Subgroups — C₃×#40650 #10659257

Order 768.

1942 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2832	C₂	1	2	yes	maximal, complemented
2	C₃×#2743	C₂	1	2	yes	maximal, complemented
3	C₃×#2696	C₂	1	2	yes	maximal, complemented
4	C₃×#2684	C₂	1	2	yes	maximal, complemented
5	C₃×#2678	C₂	1	2	yes	maximal, complemented
6	C₃×#2665	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2650	C₂	1	2	yes	maximal, complemented
8	C₃×#2635	C₂	1	2	yes	maximal, complemented
9	C₃×#2534	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2516	C₂	1	2	yes	maximal, complemented
11	C₃×#2488	C₂	1	2	yes	maximal, complemented
12	C₃×#2461	C₂	1	2	yes	maximal, complemented
13	C₃×#2459	C₂	1	2	yes	maximal, complemented
14	C₃×#2444	C₂	1	2	yes	maximal, complemented
15	C₃×#2404	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2388	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
20	#40650	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
22	C₂×C₃×#124	C₂²	1	2	yes	—
23	C₂×C₃×#123	C₂²	1	2	yes	—
24	C₂×C₃×#123	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃×#121	C₂²	1	2	yes	—
27	C₂×C₃×#120	C₂²	1	2	yes	—
28	C₂×C₃×#120	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#400	C₂²	1	2	yes	complemented
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	complemented
39	C₃×#397	C₂²	1	2	yes	—
40	C₃×#397	C₂²	1	2	yes	—
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×#395	C₂²	1	1	yes	characteristic, complemented
46	C₃×#395	C₂²	1	2	yes	complemented
47	C₃×#394	C₂²	1	2	yes	—
48	C₃×#394	C₂²	1	2	yes	—
49	C₃×#394	C₂²	1	2	yes	—
50	C₃×#394	C₂²	1	2	yes	—
51	C₃×#394	C₂²	1	2	yes	—
52	C₃×#394	C₂²	1	2	yes	complemented
53	C₃×#394	C₂²	1	1	yes	characteristic, complemented
54	C₃×#393	C₂²	1	2	yes	—
55	C₃×#393	C₂²	1	2	yes	—
56	C₃×#393	C₂²	1	2	yes	—
57	C₃×#393	C₂²	1	1	yes	characteristic, complemented
58	C₃×#393	C₂²	1	2	yes	complemented
59	C₃×#392	C₂²	1	2	yes	—
60	C₃×#392	C₂²	1	2	yes	—
61	C₃×#392	C₂²	1	2	yes	—
62	C₃×#392	C₂²	1	1	yes	characteristic, complemented
63	C₃×#391	C₂²	1	2	yes	complemented
64	C₃×#391	C₂²	1	2	yes	complemented
65	C₃×#390	C₂²	1	2	yes	—
66	C₃×#390	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	complemented
76	C₃×#388	C₂²	1	2	yes	complemented
77	C₃×#388	C₂²	1	2	yes	complemented
78	C₃×#387	C₂²	1	2	yes	complemented
79	C₃×#387	C₂²	1	2	yes	complemented
80	C₃×#387	C₂²	1	2	yes	complemented
81	C₃×#386	C₂²	1	2	yes	—
82	C₃×#386	C₂²	1	2	yes	—
83	C₃×#386	C₂²	1	2	yes	—
84	C₃×#386	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#386	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	complemented
90	C₃×#385	C₂²	1	2	yes	complemented
91	C₃×#382	C₂²	1	1	yes	characteristic, complemented
92	C₃×#381	C₂²	1	1	yes	characteristic
93	C₃×#381	C₂²	1	1	yes	characteristic
94	C₃×#381	C₂²	1	2	yes	complemented
95	C₃×#381	C₂²	1	1	yes	characteristic, complemented
96	C₃×#381	C₂²	1	2	yes	complemented
97	C₃×#380	C₂²	1	1	yes	characteristic
98	C₃×#380	C₂²	1	2	yes	—
99	C₃×#379	C₂²	1	2	yes	—
100	C₃×#379	C₂²	1	1	yes	characteristic
101	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₃×#95	C₂²	1	2	yes	complemented
108	#2832	C₂×C₃	1	2	yes	complemented
109	#2743	C₂×C₃	1	2	yes	complemented
110	#2696	C₂×C₃	1	2	yes	complemented
111	#2684	C₂×C₃	1	2	yes	complemented
112	#2678	C₂×C₃	1	2	yes	complemented
113	#2665	C₂×C₃	1	1	yes	characteristic, complemented
114	#2650	C₂×C₃	1	2	yes	complemented
115	#2635	C₂×C₃	1	2	yes	complemented
116	#2534	C₂×C₃	1	1	yes	characteristic, complemented
117	#2516	C₂×C₃	1	2	yes	complemented
118	#2488	C₂×C₃	1	2	yes	complemented
119	#2461	C₂×C₃	1	2	yes	complemented
120	#2459	C₂×C₃	1	2	yes	complemented
121	#2444	C₂×C₃	1	2	yes	complemented
122	#2404	C₂×C₃	1	1	yes	characteristic, complemented
123	#2388	C₂×C₃	1	1	yes	characteristic, complemented
124	#2357	C₂×C₃	1	1	yes	characteristic, complemented
125	#2339	C₂×C₃	1	1	yes	characteristic, complemented
126	#2312	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂×C₃×#41	—	2	4	no	—
129	C₂×C₃×#41	—	4	4	no	—
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×Q₈	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
133	C₂²×C₃×D₄	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₃×D₄	C₂³	1	2	yes	—
136	C₂²×C₃×D₄	C₂³	1	2	yes	—
137	C₂²×C₃×D₄	C₂³	1	2	yes	—
138	C₂²×C₃×D₄	C₂³	1	2	yes	—
139	C₂³×C₃×C₄	C₂³	1	2	yes	—
140	C₂³×C₃×C₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
143	C₂³×C₃×C₄	C₂³	1	2	yes	—
144	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
145	C₃×#124	—	4	4	no	—
146	C₃×#123	—	4	4	no	—
147	C₃×#123	—	4	2	no	—
148	C₃×C₂²⋊Q₈	—	4	4	no	—
149	C₃×#121	—	4	4	no	—
150	C₃×#120	—	4	2	no	—
151	C₃×#120	—	4	4	no	—
152	C₃×C₄×D₄	—	2	4	no	—
153	C₃×C₄×D₄	—	4	4	no	—
154	C₃×C₄×D₄	—	4	4	no	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₂×C₃×C₄²	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	C₂³	1	2	yes	—
200	C₂×C₃×C₄²	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	1	yes	characteristic
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	1	yes	characteristic
206	C₃×#95	C₂³	1	1	yes	characteristic
207	C₃×#95	C₂³	1	1	yes	characteristic
208	C₃×#95	C₂³	1	1	yes	characteristic
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	1	yes	characteristic
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	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
228	C₂×#124	C₂²×C₃	1	2	yes	—
229	C₂×#123	C₂²×C₃	1	2	yes	—
230	C₂×#123	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
232	C₂×#121	C₂²×C₃	1	2	yes	—
233	C₂×#120	C₂²×C₃	1	2	yes	—
234	C₂×#120	C₂²×C₃	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
237	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
238	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
239	#400	C₂²×C₃	1	2	yes	complemented
240	#400	C₂²×C₃	1	2	yes	complemented
241	#400	C₂²×C₃	1	2	yes	complemented
242	#400	C₂²×C₃	1	2	yes	complemented
243	#400	C₂²×C₃	1	2	yes	complemented
244	#399	C₂²×C₃	1	2	yes	complemented
245	#397	C₂²×C₃	1	2	yes	—
246	#397	C₂²×C₃	1	2	yes	—
247	#397	C₂²×C₃	1	2	yes	—
248	#397	C₂²×C₃	1	2	yes	complemented
249	#396	C₂²×C₃	1	2	yes	—
250	#396	C₂²×C₃	1	2	yes	—
251	#395	C₂²×C₃	1	2	yes	complemented
252	#395	C₂²×C₃	1	1	yes	characteristic, complemented
253	#394	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	—
257	#394	C₂²×C₃	1	2	yes	—
258	#394	C₂²×C₃	1	2	yes	complemented
259	#394	C₂²×C₃	1	1	yes	characteristic, complemented
260	#393	C₂²×C₃	1	2	yes	—
261	#393	C₂²×C₃	1	2	yes	—
262	#393	C₂²×C₃	1	2	yes	—
263	#393	C₂²×C₃	1	1	yes	characteristic, complemented
264	#393	C₂²×C₃	1	2	yes	complemented
265	#392	C₂²×C₃	1	2	yes	—
266	#392	C₂²×C₃	1	2	yes	—
267	#392	C₂²×C₃	1	2	yes	—
268	#392	C₂²×C₃	1	1	yes	characteristic, complemented
269	#391	C₂²×C₃	1	2	yes	complemented
270	#391	C₂²×C₃	1	2	yes	complemented
271	#390	C₂²×C₃	1	2	yes	—
272	#390	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	—
274	#388	C₂²×C₃	1	2	yes	—
275	#388	C₂²×C₃	1	2	yes	—
276	#388	C₂²×C₃	1	2	yes	—
277	#388	C₂²×C₃	1	2	yes	—
278	#388	C₂²×C₃	1	2	yes	—
279	#388	C₂²×C₃	1	2	yes	—
280	#388	C₂²×C₃	1	2	yes	—
281	#388	C₂²×C₃	1	2	yes	complemented
282	#388	C₂²×C₃	1	2	yes	complemented
283	#388	C₂²×C₃	1	2	yes	complemented
284	#387	C₂²×C₃	1	2	yes	complemented
285	#387	C₂²×C₃	1	2	yes	complemented
286	#387	C₂²×C₃	1	2	yes	complemented
287	#386	C₂²×C₃	1	2	yes	—
288	#386	C₂²×C₃	1	2	yes	—
289	#386	C₂²×C₃	1	2	yes	—
290	#386	C₂²×C₃	1	2	yes	—
291	#386	C₂²×C₃	1	2	yes	—
292	#386	C₂²×C₃	1	2	yes	—
293	#386	C₂²×C₃	1	2	yes	—
294	#386	C₂²×C₃	1	2	yes	—
295	#386	C₂²×C₃	1	2	yes	complemented
296	#385	C₂²×C₃	1	2	yes	complemented
297	#382	C₂²×C₃	1	1	yes	characteristic, complemented
298	#381	C₂²×C₃	1	1	yes	characteristic
299	#381	C₂²×C₃	1	1	yes	characteristic
300	#381	C₂²×C₃	1	2	yes	complemented
301	#381	C₂²×C₃	1	1	yes	characteristic, complemented
302	#381	C₂²×C₃	1	2	yes	complemented
303	#380	C₂²×C₃	1	2	yes	—
304	#380	C₂²×C₃	1	1	yes	characteristic
305	#379	C₂²×C₃	1	2	yes	—
306	#379	C₂²×C₃	1	1	yes	characteristic
307	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
308	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
311	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
313	C₂×#95	C₂²×C₃	1	2	yes	complemented
314	C₂⁴×C₃	—	2	2	no	—
315	C₂⁴×C₃	—	4	2	no	—
316	C₂⁴×C₃	—	4	1	no	—
317	C₂⁴×C₃	—	4	1	no	—
318	C₂⁴×C₃	—	4	2	no	—
319	C₂⁴×C₃	C₂⁴	1	2	yes	—
320	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
321	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
322	C₂⁴×C₃	C₂⁴	1	2	yes	—
323	C₃×#41	—	4	16	no	—
324	C₂×C₃×Q₈	—	2	2	no	—
325	C₂×C₃×Q₈	—	4	2	no	—
326	C₂×C₃×Q₈	—	4	2	no	—
327	C₂×C₃×Q₈	—	4	2	no	—
328	C₂×C₃×Q₈	—	4	2	no	—
329	C₂×C₃×D₄	—	2	4	no	—
330	C₂×C₃×D₄	—	2	2	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	4	no	—
336	C₂×C₃×D₄	—	2	2	no	—
337	C₂×C₃×D₄	—	2	2	no	—
338	C₂×C₃×D₄	—	4	1	no	—
339	C₂×C₃×D₄	—	4	2	no	—
340	C₂×C₃×D₄	—	4	2	no	—
341	C₂×C₃×D₄	—	4	2	no	—
342	C₂×C₃×D₄	—	4	2	no	—
343	C₂×C₃×D₄	—	4	2	no	—
344	C₂×C₃×D₄	—	4	2	no	—
345	C₂×C₃×D₄	—	4	2	no	—
346	C₂×C₃×D₄	—	4	2	no	—
347	C₂×C₃×D₄	—	4	2	no	—
348	C₂×C₃×D₄	—	4	2	no	—
349	C₂²×C₃×C₄	—	2	4	no	—
350	C₂²×C₃×C₄	—	2	2	no	—
351	C₂²×C₃×C₄	—	2	4	no	—
352	C₂²×C₃×C₄	—	2	4	no	—
353	C₂²×C₃×C₄	—	2	2	no	—
354	C₂²×C₃×C₄	—	4	2	no	—
355	C₂²×C₃×C₄	—	4	2	no	—
356	C₂²×C₃×C₄	—	4	2	no	—
357	C₂²×C₃×C₄	—	4	2	no	—
358	C₂²×C₃×C₄	—	4	2	no	—
359	C₂²×C₃×C₄	—	4	2	no	—
360	C₂²×C₃×C₄	—	4	1	no	—
361	C₂²×C₃×C₄	—	4	1	no	—
362	C₂²×C₃×C₄	—	4	2	no	—
363	C₂²×C₃×C₄	—	4	2	no	—
364	C₂²×C₃×C₄	#41	1	4	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
366	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
368	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂²×C₃×C₄	C₂⁴	1	2	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	1	yes	characteristic
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₃×C₄⋊C₄	—	2	2	no	—
381	C₃×C₄⋊C₄	—	2	4	no	—
382	C₃×C₄⋊C₄	—	2	4	no	—
383	C₃×C₄⋊C₄	—	4	2	no	—
384	C₃×C₄⋊C₄	—	4	2	no	—
385	C₃×C₄⋊C₄	—	4	2	no	—
386	C₃×C₄⋊C₄	—	4	2	no	—
387	C₃×C₄⋊C₄	—	4	2	no	—
388	C₃×C₄⋊C₄	—	4	2	no	—
389	C₃×C₄⋊C₄	—	4	2	no	—
390	C₃×C₄⋊C₄	—	4	2	no	—
391	C₃×C₂²⋊C₄	—	2	2	no	—
392	C₃×C₂²⋊C₄	—	2	4	no	—
393	C₃×C₂²⋊C₄	—	2	4	no	—
394	C₃×C₂²⋊C₄	—	2	4	no	—
395	C₃×C₂²⋊C₄	—	2	4	no	—
396	C₃×C₂²⋊C₄	—	2	2	no	—
397	C₃×C₂²⋊C₄	—	2	4	no	—
398	C₃×C₂²⋊C₄	—	2	4	no	—
399	C₃×C₂²⋊C₄	—	4	2	no	—
400	C₃×C₂²⋊C₄	—	4	2	no	—
401	C₃×C₂²⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	4	2	no	—
403	C₃×C₂²⋊C₄	—	4	2	no	—
404	C₃×C₂²⋊C₄	—	4	2	no	—
405	C₃×C₂²⋊C₄	—	4	2	no	—
406	C₃×C₂²⋊C₄	—	4	2	no	—
407	C₃×C₂²⋊C₄	—	4	2	no	—
408	C₃×C₂²⋊C₄	—	4	2	no	—
409	C₃×C₂²⋊C₄	—	4	2	no	—
410	C₃×C₂²⋊C₄	—	4	1	no	—
411	C₃×C₂²⋊C₄	—	4	2	no	—
412	C₃×C₂²⋊C₄	—	4	2	no	—
413	C₃×C₂²⋊C₄	—	4	2	no	—
414	C₃×C₂²⋊C₄	—	4	2	no	—
415	C₃×C₂²⋊C₄	—	4	2	no	—
416	C₃×C₂²⋊C₄	—	4	2	no	—
417	C₃×C₂²⋊C₄	—	4	1	no	—
418	C₃×C₂²⋊C₄	—	4	2	no	—
419	C₃×C₂²⋊C₄	—	4	2	no	—
420	C₃×C₄²	—	2	2	no	—
421	C₃×C₄²	—	4	2	no	—
422	C₃×C₄²	—	4	2	no	—
423	C₃×C₄²	—	4	2	no	—
424	C₃×C₄²	—	4	2	no	—
425	C₂⁵	C₂³×C₃	1	1	yes	characteristic
426	C₂×#41	—	2	4	no	—
427	C₂×#41	—	4	4	no	—
428	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₃	1	2	yes	—
430	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₃	1	2	yes	—
433	C₂²×D₄	C₂³×C₃	1	2	yes	—
434	C₂²×D₄	C₂³×C₃	1	2	yes	—
435	C₂²×D₄	C₂³×C₃	1	2	yes	—
436	C₂²×D₄	C₂³×C₃	1	2	yes	—
437	C₂³×C₄	C₂³×C₃	1	2	yes	—
438	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₃	1	2	yes	—
441	C₂³×C₄	C₂³×C₃	1	2	yes	—
442	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
443	#124	—	4	4	no	—
444	#123	—	4	4	no	—
445	#123	—	4	2	no	—
446	C₂²⋊Q₈	—	4	4	no	—
447	#121	—	4	4	no	—
448	#120	—	4	2	no	—
449	#120	—	4	4	no	—
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	4	4	no	—
452	C₄×D₄	—	4	4	no	—
453	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
464	C₂×C₂²⋊C₄	—	2	4	no	—
465	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
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×C₄²	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₃	1	2	yes	—
496	C₂×C₄²	C₂³×C₃	1	2	yes	—
497	C₂×C₄²	C₂³×C₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₃	1	2	yes	—
499	#95	C₂³×C₃	1	1	yes	characteristic
500	#95	C₂³×C₃	1	2	yes	—
501	#95	C₂³×C₃	1	2	yes	—
502	#95	C₂³×C₃	1	2	yes	—
503	#95	C₂³×C₃	1	1	yes	characteristic
504	#95	C₂³×C₃	1	1	yes	characteristic
505	#95	C₂³×C₃	1	1	yes	characteristic
506	#95	C₂³×C₃	1	1	yes	characteristic
507	#95	C₂³×C₃	1	2	yes	—
508	#95	C₂³×C₃	1	2	yes	—
509	#95	C₂³×C₃	1	1	yes	characteristic
510	#95	C₂³×C₃	1	2	yes	—
511	#95	C₂³×C₃	1	2	yes	—
512	#95	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	C₂³×C₃	—	2	2	no	—
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	2	1	no	—
528	C₂³×C₃	—	2	2	no	—
529	C₂³×C₃	—	2	2	no	—
530	C₂³×C₃	—	2	2	no	—
531	C₂³×C₃	—	2	2	no	—
532	C₂³×C₃	—	2	2	no	—
533	C₂³×C₃	—	2	2	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂³×C₃	—	2	2	no	—
536	C₂³×C₃	—	2	1	no	—
537	C₂³×C₃	—	2	2	no	—
538	C₂³×C₃	—	2	2	no	—
539	C₂³×C₃	—	2	2	no	—
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	—	2	2	no	—
542	C₂³×C₃	—	2	2	no	—
543	C₂³×C₃	—	2	2	no	—
544	C₂³×C₃	—	2	2	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	4	4	no	—
548	C₂³×C₃	—	8	2	no	—
549	C₂³×C₃	—	8	2	no	—
550	C₂³×C₃	—	8	4	no	—
551	C₂³×C₃	—	8	4	no	—
552	C₂³×C₃	C₂×#41	1	2	yes	—
553	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
554	C₂³×C₃	C₂⁵	1	1	yes	characteristic
555	C₃×Q₈	—	4	4	no	—
556	C₃×Q₈	—	8	4	no	—
557	C₃×D₄	—	2	8	no	—
558	C₃×D₄	—	4	4	no	—
559	C₃×D₄	—	4	8	no	—
560	C₃×D₄	—	4	8	no	—
561	C₃×D₄	—	8	4	no	—
562	C₃×D₄	—	8	4	no	—
563	C₃×D₄	—	8	4	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	2	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	2	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	2	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	2	2	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	—	4	4	no	—
603	C₂×C₃×C₄	—	4	8	no	—
604	C₂×C₃×C₄	—	8	2	no	—
605	C₂×C₃×C₄	—	8	2	no	—
606	C₂×C₃×C₄	—	8	4	no	—
607	C₂×C₃×C₄	—	8	4	no	—
608	C₂×C₃×C₄	C₂×#41	1	2	yes	—
609	C₂×C₃×C₄	C₂×#41	1	2	yes	—
610	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	4	2	no	—
613	C₂⁴	—	4	1	no	—
614	C₂⁴	—	4	2	no	—
615	C₂⁴	—	4	1	no	—
616	C₂⁴	C₂⁴×C₃	1	2	yes	—
617	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
618	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
619	C₂⁴	C₂⁴×C₃	1	2	yes	—
620	#41	—	4	16	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	4	2	no	—
623	C₂×Q₈	—	4	2	no	—
624	C₂×Q₈	—	4	2	no	—
625	C₂×Q₈	—	4	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	C₃×#41	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	4	1	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	1	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	2	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	2	no	—
722	C₂²×C₃	—	2	2	no	—
723	C₂²×C₃	—	2	4	no	—
724	C₂²×C₃	—	2	2	no	—
725	C₂²×C₃	—	2	2	no	—
726	C₂²×C₃	—	2	4	no	—
727	C₂²×C₃	—	2	4	no	—
728	C₂²×C₃	—	4	2	no	—
729	C₂²×C₃	—	4	2	no	—
730	C₂²×C₃	—	4	2	no	—
731	C₂²×C₃	—	4	2	no	—
732	C₂²×C₃	—	4	2	no	—
733	C₂²×C₃	—	4	2	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	2	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	2	no	—
738	C₂²×C₃	—	4	1	no	—
739	C₂²×C₃	—	4	2	no	—
740	C₂²×C₃	—	4	2	no	—
741	C₂²×C₃	—	4	2	no	—
742	C₂²×C₃	—	4	2	no	—
743	C₂²×C₃	—	4	2	no	—
744	C₂²×C₃	—	4	2	no	—
745	C₂²×C₃	—	4	2	no	—
746	C₂²×C₃	—	8	8	no	—
747	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
748	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
749	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂²×C₃	#585	1	2	yes	—
751	C₂²×C₃	#585	1	1	yes	characteristic
752	C₃×C₄	—	2	2	no	—
753	C₃×C₄	—	2	2	no	—
754	C₃×C₄	—	2	2	no	—
755	C₃×C₄	—	4	1	no	—
756	C₃×C₄	—	4	2	no	—
757	C₃×C₄	—	4	1	no	—
758	C₃×C₄	—	4	2	no	—
759	C₃×C₄	—	4	2	no	—
760	C₃×C₄	—	4	2	no	—
761	C₃×C₄	—	4	2	no	—
762	C₃×C₄	—	4	2	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	—	4	2	no	—
766	C₃×C₄	—	4	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	8	2	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	4	no	—
793	C₂³	—	8	4	no	—
794	C₂³	C₂×C₃×#41	1	2	yes	—
795	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
796	C₂³	C₂⁵×C₃	1	1	yes	characteristic
797	Q₈	—	4	4	no	—
798	Q₈	—	8	4	no	—
799	D₄	—	2	8	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	8	no	—
803	D₄	—	8	4	no	—
804	D₄	—	8	4	no	—
805	D₄	—	8	4	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	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	—	4	4	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	C₂×C₃×#41	1	2	yes	—
851	C₂×C₄	C₂×C₃×#41	1	2	yes	—
852	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
853	C₂×C₃	—	4	4	no	—
854	C₂×C₃	—	4	2	no	—
855	C₂×C₃	—	8	1	no	—
856	C₂×C₃	—	8	2	no	—
857	C₂×C₃	#3455	1	1	yes	characteristic
858	C₂×C₃	#3490	1	1	yes	characteristic
859	C₂×C₃	#3494	1	1	yes	characteristic
860	C₂×C₃	#3533	1	2	yes	—
861	C₂×C₃	#3558	1	2	yes	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	8	8	no	—
887	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
888	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
889	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂²	C₃×#585	1	2	yes	—
891	C₂²	C₃×#585	1	1	yes	characteristic
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₃	#40650	1	1	yes	characteristic, direct product factor, Sylow
908	C₂	—	4	2	no	—
909	C₂	—	4	4	no	—
910	C₂	—	8	2	no	—
911	C₂	—	8	1	no	—
912	C₂	C₃×#3455	1	1	yes	characteristic
913	C₂	C₃×#3490	1	1	yes	characteristic
914	C₂	C₃×#3494	1	1	yes	characteristic
915	C₂	C₃×#3533	1	2	yes	—
916	C₂	C₃×#3558	1	2	yes	—

	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×#2832	C₂	semidirect
2. C₃×#2743	C₂	semidirect
3. C₃×#2696	C₂	semidirect
4. C₃×#2684	C₂	semidirect
5. C₃×#2678	C₂	semidirect
6. C₃×#2665	C₂	semidirect
7. C₃×#2650	C₂	semidirect
8. C₃×#2635	C₂	semidirect
9. C₃×#2534	C₂	semidirect
10. C₃×#2516	C₂	semidirect
11. C₃×#2488	C₂	semidirect
12. C₃×#2461	C₂	semidirect
13. C₃×#2459	C₂	semidirect
14. C₃×#2444	C₂	semidirect
15. C₃×#2404	C₂	semidirect
16. C₃×#2388	C₂	semidirect
17. C₃×#2357	C₂	semidirect
18. C₃×#2339	C₂	semidirect
19. C₃×#2312	C₂	semidirect
20. #40650	C₃	direct (N × H)
25. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₃×C₄×D₄	C₂²	semidirect
31. C₂×C₃×C₄×D₄	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#400	C₂²	semidirect
37. C₃×#400	C₂²	semidirect
38. C₃×#399	C₂²	semidirect
42. C₃×#397	C₂²	semidirect
45. C₃×#395	C₂²	semidirect
46. C₃×#395	C₂²	semidirect
52. C₃×#394	C₂²	semidirect
53. C₃×#394	C₂²	semidirect
57. C₃×#393	C₂²	semidirect
58. C₃×#393	C₂²	semidirect
62. C₃×#392	C₂²	semidirect
63. C₃×#391	C₂²	semidirect
64. C₃×#391	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#387	C₂²	semidirect
79. C₃×#387	C₂²	semidirect
80. C₃×#387	C₂²	semidirect
89. C₃×#386	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#382	C₂²	semidirect
94. C₃×#381	C₂²	semidirect
95. C₃×#381	C₂²	semidirect
96. C₃×#381	C₂²	semidirect
101. C₃×C₄×C₄⋊C₄	C₂²	semidirect
102. C₃×C₄×C₄⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. #2832	C₂×C₃	semidirect
109. #2743	C₂×C₃	semidirect
110. #2696	C₂×C₃	semidirect
111. #2684	C₂×C₃	semidirect
112. #2678	C₂×C₃	semidirect
113. #2665	C₂×C₃	semidirect
114. #2650	C₂×C₃	semidirect
115. #2635	C₂×C₃	semidirect
116. #2534	C₂×C₃	semidirect
117. #2516	C₂×C₃	semidirect
118. #2488	C₂×C₃	semidirect
119. #2461	C₂×C₃	semidirect
120. #2459	C₂×C₃	semidirect
121. #2444	C₂×C₃	semidirect
122. #2404	C₂×C₃	semidirect
123. #2388	C₂×C₃	semidirect
124. #2357	C₂×C₃	semidirect
125. #2339	C₂×C₃	semidirect
126. #2312	C₂×C₃	semidirect
231. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
236. C₂×C₄×D₄	C₂²×C₃	semidirect
237. C₂×C₄×D₄	C₂²×C₃	semidirect
239. #400	C₂²×C₃	semidirect
240. #400	C₂²×C₃	semidirect
241. #400	C₂²×C₃	semidirect
242. #400	C₂²×C₃	semidirect
243. #400	C₂²×C₃	semidirect
244. #399	C₂²×C₃	semidirect
248. #397	C₂²×C₃	semidirect
251. #395	C₂²×C₃	semidirect
252. #395	C₂²×C₃	semidirect
258. #394	C₂²×C₃	semidirect
259. #394	C₂²×C₃	semidirect
263. #393	C₂²×C₃	semidirect
264. #393	C₂²×C₃	semidirect
268. #392	C₂²×C₃	semidirect
269. #391	C₂²×C₃	semidirect
270. #391	C₂²×C₃	semidirect
281. #388	C₂²×C₃	semidirect
282. #388	C₂²×C₃	semidirect
283. #388	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
285. #387	C₂²×C₃	semidirect
286. #387	C₂²×C₃	semidirect
295. #386	C₂²×C₃	semidirect
296. #385	C₂²×C₃	semidirect
297. #382	C₂²×C₃	semidirect
300. #381	C₂²×C₃	semidirect
301. #381	C₂²×C₃	semidirect
302. #381	C₂²×C₃	semidirect
307. C₄×C₄⋊C₄	C₂²×C₃	semidirect
308. C₄×C₄⋊C₄	C₂²×C₃	semidirect
311. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
312. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
313. C₂×#95	C₂²×C₃	semidirect
907. C₃	#40650	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×#2832	2
C₃×#2743	2
C₃×#2696	2
C₃×#2684	2
C₃×#2678	2
C₃×#2665	2
C₃×#2650	2
C₃×#2635	2
C₃×#2534	2
C₃×#2516	2
C₃×#2488	2
C₃×#2461	2
C₃×#2459	2
C₃×#2444	2
C₃×#2404	2
C₃×#2388	2
C₃×#2357	2
C₃×#2339	2
C₃×#2312	2
#40650	3

Subgroups — C3×#40650 #10659257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40650 #10659257