Subgroups — C₃×#35022 #10653629

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2852	C₂	1	2	yes	maximal, complemented
2	C₃×#2849	C₂	1	2	yes	maximal, complemented
3	C₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2617	C₂	1	1	yes	maximal, characteristic
7	C₃×#2573	C₂	1	2	yes	maximal, complemented
8	C₃×#2572	C₂	1	2	yes	maximal, complemented
9	C₃×#2554	C₂	1	2	yes	maximal, complemented
10	C₃×#2553	C₂	1	2	yes	maximal, complemented
11	C₃×#2516	C₂	1	2	yes	maximal, complemented
12	C₃×#2515	C₂	1	2	yes	maximal, complemented
13	C₃×#2458	C₂	1	2	yes	maximal, complemented
14	C₃×#2457	C₂	1	2	yes	maximal, complemented
15	C₃×#2321	C₂	1	2	yes	maximal, complemented
16	C₃×#2318	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×C₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	#35022	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₃×#123	C₂²	1	2	yes	—
24	C₂×C₃×#123	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃×#120	C₂²	1	2	yes	—
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
30	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
35	C₃×#400	C₂²	1	2	yes	complemented
36	C₃×#400	C₂²	1	2	yes	complemented
37	C₃×#400	C₂²	1	2	yes	complemented
38	C₃×#399	C₂²	1	2	yes	—
39	C₃×#398	C₂²	1	2	yes	complemented
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#397	C₂²	1	2	yes	—
42	C₃×#397	C₂²	1	2	yes	complemented
43	C₃×#396	C₂²	1	2	yes	—
44	C₃×#396	C₂²	1	2	yes	—
45	C₃×#394	C₂²	1	2	yes	—
46	C₃×#394	C₂²	1	2	yes	—
47	C₃×#394	C₂²	1	2	yes	complemented
48	C₃×#393	C₂²	1	2	yes	—
49	C₃×#393	C₂²	1	2	yes	complemented
50	C₃×#392	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	1	yes	characteristic, complemented
52	C₃×#390	C₂²	1	2	yes	—
53	C₃×#390	C₂²	1	2	yes	—
54	C₃×#390	C₂²	1	1	yes	characteristic, complemented
55	C₃×#389	C₂²	1	1	yes	characteristic, complemented
56	C₃×#389	C₂²	1	1	yes	characteristic, complemented
57	C₃×#388	C₂²	1	2	yes	—
58	C₃×#388	C₂²	1	2	yes	—
59	C₃×#388	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	2	yes	—
61	C₃×#388	C₂²	1	2	yes	complemented
62	C₃×#388	C₂²	1	2	yes	complemented
63	C₃×#388	C₂²	1	2	yes	complemented
64	C₃×#388	C₂²	1	2	yes	complemented
65	C₃×#388	C₂²	1	2	yes	complemented
66	C₃×#388	C₂²	1	2	yes	complemented
67	C₃×#387	C₂²	1	2	yes	complemented
68	C₃×#387	C₂²	1	2	yes	complemented
69	C₃×#387	C₂²	1	2	yes	complemented
70	C₃×#387	C₂²	1	2	yes	complemented
71	C₃×#387	C₂²	1	2	yes	complemented
72	C₃×#387	C₂²	1	2	yes	complemented
73	C₃×#386	C₂²	1	2	yes	—
74	C₃×#386	C₂²	1	2	yes	—
75	C₃×#386	C₂²	1	2	yes	—
76	C₃×#386	C₂²	1	2	yes	—
77	C₃×#386	C₂²	1	2	yes	—
78	C₃×#386	C₂²	1	2	yes	—
79	C₃×#386	C₂²	1	2	yes	—
80	C₃×#386	C₂²	1	2	yes	—
81	C₃×#385	C₂²	1	2	yes	—
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#383	C₂²	1	2	yes	complemented
88	C₃×#383	C₂²	1	2	yes	complemented
89	C₃×#382	C₂²	1	2	yes	complemented
90	C₃×#381	C₂²	1	2	yes	—
91	C₃×#381	C₂²	1	2	yes	—
92	C₃×#381	C₂²	1	2	yes	complemented
93	C₃×#380	C₂²	1	1	yes	characteristic
94	C₃×#380	C₂²	1	1	yes	characteristic
95	C₃×#380	C₂²	1	2	yes	complemented
96	C₃×#379	C₂²	1	2	yes	—
97	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
100	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₂×C₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic
108	#2852	C₂×C₃	1	2	yes	complemented
109	#2849	C₂×C₃	1	2	yes	complemented
110	#2646	C₂×C₃	1	1	yes	characteristic, complemented
111	#2639	C₂×C₃	1	1	yes	characteristic, complemented
112	#2626	C₂×C₃	1	1	yes	characteristic, complemented
113	#2617	C₂×C₃	1	1	yes	characteristic
114	#2573	C₂×C₃	1	2	yes	complemented
115	#2572	C₂×C₃	1	2	yes	complemented
116	#2554	C₂×C₃	1	2	yes	complemented
117	#2553	C₂×C₃	1	2	yes	complemented
118	#2516	C₂×C₃	1	2	yes	complemented
119	#2515	C₂×C₃	1	2	yes	complemented
120	#2458	C₂×C₃	1	2	yes	complemented
121	#2457	C₂×C₃	1	2	yes	complemented
122	#2321	C₂×C₃	1	2	yes	complemented
123	#2318	C₂×C₃	1	2	yes	complemented
124	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
125	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
126	C₂×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×D₄	C₂³	1	2	yes	—
130	C₂²×C₃×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×D₄	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
133	C₂³×C₃×C₄	—	2	4	no	—
134	C₂³×C₃×C₄	—	4	2	no	—
135	C₂³×C₃×C₄	—	4	2	no	—
136	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
137	C₂³×C₃×C₄	C₂³	1	2	yes	—
138	C₂³×C₃×C₄	C₂³	1	2	yes	—
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
144	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
145	C₃×#126	—	4	4	no	—
146	C₃×#123	—	4	4	no	—
147	C₃×#123	—	4	4	no	—
148	C₃×C₂²⋊Q₈	—	2	4	no	—
149	C₃×#121	—	2	4	no	—
150	C₃×#120	—	2	8	no	—
151	C₃×C₄×Q₈	—	4	2	no	—
152	C₃×C₄×D₄	—	2	8	no	—
153	C₃×C₄×D₄	—	4	2	no	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	—	4	2	no	—
196	C₂×C₃×C₄²	—	4	2	no	—
197	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄²	C₂³	1	2	yes	—
200	C₂×C₃×C₄²	C₂³	1	2	yes	—
201	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄²	C₂³	1	2	yes	—
204	C₂×C₃×C₄²	C₂³	1	2	yes	—
205	C₂×C₃×C₄²	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	2	yes	—
230	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
231	C₂×#126	C₂²×C₃	1	2	yes	complemented
232	C₂×#123	C₂²×C₃	1	2	yes	—
233	C₂×#123	C₂²×C₃	1	2	yes	—
234	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
235	C₂×#121	C₂²×C₃	1	1	yes	characteristic
236	C₂×#120	C₂²×C₃	1	2	yes	—
237	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
238	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
239	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
240	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
243	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
244	#400	C₂²×C₃	1	2	yes	complemented
245	#400	C₂²×C₃	1	2	yes	complemented
246	#400	C₂²×C₃	1	2	yes	complemented
247	#399	C₂²×C₃	1	2	yes	—
248	#398	C₂²×C₃	1	2	yes	complemented
249	#398	C₂²×C₃	1	2	yes	complemented
250	#397	C₂²×C₃	1	2	yes	—
251	#397	C₂²×C₃	1	2	yes	complemented
252	#396	C₂²×C₃	1	2	yes	—
253	#396	C₂²×C₃	1	2	yes	—
254	#394	C₂²×C₃	1	2	yes	—
255	#394	C₂²×C₃	1	2	yes	—
256	#394	C₂²×C₃	1	2	yes	complemented
257	#393	C₂²×C₃	1	2	yes	—
258	#393	C₂²×C₃	1	2	yes	complemented
259	#392	C₂²×C₃	1	2	yes	—
260	#391	C₂²×C₃	1	1	yes	characteristic, complemented
261	#390	C₂²×C₃	1	2	yes	—
262	#390	C₂²×C₃	1	2	yes	—
263	#390	C₂²×C₃	1	1	yes	characteristic, complemented
264	#389	C₂²×C₃	1	1	yes	characteristic, complemented
265	#389	C₂²×C₃	1	1	yes	characteristic, complemented
266	#388	C₂²×C₃	1	2	yes	—
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	complemented
271	#388	C₂²×C₃	1	2	yes	complemented
272	#388	C₂²×C₃	1	2	yes	complemented
273	#388	C₂²×C₃	1	2	yes	complemented
274	#388	C₂²×C₃	1	2	yes	complemented
275	#388	C₂²×C₃	1	2	yes	complemented
276	#387	C₂²×C₃	1	2	yes	complemented
277	#387	C₂²×C₃	1	2	yes	complemented
278	#387	C₂²×C₃	1	2	yes	complemented
279	#387	C₂²×C₃	1	2	yes	complemented
280	#387	C₂²×C₃	1	2	yes	complemented
281	#387	C₂²×C₃	1	2	yes	complemented
282	#386	C₂²×C₃	1	2	yes	—
283	#386	C₂²×C₃	1	2	yes	—
284	#386	C₂²×C₃	1	2	yes	—
285	#386	C₂²×C₃	1	2	yes	—
286	#386	C₂²×C₃	1	2	yes	—
287	#386	C₂²×C₃	1	2	yes	—
288	#386	C₂²×C₃	1	2	yes	—
289	#386	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	2	yes	—
291	#385	C₂²×C₃	1	2	yes	—
292	#385	C₂²×C₃	1	2	yes	—
293	#385	C₂²×C₃	1	2	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#385	C₂²×C₃	1	2	yes	—
296	#383	C₂²×C₃	1	2	yes	complemented
297	#383	C₂²×C₃	1	2	yes	complemented
298	#382	C₂²×C₃	1	2	yes	complemented
299	#381	C₂²×C₃	1	2	yes	—
300	#381	C₂²×C₃	1	2	yes	—
301	#381	C₂²×C₃	1	2	yes	complemented
302	#380	C₂²×C₃	1	1	yes	characteristic
303	#380	C₂²×C₃	1	1	yes	characteristic
304	#380	C₂²×C₃	1	2	yes	complemented
305	#379	C₂²×C₃	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
307	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
313	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
314	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
315	C₂×#95	C₂²×C₃	1	1	yes	characteristic
316	C₂×#95	C₂²×C₃	1	1	yes	characteristic
317	C₂⁴×C₃	—	2	2	no	—
318	C₂⁴×C₃	—	2	2	no	—
319	C₂⁴×C₃	—	4	1	no	—
320	C₂⁴×C₃	—	4	1	no	—
321	C₂⁴×C₃	—	4	1	no	—
322	C₂⁴×C₃	—	4	1	no	—
323	C₂⁴×C₃	#41	1	4	yes	—
324	C₂⁴×C₃	C₂⁴	1	2	yes	—
325	C₂⁴×C₃	C₂⁴	1	2	yes	—
326	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
327	C₂×C₃×Q₈	—	2	2	no	—
328	C₂×C₃×Q₈	—	4	1	no	—
329	C₂×C₃×Q₈	—	4	1	no	—
330	C₂×C₃×D₄	—	2	4	no	—
331	C₂×C₃×D₄	—	2	4	no	—
332	C₂×C₃×D₄	—	2	4	no	—
333	C₂×C₃×D₄	—	2	4	no	—
334	C₂×C₃×D₄	—	2	4	no	—
335	C₂×C₃×D₄	—	2	2	no	—
336	C₂×C₃×D₄	—	4	1	no	—
337	C₂×C₃×D₄	—	4	1	no	—
338	C₂×C₃×D₄	—	4	2	no	—
339	C₂×C₃×D₄	—	4	2	no	—
340	C₂×C₃×D₄	—	4	2	no	—
341	C₂×C₃×D₄	—	4	2	no	—
342	C₂²×C₃×C₄	—	2	2	no	—
343	C₂²×C₃×C₄	—	2	2	no	—
344	C₂²×C₃×C₄	—	2	2	no	—
345	C₂²×C₃×C₄	—	2	2	no	—
346	C₂²×C₃×C₄	—	2	2	no	—
347	C₂²×C₃×C₄	—	2	4	no	—
348	C₂²×C₃×C₄	—	2	4	no	—
349	C₂²×C₃×C₄	—	2	2	no	—
350	C₂²×C₃×C₄	—	2	4	no	—
351	C₂²×C₃×C₄	—	2	4	no	—
352	C₂²×C₃×C₄	—	2	4	no	—
353	C₂²×C₃×C₄	—	4	1	no	—
354	C₂²×C₃×C₄	—	4	1	no	—
355	C₂²×C₃×C₄	—	4	1	no	—
356	C₂²×C₃×C₄	—	4	1	no	—
357	C₂²×C₃×C₄	—	4	2	no	—
358	C₂²×C₃×C₄	—	4	2	no	—
359	C₂²×C₃×C₄	—	4	1	no	—
360	C₂²×C₃×C₄	—	4	1	no	—
361	C₂²×C₃×C₄	—	4	1	no	—
362	C₂²×C₃×C₄	—	4	1	no	—
363	C₂²×C₃×C₄	—	4	1	no	—
364	C₂²×C₃×C₄	—	4	1	no	—
365	C₂²×C₃×C₄	—	4	2	no	—
366	C₂²×C₃×C₄	—	4	2	no	—
367	C₂²×C₃×C₄	—	4	16	no	—
368	C₂²×C₃×C₄	#41	1	4	yes	—
369	C₂²×C₃×C₄	#41	1	4	yes	—
370	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
371	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₃×C₄⋊C₄	—	2	4	no	—
387	C₃×C₄⋊C₄	—	2	2	no	—
388	C₃×C₄⋊C₄	—	2	2	no	—
389	C₃×C₄⋊C₄	—	2	4	no	—
390	C₃×C₄⋊C₄	—	2	4	no	—
391	C₃×C₄⋊C₄	—	2	4	no	—
392	C₃×C₄⋊C₄	—	4	1	no	—
393	C₃×C₄⋊C₄	—	4	1	no	—
394	C₃×C₄⋊C₄	—	4	2	no	—
395	C₃×C₄⋊C₄	—	4	2	no	—
396	C₃×C₄⋊C₄	—	4	1	no	—
397	C₃×C₄⋊C₄	—	4	1	no	—
398	C₃×C₄⋊C₄	—	4	2	no	—
399	C₃×C₄⋊C₄	—	4	2	no	—
400	C₃×C₄⋊C₄	—	4	2	no	—
401	C₃×C₄⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	2	4	no	—
403	C₃×C₂²⋊C₄	—	2	4	no	—
404	C₃×C₂²⋊C₄	—	2	4	no	—
405	C₃×C₂²⋊C₄	—	2	4	no	—
406	C₃×C₂²⋊C₄	—	2	4	no	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	2	4	no	—
410	C₃×C₂²⋊C₄	—	2	4	no	—
411	C₃×C₂²⋊C₄	—	2	4	no	—
412	C₃×C₂²⋊C₄	—	2	4	no	—
413	C₃×C₂²⋊C₄	—	2	4	no	—
414	C₃×C₂²⋊C₄	—	2	4	no	—
415	C₃×C₂²⋊C₄	—	4	2	no	—
416	C₃×C₂²⋊C₄	—	4	2	no	—
417	C₃×C₂²⋊C₄	—	4	2	no	—
418	C₃×C₂²⋊C₄	—	4	2	no	—
419	C₃×C₂²⋊C₄	—	4	2	no	—
420	C₃×C₂²⋊C₄	—	4	2	no	—
421	C₃×C₂²⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	4	2	no	—
423	C₃×C₂²⋊C₄	—	4	2	no	—
424	C₃×C₂²⋊C₄	—	4	2	no	—
425	C₃×C₄²	—	2	4	no	—
426	C₃×C₄²	—	2	2	no	—
427	C₃×C₄²	—	2	2	no	—
428	C₃×C₄²	—	2	4	no	—
429	C₃×C₄²	—	4	1	no	—
430	C₃×C₄²	—	4	1	no	—
431	C₃×C₄²	—	4	2	no	—
432	C₃×C₄²	—	4	2	no	—
433	C₃×C₄²	—	4	2	no	—
434	C₂⁵	C₂³×C₃	1	1	yes	characteristic
435	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₃	1	2	yes	—
437	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
438	C₂²×D₄	C₂³×C₃	1	2	yes	—
439	C₂²×D₄	C₂³×C₃	1	2	yes	—
440	C₂³×C₄	—	2	4	no	—
441	C₂³×C₄	—	4	2	no	—
442	C₂³×C₄	—	4	2	no	—
443	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₃	1	2	yes	—
445	C₂³×C₄	C₂³×C₃	1	2	yes	—
446	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₃	1	2	yes	—
449	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
452	#126	—	4	4	no	—
453	#123	—	4	4	no	—
454	#123	—	4	4	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	#121	—	2	4	no	—
457	#120	—	2	8	no	—
458	C₄×Q₈	—	4	2	no	—
459	C₄×D₄	—	2	8	no	—
460	C₄×D₄	—	4	2	no	—
461	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₂²⋊C₄	—	2	4	no	—
478	C₂×C₂²⋊C₄	—	2	4	no	—
479	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₄²	—	4	2	no	—
503	C₂×C₄²	—	4	2	no	—
504	C₂×C₄²	C₂³×C₃	1	2	yes	—
505	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₃	1	2	yes	—
508	C₂×C₄²	C₂³×C₃	1	2	yes	—
509	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₃	1	2	yes	—
512	C₂×C₄²	C₂³×C₃	1	2	yes	—
513	#95	C₂³×C₃	1	2	yes	—
514	#95	C₂³×C₃	1	2	yes	—
515	#95	C₂³×C₃	1	2	yes	—
516	#95	C₂³×C₃	1	2	yes	—
517	#95	C₂³×C₃	1	2	yes	—
518	#95	C₂³×C₃	1	2	yes	—
519	#95	C₂³×C₃	1	2	yes	—
520	#95	C₂³×C₃	1	2	yes	—
521	#95	C₂³×C₃	1	2	yes	—
522	#95	C₂³×C₃	1	2	yes	—
523	#95	C₂³×C₃	1	2	yes	—
524	#95	C₂³×C₃	1	2	yes	—
525	#95	C₂³×C₃	1	2	yes	—
526	#95	C₂³×C₃	1	2	yes	—
527	#95	C₂³×C₃	1	2	yes	—
528	#95	C₂³×C₃	1	2	yes	—
529	#95	C₂³×C₃	1	2	yes	—
530	#95	C₂³×C₃	1	2	yes	—
531	#95	C₂³×C₃	1	2	yes	—
532	#95	C₂³×C₃	1	2	yes	—
533	#95	C₂³×C₃	1	2	yes	—
534	#95	C₂³×C₃	1	2	yes	—
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	C₂³×C₃	—	2	1	no	—
538	C₂³×C₃	—	2	1	no	—
539	C₂³×C₃	—	2	1	no	—
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	—	2	8	no	—
542	C₂³×C₃	—	2	2	no	—
543	C₂³×C₃	—	2	2	no	—
544	C₂³×C₃	—	2	2	no	—
545	C₂³×C₃	—	2	2	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	2	2	no	—
548	C₂³×C₃	—	2	2	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	2	2	no	—
553	C₂³×C₃	—	2	2	no	—
554	C₂³×C₃	—	2	2	no	—
555	C₂³×C₃	—	4	4	no	—
556	C₂³×C₃	—	4	4	no	—
557	C₂³×C₃	—	4	4	no	—
558	C₂³×C₃	—	4	4	no	—
559	C₂³×C₃	—	4	4	no	—
560	C₂³×C₃	—	4	4	no	—
561	C₂³×C₃	C₂×#41	1	4	yes	—
562	C₂³×C₃	C₂×#41	1	2	yes	—
563	C₂³×C₃	C₂×#41	1	2	yes	—
564	C₂³×C₃	C₂×#41	1	2	yes	—
565	C₂³×C₃	C₂⁵	1	1	yes	characteristic
566	C₃×Q₈	—	4	4	no	—
567	C₃×D₄	—	4	4	no	—
568	C₃×D₄	—	4	8	no	—
569	C₃×D₄	—	8	4	no	—
570	C₃×D₄	—	8	4	no	—
571	C₂×C₃×C₄	—	2	8	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	2	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	2	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	4	4	no	—
615	C₂×C₃×C₄	—	4	4	no	—
616	C₂×C₃×C₄	—	4	8	no	—
617	C₂×C₃×C₄	—	4	8	no	—
618	C₂×C₃×C₄	—	4	4	no	—
619	C₂×C₃×C₄	—	4	4	no	—
620	C₂×C₃×C₄	—	4	4	no	—
621	C₂×C₃×C₄	—	8	4	no	—
622	C₂×C₃×C₄	C₂×#41	1	2	yes	—
623	C₂×C₃×C₄	C₂×#41	1	2	yes	—
624	C₂×C₃×C₄	C₂×#41	1	2	yes	—
625	C₂×C₃×C₄	C₂×#41	1	2	yes	—
626	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
627	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	4	1	no	—
631	C₂⁴	—	4	1	no	—
632	C₂⁴	—	4	1	no	—
633	C₂⁴	—	4	1	no	—
634	C₂⁴	C₃×#41	1	4	yes	—
635	C₂⁴	C₂⁴×C₃	1	2	yes	—
636	C₂⁴	C₂⁴×C₃	1	2	yes	—
637	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	4	1	no	—
640	C₂×Q₈	—	4	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	16	no	—
679	C₂²×C₄	C₃×#41	1	4	yes	—
680	C₂²×C₄	C₃×#41	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	4	1	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	1	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	4	1	no	—
741	C₄²	—	4	1	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₂²×C₃	—	2	2	no	—
746	C₂²×C₃	—	2	2	no	—
747	C₂²×C₃	—	2	2	no	—
748	C₂²×C₃	—	2	2	no	—
749	C₂²×C₃	—	2	2	no	—
750	C₂²×C₃	—	2	2	no	—
751	C₂²×C₃	—	2	4	no	—
752	C₂²×C₃	—	2	4	no	—
753	C₂²×C₃	—	2	4	no	—
754	C₂²×C₃	—	4	16	no	—
755	C₂²×C₃	—	4	2	no	—
756	C₂²×C₃	—	4	2	no	—
757	C₂²×C₃	—	4	2	no	—
758	C₂²×C₃	—	4	2	no	—
759	C₂²×C₃	—	4	2	no	—
760	C₂²×C₃	—	4	2	no	—
761	C₂²×C₃	—	4	2	no	—
762	C₂²×C₃	—	4	2	no	—
763	C₂²×C₃	—	4	2	no	—
764	C₂²×C₃	—	4	2	no	—
765	C₂²×C₃	—	4	2	no	—
766	C₂²×C₃	#529	1	4	yes	—
767	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
768	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
769	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
770	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂²×C₃	#585	1	1	yes	characteristic
773	C₂²×C₃	#585	1	1	yes	characteristic
774	C₃×C₄	—	2	2	no	—
775	C₃×C₄	—	2	2	no	—
776	C₃×C₄	—	2	2	no	—
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	2	no	—
779	C₃×C₄	—	2	2	no	—
780	C₃×C₄	—	4	2	no	—
781	C₃×C₄	—	4	2	no	—
782	C₃×C₄	—	4	2	no	—
783	C₃×C₄	—	4	2	no	—
784	C₃×C₄	—	4	2	no	—
785	C₃×C₄	—	4	2	no	—
786	C₃×C₄	—	4	2	no	—
787	C₃×C₄	—	4	2	no	—
788	C₃×C₄	—	4	2	no	—
789	C₃×C₄	—	4	2	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	4	4	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	4	4	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	C₂×C₃×#41	1	4	yes	—
815	C₂³	C₂×C₃×#41	1	2	yes	—
816	C₂³	C₂×C₃×#41	1	2	yes	—
817	C₂³	C₂×C₃×#41	1	2	yes	—
818	C₂³	C₂⁵×C₃	1	1	yes	characteristic
819	Q₈	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	8	4	no	—
823	D₄	—	8	4	no	—
824	C₂×C₄	—	2	8	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	C₂×C₃×#41	1	2	yes	—
876	C₂×C₄	C₂×C₃×#41	1	2	yes	—
877	C₂×C₄	C₂×C₃×#41	1	2	yes	—
878	C₂×C₄	C₂×C₃×#41	1	2	yes	—
879	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
880	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
881	C₂×C₃	—	2	4	no	—
882	C₂×C₃	—	4	4	no	—
883	C₂×C₃	—	8	2	no	—
884	C₂×C₃	C₂×#529	1	1	yes	characteristic
885	C₂×C₃	#3459	1	1	yes	characteristic
886	C₂×C₃	#3460	1	1	yes	characteristic
887	C₂×C₃	#3490	1	1	yes	characteristic
888	C₂×C₃	#3491	1	1	yes	characteristic
889	C₂×C₃	#3505	1	1	yes	characteristic
890	C₂×C₃	#3506	1	1	yes	characteristic
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	4	16	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	C₃×#529	1	4	yes	—
913	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
914	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
915	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
916	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
917	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
918	C₂²	C₃×#585	1	1	yes	characteristic
919	C₂²	C₃×#585	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₃	#35022	1	1	yes	characteristic, direct product factor, Sylow
937	C₂	—	2	4	no	—
938	C₂	—	4	4	no	—
939	C₂	—	8	2	no	—
940	C₂	C₂×C₃×#529	1	1	yes	characteristic
941	C₂	C₃×#3459	1	1	yes	characteristic
942	C₂	C₃×#3460	1	1	yes	characteristic
943	C₂	C₃×#3490	1	1	yes	characteristic
944	C₂	C₃×#3491	1	1	yes	characteristic
945	C₂	C₃×#3505	1	1	yes	characteristic
946	C₂	C₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2617	C₂
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×#2852	C₂	semidirect
2. C₃×#2849	C₂	semidirect
3. C₃×#2646	C₂	semidirect
4. C₃×#2639	C₂	semidirect
5. C₃×#2626	C₂	semidirect
7. C₃×#2573	C₂	semidirect
8. C₃×#2572	C₂	semidirect
9. C₃×#2554	C₂	semidirect
10. C₃×#2553	C₂	semidirect
11. C₃×#2516	C₂	semidirect
12. C₃×#2515	C₂	semidirect
13. C₃×#2458	C₂	semidirect
14. C₃×#2457	C₂	semidirect
15. C₃×#2321	C₂	semidirect
16. C₃×#2318	C₂	semidirect
17. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
18. C₃×C₄×#121	C₂	semidirect
19. C₂×C₃×C₄×C₂²⋊C₄	C₂	semidirect
20. #35022	C₃	direct (N × H)
22. C₂×C₃×#126	C₂²	semidirect
28. C₂×C₃×C₄×Q₈	C₂²	semidirect
30. C₂×C₃×C₄×D₄	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#400	C₂²	semidirect
37. C₃×#400	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
42. C₃×#397	C₂²	semidirect
47. C₃×#394	C₂²	semidirect
49. C₃×#393	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
54. C₃×#390	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
63. C₃×#388	C₂²	semidirect
64. C₃×#388	C₂²	semidirect
65. C₃×#388	C₂²	semidirect
66. C₃×#388	C₂²	semidirect
67. C₃×#387	C₂²	semidirect
68. C₃×#387	C₂²	semidirect
69. C₃×#387	C₂²	semidirect
70. C₃×#387	C₂²	semidirect
71. C₃×#387	C₂²	semidirect
72. C₃×#387	C₂²	semidirect
87. C₃×#383	C₂²	semidirect
88. C₃×#383	C₂²	semidirect
89. C₃×#382	C₂²	semidirect
92. C₃×#381	C₂²	semidirect
95. C₃×#380	C₂²	semidirect
97. C₃×C₄×C₄⋊C₄	C₂²	semidirect
98. C₃×C₄×C₄⋊C₄	C₂²	semidirect
99. C₃×C₄×C₄⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
108. #2852	C₂×C₃	semidirect
109. #2849	C₂×C₃	semidirect
110. #2646	C₂×C₃	semidirect
111. #2639	C₂×C₃	semidirect
112. #2626	C₂×C₃	semidirect
114. #2573	C₂×C₃	semidirect
115. #2572	C₂×C₃	semidirect
116. #2554	C₂×C₃	semidirect
117. #2553	C₂×C₃	semidirect
118. #2516	C₂×C₃	semidirect
119. #2515	C₂×C₃	semidirect
120. #2458	C₂×C₃	semidirect
121. #2457	C₂×C₃	semidirect
122. #2321	C₂×C₃	semidirect
123. #2318	C₂×C₃	semidirect
124. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
125. C₄×#121	C₂×C₃	semidirect
126. C₂×C₄×C₂²⋊C₄	C₂×C₃	semidirect
231. C₂×#126	C₂²×C₃	semidirect
237. C₂×C₄×Q₈	C₂²×C₃	semidirect
239. C₂×C₄×D₄	C₂²×C₃	semidirect
244. #400	C₂²×C₃	semidirect
245. #400	C₂²×C₃	semidirect
246. #400	C₂²×C₃	semidirect
248. #398	C₂²×C₃	semidirect
249. #398	C₂²×C₃	semidirect
251. #397	C₂²×C₃	semidirect
256. #394	C₂²×C₃	semidirect
258. #393	C₂²×C₃	semidirect
260. #391	C₂²×C₃	semidirect
263. #390	C₂²×C₃	semidirect
264. #389	C₂²×C₃	semidirect
265. #389	C₂²×C₃	semidirect
270. #388	C₂²×C₃	semidirect
271. #388	C₂²×C₃	semidirect
272. #388	C₂²×C₃	semidirect
273. #388	C₂²×C₃	semidirect
274. #388	C₂²×C₃	semidirect
275. #388	C₂²×C₃	semidirect
276. #387	C₂²×C₃	semidirect
277. #387	C₂²×C₃	semidirect
278. #387	C₂²×C₃	semidirect
279. #387	C₂²×C₃	semidirect
280. #387	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
296. #383	C₂²×C₃	semidirect
297. #383	C₂²×C₃	semidirect
298. #382	C₂²×C₃	semidirect
301. #381	C₂²×C₃	semidirect
304. #380	C₂²×C₃	semidirect
306. C₄×C₄⋊C₄	C₂²×C₃	semidirect
307. C₄×C₄⋊C₄	C₂²×C₃	semidirect
308. C₄×C₄⋊C₄	C₂²×C₃	semidirect
314. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
936. C₃	#35022	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×#2852	2
C₃×#2849	2
C₃×#2646	2
C₃×#2639	2
C₃×#2626	2
C₃×#2617	2
C₃×#2573	2
C₃×#2572	2
C₃×#2554	2
C₃×#2553	2
C₃×#2516	2
C₃×#2515	2
C₃×#2458	2
C₃×#2457	2
C₃×#2321	2
C₃×#2318	2
C₃×C₄×C₂²⋊Q₈	2
C₃×C₄×#121	2
C₂×C₃×C₄×C₂²⋊C₄	2
#35022	3

Subgroups — C3×#35022 #10653629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35022 #10653629