Subgroups — C₃×#40608 #10659215

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2841	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2840	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2804	C₂	1	2	yes	maximal, complemented
4	C₃×#2784	C₂	1	2	yes	maximal, complemented
5	C₃×#2692	C₂	1	2	yes	maximal, complemented
6	C₃×#2692	C₂	1	2	yes	maximal, complemented
7	C₃×#2665	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×#2564	C₂	1	2	yes	maximal, complemented
12	C₃×#2450	C₂	1	2	yes	maximal, complemented
13	C₃×#2450	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×#2409	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#393	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	#40608	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
29	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
30	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×#399	C₂²	1	1	yes	characteristic
38	C₃×#399	C₂²	1	2	yes	—
39	C₃×#399	C₂²	1	1	yes	characteristic, complemented
40	C₃×#399	C₂²	1	2	yes	complemented
41	C₃×#398	C₂²	1	2	yes	complemented
42	C₃×#398	C₂²	1	2	yes	complemented
43	C₃×#396	C₂²	1	2	yes	—
44	C₃×#396	C₂²	1	2	yes	—
45	C₃×#396	C₂²	1	2	yes	—
46	C₃×#396	C₂²	1	2	yes	complemented
47	C₃×#396	C₂²	1	2	yes	complemented
48	C₃×#396	C₂²	1	2	yes	complemented
49	C₃×#395	C₂²	1	2	yes	complemented
50	C₃×#395	C₂²	1	2	yes	complemented
51	C₃×#395	C₂²	1	2	yes	complemented
52	C₃×#393	C₂²	1	2	yes	—
53	C₃×#393	C₂²	1	1	yes	characteristic
54	C₃×#393	C₂²	1	1	yes	characteristic
55	C₃×#393	C₂²	1	1	yes	characteristic
56	C₃×#393	C₂²	1	2	yes	—
57	C₃×#393	C₂²	1	2	yes	complemented
58	C₃×#393	C₂²	1	1	yes	characteristic, complemented
59	C₃×#393	C₂²	1	1	yes	characteristic, complemented
60	C₃×#393	C₂²	1	2	yes	complemented
61	C₃×#393	C₂²	1	1	yes	characteristic, complemented
62	C₃×#393	C₂²	1	2	yes	complemented
63	C₃×#393	C₂²	1	2	yes	complemented
64	C₃×#393	C₂²	1	2	yes	complemented
65	C₃×#393	C₂²	1	2	yes	complemented
66	C₃×#391	C₂²	1	2	yes	complemented
67	C₃×#391	C₂²	1	2	yes	complemented
68	C₃×#391	C₂²	1	2	yes	complemented
69	C₃×#391	C₂²	1	2	yes	complemented
70	C₃×#390	C₂²	1	2	yes	—
71	C₃×#390	C₂²	1	2	yes	—
72	C₃×#387	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×#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×#386	C₂²	1	2	yes	—
82	C₃×#386	C₂²	1	2	yes	—
83	C₃×#386	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	complemented
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×#381	C₂²	1	1	yes	characteristic
94	C₃×#381	C₂²	1	1	yes	characteristic
95	C₃×#380	C₂²	1	2	yes	—
96	C₃×#380	C₂²	1	2	yes	complemented
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×#379	C₂²	1	1	yes	characteristic
102	C₃×#379	C₂²	1	2	yes	—
103	C₃×#379	C₂²	1	2	yes	—
104	C₃×#379	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₃×#95	C₂²	1	2	yes	complemented
108	#2841	C₂×C₃	1	1	yes	characteristic, complemented
109	#2840	C₂×C₃	1	1	yes	characteristic, complemented
110	#2804	C₂×C₃	1	2	yes	complemented
111	#2784	C₂×C₃	1	2	yes	complemented
112	#2692	C₂×C₃	1	2	yes	complemented
113	#2692	C₂×C₃	1	2	yes	complemented
114	#2665	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	#2564	C₂×C₃	1	2	yes	complemented
119	#2450	C₂×C₃	1	2	yes	complemented
120	#2450	C₂×C₃	1	2	yes	complemented
121	#2437	C₂×C₃	1	2	yes	complemented
122	#2437	C₂×C₃	1	1	yes	characteristic, complemented
123	#2409	C₂×C₃	1	2	yes	complemented
124	C₂×#393	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	—	4	2	no	—
130	C₂²×C₃×Q₈	—	4	4	no	—
131	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₃×Q₈	C₂³	1	2	yes	—
133	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
135	C₂²×C₃×Q₈	C₂³	1	2	yes	—
136	C₂²×C₃×D₄	—	4	2	no	—
137	C₂²×C₃×D₄	—	4	2	no	—
138	C₂²×C₃×D₄	Q₈	1	8	yes	complemented
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂²×C₃×D₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	2	yes	—
142	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
143	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
144	C₂³×C₃×C₄	C₂³	1	2	yes	—
145	C₂³×C₃×C₄	C₂³	1	2	yes	—
146	C₂³×C₃×C₄	C₂³	1	2	yes	—
147	C₂³×C₃×C₄	C₂³	1	2	yes	—
148	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
149	C₃×C₂²⋊Q₈	—	4	4	no	—
150	C₃×C₂²⋊Q₈	—	4	2	no	—
151	C₃×C₂²⋊Q₈	—	4	4	no	—
152	C₃×C₂²⋊Q₈	—	4	4	no	—
153	C₃×C₂²⋊Q₈	—	4	4	no	—
154	C₃×C₄×D₄	—	4	4	no	—
155	C₃×C₄×D₄	—	4	4	no	—
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	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
173	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
174	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
175	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
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	1	yes	characteristic
190	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄²	C₂³	1	2	yes	—
204	C₂×C₃×C₄²	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
231	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
233	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
234	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
235	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
236	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
237	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
239	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
243	#400	C₂²×C₃	1	2	yes	complemented
244	#400	C₂²×C₃	1	2	yes	complemented
245	#400	C₂²×C₃	1	2	yes	complemented
246	#399	C₂²×C₃	1	1	yes	characteristic
247	#399	C₂²×C₃	1	2	yes	—
248	#399	C₂²×C₃	1	2	yes	complemented
249	#399	C₂²×C₃	1	1	yes	characteristic, complemented
250	#398	C₂²×C₃	1	2	yes	complemented
251	#398	C₂²×C₃	1	2	yes	complemented
252	#396	C₂²×C₃	1	2	yes	—
253	#396	C₂²×C₃	1	2	yes	—
254	#396	C₂²×C₃	1	2	yes	—
255	#396	C₂²×C₃	1	2	yes	complemented
256	#396	C₂²×C₃	1	2	yes	complemented
257	#396	C₂²×C₃	1	2	yes	complemented
258	#395	C₂²×C₃	1	2	yes	complemented
259	#395	C₂²×C₃	1	2	yes	complemented
260	#395	C₂²×C₃	1	2	yes	complemented
261	#393	C₂²×C₃	1	1	yes	characteristic
262	#393	C₂²×C₃	1	1	yes	characteristic
263	#393	C₂²×C₃	1	2	yes	—
264	#393	C₂²×C₃	1	1	yes	characteristic
265	#393	C₂²×C₃	1	2	yes	—
266	#393	C₂²×C₃	1	2	yes	complemented
267	#393	C₂²×C₃	1	2	yes	complemented
268	#393	C₂²×C₃	1	2	yes	complemented
269	#393	C₂²×C₃	1	2	yes	complemented
270	#393	C₂²×C₃	1	2	yes	complemented
271	#393	C₂²×C₃	1	1	yes	characteristic, complemented
272	#393	C₂²×C₃	1	1	yes	characteristic, complemented
273	#393	C₂²×C₃	1	2	yes	complemented
274	#393	C₂²×C₃	1	1	yes	characteristic, complemented
275	#391	C₂²×C₃	1	2	yes	complemented
276	#391	C₂²×C₃	1	2	yes	complemented
277	#391	C₂²×C₃	1	2	yes	complemented
278	#391	C₂²×C₃	1	2	yes	complemented
279	#390	C₂²×C₃	1	2	yes	—
280	#390	C₂²×C₃	1	2	yes	—
281	#387	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	#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	#386	C₂²×C₃	1	2	yes	—
291	#386	C₂²×C₃	1	2	yes	—
292	#386	C₂²×C₃	1	2	yes	—
293	#385	C₂²×C₃	1	2	yes	complemented
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	#381	C₂²×C₃	1	1	yes	characteristic
303	#381	C₂²×C₃	1	1	yes	characteristic
304	#380	C₂²×C₃	1	2	yes	—
305	#380	C₂²×C₃	1	1	yes	characteristic, complemented
306	#380	C₂²×C₃	1	2	yes	complemented
307	#380	C₂²×C₃	1	2	yes	complemented
308	#380	C₂²×C₃	1	2	yes	complemented
309	#380	C₂²×C₃	1	2	yes	complemented
310	#379	C₂²×C₃	1	1	yes	characteristic
311	#379	C₂²×C₃	1	1	yes	characteristic
312	#379	C₂²×C₃	1	2	yes	—
313	#379	C₂²×C₃	1	2	yes	—
314	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
315	C₂×#95	C₂²×C₃	1	2	yes	complemented
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	complemented
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	—	2	4	no	—
333	C₂×C₃×Q₈	—	4	1	no	—
334	C₂×C₃×Q₈	—	4	2	no	—
335	C₂×C₃×Q₈	—	4	2	no	—
336	C₂×C₃×Q₈	—	4	1	no	—
337	C₂×C₃×Q₈	—	4	2	no	—
338	C₂×C₃×Q₈	—	4	1	no	—
339	C₂×C₃×Q₈	—	4	2	no	—
340	C₂×C₃×Q₈	—	4	2	no	—
341	C₂×C₃×Q₈	—	4	2	no	—
342	C₂×C₃×Q₈	—	4	2	no	—
343	C₂×C₃×Q₈	—	4	16	no	—
344	C₂×C₃×D₄	—	2	4	no	—
345	C₂×C₃×D₄	—	2	4	no	—
346	C₂×C₃×D₄	—	4	2	no	—
347	C₂×C₃×D₄	—	4	2	no	—
348	C₂×C₃×D₄	—	4	16	no	—
349	C₂×C₃×D₄	C₂×Q₈	1	8	yes	—
350	C₂×C₃×D₄	C₂×Q₈	1	8	yes	complemented
351	C₂²×C₃×C₄	—	2	2	no	—
352	C₂²×C₃×C₄	—	2	4	no	—
353	C₂²×C₃×C₄	—	2	2	no	—
354	C₂²×C₃×C₄	—	2	4	no	—
355	C₂²×C₃×C₄	—	2	4	no	—
356	C₂²×C₃×C₄	—	2	4	no	—
357	C₂²×C₃×C₄	—	4	1	no	—
358	C₂²×C₃×C₄	—	4	1	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	—	4	2	no	—
365	C₂²×C₃×C₄	—	4	2	no	—
366	C₂²×C₃×C₄	—	4	2	no	—
367	C₂²×C₃×C₄	—	4	2	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	—	4	2	no	—
370	C₂²×C₃×C₄	—	4	2	no	—
371	C₂²×C₃×C₄	—	4	2	no	—
372	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	complemented
373	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
388	C₃×C₄⋊C₄	—	2	4	no	—
389	C₃×C₄⋊C₄	—	2	4	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	2	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	1	no	—
402	C₃×C₄⋊C₄	—	4	2	no	—
403	C₃×C₄⋊C₄	—	4	2	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	—	4	2	no	—
411	C₃×C₂²⋊C₄	—	4	2	no	—
412	C₃×C₂²⋊C₄	—	4	1	no	—
413	C₃×C₂²⋊C₄	—	4	2	no	—
414	C₃×C₂²⋊C₄	—	4	1	no	—
415	C₃×C₂²⋊C₄	—	4	2	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	1	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×C₂²⋊C₄	—	4	2	no	—
431	C₃×C₄²	—	4	2	no	—
432	C₃×C₄²	—	4	2	no	—
433	C₂⁵	C₂³×C₃	1	1	yes	characteristic
434	C₂⁵	C₂³×C₃	1	1	yes	characteristic
435	C₂²×Q₈	—	4	2	no	—
436	C₂²×Q₈	—	4	4	no	—
437	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₃	1	2	yes	—
439	C₂²×Q₈	C₂³×C₃	1	2	yes	—
440	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
441	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
442	C₂²×D₄	—	4	2	no	—
443	C₂²×D₄	—	4	2	no	—
444	C₂²×D₄	C₃×Q₈	1	8	yes	complemented
445	C₂²×D₄	C₂³×C₃	1	2	yes	—
446	C₂²×D₄	C₂³×C₃	1	2	yes	—
447	C₂³×C₄	C₂³×C₃	1	2	yes	—
448	C₂³×C₄	C₂³×C₃	1	2	yes	—
449	C₂³×C₄	C₂³×C₃	1	2	yes	—
450	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₃	1	2	yes	—
453	C₂³×C₄	C₂³×C₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
455	C₂²⋊Q₈	—	4	4	no	—
456	C₂²⋊Q₈	—	4	2	no	—
457	C₂²⋊Q₈	—	4	4	no	—
458	C₂²⋊Q₈	—	4	4	no	—
459	C₂²⋊Q₈	—	4	4	no	—
460	C₄×D₄	—	4	4	no	—
461	C₄×D₄	—	4	4	no	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
478	C₂×C₂²⋊C₄	—	4	4	no	—
479	C₂×C₂²⋊C₄	—	4	4	no	—
480	C₂×C₂²⋊C₄	—	4	2	no	—
481	C₂×C₂²⋊C₄	—	4	2	no	—
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	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×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×C₄²	C₂³×C₃	1	2	yes	—
510	C₂×C₄²	C₂³×C₃	1	2	yes	—
511	#95	C₂³×C₃	1	1	yes	characteristic
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	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	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	1	yes	characteristic
527	#95	C₂³×C₃	1	1	yes	characteristic
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	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	2	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	2	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	2	1	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	8	no	—
553	C₂³×C₃	—	4	4	no	—
554	C₂³×C₃	—	4	8	no	—
555	C₂³×C₃	—	4	8	no	—
556	C₂³×C₃	—	8	2	no	—
557	C₂³×C₃	—	8	2	no	—
558	C₂³×C₃	—	8	4	no	—
559	C₂³×C₃	—	8	2	no	—
560	C₂³×C₃	—	8	2	no	—
561	C₂³×C₃	—	8	4	no	—
562	C₂³×C₃	C₂²×Q₈	1	2	yes	—
563	C₂³×C₃	C₂²×Q₈	1	4	yes	—
564	C₂³×C₃	C₂²×Q₈	1	2	yes	—
565	C₂³×C₃	C₂²×Q₈	1	2	yes	—
566	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
567	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
568	C₂³×C₃	C₂⁵	1	1	yes	characteristic
569	C₃×Q₈	—	4	4	no	—
570	C₃×Q₈	—	4	8	no	—
571	C₃×Q₈	—	4	4	no	—
572	C₃×Q₈	—	8	2	no	—
573	C₃×Q₈	—	8	4	no	—
574	C₃×D₄	—	2	16	no	—
575	C₃×D₄	—	4	8	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	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	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	—	2	2	no	—
615	C₂×C₃×C₄	—	4	4	no	—
616	C₂×C₃×C₄	—	4	8	no	—
617	C₂×C₃×C₄	—	4	4	no	—
618	C₂×C₃×C₄	—	8	4	no	—
619	C₂×C₃×C₄	—	8	2	no	—
620	C₂×C₃×C₄	—	8	4	no	—
621	C₂×C₃×C₄	—	8	4	no	—
622	C₂×C₃×C₄	—	8	4	no	—
623	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
624	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
625	C₂⁴	—	2	2	no	—
626	C₂⁴	—	2	2	no	—
627	C₂⁴	—	4	2	no	—
628	C₂⁴	—	4	2	no	—
629	C₂⁴	—	4	1	no	—
630	C₂⁴	—	4	1	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
634	C₂⁴	C₂×C₃×Q₈	1	4	yes	complemented
635	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
636	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
637	C₂⁴	C₂⁴×C₃	1	2	yes	—
638	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	2	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×Q₈	—	4	1	no	—
647	C₂×Q₈	—	4	2	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	2	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×Q₈	—	4	16	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	16	no	—
657	C₂×D₄	C₂×C₃×Q₈	1	8	yes	—
658	C₂×D₄	C₂×C₃×Q₈	1	8	yes	complemented
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	complemented
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	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	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	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	1	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	1	no	—
725	C₂²⋊C₄	—	4	1	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	4	1	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	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₂²×C₃	—	2	4	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	2	2	no	—
744	C₂²×C₃	—	2	4	no	—
745	C₂²×C₃	—	2	2	no	—
746	C₂²×C₃	—	2	4	no	—
747	C₂²×C₃	—	2	2	no	—
748	C₂²×C₃	—	2	4	no	—
749	C₂²×C₃	—	2	4	no	—
750	C₂²×C₃	—	2	4	no	—
751	C₂²×C₃	—	2	4	no	—
752	C₂²×C₃	—	4	2	no	—
753	C₂²×C₃	—	4	1	no	—
754	C₂²×C₃	—	4	1	no	—
755	C₂²×C₃	—	4	1	no	—
756	C₂²×C₃	—	4	2	no	—
757	C₂²×C₃	—	4	1	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	—	8	8	no	—
763	C₂²×C₃	—	8	8	no	—
764	C₂²×C₃	#543	1	4	yes	—
765	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
766	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
768	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
769	C₂²×C₃	#585	1	2	yes	—
770	C₃×C₄	—	2	4	no	—
771	C₃×C₄	—	2	4	no	—
772	C₃×C₄	—	4	2	no	—
773	C₃×C₄	—	4	1	no	—
774	C₃×C₄	—	4	1	no	—
775	C₃×C₄	—	4	2	no	—
776	C₃×C₄	—	4	1	no	—
777	C₃×C₄	—	4	1	no	—
778	C₃×C₄	—	4	2	no	—
779	C₃×C₄	—	4	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	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	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	1	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	8	no	—
802	C₂³	—	4	4	no	—
803	C₂³	—	4	8	no	—
804	C₂³	—	4	8	no	—
805	C₂³	—	8	2	no	—
806	C₂³	—	8	2	no	—
807	C₂³	—	8	4	no	—
808	C₂³	—	8	2	no	—
809	C₂³	—	8	2	no	—
810	C₂³	—	8	4	no	—
811	C₂³	C₂²×C₃×Q₈	1	2	yes	—
812	C₂³	C₂²×C₃×Q₈	1	4	yes	—
813	C₂³	C₂²×C₃×Q₈	1	2	yes	—
814	C₂³	C₂²×C₃×Q₈	1	2	yes	—
815	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
816	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
817	C₂³	C₂⁵×C₃	1	1	yes	characteristic
818	Q₈	—	4	4	no	—
819	Q₈	—	4	8	no	—
820	Q₈	—	4	4	no	—
821	Q₈	—	8	2	no	—
822	Q₈	—	8	4	no	—
823	D₄	—	2	16	no	—
824	D₄	—	4	8	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	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	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	—	4	4	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	8	4	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	4	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
873	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
874	C₂×C₃	—	2	4	no	—
875	C₂×C₃	—	4	4	no	—
876	C₂×C₃	—	4	2	no	—
877	C₂×C₃	—	4	2	no	—
878	C₂×C₃	C₂×#543	1	1	yes	characteristic
879	C₂×C₃	#3501	1	2	yes	—
880	C₂×C₃	#3532	1	1	yes	characteristic
881	C₂×C₃	#3545	1	1	yes	characteristic
882	C₂×C₃	#3558	1	2	yes	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	8	8	no	—
905	C₂²	—	8	8	no	—
906	C₂²	C₃×#543	1	4	yes	—
907	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
908	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
909	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
911	C₂²	C₃×#585	1	2	yes	—
912	C₄	—	2	4	no	—
913	C₄	—	2	4	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₃	#40608	1	1	yes	characteristic, direct product factor, Sylow
928	C₂	—	2	4	no	—
929	C₂	—	4	2	no	—
930	C₂	—	4	4	no	—
931	C₂	—	4	2	no	—
932	C₂	C₂×C₃×#543	1	1	yes	characteristic
933	C₂	C₃×#3501	1	2	yes	—
934	C₂	C₃×#3532	1	1	yes	characteristic
935	C₂	C₃×#3545	1	1	yes	characteristic
936	C₂	C₃×#3558	1	2	yes	—

	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×#2841	C₂	semidirect
2. C₃×#2840	C₂	semidirect
3. C₃×#2804	C₂	semidirect
4. C₃×#2784	C₂	semidirect
5. C₃×#2692	C₂	semidirect
6. C₃×#2692	C₂	semidirect
7. C₃×#2665	C₂	semidirect
8. C₃×#2626	C₂	semidirect
9. C₃×#2626	C₂	semidirect
10. C₃×#2607	C₂	semidirect
11. C₃×#2564	C₂	semidirect
12. C₃×#2450	C₂	semidirect
13. C₃×#2450	C₂	semidirect
14. C₃×#2437	C₂	semidirect
15. C₃×#2437	C₂	semidirect
16. C₃×#2409	C₂	semidirect
17. C₂×C₃×#393	C₂	semidirect
20. #40608	C₃	direct (N × H)
21. C₂³×C₃×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
27. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#400	C₂²	semidirect
39. C₃×#399	C₂²	semidirect
40. C₃×#399	C₂²	semidirect
41. C₃×#398	C₂²	semidirect
42. C₃×#398	C₂²	semidirect
46. C₃×#396	C₂²	semidirect
47. C₃×#396	C₂²	semidirect
48. C₃×#396	C₂²	semidirect
49. C₃×#395	C₂²	semidirect
50. C₃×#395	C₂²	semidirect
51. C₃×#395	C₂²	semidirect
57. C₃×#393	C₂²	semidirect
58. C₃×#393	C₂²	semidirect
59. C₃×#393	C₂²	semidirect
60. C₃×#393	C₂²	semidirect
61. C₃×#393	C₂²	semidirect
62. C₃×#393	C₂²	semidirect
63. C₃×#393	C₂²	semidirect
64. C₃×#393	C₂²	semidirect
65. C₃×#393	C₂²	semidirect
66. C₃×#391	C₂²	semidirect
67. C₃×#391	C₂²	semidirect
68. C₃×#391	C₂²	semidirect
69. C₃×#391	C₂²	semidirect
72. C₃×#387	C₂²	semidirect
73. C₃×#387	C₂²	semidirect
74. C₃×#387	C₂²	semidirect
75. C₃×#387	C₂²	semidirect
84. C₃×#385	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
96. C₃×#380	C₂²	semidirect
97. C₃×#380	C₂²	semidirect
98. C₃×#380	C₂²	semidirect
99. C₃×#380	C₂²	semidirect
100. C₃×#380	C₂²	semidirect
106. C₂×C₃×#95	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. #2841	C₂×C₃	semidirect
109. #2840	C₂×C₃	semidirect
110. #2804	C₂×C₃	semidirect
111. #2784	C₂×C₃	semidirect
112. #2692	C₂×C₃	semidirect
113. #2692	C₂×C₃	semidirect
114. #2665	C₂×C₃	semidirect
115. #2626	C₂×C₃	semidirect
116. #2626	C₂×C₃	semidirect
117. #2607	C₂×C₃	semidirect
118. #2564	C₂×C₃	semidirect
119. #2450	C₂×C₃	semidirect
120. #2450	C₂×C₃	semidirect
121. #2437	C₂×C₃	semidirect
122. #2437	C₂×C₃	semidirect
123. #2409	C₂×C₃	semidirect
124. C₂×#393	C₂×C₃	semidirect
138. C₂²×C₃×D₄	Q₈	semidirect
230. C₂³×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
236. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
243. #400	C₂²×C₃	semidirect
244. #400	C₂²×C₃	semidirect
245. #400	C₂²×C₃	semidirect
248. #399	C₂²×C₃	semidirect
249. #399	C₂²×C₃	semidirect
250. #398	C₂²×C₃	semidirect
251. #398	C₂²×C₃	semidirect
255. #396	C₂²×C₃	semidirect
256. #396	C₂²×C₃	semidirect
257. #396	C₂²×C₃	semidirect
258. #395	C₂²×C₃	semidirect
259. #395	C₂²×C₃	semidirect
260. #395	C₂²×C₃	semidirect
266. #393	C₂²×C₃	semidirect
267. #393	C₂²×C₃	semidirect
268. #393	C₂²×C₃	semidirect
269. #393	C₂²×C₃	semidirect
270. #393	C₂²×C₃	semidirect
271. #393	C₂²×C₃	semidirect
272. #393	C₂²×C₃	semidirect
273. #393	C₂²×C₃	semidirect
274. #393	C₂²×C₃	semidirect
275. #391	C₂²×C₃	semidirect
276. #391	C₂²×C₃	semidirect
277. #391	C₂²×C₃	semidirect
278. #391	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
293. #385	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
305. #380	C₂²×C₃	semidirect
306. #380	C₂²×C₃	semidirect
307. #380	C₂²×C₃	semidirect
308. #380	C₂²×C₃	semidirect
309. #380	C₂²×C₃	semidirect
315. C₂×#95	C₂²×C₃	semidirect
316. C₂×#95	C₂²×C₃	semidirect
326. C₂⁴×C₃	C₂×Q₈	semidirect
350. C₂×C₃×D₄	C₂×Q₈	semidirect
372. C₂²×C₃×C₄	C₂×Q₈	semidirect
444. C₂²×D₄	C₃×Q₈	semidirect
634. C₂⁴	C₂×C₃×Q₈	semidirect
658. C₂×D₄	C₂×C₃×Q₈	semidirect
680. C₂²×C₄	C₂×C₃×Q₈	semidirect
927. C₃	#40608	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×#2841	2
C₃×#2840	2
C₃×#2804	2
C₃×#2784	2
C₃×#2692	2
C₃×#2665	2
C₃×#2626	2
C₃×#2607	2
C₃×#2564	2
C₃×#2450	2
C₃×#2437	2
C₃×#2409	2
C₂×C₃×#393	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2308	2
#40608	3

Subgroups — C3×#40608 #10659215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40608 #10659215