Subgroups — C₃×#40612 #10659219

Order 768.

2066 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2842	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2841	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2780	C₂	1	2	yes	maximal, complemented
4	C₃×#2748	C₂	1	2	yes	maximal, complemented
5	C₃×#2732	C₂	1	2	yes	maximal, complemented
6	C₃×#2692	C₂	1	2	yes	maximal, complemented
7	C₃×#2667	C₂	1	2	yes	maximal, complemented
8	C₃×#2626	C₂	1	2	yes	maximal, complemented
9	C₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2607	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2579	C₂	1	2	yes	maximal, complemented
12	C₃×#2450	C₂	1	2	yes	maximal, complemented
13	C₃×#2449	C₂	1	2	yes	maximal, complemented
14	C₃×#2437	C₂	1	2	yes	maximal, complemented
15	C₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2417	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal
19	C₃×#2308	C₂	1	1	yes	maximal, characteristic
20	#40612	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
29	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×#400	C₂²	1	2	yes	complemented
36	C₃×#399	C₂²	1	2	yes	—
37	C₃×#399	C₂²	1	1	yes	characteristic
38	C₃×#399	C₂²	1	1	yes	characteristic
39	C₃×#399	C₂²	1	1	yes	characteristic
40	C₃×#399	C₂²	1	2	yes	—
41	C₃×#399	C₂²	1	2	yes	complemented
42	C₃×#399	C₂²	1	1	yes	characteristic, complemented
43	C₃×#399	C₂²	1	2	yes	complemented
44	C₃×#399	C₂²	1	1	yes	characteristic, complemented
45	C₃×#399	C₂²	1	1	yes	characteristic, complemented
46	C₃×#398	C₂²	1	2	yes	complemented
47	C₃×#398	C₂²	1	2	yes	complemented
48	C₃×#398	C₂²	1	2	yes	complemented
49	C₃×#398	C₂²	1	2	yes	complemented
50	C₃×#398	C₂²	1	2	yes	complemented
51	C₃×#398	C₂²	1	2	yes	complemented
52	C₃×#396	C₂²	1	2	yes	—
53	C₃×#396	C₂²	1	2	yes	—
54	C₃×#396	C₂²	1	2	yes	—
55	C₃×#396	C₂²	1	2	yes	complemented
56	C₃×#396	C₂²	1	2	yes	complemented
57	C₃×#396	C₂²	1	2	yes	complemented
58	C₃×#396	C₂²	1	2	yes	complemented
59	C₃×#396	C₂²	1	2	yes	complemented
60	C₃×#396	C₂²	1	2	yes	complemented
61	C₃×#396	C₂²	1	2	yes	complemented
62	C₃×#395	C₂²	1	2	yes	complemented
63	C₃×#393	C₂²	1	1	yes	characteristic
64	C₃×#393	C₂²	1	2	yes	—
65	C₃×#393	C₂²	1	1	yes	characteristic, complemented
66	C₃×#393	C₂²	1	2	yes	complemented
67	C₃×#391	C₂²	1	2	yes	complemented
68	C₃×#391	C₂²	1	2	yes	complemented
69	C₃×#390	C₂²	1	2	yes	—
70	C₃×#390	C₂²	1	2	yes	—
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#389	C₂²	1	2	yes	complemented
73	C₃×#387	C₂²	1	2	yes	complemented
74	C₃×#387	C₂²	1	2	yes	complemented
75	C₃×#387	C₂²	1	2	yes	complemented
76	C₃×#387	C₂²	1	2	yes	complemented
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×#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×#385	C₂²	1	2	yes	complemented
86	C₃×#385	C₂²	1	2	yes	complemented
87	C₃×#385	C₂²	1	2	yes	complemented
88	C₃×#385	C₂²	1	2	yes	complemented
89	C₃×#385	C₂²	1	2	yes	complemented
90	C₃×#385	C₂²	1	2	yes	complemented
91	C₃×#385	C₂²	1	2	yes	complemented
92	C₃×#385	C₂²	1	2	yes	complemented
93	C₃×#385	C₂²	1	2	yes	complemented
94	C₃×#381	C₂²	1	1	yes	characteristic
95	C₃×#381	C₂²	1	1	yes	characteristic
96	C₃×#380	C₂²	1	2	yes	—
97	C₃×#380	C₂²	1	1	yes	characteristic, complemented
98	C₃×#380	C₂²	1	2	yes	complemented
99	C₃×#380	C₂²	1	2	yes	complemented
100	C₃×#380	C₂²	1	2	yes	complemented
101	C₃×#380	C₂²	1	2	yes	complemented
102	C₃×#379	C₂²	1	1	yes	characteristic
103	C₃×#379	C₂²	1	2	yes	—
104	C₃×#379	C₂²	1	2	yes	—
105	C₃×#379	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
108	#2842	C₂×C₃	1	1	yes	characteristic, complemented
109	#2841	C₂×C₃	1	1	yes	characteristic, complemented
110	#2780	C₂×C₃	1	2	yes	complemented
111	#2748	C₂×C₃	1	2	yes	complemented
112	#2732	C₂×C₃	1	2	yes	complemented
113	#2692	C₂×C₃	1	2	yes	complemented
114	#2667	C₂×C₃	1	2	yes	complemented
115	#2626	C₂×C₃	1	1	yes	characteristic, complemented
116	#2626	C₂×C₃	1	2	yes	complemented
117	#2607	C₂×C₃	1	1	yes	characteristic, complemented
118	#2579	C₂×C₃	1	2	yes	complemented
119	#2450	C₂×C₃	1	2	yes	complemented
120	#2449	C₂×C₃	1	2	yes	complemented
121	#2437	C₂×C₃	1	2	yes	complemented
122	#2437	C₂×C₃	1	1	yes	characteristic, complemented
123	#2417	C₂×C₃	1	2	yes	complemented
124	C₂×#399	C₂×C₃	1	1	yes	characteristic, complemented
125	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
126	#2308	C₂×C₃	1	1	yes	characteristic
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×D₄	—	4	2	no	—
132	C₂²×C₃×D₄	—	4	2	no	—
133	C₂²×C₃×D₄	Q₈	1	8	yes	complemented
134	C₂²×C₃×D₄	C₂³	1	2	yes	—
135	C₂²×C₃×D₄	C₂³	1	2	yes	—
136	C₂³×C₃×C₄	C₂³	1	2	yes	—
137	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂³	1	2	yes	—
139	C₂³×C₃×C₄	C₂³	1	2	yes	—
140	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂³	1	2	yes	—
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
144	C₃×C₂²⋊Q₈	—	4	4	no	—
145	C₃×C₂²⋊Q₈	—	4	2	no	—
146	C₃×C₂²⋊Q₈	—	4	4	no	—
147	C₃×C₂²⋊Q₈	—	4	4	no	—
148	C₃×C₂²⋊Q₈	—	4	4	no	—
149	C₃×C₄×D₄	—	4	4	no	—
150	C₃×C₄×D₄	—	4	4	no	—
151	C₂×C₃×C₄⋊C₄	—	4	4	no	—
152	C₂×C₃×C₄⋊C₄	—	4	2	no	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
177	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
178	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
179	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
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	1	yes	characteristic
194	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊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	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄²	C₂³	1	2	yes	—
208	C₂×C₃×C₄²	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
232	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
234	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
235	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
236	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
238	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
239	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
240	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
244	#400	C₂²×C₃	1	2	yes	complemented
245	#399	C₂²×C₃	1	1	yes	characteristic
246	#399	C₂²×C₃	1	1	yes	characteristic
247	#399	C₂²×C₃	1	2	yes	—
248	#399	C₂²×C₃	1	1	yes	characteristic
249	#399	C₂²×C₃	1	2	yes	—
250	#399	C₂²×C₃	1	2	yes	complemented
251	#399	C₂²×C₃	1	1	yes	characteristic, complemented
252	#399	C₂²×C₃	1	2	yes	complemented
253	#399	C₂²×C₃	1	1	yes	characteristic, complemented
254	#399	C₂²×C₃	1	1	yes	characteristic, complemented
255	#398	C₂²×C₃	1	2	yes	complemented
256	#398	C₂²×C₃	1	2	yes	complemented
257	#398	C₂²×C₃	1	2	yes	complemented
258	#398	C₂²×C₃	1	2	yes	complemented
259	#398	C₂²×C₃	1	2	yes	complemented
260	#398	C₂²×C₃	1	2	yes	complemented
261	#396	C₂²×C₃	1	2	yes	—
262	#396	C₂²×C₃	1	2	yes	—
263	#396	C₂²×C₃	1	2	yes	—
264	#396	C₂²×C₃	1	2	yes	complemented
265	#396	C₂²×C₃	1	2	yes	complemented
266	#396	C₂²×C₃	1	2	yes	complemented
267	#396	C₂²×C₃	1	2	yes	complemented
268	#396	C₂²×C₃	1	2	yes	complemented
269	#396	C₂²×C₃	1	2	yes	complemented
270	#396	C₂²×C₃	1	2	yes	complemented
271	#395	C₂²×C₃	1	2	yes	complemented
272	#393	C₂²×C₃	1	1	yes	characteristic
273	#393	C₂²×C₃	1	2	yes	—
274	#393	C₂²×C₃	1	1	yes	characteristic, complemented
275	#393	C₂²×C₃	1	2	yes	complemented
276	#391	C₂²×C₃	1	2	yes	complemented
277	#391	C₂²×C₃	1	2	yes	complemented
278	#390	C₂²×C₃	1	2	yes	—
279	#390	C₂²×C₃	1	2	yes	—
280	#389	C₂²×C₃	1	2	yes	complemented
281	#389	C₂²×C₃	1	2	yes	complemented
282	#387	C₂²×C₃	1	2	yes	complemented
283	#387	C₂²×C₃	1	2	yes	complemented
284	#387	C₂²×C₃	1	2	yes	complemented
285	#387	C₂²×C₃	1	2	yes	complemented
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	#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	#385	C₂²×C₃	1	2	yes	complemented
295	#385	C₂²×C₃	1	2	yes	complemented
296	#385	C₂²×C₃	1	2	yes	complemented
297	#385	C₂²×C₃	1	2	yes	complemented
298	#385	C₂²×C₃	1	2	yes	complemented
299	#385	C₂²×C₃	1	2	yes	complemented
300	#385	C₂²×C₃	1	2	yes	complemented
301	#385	C₂²×C₃	1	2	yes	complemented
302	#385	C₂²×C₃	1	2	yes	complemented
303	#381	C₂²×C₃	1	1	yes	characteristic
304	#381	C₂²×C₃	1	1	yes	characteristic
305	#380	C₂²×C₃	1	2	yes	—
306	#380	C₂²×C₃	1	2	yes	complemented
307	#380	C₂²×C₃	1	1	yes	characteristic, complemented
308	#380	C₂²×C₃	1	2	yes	complemented
309	#380	C₂²×C₃	1	2	yes	complemented
310	#380	C₂²×C₃	1	2	yes	complemented
311	#379	C₂²×C₃	1	1	yes	characteristic
312	#379	C₂²×C₃	1	1	yes	characteristic
313	#379	C₂²×C₃	1	2	yes	—
314	#379	C₂²×C₃	1	2	yes	—
315	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
316	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
317	C₂⁴×C₃	—	2	2	no	—
318	C₂⁴×C₃	—	2	2	no	—
319	C₂⁴×C₃	—	4	2	no	—
320	C₂⁴×C₃	—	4	2	no	—
321	C₂⁴×C₃	—	4	2	no	—
322	C₂⁴×C₃	—	4	2	no	—
323	C₂⁴×C₃	—	4	1	no	—
324	C₂⁴×C₃	—	4	1	no	—
325	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
326	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
327	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
328	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
329	C₂⁴×C₃	C₂⁴	1	2	yes	—
330	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
331	C₂×C₃×Q₈	—	2	4	no	—
332	C₂×C₃×Q₈	—	4	2	no	—
333	C₂×C₃×Q₈	—	4	2	no	—
334	C₂×C₃×Q₈	—	4	1	no	—
335	C₂×C₃×Q₈	—	4	2	no	—
336	C₂×C₃×D₄	—	2	4	no	—
337	C₂×C₃×D₄	—	2	4	no	—
338	C₂×C₃×D₄	—	4	2	no	—
339	C₂×C₃×D₄	—	4	2	no	—
340	C₂×C₃×D₄	—	4	16	no	—
341	C₂×C₃×D₄	C₂×Q₈	1	8	yes	—
342	C₂×C₃×D₄	C₂×Q₈	1	8	yes	—
343	C₂²×C₃×C₄	—	2	2	no	—
344	C₂²×C₃×C₄	—	2	4	no	—
345	C₂²×C₃×C₄	—	2	2	no	—
346	C₂²×C₃×C₄	—	2	4	no	—
347	C₂²×C₃×C₄	—	2	4	no	—
348	C₂²×C₃×C₄	—	2	4	no	—
349	C₂²×C₃×C₄	—	4	2	no	—
350	C₂²×C₃×C₄	—	4	2	no	—
351	C₂²×C₃×C₄	—	4	1	no	—
352	C₂²×C₃×C₄	—	4	1	no	—
353	C₂²×C₃×C₄	—	4	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	2	no	—
361	C₂²×C₃×C₄	—	4	2	no	—
362	C₂²×C₃×C₄	—	4	2	no	—
363	C₂²×C₃×C₄	—	4	2	no	—
364	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₃×C₄⋊C₄	—	2	4	no	—
381	C₃×C₄⋊C₄	—	2	4	no	—
382	C₃×C₄⋊C₄	—	2	4	no	—
383	C₃×C₄⋊C₄	—	4	1	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	1	no	—
388	C₃×C₄⋊C₄	—	4	2	no	—
389	C₃×C₄⋊C₄	—	4	2	no	—
390	C₃×C₄⋊C₄	—	4	2	no	—
391	C₃×C₄⋊C₄	—	4	2	no	—
392	C₃×C₄⋊C₄	—	4	2	no	—
393	C₃×C₄⋊C₄	—	4	2	no	—
394	C₃×C₄⋊C₄	—	4	1	no	—
395	C₃×C₄⋊C₄	—	4	2	no	—
396	C₃×C₄⋊C₄	—	4	2	no	—
397	C₃×C₄⋊C₄	—	4	2	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×C₄⋊C₄	—	4	2	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	—	4	2	no	—
410	C₃×C₂²⋊C₄	—	4	2	no	—
411	C₃×C₂²⋊C₄	—	4	1	no	—
412	C₃×C₂²⋊C₄	—	4	2	no	—
413	C₃×C₂²⋊C₄	—	4	1	no	—
414	C₃×C₂²⋊C₄	—	4	2	no	—
415	C₃×C₂²⋊C₄	—	4	1	no	—
416	C₃×C₂²⋊C₄	—	4	1	no	—
417	C₃×C₂²⋊C₄	—	4	1	no	—
418	C₃×C₂²⋊C₄	—	4	1	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×C₂²⋊C₄	—	4	2	no	—
426	C₃×C₂²⋊C₄	—	4	2	no	—
427	C₃×C₂²⋊C₄	—	4	2	no	—
428	C₃×C₂²⋊C₄	—	4	2	no	—
429	C₃×C₂²⋊C₄	—	4	2	no	—
430	C₃×C₄²	—	4	2	no	—
431	C₃×C₄²	—	4	2	no	—
432	C₂⁵	C₂³×C₃	1	1	yes	characteristic
433	C₂⁵	C₂³×C₃	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₃	1	2	yes	—
435	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
436	C₂²×D₄	—	4	2	no	—
437	C₂²×D₄	—	4	2	no	—
438	C₂²×D₄	C₃×Q₈	1	8	yes	complemented
439	C₂²×D₄	C₂³×C₃	1	2	yes	—
440	C₂²×D₄	C₂³×C₃	1	2	yes	—
441	C₂³×C₄	C₂³×C₃	1	2	yes	—
442	C₂³×C₄	C₂³×C₃	1	2	yes	—
443	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₃	1	2	yes	—
446	C₂³×C₄	C₂³×C₃	1	2	yes	—
447	C₂³×C₄	C₂³×C₃	1	2	yes	—
448	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
449	C₂²⋊Q₈	—	4	4	no	—
450	C₂²⋊Q₈	—	4	2	no	—
451	C₂²⋊Q₈	—	4	4	no	—
452	C₂²⋊Q₈	—	4	4	no	—
453	C₂²⋊Q₈	—	4	4	no	—
454	C₄×D₄	—	4	4	no	—
455	C₄×D₄	—	4	4	no	—
456	C₂×C₄⋊C₄	—	4	4	no	—
457	C₂×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₂²⋊C₄	—	4	4	no	—
482	C₂×C₂²⋊C₄	—	4	4	no	—
483	C₂×C₂²⋊C₄	—	4	2	no	—
484	C₂×C₂²⋊C₄	—	4	2	no	—
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	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄²	C₂³×C₃	1	2	yes	—
513	C₂×C₄²	C₂³×C₃	1	2	yes	—
514	#95	C₂³×C₃	1	2	yes	—
515	#95	C₂³×C₃	1	1	yes	characteristic
516	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	C₂³×C₃	—	2	2	no	—
536	C₂³×C₃	—	2	2	no	—
537	C₂³×C₃	—	2	2	no	—
538	C₂³×C₃	—	2	2	no	—
539	C₂³×C₃	—	2	2	no	—
540	C₂³×C₃	—	2	2	no	—
541	C₂³×C₃	—	2	1	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	2	no	—
545	C₂³×C₃	—	2	2	no	—
546	C₂³×C₃	—	2	1	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	8	no	—
552	C₂³×C₃	—	4	4	no	—
553	C₂³×C₃	—	4	8	no	—
554	C₂³×C₃	—	4	8	no	—
555	C₂³×C₃	—	8	2	no	—
556	C₂³×C₃	—	8	4	no	—
557	C₂³×C₃	—	8	2	no	—
558	C₂³×C₃	—	8	2	no	—
559	C₂³×C₃	—	8	4	no	—
560	C₂³×C₃	—	8	2	no	—
561	C₂³×C₃	C₂²×Q₈	1	2	yes	—
562	C₂³×C₃	C₂²×Q₈	1	4	yes	—
563	C₂³×C₃	C₂²×Q₈	1	2	yes	—
564	C₂³×C₃	C₂²×Q₈	1	2	yes	—
565	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
566	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
567	C₂³×C₃	C₂⁵	1	1	yes	characteristic
568	C₃×Q₈	—	8	4	no	—
569	C₃×Q₈	—	8	2	no	—
570	C₃×D₄	—	2	16	no	—
571	C₃×D₄	—	4	8	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	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	1	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	—	4	4	no	—
612	C₂×C₃×C₄	—	4	8	no	—
613	C₂×C₃×C₄	—	4	4	no	—
614	C₂×C₃×C₄	—	8	4	no	—
615	C₂×C₃×C₄	—	8	4	no	—
616	C₂×C₃×C₄	—	8	2	no	—
617	C₂×C₃×C₄	—	8	4	no	—
618	C₂×C₃×C₄	—	8	4	no	—
619	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
620	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	2	2	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	2	no	—
625	C₂⁴	—	4	1	no	—
626	C₂⁴	—	4	1	no	—
627	C₂⁴	—	4	2	no	—
628	C₂⁴	—	4	2	no	—
629	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
630	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
631	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
632	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
633	C₂⁴	C₂⁴×C₃	1	2	yes	—
634	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
635	C₂×Q₈	—	2	4	no	—
636	C₂×Q₈	—	4	2	no	—
637	C₂×Q₈	—	4	2	no	—
638	C₂×Q₈	—	4	1	no	—
639	C₂×Q₈	—	4	2	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	16	no	—
645	C₂×D₄	C₂×C₃×Q₈	1	8	yes	—
646	C₂×D₄	C₂×C₃×Q₈	1	8	yes	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	4	1	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	1	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	1	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	1	no	—
722	C₂²⋊C₄	—	4	1	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	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	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₂²×C₃	—	2	4	no	—
737	C₂²×C₃	—	2	2	no	—
738	C₂²×C₃	—	2	4	no	—
739	C₂²×C₃	—	2	2	no	—
740	C₂²×C₃	—	2	2	no	—
741	C₂²×C₃	—	2	4	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	2	4	no	—
744	C₂²×C₃	—	2	4	no	—
745	C₂²×C₃	—	2	4	no	—
746	C₂²×C₃	—	2	4	no	—
747	C₂²×C₃	—	4	1	no	—
748	C₂²×C₃	—	4	2	no	—
749	C₂²×C₃	—	4	1	no	—
750	C₂²×C₃	—	4	2	no	—
751	C₂²×C₃	—	4	2	no	—
752	C₂²×C₃	—	4	2	no	—
753	C₂²×C₃	—	4	2	no	—
754	C₂²×C₃	—	4	2	no	—
755	C₂²×C₃	—	4	1	no	—
756	C₂²×C₃	—	4	1	no	—
757	C₂²×C₃	—	8	8	no	—
758	C₂²×C₃	—	8	8	no	—
759	C₂²×C₃	#543	1	4	yes	—
760	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
761	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
762	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
764	C₂²×C₃	#585	1	2	yes	—
765	C₃×C₄	—	2	4	no	—
766	C₃×C₄	—	2	4	no	—
767	C₃×C₄	—	4	2	no	—
768	C₃×C₄	—	4	1	no	—
769	C₃×C₄	—	4	1	no	—
770	C₃×C₄	—	4	2	no	—
771	C₃×C₄	—	4	2	no	—
772	C₃×C₄	—	4	2	no	—
773	C₃×C₄	—	4	2	no	—
774	C₃×C₄	—	4	2	no	—
775	C₃×C₄	—	4	2	no	—
776	C₃×C₄	—	4	1	no	—
777	C₃×C₄	—	4	2	no	—
778	C₃×C₄	—	4	2	no	—
779	C₃×C₄	—	4	1	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	4	4	no	—
798	C₂³	—	4	8	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	8	2	no	—
801	C₂³	—	8	4	no	—
802	C₂³	—	8	2	no	—
803	C₂³	—	8	2	no	—
804	C₂³	—	8	4	no	—
805	C₂³	—	8	2	no	—
806	C₂³	C₂²×C₃×Q₈	1	2	yes	—
807	C₂³	C₂²×C₃×Q₈	1	4	yes	—
808	C₂³	C₂²×C₃×Q₈	1	2	yes	—
809	C₂³	C₂²×C₃×Q₈	1	2	yes	—
810	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
811	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
812	C₂³	C₂⁵×C₃	1	1	yes	characteristic
813	Q₈	—	8	4	no	—
814	Q₈	—	8	2	no	—
815	D₄	—	2	16	no	—
816	D₄	—	4	8	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	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	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	—	4	4	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	8	4	no	—
860	C₂×C₄	—	8	4	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	4	no	—
863	C₂×C₄	—	8	4	no	—
864	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
865	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
866	C₂×C₃	—	2	4	no	—
867	C₂×C₃	—	4	4	no	—
868	C₂×C₃	—	4	2	no	—
869	C₂×C₃	—	4	2	no	—
870	C₂×C₃	C₂×#543	1	1	yes	characteristic
871	C₂×C₃	#3501	1	2	yes	—
872	C₂×C₃	#3533	1	1	yes	characteristic
873	C₂×C₃	#3534	1	2	yes	—
874	C₂×C₃	#3543	1	1	yes	characteristic
875	C₂²	—	2	4	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	8	8	no	—
897	C₂²	—	8	8	no	—
898	C₂²	C₃×#543	1	4	yes	—
899	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
900	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
903	C₂²	C₃×#585	1	2	yes	—
904	C₄	—	2	4	no	—
905	C₄	—	2	4	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	1	no	—
919	C₃	#40612	1	1	yes	characteristic, direct product factor, Sylow
920	C₂	—	2	4	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	4	no	—
923	C₂	—	4	2	no	—
924	C₂	C₂×C₃×#543	1	1	yes	characteristic
925	C₂	C₃×#3501	1	2	yes	—
926	C₂	C₃×#3533	1	1	yes	characteristic
927	C₂	C₃×#3534	1	2	yes	—
928	C₂	C₃×#3543	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
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×#2842	C₂	semidirect
2. C₃×#2841	C₂	semidirect
3. C₃×#2780	C₂	semidirect
4. C₃×#2748	C₂	semidirect
5. C₃×#2732	C₂	semidirect
6. C₃×#2692	C₂	semidirect
7. C₃×#2667	C₂	semidirect
8. C₃×#2626	C₂	semidirect
9. C₃×#2626	C₂	semidirect
10. C₃×#2607	C₂	semidirect
11. C₃×#2579	C₂	semidirect
12. C₃×#2450	C₂	semidirect
13. C₃×#2449	C₂	semidirect
14. C₃×#2437	C₂	semidirect
15. C₃×#2437	C₂	semidirect
16. C₃×#2417	C₂	semidirect
17. C₂×C₃×#399	C₂	semidirect
20. #40612	C₃	direct (N × H)
22. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
41. C₃×#399	C₂²	semidirect
42. C₃×#399	C₂²	semidirect
43. C₃×#399	C₂²	semidirect
44. C₃×#399	C₂²	semidirect
45. C₃×#399	C₂²	semidirect
46. C₃×#398	C₂²	semidirect
47. C₃×#398	C₂²	semidirect
48. C₃×#398	C₂²	semidirect
49. C₃×#398	C₂²	semidirect
50. C₃×#398	C₂²	semidirect
51. C₃×#398	C₂²	semidirect
55. C₃×#396	C₂²	semidirect
56. C₃×#396	C₂²	semidirect
57. C₃×#396	C₂²	semidirect
58. C₃×#396	C₂²	semidirect
59. C₃×#396	C₂²	semidirect
60. C₃×#396	C₂²	semidirect
61. C₃×#396	C₂²	semidirect
62. C₃×#395	C₂²	semidirect
65. C₃×#393	C₂²	semidirect
66. C₃×#393	C₂²	semidirect
67. C₃×#391	C₂²	semidirect
68. C₃×#391	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
73. C₃×#387	C₂²	semidirect
74. C₃×#387	C₂²	semidirect
75. C₃×#387	C₂²	semidirect
76. C₃×#387	C₂²	semidirect
85. C₃×#385	C₂²	semidirect
86. C₃×#385	C₂²	semidirect
87. C₃×#385	C₂²	semidirect
88. C₃×#385	C₂²	semidirect
89. C₃×#385	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#385	C₂²	semidirect
92. C₃×#385	C₂²	semidirect
93. C₃×#385	C₂²	semidirect
97. C₃×#380	C₂²	semidirect
98. C₃×#380	C₂²	semidirect
99. C₃×#380	C₂²	semidirect
100. C₃×#380	C₂²	semidirect
101. C₃×#380	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. #2842	C₂×C₃	semidirect
109. #2841	C₂×C₃	semidirect
110. #2780	C₂×C₃	semidirect
111. #2748	C₂×C₃	semidirect
112. #2732	C₂×C₃	semidirect
113. #2692	C₂×C₃	semidirect
114. #2667	C₂×C₃	semidirect
115. #2626	C₂×C₃	semidirect
116. #2626	C₂×C₃	semidirect
117. #2607	C₂×C₃	semidirect
118. #2579	C₂×C₃	semidirect
119. #2450	C₂×C₃	semidirect
120. #2449	C₂×C₃	semidirect
121. #2437	C₂×C₃	semidirect
122. #2437	C₂×C₃	semidirect
123. #2417	C₂×C₃	semidirect
124. C₂×#399	C₂×C₃	semidirect
133. C₂²×C₃×D₄	Q₈	semidirect
231. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
232. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
233. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
234. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
235. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
238. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
239. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
244. #400	C₂²×C₃	semidirect
250. #399	C₂²×C₃	semidirect
251. #399	C₂²×C₃	semidirect
252. #399	C₂²×C₃	semidirect
253. #399	C₂²×C₃	semidirect
254. #399	C₂²×C₃	semidirect
255. #398	C₂²×C₃	semidirect
256. #398	C₂²×C₃	semidirect
257. #398	C₂²×C₃	semidirect
258. #398	C₂²×C₃	semidirect
259. #398	C₂²×C₃	semidirect
260. #398	C₂²×C₃	semidirect
264. #396	C₂²×C₃	semidirect
265. #396	C₂²×C₃	semidirect
266. #396	C₂²×C₃	semidirect
267. #396	C₂²×C₃	semidirect
268. #396	C₂²×C₃	semidirect
269. #396	C₂²×C₃	semidirect
270. #396	C₂²×C₃	semidirect
271. #395	C₂²×C₃	semidirect
274. #393	C₂²×C₃	semidirect
275. #393	C₂²×C₃	semidirect
276. #391	C₂²×C₃	semidirect
277. #391	C₂²×C₃	semidirect
280. #389	C₂²×C₃	semidirect
281. #389	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
285. #387	C₂²×C₃	semidirect
294. #385	C₂²×C₃	semidirect
295. #385	C₂²×C₃	semidirect
296. #385	C₂²×C₃	semidirect
297. #385	C₂²×C₃	semidirect
298. #385	C₂²×C₃	semidirect
299. #385	C₂²×C₃	semidirect
300. #385	C₂²×C₃	semidirect
301. #385	C₂²×C₃	semidirect
302. #385	C₂²×C₃	semidirect
306. #380	C₂²×C₃	semidirect
307. #380	C₂²×C₃	semidirect
308. #380	C₂²×C₃	semidirect
309. #380	C₂²×C₃	semidirect
310. #380	C₂²×C₃	semidirect
316. C₂×#95	C₂²×C₃	semidirect
438. C₂²×D₄	C₃×Q₈	semidirect
919. C₃	#40612	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×#2842	2
C₃×#2841	2
C₃×#2780	2
C₃×#2748	2
C₃×#2732	2
C₃×#2692	2
C₃×#2667	2
C₃×#2626	2
C₃×#2607	2
C₃×#2579	2
C₃×#2450	2
C₃×#2449	2
C₃×#2437	2
C₃×#2417	2
C₂×C₃×#399	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2308	2
#40612	3

Subgroups — C3×#40612 #10659219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40612 #10659219