Subgroups — C₂×C₃×#3201 #10679352

Order 768.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#537	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3201	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#3201	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
27	C₃×#537	—	2	4	no	—
28	C₃×#537	C₂²	1	8	yes	—
29	C₃×#536	—	2	4	no	—
30	C₃×#536	C₂²	1	8	yes	complemented
31	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
32	C₂×C₃×#124	—	2	1	no	—
33	C₂×C₃×#123	—	2	1	no	—
34	C₂×C₃×#123	—	2	1	no	—
35	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	—	2	1	no	—
43	C₂×C₃×#121	—	2	1	no	—
44	C₂×C₃×#121	—	2	1	no	—
45	C₂×C₃×#121	C₂²	1	1	yes	characteristic
46	C₂×C₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃×#117	C₂²	1	1	yes	characteristic
48	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×#485	C₂²	1	8	yes	complemented
50	C₃×#484	C₂²	1	8	yes	complemented
51	C₃×#483	C₂²	1	8	yes	complemented
52	C₃×#482	C₂²	1	8	yes	complemented
53	C₃×#470	C₂²	1	8	yes	complemented
54	C₃×#468	C₂²	1	8	yes	complemented
55	C₃×#467	C₂²	1	8	yes	complemented
56	C₃×#465	C₂²	1	8	yes	complemented
57	C₃×#452	C₂²	1	8	yes	complemented
58	C₃×#452	C₂²	1	8	yes	complemented
59	C₃×#451	C₂²	1	8	yes	complemented
60	C₃×#448	C₂²	1	8	yes	complemented
61	C₂×C₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₃×#107	C₂²	1	1	yes	characteristic
63	C₂×C₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₃×#102	C₂²	1	1	yes	characteristic
73	C₃×#408	C₂²	1	8	yes	complemented
74	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
78	C₂×#537	C₂×C₃	1	1	yes	characteristic
79	C₂×#536	C₂×C₃	1	1	yes	characteristic, complemented
80	#3201	C₂×C₃	1	16	yes	direct product factor
81	C₂×#484	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#485	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#482	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#483	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#470	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂×#468	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#467	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂×#465	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×#452	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×#452	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#451	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×#448	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#408	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃×#41	—	2	2	no	—
95	C₂×C₃×#41	—	4	2	no	—
96	C₂×C₃×#41	—	4	2	no	—
97	C₂×C₃×#41	—	4	2	no	—
98	C₂×C₃×#41	—	4	2	no	—
99	C₂×C₃×#41	D₄	1	4	yes	—
100	C₂×C₃×#41	C₂³	1	4	yes	—
101	C₂×C₃×#41	C₂³	1	4	yes	—
102	C₂²×C₃×Q₈	—	2	1	no	—
103	C₂²×C₃×Q₈	—	2	2	no	—
104	C₂²×C₃×Q₈	—	4	2	no	—
105	C₂²×C₃×Q₈	—	4	2	no	—
106	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
107	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₃×Q₈	C₂³	1	4	yes	—
111	C₂²×C₃×D₄	—	2	1	no	—
112	C₂²×C₃×D₄	—	2	1	no	—
113	C₂²×C₃×D₄	—	2	1	no	—
114	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
115	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
116	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
117	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
118	C₂³×C₃×C₄	—	2	1	no	—
119	C₂³×C₃×C₄	—	2	1	no	—
120	C₂³×C₃×C₄	—	2	1	no	—
121	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
124	C₂×C₃×Q₁₆	—	4	2	no	—
125	C₂×C₃×Q₁₆	—	4	2	no	—
126	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
127	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
128	C₂×C₃×SD₁₆	—	4	2	no	—
129	C₂×C₃×SD₁₆	—	4	2	no	—
130	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
132	C₂×C₃×M₁₆	—	4	2	no	—
133	C₂×C₃×M₁₆	C₂³	1	4	yes	—
134	C₂²×C₃×C₈	—	4	2	no	—
135	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
136	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
137	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₃×C₈	C₂³	1	4	yes	—
140	C₃×C₄⋊Q₈	—	2	8	no	—
141	C₃×#124	—	2	8	no	—
142	C₃×#123	—	2	8	no	—
143	C₃×#123	—	2	8	no	—
144	C₃×C₂²⋊Q₈	—	2	8	no	—
145	C₃×C₂²⋊Q₈	—	2	2	no	—
146	C₃×C₂²⋊Q₈	—	2	2	no	—
147	C₃×C₂²⋊Q₈	—	2	2	no	—
148	C₃×C₂²⋊Q₈	—	2	2	no	—
149	C₃×C₂²⋊Q₈	—	2	2	no	—
150	C₃×C₂²⋊Q₈	—	2	2	no	—
151	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₃×#121	—	2	8	no	—
158	C₃×#121	—	2	8	no	—
159	C₃×#121	—	2	8	no	—
160	C₃×#121	—	2	2	no	—
161	C₃×#121	—	2	2	no	—
162	C₃×#121	C₂³	1	4	yes	—
163	C₃×#121	C₂³	1	4	yes	—
164	C₃×#117	—	2	2	no	—
165	C₃×#117	C₂³	1	4	yes	—
166	C₂×C₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₃×C₄⋊C₄	—	2	2	no	—
168	C₂×C₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₃×C₄⋊C₄	—	2	1	no	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
179	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₃×C₄²	—	2	1	no	—
189	C₃×#107	C₂³	1	4	yes	—
190	C₃×#107	C₂³	1	4	yes	—
191	C₃×#106	C₂³	1	4	yes	—
192	C₃×#106	C₂³	1	4	yes	—
193	C₃×#103	C₂³	1	4	yes	—
194	C₃×#103	C₂³	1	4	yes	—
195	C₃×#103	C₂³	1	4	yes	—
196	C₃×#103	C₂³	1	4	yes	—
197	C₃×#103	C₂³	1	4	yes	—
198	C₃×#103	C₂³	1	4	yes	—
199	C₃×#102	C₂³	1	4	yes	—
200	C₃×#102	C₂³	1	4	yes	—
201	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
202	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
203	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
206	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
207	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
213	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
214	#537	—	2	4	no	—
215	#537	C₂²×C₃	1	8	yes	—
216	#536	—	2	4	no	—
217	#536	C₂²×C₃	1	8	yes	complemented
218	C₂×C₄⋊Q₈	—	2	1	no	—
219	C₂×#124	—	2	1	no	—
220	C₂×#123	—	2	1	no	—
221	C₂×#123	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
228	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
229	C₂×#121	—	2	1	no	—
230	C₂×#121	—	2	1	no	—
231	C₂×#121	—	2	1	no	—
232	C₂×#121	C₂²×C₃	1	1	yes	characteristic
233	C₂×#121	C₂²×C₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₃	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
236	#485	C₂²×C₃	1	8	yes	complemented
237	#484	C₂²×C₃	1	8	yes	complemented
238	#483	C₂²×C₃	1	8	yes	complemented
239	#482	C₂²×C₃	1	8	yes	complemented
240	#470	C₂²×C₃	1	8	yes	complemented
241	#468	C₂²×C₃	1	8	yes	complemented
242	#467	C₂²×C₃	1	8	yes	complemented
243	#465	C₂²×C₃	1	8	yes	complemented
244	#452	C₂²×C₃	1	8	yes	complemented
245	#452	C₂²×C₃	1	8	yes	complemented
246	#451	C₂²×C₃	1	8	yes	complemented
247	#448	C₂²×C₃	1	8	yes	complemented
248	C₂×#107	C₂²×C₃	1	1	yes	characteristic
249	C₂×#107	C₂²×C₃	1	1	yes	characteristic
250	C₂×#106	C₂²×C₃	1	1	yes	characteristic
251	C₂×#106	C₂²×C₃	1	1	yes	characteristic
252	C₂×#103	C₂²×C₃	1	1	yes	characteristic
253	C₂×#103	C₂²×C₃	1	1	yes	characteristic
254	C₂×#103	C₂²×C₃	1	1	yes	characteristic
255	C₂×#103	C₂²×C₃	1	1	yes	characteristic
256	C₂×#103	C₂²×C₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₃	1	1	yes	characteristic
258	C₂×#102	C₂²×C₃	1	1	yes	characteristic
259	C₂×#102	C₂²×C₃	1	1	yes	characteristic
260	#408	C₂²×C₃	1	8	yes	complemented
261	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
265	C₂⁴×C₃	—	2	1	no	—
266	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
267	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
268	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
269	C₃×#41	—	4	8	no	—
270	C₃×#41	—	4	4	no	—
271	C₃×#41	—	4	4	no	—
272	C₃×#41	—	4	4	no	—
273	C₃×#41	—	4	4	no	—
274	C₃×#41	—	4	8	no	—
275	C₂×C₃×Q₈	—	2	1	no	—
276	C₂×C₃×Q₈	—	2	1	no	—
277	C₂×C₃×Q₈	—	2	1	no	—
278	C₂×C₃×Q₈	—	2	4	no	—
279	C₂×C₃×Q₈	—	2	2	no	—
280	C₂×C₃×Q₈	—	2	2	no	—
281	C₂×C₃×Q₈	—	2	2	no	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	—	2	2	no	—
285	C₂×C₃×Q₈	—	4	2	no	—
286	C₂×C₃×Q₈	—	4	4	no	—
287	C₂×C₃×Q₈	—	4	4	no	—
288	C₂×C₃×Q₈	—	4	4	no	—
289	C₂×C₃×Q₈	—	4	8	no	—
290	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
291	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
292	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
293	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
294	C₂×C₃×D₄	—	2	4	no	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	4	no	—
297	C₂×C₃×D₄	—	2	1	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	4	2	no	—
301	C₂×C₃×D₄	—	4	2	no	—
302	C₂×C₃×D₄	—	4	2	no	—
303	C₂×C₃×D₄	—	4	4	no	—
304	C₂×C₃×D₄	—	8	2	no	—
305	C₂×C₃×D₄	—	8	2	no	—
306	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
307	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
308	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
309	C₂×C₃×D₄	C₂⁴	1	2	yes	—
310	C₂²×C₃×C₄	—	2	2	no	—
311	C₂²×C₃×C₄	—	2	2	no	—
312	C₂²×C₃×C₄	—	2	2	no	—
313	C₂²×C₃×C₄	—	2	2	no	—
314	C₂²×C₃×C₄	—	2	2	no	—
315	C₂²×C₃×C₄	—	2	2	no	—
316	C₂²×C₃×C₄	—	2	4	no	—
317	C₂²×C₃×C₄	—	2	1	no	—
318	C₂²×C₃×C₄	—	2	1	no	—
319	C₂²×C₃×C₄	—	2	1	no	—
320	C₂²×C₃×C₄	—	2	1	no	—
321	C₂²×C₃×C₄	—	2	1	no	—
322	C₂²×C₃×C₄	—	2	1	no	—
323	C₂²×C₃×C₄	—	2	1	no	—
324	C₂²×C₃×C₄	—	2	4	no	—
325	C₂²×C₃×C₄	—	2	4	no	—
326	C₂²×C₃×C₄	—	4	4	no	—
327	C₂²×C₃×C₄	—	4	4	no	—
328	C₂²×C₃×C₄	—	8	2	no	—
329	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
330	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
331	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
332	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₃×Q₁₆	—	4	4	no	—
340	C₃×Q₁₆	—	4	4	no	—
341	C₃×SD₁₆	—	4	4	no	—
342	C₃×SD₁₆	—	4	4	no	—
343	C₃×M₁₆	—	4	4	no	—
344	C₂×C₃×C₈	—	2	2	no	—
345	C₂×C₃×C₈	—	2	2	no	—
346	C₂×C₃×C₈	—	2	2	no	—
347	C₂×C₃×C₈	—	2	2	no	—
348	C₂×C₃×C₈	—	4	4	no	—
349	C₂×C₃×C₈	C₂⁴	1	2	yes	—
350	C₂×C₃×C₈	C₂⁴	1	2	yes	—
351	C₂×C₃×C₈	C₂⁴	1	2	yes	—
352	C₂×C₃×C₈	C₂⁴	1	2	yes	—
353	C₃×C₄⋊C₄	—	2	4	no	—
354	C₃×C₄⋊C₄	—	2	1	no	—
355	C₃×C₄⋊C₄	—	2	1	no	—
356	C₃×C₄⋊C₄	—	2	4	no	—
357	C₃×C₄⋊C₄	—	2	4	no	—
358	C₃×C₄⋊C₄	—	2	4	no	—
359	C₃×C₄⋊C₄	—	2	4	no	—
360	C₃×C₄⋊C₄	—	2	4	no	—
361	C₃×C₄⋊C₄	—	2	4	no	—
362	C₃×C₄⋊C₄	—	2	1	no	—
363	C₃×C₄⋊C₄	—	2	1	no	—
364	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	2	4	no	—
370	C₃×C₂²⋊C₄	—	2	4	no	—
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	4	no	—
374	C₃×C₂²⋊C₄	—	2	4	no	—
375	C₃×C₂²⋊C₄	—	2	4	no	—
376	C₃×C₂²⋊C₄	—	2	4	no	—
377	C₃×C₄²	—	2	4	no	—
378	C₂×#41	—	2	2	no	—
379	C₂×#41	—	4	2	no	—
380	C₂×#41	—	4	2	no	—
381	C₂×#41	—	4	2	no	—
382	C₂×#41	—	4	2	no	—
383	C₂×#41	C₃×D₄	1	4	yes	—
384	C₂×#41	C₂³×C₃	1	4	yes	—
385	C₂×#41	C₂³×C₃	1	4	yes	—
386	C₂²×Q₈	—	2	1	no	—
387	C₂²×Q₈	—	2	2	no	—
388	C₂²×Q₈	—	4	2	no	—
389	C₂²×Q₈	—	4	2	no	—
390	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
393	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₃	1	4	yes	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
399	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
400	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
401	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
408	C₂×Q₁₆	—	4	2	no	—
409	C₂×Q₁₆	—	4	2	no	—
410	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
411	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
412	C₂×SD₁₆	—	4	2	no	—
413	C₂×SD₁₆	—	4	2	no	—
414	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
415	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
416	C₂×M₁₆	—	4	2	no	—
417	C₂×M₁₆	C₂³×C₃	1	4	yes	—
418	C₂²×C₈	—	4	2	no	—
419	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₃	1	4	yes	—
424	C₄⋊Q₈	—	2	8	no	—
425	#124	—	2	8	no	—
426	#123	—	2	8	no	—
427	#123	—	2	8	no	—
428	C₂²⋊Q₈	—	2	8	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
436	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
437	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
438	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
439	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
440	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
441	#121	—	2	8	no	—
442	#121	—	2	8	no	—
443	#121	—	2	8	no	—
444	#121	—	2	2	no	—
445	#121	—	2	2	no	—
446	#121	C₂³×C₃	1	4	yes	—
447	#121	C₂³×C₃	1	4	yes	—
448	#117	—	2	2	no	—
449	#117	C₂³×C₃	1	4	yes	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	2	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₄²	—	2	1	no	—
473	#107	C₂³×C₃	1	4	yes	—
474	#107	C₂³×C₃	1	4	yes	—
475	#106	C₂³×C₃	1	4	yes	—
476	#106	C₂³×C₃	1	4	yes	—
477	#103	C₂³×C₃	1	4	yes	—
478	#103	C₂³×C₃	1	4	yes	—
479	#103	C₂³×C₃	1	4	yes	—
480	#103	C₂³×C₃	1	4	yes	—
481	#103	C₂³×C₃	1	4	yes	—
482	#103	C₂³×C₃	1	4	yes	—
483	#102	C₂³×C₃	1	4	yes	—
484	#102	C₂³×C₃	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
487	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
488	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
489	C₂³×C₃	—	2	2	no	—
490	C₂³×C₃	—	2	2	no	—
491	C₂³×C₃	—	2	2	no	—
492	C₂³×C₃	—	2	2	no	—
493	C₂³×C₃	—	2	2	no	—
494	C₂³×C₃	—	2	2	no	—
495	C₂³×C₃	—	2	2	no	—
496	C₂³×C₃	—	2	2	no	—
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	2	no	—
499	C₂³×C₃	—	4	2	no	—
500	C₂³×C₃	—	4	2	no	—
501	C₂³×C₃	—	4	2	no	—
502	C₂³×C₃	C₂²×D₄	1	2	yes	—
503	C₂³×C₃	C₂²×D₄	1	2	yes	—
504	C₂³×C₃	C₂²×D₄	1	2	yes	—
505	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
506	C₃×Q₈	—	2	2	no	—
507	C₃×Q₈	—	2	2	no	—
508	C₃×Q₈	—	2	2	no	—
509	C₃×Q₈	—	2	2	no	—
510	C₃×Q₈	—	2	2	no	—
511	C₃×Q₈	—	2	2	no	—
512	C₃×Q₈	—	4	4	no	—
513	C₃×Q₈	—	4	8	no	—
514	C₃×Q₈	—	4	2	no	—
515	C₃×Q₈	—	4	2	no	—
516	C₃×Q₈	—	4	2	no	—
517	C₃×D₄	—	2	2	no	—
518	C₃×D₄	—	2	2	no	—
519	C₃×D₄	—	4	4	no	—
520	C₃×D₄	—	4	4	no	—
521	C₃×D₄	—	4	4	no	—
522	C₃×D₄	—	4	8	no	—
523	C₃×D₄	—	4	2	no	—
524	C₃×D₄	—	8	4	no	—
525	C₃×D₄	—	8	4	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	4	no	—
530	C₂×C₃×C₄	—	2	4	no	—
531	C₂×C₃×C₄	—	2	4	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	4	8	no	—
546	C₂×C₃×C₄	—	4	8	no	—
547	C₂×C₃×C₄	—	4	2	no	—
548	C₂×C₃×C₄	—	4	2	no	—
549	C₂×C₃×C₄	—	4	2	no	—
550	C₂×C₃×C₄	—	4	2	no	—
551	C₂×C₃×C₄	—	4	2	no	—
552	C₂×C₃×C₄	—	4	2	no	—
553	C₂×C₃×C₄	—	4	2	no	—
554	C₂×C₃×C₄	—	8	4	no	—
555	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
556	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
557	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
558	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
560	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
561	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
562	C₃×C₈	—	2	2	no	—
563	C₃×C₈	—	2	2	no	—
564	C₃×C₈	—	2	2	no	—
565	C₃×C₈	—	2	2	no	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
568	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
569	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
570	#41	—	4	8	no	—
571	#41	—	4	4	no	—
572	#41	—	4	4	no	—
573	#41	—	4	4	no	—
574	#41	—	4	4	no	—
575	#41	—	4	8	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	4	2	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	—	4	8	no	—
591	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
592	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
593	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
594	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	8	2	no	—
606	C₂×D₄	—	8	2	no	—
607	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
608	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
609	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
610	C₂×D₄	C₂⁴×C₃	1	2	yes	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	8	2	no	—
630	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
631	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
632	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
633	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
634	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
635	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
640	Q₁₆	—	4	4	no	—
641	Q₁₆	—	4	4	no	—
642	SD₁₆	—	4	4	no	—
643	SD₁₆	—	4	4	no	—
644	M₁₆	—	4	4	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	4	4	no	—
650	C₂×C₈	C₂⁴×C₃	1	2	yes	—
651	C₂×C₈	C₂⁴×C₃	1	2	yes	—
652	C₂×C₈	C₂⁴×C₃	1	2	yes	—
653	C₂×C₈	C₂⁴×C₃	1	2	yes	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₂²×C₃	—	2	2	no	—
680	C₂²×C₃	—	2	2	no	—
681	C₂²×C₃	—	2	2	no	—
682	C₂²×C₃	—	2	2	no	—
683	C₂²×C₃	—	2	2	no	—
684	C₂²×C₃	—	2	2	no	—
685	C₂²×C₃	—	2	2	no	—
686	C₂²×C₃	—	2	2	no	—
687	C₂²×C₃	—	2	2	no	—
688	C₂²×C₃	—	4	4	no	—
689	C₂²×C₃	—	4	4	no	—
690	C₂²×C₃	—	4	4	no	—
691	C₂²×C₃	—	4	2	no	—
692	C₂²×C₃	—	4	2	no	—
693	C₂²×C₃	—	4	2	no	—
694	C₂²×C₃	—	8	4	no	—
695	C₂²×C₃	#534	1	2	yes	—
696	C₂²×C₃	#577	1	2	yes	—
697	C₂²×C₃	#578	1	2	yes	—
698	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
699	C₃×C₄	—	2	2	no	—
700	C₃×C₄	—	2	2	no	—
701	C₃×C₄	—	2	2	no	—
702	C₃×C₄	—	4	2	no	—
703	C₃×C₄	—	4	2	no	—
704	C₃×C₄	—	4	2	no	—
705	C₃×C₄	—	4	2	no	—
706	C₃×C₄	—	4	2	no	—
707	C₃×C₄	—	4	2	no	—
708	C₃×C₄	—	4	2	no	—
709	C₃×C₄	#534	1	2	yes	—
710	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
711	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	4	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	4	2	no	—
725	C₂³	C₂²×C₃×D₄	1	2	yes	—
726	C₂³	C₂²×C₃×D₄	1	2	yes	—
727	C₂³	C₂²×C₃×D₄	1	2	yes	—
728	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
729	Q₈	—	2	2	no	—
730	Q₈	—	2	2	no	—
731	Q₈	—	2	2	no	—
732	Q₈	—	2	2	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	2	no	—
735	Q₈	—	4	4	no	—
736	Q₈	—	4	8	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	4	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	4	no	—
745	D₄	—	4	8	no	—
746	D₄	—	4	2	no	—
747	D₄	—	8	4	no	—
748	D₄	—	8	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	8	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
779	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
780	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
781	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
782	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
783	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
784	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
785	C₈	—	2	2	no	—
786	C₈	—	2	2	no	—
787	C₈	—	2	2	no	—
788	C₈	—	2	2	no	—
789	C₂×C₃	—	4	2	no	—
790	C₂×C₃	—	4	2	no	—
791	C₂×C₃	—	4	2	no	—
792	C₂×C₃	—	8	2	no	—
793	C₂×C₃	#3201	1	4	yes	direct product factor
794	C₂×C₃	C₂×#534	1	1	yes	characteristic
795	C₂×C₃	C₂×#577	1	1	yes	characteristic
796	C₂×C₃	C₂×#578	1	1	yes	characteristic
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	8	4	no	—
813	C₂²	C₃×#534	1	2	yes	—
814	C₂²	C₃×#577	1	2	yes	—
815	C₂²	C₃×#578	1	2	yes	—
816	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	C₃×#534	1	2	yes	—
828	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
829	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₃	C₂×#3201	1	1	yes	characteristic, direct product factor, Sylow
831	C₂	—	4	2	no	—
832	C₂	—	4	2	no	—
833	C₂	—	4	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₃×#3201	1	4	yes	direct product factor
836	C₂	C₂×C₃×#534	1	1	yes	characteristic
837	C₂	C₂×C₃×#577	1	1	yes	characteristic
838	C₂	C₂×C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×#536	C₂	semidirect
3. C₃×#3201	C₂	direct (N × H)
4. C₂×C₃×#484	C₂	semidirect
5. C₂×C₃×#485	C₂	semidirect
6. C₂×C₃×#482	C₂	semidirect
7. C₂×C₃×#483	C₂	semidirect
8. C₂×C₃×#470	C₂	semidirect
9. C₂×C₃×#468	C₂	semidirect
10. C₂×C₃×#467	C₂	semidirect
11. C₂×C₃×#465	C₂	semidirect
12. C₂×C₃×#452	C₂	semidirect
13. C₂×C₃×#452	C₂	semidirect
14. C₂×C₃×#451	C₂	semidirect
15. C₂×C₃×#448	C₂	semidirect
16. C₂×C₃×#408	C₂	semidirect
17. C₂×#3201	C₃	direct (N × H)
30. C₃×#536	C₂²	semidirect
49. C₃×#485	C₂²	semidirect
50. C₃×#484	C₂²	semidirect
51. C₃×#483	C₂²	semidirect
52. C₃×#482	C₂²	semidirect
53. C₃×#470	C₂²	semidirect
54. C₃×#468	C₂²	semidirect
55. C₃×#467	C₂²	semidirect
56. C₃×#465	C₂²	semidirect
57. C₃×#452	C₂²	semidirect
58. C₃×#452	C₂²	semidirect
59. C₃×#451	C₂²	semidirect
60. C₃×#448	C₂²	semidirect
73. C₃×#408	C₂²	semidirect
79. C₂×#536	C₂×C₃	semidirect
80. #3201	C₂×C₃	direct (N × H)
81. C₂×#484	C₂×C₃	semidirect
82. C₂×#485	C₂×C₃	semidirect
83. C₂×#482	C₂×C₃	semidirect
84. C₂×#483	C₂×C₃	semidirect
85. C₂×#470	C₂×C₃	semidirect
86. C₂×#468	C₂×C₃	semidirect
87. C₂×#467	C₂×C₃	semidirect
88. C₂×#465	C₂×C₃	semidirect
89. C₂×#452	C₂×C₃	semidirect
90. C₂×#452	C₂×C₃	semidirect
91. C₂×#451	C₂×C₃	semidirect
92. C₂×#448	C₂×C₃	semidirect
93. C₂×#408	C₂×C₃	semidirect
217. #536	C₂²×C₃	semidirect
236. #485	C₂²×C₃	semidirect
237. #484	C₂²×C₃	semidirect
238. #483	C₂²×C₃	semidirect
239. #482	C₂²×C₃	semidirect
240. #470	C₂²×C₃	semidirect
241. #468	C₂²×C₃	semidirect
242. #467	C₂²×C₃	semidirect
243. #465	C₂²×C₃	semidirect
244. #452	C₂²×C₃	semidirect
245. #452	C₂²×C₃	semidirect
246. #451	C₂²×C₃	semidirect
247. #448	C₂²×C₃	semidirect
260. #408	C₂²×C₃	semidirect
793. C₂×C₃	#3201	direct (N × H)
830. C₃	C₂×#3201	direct (N × H)
835. C₂	C₃×#3201	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#537	2
C₂×C₃×#536	2
C₃×#3201	2
C₂×C₃×#484	2
C₂×C₃×#485	2
C₂×C₃×#482	2
C₂×C₃×#483	2
C₂×C₃×#470	2
C₂×C₃×#468	2
C₂×C₃×#467	2
C₂×C₃×#465	2
C₂×C₃×#452	2
C₂×C₃×#451	2
C₂×C₃×#448	2
C₂×C₃×#408	2
C₂×#3201	3

Subgroups — C2×C3×#3201 #10679352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3201 #10679352