Subgroups — C₃×#42906 #10661513

Order 768.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2828	C₂	1	2	yes	maximal, complemented
2	C₃×#2803	C₂	1	2	yes	maximal, complemented
3	C₃×#2803	C₂	1	2	yes	maximal, complemented
4	C₃×#2770	C₂	1	2	yes	maximal, complemented
5	C₃×#2756	C₂	1	2	yes	maximal, complemented
6	C₃×#2651	C₂	1	2	yes	maximal, complemented
7	C₃×#2649	C₂	1	2	yes	maximal, complemented
8	C₃×#2624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2595	C₂	1	2	yes	maximal, complemented
10	C₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
24	#42906	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃×#117	C₂²	1	1	yes	characteristic
38	C₃×#400	C₂²	1	2	yes	—
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	2	yes	—
41	C₃×#399	C₂²	1	2	yes	—
42	C₃×#398	C₂²	1	1	yes	characteristic
43	C₃×#398	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	1	yes	characteristic
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	2	yes	—
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#396	C₂²	1	1	yes	characteristic
53	C₃×#396	C₂²	1	1	yes	characteristic
54	C₃×#394	C₂²	1	2	yes	—
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	1	yes	characteristic
57	C₃×#394	C₂²	1	1	yes	characteristic
58	C₃×#394	C₂²	1	1	yes	characteristic
59	C₃×#394	C₂²	1	2	yes	—
60	C₃×#394	C₂²	1	2	yes	—
61	C₃×#394	C₂²	1	2	yes	—
62	C₃×#394	C₂²	1	2	yes	—
63	C₃×#394	C₂²	1	2	yes	—
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	—
66	C₃×#392	C₂²	1	1	yes	characteristic
67	C₃×#392	C₂²	1	2	yes	—
68	C₃×#392	C₂²	1	2	yes	—
69	C₃×#392	C₂²	1	2	yes	—
70	C₃×#391	C₂²	1	1	yes	characteristic
71	C₃×#391	C₂²	1	1	yes	characteristic
72	C₃×#390	C₂²	1	1	yes	characteristic
73	C₃×#390	C₂²	1	1	yes	characteristic
74	C₃×#390	C₂²	1	2	yes	—
75	C₃×#390	C₂²	1	1	yes	characteristic
76	C₃×#390	C₂²	1	1	yes	characteristic
77	C₃×#390	C₂²	1	2	yes	—
78	C₃×#390	C₂²	1	2	yes	—
79	C₃×#390	C₂²	1	2	yes	—
80	C₃×#389	C₂²	1	1	yes	characteristic
81	C₃×#389	C₂²	1	1	yes	characteristic
82	C₃×#389	C₂²	1	2	yes	—
83	C₃×#389	C₂²	1	1	yes	characteristic
84	C₃×#389	C₂²	1	1	yes	characteristic
85	C₃×#389	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×#388	C₂²	1	2	yes	—
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#388	C₂²	1	2	yes	—
96	C₃×#388	C₂²	1	2	yes	—
97	C₃×#388	C₂²	1	2	yes	—
98	C₃×#388	C₂²	1	2	yes	—
99	C₃×#388	C₂²	1	2	yes	—
100	C₃×#387	C₂²	1	2	yes	—
101	C₃×#387	C₂²	1	2	yes	—
102	C₃×#387	C₂²	1	2	yes	—
103	C₃×#387	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	2	yes	—
105	C₃×#386	C₂²	1	2	yes	—
106	C₃×#385	C₂²	1	2	yes	—
107	C₃×#385	C₂²	1	2	yes	—
108	C₃×#383	C₂²	1	2	yes	—
109	C₃×#382	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	2	yes	—
117	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊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	#2828	C₂×C₃	1	2	yes	complemented
125	#2803	C₂×C₃	1	2	yes	complemented
126	#2803	C₂×C₃	1	2	yes	complemented
127	#2770	C₂×C₃	1	2	yes	complemented
128	#2756	C₂×C₃	1	2	yes	complemented
129	#2651	C₂×C₃	1	2	yes	complemented
130	#2649	C₂×C₃	1	2	yes	complemented
131	#2624	C₂×C₃	1	1	yes	characteristic, complemented
132	#2595	C₂×C₃	1	2	yes	complemented
133	#2562	C₂×C₃	1	1	yes	characteristic, complemented
134	#2536	C₂×C₃	1	1	yes	characteristic, complemented
135	#2513	C₂×C₃	1	1	yes	characteristic, complemented
136	#2495	C₂×C₃	1	1	yes	characteristic, complemented
137	#2490	C₂×C₃	1	1	yes	characteristic, complemented
138	#2485	C₂×C₃	1	1	yes	characteristic, complemented
139	#2453	C₂×C₃	1	1	yes	characteristic, complemented
140	#2414	C₂×C₃	1	1	yes	characteristic, complemented
141	#2407	C₂×C₃	1	1	yes	characteristic, complemented
142	#2407	C₂×C₃	1	1	yes	characteristic, complemented
143	#2392	C₂×C₃	1	1	yes	characteristic, complemented
144	#2362	C₂×C₃	1	1	yes	characteristic, complemented
145	#2341	C₂×C₃	1	1	yes	characteristic, complemented
146	#2323	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×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	C₂³	1	2	yes	—
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	2	yes	—
162	C₃×#125	—	4	2	no	—
163	C₃×C₂²⋊Q₈	—	2	4	no	—
164	C₃×C₂²⋊Q₈	—	2	4	no	—
165	C₃×#121	—	4	2	no	—
166	C₃×#121	—	4	2	no	—
167	C₃×C₄×Q₈	—	4	2	no	—
168	C₃×C₄×Q₈	—	4	2	no	—
169	C₃×C₄×D₄	—	4	2	no	—
170	C₃×C₄×D₄	—	4	2	no	—
171	C₃×C₄×D₄	—	4	2	no	—
172	C₃×#117	—	4	2	no	—
173	C₃×#117	—	4	2	no	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊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	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	2	yes	—
233	C₂×C₃×C₄²	C₂³	1	2	yes	—
234	C₂×C₃×C₄²	C₂³	1	2	yes	—
235	C₂×C₃×C₄²	C₂³	1	2	yes	—
236	C₂×C₃×C₄²	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	1	yes	characteristic
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
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	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
262	C₂×#125	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
265	C₂×#121	C₂²×C₃	1	1	yes	characteristic
266	C₂×#121	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
272	C₂×#117	C₂²×C₃	1	1	yes	characteristic
273	C₂×#117	C₂²×C₃	1	1	yes	characteristic
274	#400	C₂²×C₃	1	2	yes	—
275	#400	C₂²×C₃	1	2	yes	—
276	#400	C₂²×C₃	1	2	yes	—
277	#399	C₂²×C₃	1	2	yes	—
278	#398	C₂²×C₃	1	1	yes	characteristic
279	#398	C₂²×C₃	1	2	yes	—
280	#398	C₂²×C₃	1	2	yes	—
281	#397	C₂²×C₃	1	2	yes	—
282	#397	C₂²×C₃	1	2	yes	—
283	#397	C₂²×C₃	1	1	yes	characteristic
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	#396	C₂²×C₃	1	1	yes	characteristic
289	#396	C₂²×C₃	1	1	yes	characteristic
290	#394	C₂²×C₃	1	2	yes	—
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	2	yes	—
295	#394	C₂²×C₃	1	2	yes	—
296	#394	C₂²×C₃	1	1	yes	characteristic
297	#394	C₂²×C₃	1	1	yes	characteristic
298	#394	C₂²×C₃	1	1	yes	characteristic
299	#394	C₂²×C₃	1	2	yes	—
300	#394	C₂²×C₃	1	2	yes	—
301	#394	C₂²×C₃	1	2	yes	—
302	#392	C₂²×C₃	1	1	yes	characteristic
303	#392	C₂²×C₃	1	2	yes	—
304	#392	C₂²×C₃	1	2	yes	—
305	#392	C₂²×C₃	1	2	yes	—
306	#391	C₂²×C₃	1	1	yes	characteristic
307	#391	C₂²×C₃	1	1	yes	characteristic
308	#390	C₂²×C₃	1	2	yes	—
309	#390	C₂²×C₃	1	2	yes	—
310	#390	C₂²×C₃	1	1	yes	characteristic
311	#390	C₂²×C₃	1	1	yes	characteristic
312	#390	C₂²×C₃	1	2	yes	—
313	#390	C₂²×C₃	1	1	yes	characteristic
314	#390	C₂²×C₃	1	1	yes	characteristic
315	#390	C₂²×C₃	1	2	yes	—
316	#389	C₂²×C₃	1	1	yes	characteristic
317	#389	C₂²×C₃	1	2	yes	—
318	#389	C₂²×C₃	1	1	yes	characteristic
319	#389	C₂²×C₃	1	1	yes	characteristic
320	#389	C₂²×C₃	1	2	yes	—
321	#389	C₂²×C₃	1	1	yes	characteristic
322	#388	C₂²×C₃	1	2	yes	—
323	#388	C₂²×C₃	1	2	yes	—
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	#388	C₂²×C₃	1	2	yes	—
333	#388	C₂²×C₃	1	2	yes	—
334	#388	C₂²×C₃	1	2	yes	—
335	#388	C₂²×C₃	1	2	yes	—
336	#387	C₂²×C₃	1	2	yes	—
337	#387	C₂²×C₃	1	2	yes	—
338	#387	C₂²×C₃	1	2	yes	—
339	#387	C₂²×C₃	1	2	yes	—
340	#386	C₂²×C₃	1	2	yes	—
341	#386	C₂²×C₃	1	2	yes	—
342	#385	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	#380	C₂²×C₃	1	1	yes	characteristic
347	#380	C₂²×C₃	1	1	yes	characteristic
348	#380	C₂²×C₃	1	1	yes	characteristic
349	#380	C₂²×C₃	1	1	yes	characteristic
350	#380	C₂²×C₃	1	2	yes	—
351	#380	C₂²×C₃	1	1	yes	characteristic
352	#380	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
357	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
360	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
361	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
362	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
363	C₂⁴×C₃	C₂⁴	1	2	yes	—
364	C₃×#41	—	4	16	no	—
365	C₂×C₃×Q₈	—	2	2	no	—
366	C₂×C₃×Q₈	—	2	2	no	—
367	C₂×C₃×Q₈	#41	1	4	yes	—
368	C₂×C₃×D₄	—	2	4	no	—
369	C₂×C₃×D₄	—	2	2	no	—
370	C₂×C₃×D₄	—	2	2	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	4	1	no	—
373	C₂×C₃×D₄	—	4	1	no	—
374	C₂×C₃×D₄	—	4	1	no	—
375	C₂×C₃×D₄	—	4	1	no	—
376	C₂×C₃×D₄	—	4	1	no	—
377	C₂×C₃×D₄	—	4	1	no	—
378	C₂×C₃×D₄	—	4	1	no	—
379	C₂×C₃×D₄	—	4	1	no	—
380	C₂×C₃×D₄	—	4	1	no	—
381	C₂×C₃×D₄	—	4	2	no	—
382	C₂×C₃×D₄	—	4	2	no	—
383	C₂×C₃×D₄	—	4	2	no	—
384	C₂×C₃×D₄	—	4	2	no	—
385	C₂×C₃×D₄	—	4	2	no	—
386	C₂×C₃×D₄	—	4	2	no	—
387	C₂×C₃×D₄	—	4	2	no	—
388	C₂×C₃×D₄	—	4	2	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	2	2	no	—
391	C₂²×C₃×C₄	—	2	4	no	—
392	C₂²×C₃×C₄	—	2	2	no	—
393	C₂²×C₃×C₄	—	2	2	no	—
394	C₂²×C₃×C₄	—	2	2	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	2	no	—
399	C₂²×C₃×C₄	—	4	2	no	—
400	C₂²×C₃×C₄	—	4	2	no	—
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
409	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	4	no	—
423	C₃×C₄⋊C₄	—	2	4	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	2	2	no	—
426	C₃×C₄⋊C₄	—	2	2	no	—
427	C₃×C₄⋊C₄	—	2	2	no	—
428	C₃×C₄⋊C₄	—	4	2	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	—	4	1	no	—
431	C₃×C₄⋊C₄	—	4	1	no	—
432	C₃×C₄⋊C₄	—	4	2	no	—
433	C₃×C₄⋊C₄	—	4	2	no	—
434	C₃×C₄⋊C₄	—	4	1	no	—
435	C₃×C₄⋊C₄	—	4	1	no	—
436	C₃×C₄⋊C₄	—	4	1	no	—
437	C₃×C₄⋊C₄	—	4	1	no	—
438	C₃×C₄⋊C₄	—	4	1	no	—
439	C₃×C₄⋊C₄	—	4	2	no	—
440	C₃×C₄⋊C₄	—	4	2	no	—
441	C₃×C₄⋊C₄	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	2	no	—
443	C₃×C₂²⋊C₄	—	2	4	no	—
444	C₃×C₂²⋊C₄	—	2	4	no	—
445	C₃×C₂²⋊C₄	—	4	1	no	—
446	C₃×C₂²⋊C₄	—	4	1	no	—
447	C₃×C₂²⋊C₄	—	4	2	no	—
448	C₃×C₂²⋊C₄	—	4	2	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₂²⋊C₄	—	4	2	no	—
451	C₃×C₂²⋊C₄	—	4	2	no	—
452	C₃×C₂²⋊C₄	—	4	2	no	—
453	C₃×C₂²⋊C₄	—	4	2	no	—
454	C₃×C₂²⋊C₄	—	4	2	no	—
455	C₃×C₂²⋊C₄	—	4	2	no	—
456	C₃×C₂²⋊C₄	—	4	2	no	—
457	C₃×C₂²⋊C₄	—	4	2	no	—
458	C₃×C₂²⋊C₄	—	4	1	no	—
459	C₃×C₂²⋊C₄	—	4	2	no	—
460	C₃×C₂²⋊C₄	—	4	2	no	—
461	C₃×C₂²⋊C₄	—	4	2	no	—
462	C₃×C₂²⋊C₄	—	4	1	no	—
463	C₃×C₂²⋊C₄	—	4	1	no	—
464	C₃×C₂²⋊C₄	—	4	1	no	—
465	C₃×C₂²⋊C₄	—	4	2	no	—
466	C₃×C₂²⋊C₄	—	4	1	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	C₃×C₂²⋊C₄	—	4	1	no	—
469	C₃×C₂²⋊C₄	—	4	1	no	—
470	C₃×C₂²⋊C₄	—	4	1	no	—
471	C₃×C₂²⋊C₄	—	4	1	no	—
472	C₃×C₂²⋊C₄	—	4	2	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₄²	—	2	2	no	—
475	C₃×C₄²	—	2	2	no	—
476	C₃×C₄²	—	2	2	no	—
477	C₃×C₄²	—	2	2	no	—
478	C₃×C₄²	—	4	2	no	—
479	C₃×C₄²	—	4	2	no	—
480	C₃×C₄²	—	4	2	no	—
481	C₃×C₄²	—	4	2	no	—
482	C₃×C₄²	—	4	2	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	4	2	no	—
485	C₂×#41	—	4	2	no	—
486	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₃	1	2	yes	—
489	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₃	1	2	yes	—
493	C₂²×D₄	C₂³×C₃	1	2	yes	—
494	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₃	1	2	yes	—
498	#125	—	4	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	#121	—	4	2	no	—
502	#121	—	4	2	no	—
503	C₄×Q₈	—	4	2	no	—
504	C₄×Q₈	—	4	2	no	—
505	C₄×D₄	—	4	2	no	—
506	C₄×D₄	—	4	2	no	—
507	C₄×D₄	—	4	2	no	—
508	#117	—	4	2	no	—
509	#117	—	4	2	no	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₃	1	2	yes	—
570	C₂×C₄²	C₂³×C₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	1	yes	characteristic
574	#95	C₂³×C₃	1	1	yes	characteristic
575	#95	C₂³×C₃	1	1	yes	characteristic
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	1	yes	characteristic
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	1	yes	characteristic
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	1	yes	characteristic
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	2	yes	—
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	2	yes	—
587	#95	C₂³×C₃	1	2	yes	—
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	2	yes	—
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	2	yes	—
595	#95	C₂³×C₃	1	2	yes	—
596	#95	C₂³×C₃	1	2	yes	—
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	1	no	—
602	C₂³×C₃	—	2	1	no	—
603	C₂³×C₃	—	2	1	no	—
604	C₂³×C₃	—	2	1	no	—
605	C₂³×C₃	—	2	1	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	2	no	—
608	C₂³×C₃	—	2	2	no	—
609	C₂³×C₃	—	2	2	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	2	no	—
616	C₂³×C₃	—	2	2	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	2	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	1	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	C₂⁵	1	1	yes	characteristic
626	C₃×Q₈	—	2	8	no	—
627	C₃×D₄	—	4	8	no	—
628	C₃×D₄	—	4	4	no	—
629	C₃×D₄	—	4	4	no	—
630	C₃×D₄	—	4	4	no	—
631	C₃×D₄	—	4	4	no	—
632	C₃×D₄	—	8	4	no	—
633	C₃×D₄	—	8	4	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	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	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	1	no	—
684	C₂×C₃×C₄	—	2	1	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	4	8	no	—
688	C₂×C₃×C₄	—	4	4	no	—
689	C₂×C₃×C₄	—	4	4	no	—
690	C₂×C₃×C₄	—	4	4	no	—
691	C₂×C₃×C₄	C₂×#41	1	4	yes	—
692	C₂×C₃×C₄	C₂×#41	1	2	yes	—
693	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
694	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
695	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
696	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
697	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
698	C₂⁴	C₂⁴×C₃	1	2	yes	—
699	#41	—	4	16	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	C₃×#41	1	4	yes	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	1	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	2	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	1	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	1	no	—
784	C₂²⋊C₄	—	4	1	no	—
785	C₂²⋊C₄	—	4	1	no	—
786	C₂²⋊C₄	—	4	1	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	1	no	—
792	C₂²⋊C₄	—	4	1	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	1	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₂²×C₃	—	4	2	no	—
819	C₂²×C₃	—	4	1	no	—
820	C₂²×C₃	—	4	1	no	—
821	C₂²×C₃	—	4	1	no	—
822	C₂²×C₃	—	4	1	no	—
823	C₂²×C₃	—	4	1	no	—
824	C₂²×C₃	—	4	1	no	—
825	C₂²×C₃	—	4	1	no	—
826	C₂²×C₃	—	4	1	no	—
827	C₂²×C₃	—	4	2	no	—
828	C₂²×C₃	—	4	1	no	—
829	C₂²×C₃	—	4	2	no	—
830	C₂²×C₃	—	4	1	no	—
831	C₂²×C₃	—	4	1	no	—
832	C₂²×C₃	—	4	1	no	—
833	C₂²×C₃	—	4	1	no	—
834	C₂²×C₃	—	4	1	no	—
835	C₂²×C₃	—	4	1	no	—
836	C₂²×C₃	—	4	2	no	—
837	C₂²×C₃	—	4	2	no	—
838	C₂²×C₃	—	4	1	no	—
839	C₂²×C₃	—	4	1	no	—
840	C₂²×C₃	—	4	1	no	—
841	C₂²×C₃	—	4	2	no	—
842	C₂²×C₃	—	4	1	no	—
843	C₂²×C₃	—	4	2	no	—
844	C₂²×C₃	—	4	1	no	—
845	C₂²×C₃	—	4	1	no	—
846	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
847	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
848	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂²×C₃	#585	1	1	yes	characteristic
850	C₂²×C₃	#585	1	1	yes	characteristic
851	C₂²×C₃	#585	1	1	yes	characteristic
852	C₂²×C₃	#585	1	1	yes	characteristic
853	C₃×C₄	—	2	4	no	—
854	C₃×C₄	—	4	1	no	—
855	C₃×C₄	—	4	1	no	—
856	C₃×C₄	—	4	1	no	—
857	C₃×C₄	—	4	2	no	—
858	C₃×C₄	—	4	2	no	—
859	C₃×C₄	—	4	1	no	—
860	C₃×C₄	—	4	1	no	—
861	C₃×C₄	—	4	2	no	—
862	C₃×C₄	—	4	2	no	—
863	C₃×C₄	—	4	1	no	—
864	C₃×C₄	—	4	1	no	—
865	C₃×C₄	—	4	1	no	—
866	C₃×C₄	—	4	1	no	—
867	C₃×C₄	—	4	2	no	—
868	C₃×C₄	—	4	1	no	—
869	C₃×C₄	—	4	1	no	—
870	C₃×C₄	—	4	2	no	—
871	C₃×C₄	#538	1	4	yes	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	C₂⁵×C₃	1	1	yes	characteristic
901	Q₈	—	2	8	no	—
902	D₄	—	4	8	no	—
903	D₄	—	4	4	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	4	no	—
906	D₄	—	4	4	no	—
907	D₄	—	8	4	no	—
908	D₄	—	8	4	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	4	8	no	—
963	C₂×C₄	—	4	4	no	—
964	C₂×C₄	—	4	4	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	C₂×C₃×#41	1	4	yes	—
967	C₂×C₄	C₂×C₃×#41	1	2	yes	—
968	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
969	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
970	C₂×C₃	—	8	1	no	—
971	C₂×C₃	—	8	2	no	—
972	C₂×C₃	—	8	1	no	—
973	C₂×C₃	—	8	1	no	—
974	C₂×C₃	C₂×#538	1	1	yes	characteristic
975	C₂×C₃	#3524	1	1	yes	characteristic
976	C₂×C₃	#3524	1	1	yes	characteristic
977	C₂×C₃	#3539	1	1	yes	characteristic
978	C₂×C₃	#3539	1	1	yes	characteristic
979	C₂×C₃	#3540	1	1	yes	characteristic
980	C₂×C₃	#3551	1	1	yes	characteristic
981	C₂²	—	4	2	no	—
982	C₂²	—	4	1	no	—
983	C₂²	—	4	1	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1010	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1011	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₂²	C₃×#585	1	1	yes	characteristic
1013	C₂²	C₃×#585	1	1	yes	characteristic
1014	C₂²	C₃×#585	1	1	yes	characteristic
1015	C₂²	C₃×#585	1	1	yes	characteristic
1016	C₄	—	2	4	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	1	no	—
1034	C₄	C₃×#538	1	4	yes	—
1035	C₃	#42906	1	1	yes	characteristic, direct product factor, Sylow
1036	C₂	—	8	1	no	—
1037	C₂	—	8	2	no	—
1038	C₂	—	8	1	no	—
1039	C₂	—	8	1	no	—
1040	C₂	C₂×C₃×#538	1	1	yes	characteristic
1041	C₂	C₃×#3524	1	1	yes	characteristic
1042	C₂	C₃×#3524	1	1	yes	characteristic
1043	C₂	C₃×#3539	1	1	yes	characteristic
1044	C₂	C₃×#3539	1	1	yes	characteristic
1045	C₂	C₃×#3540	1	1	yes	characteristic
1046	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×#2828	C₂	semidirect
2. C₃×#2803	C₂	semidirect
3. C₃×#2803	C₂	semidirect
4. C₃×#2770	C₂	semidirect
5. C₃×#2756	C₂	semidirect
6. C₃×#2651	C₂	semidirect
7. C₃×#2649	C₂	semidirect
8. C₃×#2624	C₂	semidirect
9. C₃×#2595	C₂	semidirect
10. C₃×#2562	C₂	semidirect
11. C₃×#2536	C₂	semidirect
12. C₃×#2513	C₂	semidirect
13. C₃×#2495	C₂	semidirect
14. C₃×#2490	C₂	semidirect
15. C₃×#2485	C₂	semidirect
16. C₃×#2453	C₂	semidirect
17. C₃×#2414	C₂	semidirect
18. C₃×#2407	C₂	semidirect
19. C₃×#2407	C₂	semidirect
20. C₃×#2392	C₂	semidirect
21. C₃×#2362	C₂	semidirect
22. C₃×#2341	C₂	semidirect
23. C₃×#2323	C₂	semidirect
24. #42906	C₃	direct (N × H)
124. #2828	C₂×C₃	semidirect
125. #2803	C₂×C₃	semidirect
126. #2803	C₂×C₃	semidirect
127. #2770	C₂×C₃	semidirect
128. #2756	C₂×C₃	semidirect
129. #2651	C₂×C₃	semidirect
130. #2649	C₂×C₃	semidirect
131. #2624	C₂×C₃	semidirect
132. #2595	C₂×C₃	semidirect
133. #2562	C₂×C₃	semidirect
134. #2536	C₂×C₃	semidirect
135. #2513	C₂×C₃	semidirect
136. #2495	C₂×C₃	semidirect
137. #2490	C₂×C₃	semidirect
138. #2485	C₂×C₃	semidirect
139. #2453	C₂×C₃	semidirect
140. #2414	C₂×C₃	semidirect
141. #2407	C₂×C₃	semidirect
142. #2407	C₂×C₃	semidirect
143. #2392	C₂×C₃	semidirect
144. #2362	C₂×C₃	semidirect
145. #2341	C₂×C₃	semidirect
146. #2323	C₂×C₃	semidirect
1035. C₃	#42906	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×#2828	2
C₃×#2803	2
C₃×#2770	2
C₃×#2756	2
C₃×#2651	2
C₃×#2649	2
C₃×#2624	2
C₃×#2595	2
C₃×#2562	2
C₃×#2536	2
C₃×#2513	2
C₃×#2495	2
C₃×#2490	2
C₃×#2485	2
C₃×#2453	2
C₃×#2414	2
C₃×#2407	2
C₃×#2392	2
C₃×#2362	2
C₃×#2341	2
C₃×#2323	2
#42906	3

Subgroups — C3×#42906 #10661513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42906 #10661513