₄	—	8	4	no	—
719	C₂×C₃×C₄	—	8	4	no	—
720	C₂×C₃×C₄	C₂×#41	1	2	yes	—
721	C₂×C₃×C₄	C₂×#41	1	2	yes	—
722	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
723	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
724	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
725	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
726	C₂⁴	C₂⁴×C₃	1	2	yes	—
727	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
728	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
729	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
730	#41	—	4	16	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	4	1	no	—
734	C₂×Q₈	—	4	1	no	—
735	C₂×Q₈	—	4	2	no	—
736	C₂×Q₈	—	4	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	4	1	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	1	no	—
749	C₂×D₄	—	4	1	no	—
750	C₂×D₄	—	4	1	no	—
751	C₂×D₄	—	4	1	no	—
752	C₂×D₄	—	4	1	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	1	no	—
755	C₂×D₄	—	4	1	no	—
756	C₂×D₄	—	4	1	no	—
757	C₂×D₄	—	4	1	no	—
758	C₂×D₄	—	4	1	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	1	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	C₃×#41	1	4	yes	—
788	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	1	no	—
831	C₂²⋊C₄	—	4	1	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	1	no	—
834	C₂²⋊C₄	—	4	1	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	—	4	1	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	1	no	—
848	C₂²⋊C₄	—	4	1	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	1	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	4	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	4	2	no	—
859	C₄²	—	4	2	no	—
860	C₄²	—	4	2	no	—
861	C₂²×C₃	—	2	2	no	—
862	C₂²×C₃	—	2	2	no	—
863	C₂²×C₃	—	2	2	no	—
864	C₂²×C₃	—	4	1	no	—
865	C₂²×C₃	—	4	1	no	—
866	C₂²×C₃	—	4	1	no	—
867	C₂²×C₃	—	4	1	no	—
868	C₂²×C₃	—	4	1	no	—
869	C₂²×C₃	—	4	1	no	—
870	C₂²×C₃	—	4	1	no	—
871	C₂²×C₃	—	4	2	no	—
872	C₂²×C₃	—	4	1	no	—
873	C₂²×C₃	—	4	2	no	—
874	C₂²×C₃	—	4	1	no	—
875	C₂²×C₃	—	4	1	no	—
876	C₂²×C₃	—	4	2	no	—
877	C₂²×C₃	—	4	1	no	—
878	C₂²×C₃	—	4	1	no	—
879	C₂²×C₃	—	4	1	no	—
880	C₂²×C₃	—	4	1	no	—
881	C₂²×C₃	—	4	1	no	—
882	C₂²×C₃	—	4	1	no	—
883	C₂²×C₃	—	4	2	no	—
884	C₂²×C₃	—	4	1	no	—
885	C₂²×C₃	—	4	1	no	—
886	C₂²×C₃	—	4	1	no	—
887	C₂²×C₃	—	4	2	no	—
888	C₂²×C₃	—	4	2	no	—
889	C₂²×C₃	—	4	1	no	—
890	C₂²×C₃	—	4	1	no	—
891	C₂²×C₃	—	4	1	no	—
892	C₂²×C₃	—	4	1	no	—
893	C₂²×C₃	—	4	2	no	—
894	C₂²×C₃	—	4	1	no	—
895	C₂²×C₃	—	4	1	no	—
896	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
897	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
898	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
899	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
900	C₂²×C₃	#585	1	1	yes	characteristic
901	C₂²×C₃	#585	1	1	yes	characteristic
902	C₂²×C₃	#585	1	1	yes	characteristic
903	C₃×C₄	—	2	2	no	—
904	C₃×C₄	—	2	2	no	—
905	C₃×C₄	—	4	1	no	—
906	C₃×C₄	—	4	1	no	—
907	C₃×C₄	—	4	1	no	—
908	C₃×C₄	—	4	1	no	—
909	C₃×C₄	—	4	1	no	—
910	C₃×C₄	—	4	2	no	—
911	C₃×C₄	—	4	1	no	—
912	C₃×C₄	—	4	2	no	—
913	C₃×C₄	—	4	2	no	—
914	C₃×C₄	—	4	2	no	—
915	C₃×C₄	—	4	2	no	—
916	C₃×C₄	—	4	1	no	—
917	C₃×C₄	—	4	2	no	—
918	C₃×C₄	—	4	1	no	—
919	C₃×C₄	—	4	2	no	—
920	C₃×C₄	#538	1	4	yes	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	1	no	—
955	C₂³	C₂×C₃×#41	1	2	yes	—
956	C₂³	C₂⁵×C₃	1	1	yes	characteristic
957	Q₈	—	4	4	no	—
958	Q₈	—	8	4	no	—
959	D₄	—	4	4	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	4	no	—
962	D₄	—	4	4	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	8	no	—
965	D₄	—	4	4	no	—
966	D₄	—	4	4	no	—
967	D₄	—	8	4	no	—
968	D₄	—	8	4	no	—
969	D₄	—	8	4	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	8	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	8	4	no	—
1024	C₂×C₄	—	8	4	no	—
1025	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1026	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1027	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1028	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1029	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1030	C₂×C₃	—	4	2	no	—
1031	C₂×C₃	—	8	1	no	—
1032	C₂×C₃	—	8	1	no	—
1033	C₂×C₃	—	8	1	no	—
1034	C₂×C₃	—	8	2	no	—
1035	C₂×C₃	C₂×#538	1	1	yes	characteristic
1036	C₂×C₃	#3493	1	1	yes	characteristic
1037	C₂×C₃	#3506	1	1	yes	characteristic
1038	C₂×C₃	#3540	1	1	yes	characteristic
1039	C₂×C₃	#3542	1	1	yes	characteristic
1040	C₂×C₃	#3546	1	1	yes	characteristic
1041	C₂×C₃	#3551	1	1	yes	characteristic
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1078	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1079	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1080	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1081	C₂²	C₃×#585	1	1	yes	characteristic
1082	C₂²	C₃×#585	1	1	yes	characteristic
1083	C₂²	C₃×#585	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	C₃×#538	1	4	yes	—
1102	C₃	#42463	1	1	yes	characteristic, direct product factor, Sylow
1103	C₂	—	4	2	no	—
1104	C₂	—	8	1	no	—
1105	C₂	—	8	1	no	—
1106	C₂	—	8	1	no	—
1107	C₂	—	8	2	no	—
1108	C₂	C₂×C₃×#538	1	1	yes	characteristic
1109	C₂	C₃×#3493	1	1	yes	characteristic
1110	C₂	C₃×#3506	1	1	yes	characteristic
1111	C₂	C₃×#3540	1	1	yes	characteristic
1112	C₂	C₃×#3542	1	1	yes	characteristic
1113	C₂	C₃×#3546	1	1	yes	characteristic
1114	C₂	C₃×#3551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2825	C₂	semidirect
2. C₃×#2797	C₂	semidirect
3. C₃×#2759	C₂	semidirect
4. C₃×#2751	C₂	semidirect
5. C₃×#2733	C₂	semidirect
6. C₃×#2648	C₂	semidirect
7. C₃×#2631	C₂	semidirect
8. C₃×#2615	C₂	semidirect
9. C₃×#2547	C₂	semidirect
10. C₃×#2535	C₂	semidirect
11. C₃×#2495	C₂	semidirect
12. C₃×#2494	C₂	semidirect
13. C₃×#2491	C₂	semidirect
14. C₃×#2485	C₂	semidirect
15. C₃×#2459	C₂	semidirect
16. C₃×#2439	C₂	semidirect
17. C₃×#2420	C₂	semidirect
18. C₃×#2414	C₂	semidirect
19. C₃×#2414	C₂	semidirect
20. C₃×#2388	C₂	semidirect
21. C₃×#2361	C₂	semidirect
22. C₃×#2352	C₂	semidirect
23. C₃×#2311	C₂	semidirect
24. #42463	C₃	direct (N × H)
124. #2825	C₂×C₃	semidirect
125. #2797	C₂×C₃	semidirect
126. #2759	C₂×C₃	semidirect
127. #2751	C₂×C₃	semidirect
128. #2733	C₂×C₃	semidirect
129. #2648	C₂×C₃	semidirect
130. #2631	C₂×C₃	semidirect
131. #2615	C₂×C₃	semidirect
132. #2547	C₂×C₃	semidirect
133. #2535	C₂×C₃	semidirect
134. #2495	C₂×C₃	semidirect
135. #2494	C₂×C₃	semidirect
136. #2491	C₂×C₃	semidirect
137. #2485	C₂×C₃	semidirect
138. #2459	C₂×C₃	semidirect
139. #2439	C₂×C₃	semidirect
140. #2420	C₂×C₃	semidirect
141. #2414	C₂×C₃	semidirect
142. #2414	C₂×C₃	semidirect
143. #2388	C₂×C₃	semidirect
144. #2361	C₂×C₃	semidirect
145. #2352	C₂×C₃	semidirect
146. #2311	C₂×C₃	semidirect
1102. C₃	#42463	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×#2825	2
C₃×#2797	2
C₃×#2759	2
C₃×#2751	2
C₃×#2733	2
C₃×#2648	2
C₃×#2631	2
C₃×#2615	2
C₃×#2547	2
C₃×#2535	2
C₃×#2495	2
C₃×#2494	2
C₃×#2491	2
C₃×#2485	2
C₃×#2459	2
C₃×#2439	2
C₃×#2420	2
C₃×#2414	2
C₃×#2388	2
C₃×#2361	2
C₃×#2352	2
C₃×#2311	2
#42463	3

Subgroups — C3×#42463 #10661070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42463 #10661070