Subgroups — C₃×#36161 #10654768

Order 768.

2816 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×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2848	C₂	1	2	yes	maximal, complemented
5	C₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2485	C₂	1	2	yes	maximal, complemented
8	C₃×#2480	C₂	1	4	yes	maximal, complemented
9	C₃×#2466	C₂	1	4	yes	maximal, complemented
10	C₃×#2447	C₂	1	2	yes	maximal, complemented
11	C₃×#2435	C₂	1	2	yes	maximal
12	C₃×#2415	C₂	1	2	yes	maximal, complemented
13	C₃×#2367	C₂	1	2	yes	maximal, complemented
14	C₃×#2360	C₂	1	2	yes	maximal, complemented
15	C₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2280	C₂	1	2	yes	maximal, complemented
18	#36161	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
20	C₂⁴×C₃×C₄	C₂²	1	2	yes	—
21	C₃×#556	—	2	8	no	—
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#126	C₂²	1	4	yes	complemented
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#124	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄×D₄	—	2	8	no	—
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	2	yes	complemented
40	C₂×C₃×#117	C₂²	1	2	yes	complemented
41	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
44	C₃×#397	C₂²	1	4	yes	complemented
45	C₃×#397	C₂²	1	4	yes	complemented
46	C₃×#397	C₂²	1	4	yes	complemented
47	C₃×#396	C₂²	1	4	yes	complemented
48	C₃×#394	C₂²	1	4	yes	—
49	C₃×#394	C₂²	1	4	yes	—
50	C₃×#391	C₂²	1	2	yes	complemented
51	C₃×#391	C₂²	1	2	yes	complemented
52	C₃×#391	C₂²	1	1	yes	characteristic, complemented
53	C₃×#390	C₂²	1	2	yes	—
54	C₃×#390	C₂²	1	2	yes	—
55	C₃×#389	C₂²	1	4	yes	complemented
56	C₃×#389	C₂²	1	2	yes	complemented
57	C₃×#389	C₂²	1	2	yes	complemented
58	C₃×#389	C₂²	1	2	yes	complemented
59	C₃×#389	C₂²	1	1	yes	characteristic, complemented
60	C₃×#388	C₂²	1	4	yes	complemented
61	C₃×#388	C₂²	1	4	yes	complemented
62	C₃×#388	C₂²	1	4	yes	complemented
63	C₃×#387	C₂²	1	4	yes	complemented
64	C₃×#387	C₂²	1	2	yes	complemented
65	C₃×#385	C₂²	1	4	yes	—
66	C₃×#385	C₂²	1	2	yes	—
67	C₃×#385	C₂²	1	4	yes	complemented
68	C₃×#385	C₂²	1	4	yes	complemented
69	C₃×#384	C₂²	1	1	yes	characteristic, complemented
70	C₃×#381	C₂²	1	4	yes	complemented
71	C₃×#380	C₂²	1	2	yes	—
72	C₃×#380	C₂²	1	1	yes	characteristic
73	C₃×#380	C₂²	1	2	yes	—
74	C₃×#380	C₂²	1	2	yes	complemented
75	C₃×#380	C₂²	1	2	yes	complemented
76	C₃×#380	C₂²	1	2	yes	complemented
77	C₃×#380	C₂²	1	2	yes	complemented
78	C₃×#379	C₂²	1	4	yes	—
79	C₃×#379	C₂²	1	4	yes	—
80	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
85	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
86	C₂×#556	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
88	#2857	C₂×C₃	1	1	yes	characteristic, complemented
89	#2848	C₂×C₃	1	2	yes	complemented
90	#2547	C₂×C₃	1	1	yes	characteristic, complemented
91	#2538	C₂×C₃	1	1	yes	characteristic, complemented
92	#2485	C₂×C₃	1	2	yes	complemented
93	#2480	C₂×C₃	1	4	yes	complemented
94	#2466	C₂×C₃	1	4	yes	complemented
95	#2447	C₂×C₃	1	2	yes	complemented
96	#2435	C₂×C₃	1	2	yes	—
97	#2415	C₂×C₃	1	2	yes	complemented
98	#2367	C₂×C₃	1	2	yes	complemented
99	#2360	C₂×C₃	1	2	yes	complemented
100	#2354	C₂×C₃	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
102	#2280	C₂×C₃	1	2	yes	complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂²×C₃×Q₈	C₂³	1	2	yes	—
105	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×D₄	—	2	4	no	—
107	C₂²×C₃×D₄	—	2	4	no	—
108	C₂²×C₃×D₄	—	2	4	no	—
109	C₂²×C₃×D₄	C₂³	1	2	yes	—
110	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
111	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
112	C₂³×C₃×C₄	—	2	8	no	—
113	C₂³×C₃×C₄	—	2	8	no	—
114	C₂³×C₃×C₄	—	4	4	no	—
115	C₂³×C₃×C₄	C₂³	1	2	yes	—
116	C₂³×C₃×C₄	C₂³	1	2	yes	—
117	C₂³×C₃×C₄	C₂³	1	2	yes	—
118	C₂³×C₃×C₄	C₂³	1	2	yes	—
119	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂³×C₃×C₄	C₂³	1	2	yes	—
121	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
123	C₃×C₄⋊Q₈	—	2	4	no	—
124	C₃×#126	—	2	16	no	—
125	C₃×#124	—	2	8	no	—
126	C₃×#124	—	2	8	no	—
127	C₃×C₂²⋊Q₈	—	2	8	no	—
128	C₃×C₂²⋊Q₈	—	2	8	no	—
129	C₃×C₂²⋊Q₈	—	2	4	no	—
130	C₃×C₂²⋊Q₈	—	4	4	no	—
131	C₃×C₄×Q₈	—	2	8	no	—
132	C₃×C₄×Q₈	—	2	4	no	—
133	C₃×C₄×D₄	—	2	4	no	—
134	C₃×C₄×D₄	—	2	8	no	—
135	C₃×C₄×D₄	—	2	4	no	—
136	C₃×C₄×D₄	—	2	8	no	—
137	C₃×C₄×D₄	—	2	4	no	—
138	C₃×C₄×D₄	D₄	1	8	yes	—
139	C₃×#117	—	2	8	no	—
140	C₃×#117	—	4	4	no	—
141	C₂×C₃×C₄⋊C₄	—	2	4	no	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	4	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄²	—	2	4	no	—
176	C₂×C₃×C₄²	C₂³	1	4	yes	—
177	C₂×C₃×C₄²	C₂³	1	2	yes	—
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂³	1	4	yes	—
183	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
184	C₃×#95	C₂³	1	4	yes	—
185	C₃×#95	C₂³	1	4	yes	—
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	2	yes	—
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	2	yes	—
192	C₃×#95	C₂³	1	2	yes	—
193	C₃×#95	C₂³	1	4	yes	—
194	C₃×#95	C₂³	1	4	yes	—
195	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
196	C₂⁴×C₄	C₂²×C₃	1	2	yes	—
197	#556	—	2	8	no	—
198	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₂×#126	C₂²×C₃	1	4	yes	complemented
200	C₂×#124	C₂²×C₃	1	2	yes	—
201	C₂×#124	C₂²×C₃	1	2	yes	—
202	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
203	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
204	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
205	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
206	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
207	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂×C₄×D₄	—	2	8	no	—
209	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
213	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
215	C₂×#117	C₂²×C₃	1	2	yes	complemented
216	C₂×#117	C₂²×C₃	1	2	yes	complemented
217	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
218	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
219	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
220	#397	C₂²×C₃	1	4	yes	complemented
221	#397	C₂²×C₃	1	4	yes	complemented
222	#397	C₂²×C₃	1	4	yes	complemented
223	#396	C₂²×C₃	1	4	yes	complemented
224	#394	C₂²×C₃	1	4	yes	—
225	#394	C₂²×C₃	1	4	yes	—
226	#391	C₂²×C₃	1	2	yes	complemented
227	#391	C₂²×C₃	1	2	yes	complemented
228	#391	C₂²×C₃	1	1	yes	characteristic, complemented
229	#390	C₂²×C₃	1	2	yes	—
230	#390	C₂²×C₃	1	2	yes	—
231	#389	C₂²×C₃	1	2	yes	complemented
232	#389	C₂²×C₃	1	2	yes	complemented
233	#389	C₂²×C₃	1	4	yes	complemented
234	#389	C₂²×C₃	1	2	yes	complemented
235	#389	C₂²×C₃	1	1	yes	characteristic, complemented
236	#388	C₂²×C₃	1	4	yes	complemented
237	#388	C₂²×C₃	1	4	yes	complemented
238	#388	C₂²×C₃	1	4	yes	complemented
239	#387	C₂²×C₃	1	4	yes	complemented
240	#387	C₂²×C₃	1	2	yes	complemented
241	#385	C₂²×C₃	1	4	yes	—
242	#385	C₂²×C₃	1	2	yes	—
243	#385	C₂²×C₃	1	4	yes	complemented
244	#385	C₂²×C₃	1	4	yes	complemented
245	#384	C₂²×C₃	1	1	yes	characteristic, complemented
246	#381	C₂²×C₃	1	4	yes	complemented
247	#380	C₂²×C₃	1	2	yes	—
248	#380	C₂²×C₃	1	2	yes	—
249	#380	C₂²×C₃	1	1	yes	characteristic
250	#380	C₂²×C₃	1	2	yes	complemented
251	#380	C₂²×C₃	1	2	yes	complemented
252	#380	C₂²×C₃	1	2	yes	complemented
253	#380	C₂²×C₃	1	2	yes	complemented
254	#379	C₂²×C₃	1	4	yes	—
255	#379	C₂²×C₃	1	4	yes	—
256	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
257	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
258	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
259	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
260	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
261	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
262	C₂⁴×C₃	—	2	4	no	—
263	C₂⁴×C₃	—	2	4	no	—
264	C₂⁴×C₃	—	2	4	no	—
265	C₂⁴×C₃	—	2	4	no	—
266	C₂⁴×C₃	—	2	4	no	—
267	C₂⁴×C₃	—	4	2	no	—
268	C₂⁴×C₃	—	4	2	no	—
269	C₂⁴×C₃	C₂⁴	1	2	yes	—
270	C₂⁴×C₃	C₂⁴	1	2	yes	—
271	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×Q₈	—	2	2	no	—
273	C₂×C₃×Q₈	—	2	4	no	—
274	C₂×C₃×Q₈	—	2	4	no	—
275	C₂×C₃×Q₈	—	2	2	no	—
276	C₂×C₃×Q₈	—	2	4	no	—
277	C₂×C₃×Q₈	—	2	2	no	—
278	C₂×C₃×D₄	—	2	32	no	—
279	C₂×C₃×D₄	—	2	4	no	—
280	C₂×C₃×D₄	—	2	4	no	—
281	C₂×C₃×D₄	—	2	2	no	—
282	C₂×C₃×D₄	—	2	4	no	—
283	C₂×C₃×D₄	—	2	2	no	—
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	—	2	2	no	—
286	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
287	C₂×C₃×D₄	#41	1	4	yes	—
288	C₂²×C₃×C₄	—	2	2	no	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	4	no	—
291	C₂²×C₃×C₄	—	2	2	no	—
292	C₂²×C₃×C₄	—	2	4	no	—
293	C₂²×C₃×C₄	—	2	2	no	—
294	C₂²×C₃×C₄	—	2	4	no	—
295	C₂²×C₃×C₄	—	2	4	no	—
296	C₂²×C₃×C₄	—	2	2	no	—
297	C₂²×C₃×C₄	—	2	2	no	—
298	C₂²×C₃×C₄	—	2	4	no	—
299	C₂²×C₃×C₄	—	2	4	no	—
300	C₂²×C₃×C₄	—	2	4	no	—
301	C₂²×C₃×C₄	—	2	4	no	—
302	C₂²×C₃×C₄	—	2	4	no	—
303	C₂²×C₃×C₄	—	2	4	no	—
304	C₂²×C₃×C₄	—	2	4	no	—
305	C₂²×C₃×C₄	—	4	2	no	—
306	C₂²×C₃×C₄	—	4	2	no	—
307	C₂²×C₃×C₄	—	4	2	no	—
308	C₂²×C₃×C₄	—	4	1	no	—
309	C₂²×C₃×C₄	—	4	32	no	—
310	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
311	C₂²×C₃×C₄	#41	1	4	yes	—
312	C₂²×C₃×C₄	#41	1	4	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
321	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
322	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	—	2	2	no	—
329	C₃×C₄⋊C₄	—	2	2	no	—
330	C₃×C₄⋊C₄	—	2	4	no	—
331	C₃×C₄⋊C₄	—	2	8	no	—
332	C₃×C₄⋊C₄	—	2	4	no	—
333	C₃×C₄⋊C₄	—	2	4	no	—
334	C₃×C₄⋊C₄	—	2	4	no	—
335	C₃×C₄⋊C₄	—	2	2	no	—
336	C₃×C₄⋊C₄	—	2	8	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	4	no	—
340	C₃×C₄⋊C₄	—	4	2	no	—
341	C₃×C₄⋊C₄	—	4	2	no	—
342	C₃×C₄⋊C₄	—	4	4	no	—
343	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	2	8	no	—
346	C₃×C₂²⋊C₄	—	2	8	no	—
347	C₃×C₂²⋊C₄	—	2	8	no	—
348	C₃×C₂²⋊C₄	—	2	4	no	—
349	C₃×C₂²⋊C₄	—	2	8	no	—
350	C₃×C₂²⋊C₄	—	2	8	no	—
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	4	4	no	—
355	C₃×C₂²⋊C₄	—	4	4	no	—
356	C₃×C₂²⋊C₄	—	4	4	no	—
357	C₃×C₂²⋊C₄	—	4	4	no	—
358	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
359	C₃×C₄²	—	2	2	no	—
360	C₃×C₄²	—	2	2	no	—
361	C₃×C₄²	—	2	2	no	—
362	C₃×C₄²	—	2	8	no	—
363	C₃×C₄²	—	2	4	no	—
364	C₃×C₄²	—	2	4	no	—
365	C₃×C₄²	—	4	4	no	—
366	C₃×C₄²	C₂×D₄	1	4	yes	—
367	C₂⁵	C₂³×C₃	1	2	yes	—
368	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₃	1	2	yes	—
370	C₂²×D₄	—	2	4	no	—
371	C₂²×D₄	—	2	4	no	—
372	C₂²×D₄	—	2	4	no	—
373	C₂²×D₄	C₂³×C₃	1	2	yes	—
374	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
376	C₂³×C₄	—	2	8	no	—
377	C₂³×C₄	—	2	8	no	—
378	C₂³×C₄	—	4	4	no	—
379	C₂³×C₄	C₂³×C₃	1	2	yes	—
380	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₃	1	2	yes	—
382	C₂³×C₄	C₂³×C₃	1	2	yes	—
383	C₂³×C₄	C₂³×C₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₃	1	2	yes	—
385	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
387	C₄⋊Q₈	—	2	4	no	—
388	#126	—	2	16	no	—
389	#124	—	2	8	no	—
390	#124	—	2	8	no	—
391	C₂²⋊Q₈	—	2	8	no	—
392	C₂²⋊Q₈	—	2	8	no	—
393	C₂²⋊Q₈	—	2	4	no	—
394	C₂²⋊Q₈	—	4	4	no	—
395	C₄×Q₈	—	2	8	no	—
396	C₄×Q₈	—	2	4	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	8	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	8	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	C₃×D₄	1	8	yes	—
403	#117	—	2	8	no	—
404	#117	—	4	4	no	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄²	—	2	4	no	—
440	C₂×C₄²	C₂³×C₃	1	4	yes	—
441	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₃	1	2	yes	—
445	C₂×C₄²	C₂³×C₃	1	2	yes	—
446	C₂×C₄²	C₂³×C₃	1	4	yes	—
447	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
448	#95	C₂³×C₃	1	4	yes	—
449	#95	C₂³×C₃	1	4	yes	—
450	#95	C₂³×C₃	1	2	yes	—
451	#95	C₂³×C₃	1	2	yes	—
452	#95	C₂³×C₃	1	2	yes	—
453	#95	C₂³×C₃	1	4	yes	—
454	#95	C₂³×C₃	1	4	yes	—
455	#95	C₂³×C₃	1	2	yes	—
456	#95	C₂³×C₃	1	2	yes	—
457	#95	C₂³×C₃	1	4	yes	—
458	#95	C₂³×C₃	1	4	yes	—
459	C₂³×C₃	—	2	1	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	1	no	—
462	C₂³×C₃	—	2	1	no	—
463	C₂³×C₃	—	2	16	no	—
464	C₂³×C₃	—	2	2	no	—
465	C₂³×C₃	—	2	2	no	—
466	C₂³×C₃	—	2	2	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	2	2	no	—
470	C₂³×C₃	—	2	2	no	—
471	C₂³×C₃	—	2	2	no	—
472	C₂³×C₃	—	2	2	no	—
473	C₂³×C₃	—	2	2	no	—
474	C₂³×C₃	—	2	2	no	—
475	C₂³×C₃	—	2	2	no	—
476	C₂³×C₃	—	4	8	no	—
477	C₂³×C₃	—	4	8	no	—
478	C₂³×C₃	—	4	8	no	—
479	C₂³×C₃	—	4	8	no	—
480	C₂³×C₃	—	4	8	no	—
481	C₂³×C₃	—	4	8	no	—
482	C₂³×C₃	C₂²×D₄	1	4	yes	—
483	C₂³×C₃	C₂×#41	1	4	yes	—
484	C₂³×C₃	C₂×#41	1	2	yes	—
485	C₂³×C₃	C₂×#41	1	2	yes	—
486	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
487	C₂³×C₃	C₂⁵	1	1	yes	characteristic
488	C₃×Q₈	—	4	8	no	—
489	C₃×Q₈	—	4	4	no	—
490	C₃×D₄	—	2	16	no	—
491	C₃×D₄	—	2	8	no	—
492	C₃×D₄	—	2	8	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	8	no	—
502	C₂×C₃×C₄	—	2	8	no	—
503	C₂×C₃×C₄	—	2	16	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	4	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	2	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	4	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	4	no	—
514	C₂×C₃×C₄	—	2	4	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	4	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	4	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	4	8	no	—
529	C₂×C₃×C₄	—	4	4	no	—
530	C₂×C₃×C₄	—	4	8	no	—
531	C₂×C₃×C₄	—	4	8	no	—
532	C₂×C₃×C₄	—	4	8	no	—
533	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
534	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
535	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
536	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
537	C₂×C₃×C₄	C₂×#41	1	2	yes	—
538	C₂×C₃×C₄	C₂×#41	1	2	yes	—
539	C₂×C₃×C₄	C₂×#41	1	2	yes	—
540	C₂×C₃×C₄	C₂×#41	1	2	yes	—
541	C₂×C₃×C₄	C₂×#41	1	2	yes	—
542	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
543	C₂⁴	—	2	4	no	—
544	C₂⁴	—	2	4	no	—
545	C₂⁴	—	2	4	no	—
546	C₂⁴	—	2	4	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	4	2	no	—
549	C₂⁴	—	4	2	no	—
550	C₂⁴	C₂⁴×C₃	1	2	yes	—
551	C₂⁴	C₂⁴×C₃	1	2	yes	—
552	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×D₄	—	2	32	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
568	C₂×D₄	C₃×#41	1	4	yes	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	32	no	—
591	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
592	C₂²×C₄	C₃×#41	1	4	yes	—
593	C₂²×C₄	C₃×#41	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	8	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	8	no	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	8	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	4	no	—
647	C₄²	C₂×C₃×D₄	1	4	yes	—
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	2	2	no	—
651	C₂²×C₃	—	2	2	no	—
652	C₂²×C₃	—	2	2	no	—
653	C₂²×C₃	—	2	2	no	—
654	C₂²×C₃	—	2	4	no	—
655	C₂²×C₃	—	2	4	no	—
656	C₂²×C₃	—	2	4	no	—
657	C₂²×C₃	—	2	4	no	—
658	C₂²×C₃	—	2	4	no	—
659	C₂²×C₃	—	2	4	no	—
660	C₂²×C₃	—	4	32	no	—
661	C₂²×C₃	—	4	2	no	—
662	C₂²×C₃	—	4	2	no	—
663	C₂²×C₃	—	4	2	no	—
664	C₂²×C₃	—	4	2	no	—
665	C₂²×C₃	—	4	2	no	—
666	C₂²×C₃	—	4	2	no	—
667	C₂²×C₃	—	4	2	no	—
668	C₂²×C₃	—	4	2	no	—
669	C₂²×C₃	#556	1	4	yes	complemented
670	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
671	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
672	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
673	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
674	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
676	C₂²×C₃	#585	1	1	yes	characteristic
677	C₃×C₄	—	2	2	no	—
678	C₃×C₄	—	2	2	no	—
679	C₃×C₄	—	2	4	no	—
680	C₃×C₄	—	2	2	no	—
681	C₃×C₄	—	4	4	no	—
682	C₃×C₄	—	4	2	no	—
683	C₃×C₄	—	4	2	no	—
684	C₃×C₄	—	4	2	no	—
685	C₃×C₄	—	4	2	no	—
686	C₃×C₄	—	4	1	no	—
687	C₃×C₄	—	4	4	no	—
688	C₃×C₄	—	4	2	no	—
689	C₃×C₄	#525	1	4	yes	—
690	C₃×C₄	#546	1	4	yes	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	16	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	4	8	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	8	no	—
714	C₂³	C₂²×C₃×D₄	1	4	yes	—
715	C₂³	C₂×C₃×#41	1	4	yes	—
716	C₂³	C₂×C₃×#41	1	2	yes	—
717	C₂³	C₂×C₃×#41	1	2	yes	—
718	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
719	C₂³	C₂⁵×C₃	1	1	yes	characteristic
720	Q₈	—	4	8	no	—
721	Q₈	—	4	4	no	—
722	D₄	—	2	16	no	—
723	D₄	—	2	8	no	—
724	D₄	—	2	8	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	8	no	—
734	C₂×C₄	—	2	8	no	—
735	C₂×C₄	—	2	16	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	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	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
766	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
767	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
768	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
769	C₂×C₄	C₂×C₃×#41	1	2	yes	—
770	C₂×C₄	C₂×C₃×#41	1	2	yes	—
771	C₂×C₄	C₂×C₃×#41	1	2	yes	—
772	C₂×C₄	C₂×C₃×#41	1	2	yes	—
773	C₂×C₄	C₂×C₃×#41	1	2	yes	—
774	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
775	C₂×C₃	—	2	4	no	—
776	C₂×C₃	—	4	4	no	—
777	C₂×C₃	—	4	4	no	—
778	C₂×C₃	C₂×#525	1	1	yes	characteristic
779	C₂×C₃	C₂×#546	1	1	yes	characteristic
780	C₂×C₃	C₂×#556	1	1	yes	characteristic
781	C₂×C₃	#3475	1	1	yes	characteristic
782	C₂×C₃	#3489	1	1	yes	characteristic
783	C₂×C₃	#3506	1	1	yes	characteristic
784	C₂×C₃	#3520	1	1	yes	characteristic
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	4	32	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	C₃×#556	1	4	yes	complemented
807	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
808	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
809	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
810	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
811	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
812	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
813	C₂²	C₃×#585	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	4	no	—
817	C₄	—	2	2	no	—
818	C₄	—	4	4	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	2	no	—
826	C₄	C₃×#525	1	4	yes	—
827	C₄	C₃×#546	1	4	yes	—
828	C₃	#36161	1	1	yes	characteristic, direct product factor, Sylow
829	C₂	—	2	4	no	—
830	C₂	—	4	4	no	—
831	C₂	—	4	4	no	—
832	C₂	C₂×C₃×#525	1	1	yes	characteristic
833	C₂	C₂×C₃×#546	1	1	yes	characteristic
834	C₂	C₂×C₃×#556	1	1	yes	characteristic
835	C₂	C₃×#3475	1	1	yes	characteristic
836	C₂	C₃×#3489	1	1	yes	characteristic
837	C₂	C₃×#3506	1	1	yes	characteristic
838	C₂	C₃×#3520	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. C₂×C₃×#556	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2848	C₂	semidirect
5. C₃×#2547	C₂	semidirect
6. C₃×#2538	C₂	semidirect
7. C₃×#2485	C₂	semidirect
8. C₃×#2480	C₂	semidirect
9. C₃×#2466	C₂	semidirect
10. C₃×#2447	C₂	semidirect
12. C₃×#2415	C₂	semidirect
13. C₃×#2367	C₂	semidirect
14. C₃×#2360	C₂	semidirect
15. C₃×#2354	C₂	semidirect
16. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
17. C₃×#2280	C₂	semidirect
18. #36161	C₃	direct (N × H)
22. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₃×#126	C₂²	semidirect
28. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₃×C₄×Q₈	C₂²	semidirect
31. C₂×C₃×C₄×Q₈	C₂²	semidirect
39. C₂×C₃×#117	C₂²	semidirect
40. C₂×C₃×#117	C₂²	semidirect
44. C₃×#397	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
47. C₃×#396	C₂²	semidirect
50. C₃×#391	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
52. C₃×#391	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
57. C₃×#389	C₂²	semidirect
58. C₃×#389	C₂²	semidirect
59. C₃×#389	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
63. C₃×#387	C₂²	semidirect
64. C₃×#387	C₂²	semidirect
67. C₃×#385	C₂²	semidirect
68. C₃×#385	C₂²	semidirect
69. C₃×#384	C₂²	semidirect
70. C₃×#381	C₂²	semidirect
74. C₃×#380	C₂²	semidirect
75. C₃×#380	C₂²	semidirect
76. C₃×#380	C₂²	semidirect
77. C₃×#380	C₂²	semidirect
80. C₃×C₄×C₄⋊C₄	C₂²	semidirect
81. C₃×C₄×C₄⋊C₄	C₂²	semidirect
82. C₃×C₄×C₄⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×#556	C₂×C₃	semidirect
88. #2857	C₂×C₃	semidirect
89. #2848	C₂×C₃	semidirect
90. #2547	C₂×C₃	semidirect
91. #2538	C₂×C₃	semidirect
92. #2485	C₂×C₃	semidirect
93. #2480	C₂×C₃	semidirect
94. #2466	C₂×C₃	semidirect
95. #2447	C₂×C₃	semidirect
97. #2415	C₂×C₃	semidirect
98. #2367	C₂×C₃	semidirect
99. #2360	C₂×C₃	semidirect
100. #2354	C₂×C₃	semidirect
101. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
102. #2280	C₂×C₃	semidirect
198. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
199. C₂×#126	C₂²×C₃	semidirect
204. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
205. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
206. C₂×C₄×Q₈	C₂²×C₃	semidirect
207. C₂×C₄×Q₈	C₂²×C₃	semidirect
215. C₂×#117	C₂²×C₃	semidirect
216. C₂×#117	C₂²×C₃	semidirect
220. #397	C₂²×C₃	semidirect
221. #397	C₂²×C₃	semidirect
222. #397	C₂²×C₃	semidirect
223. #396	C₂²×C₃	semidirect
226. #391	C₂²×C₃	semidirect
227. #391	C₂²×C₃	semidirect
228. #391	C₂²×C₃	semidirect
231. #389	C₂²×C₃	semidirect
232. #389	C₂²×C₃	semidirect
233. #389	C₂²×C₃	semidirect
234. #389	C₂²×C₃	semidirect
235. #389	C₂²×C₃	semidirect
236. #388	C₂²×C₃	semidirect
237. #388	C₂²×C₃	semidirect
238. #388	C₂²×C₃	semidirect
239. #387	C₂²×C₃	semidirect
240. #387	C₂²×C₃	semidirect
243. #385	C₂²×C₃	semidirect
244. #385	C₂²×C₃	semidirect
245. #384	C₂²×C₃	semidirect
246. #381	C₂²×C₃	semidirect
250. #380	C₂²×C₃	semidirect
251. #380	C₂²×C₃	semidirect
252. #380	C₂²×C₃	semidirect
253. #380	C₂²×C₃	semidirect
256. C₄×C₄⋊C₄	C₂²×C₃	semidirect
257. C₄×C₄⋊C₄	C₂²×C₃	semidirect
258. C₄×C₄⋊C₄	C₂²×C₃	semidirect
261. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
669. C₂²×C₃	#556	semidirect
806. C₂²	C₃×#556	semidirect
828. C₃	#36161	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×#556	2
C₂²×C₃×C₄×D₄	2
C₃×#2857	2
C₃×#2848	2
C₃×#2547	2
C₃×#2538	2
C₃×#2485	2
C₃×#2480	2
C₃×#2466	2
C₃×#2447	2
C₃×#2435	2
C₃×#2415	2
C₃×#2367	2
C₃×#2360	2
C₃×#2354	2
C₃×C₄×C₂²⋊Q₈	2
C₃×#2280	2
#36161	3

Subgroups — C3×#36161 #10654768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36161 #10654768