Subgroups — C₃×#41989 #10660596

Order 768.

2654 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2816	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2814	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2705	C₂	1	2	yes	maximal, complemented
6	C₃×#2697	C₂	1	2	yes	maximal, complemented
7	C₃×#2681	C₂	1	2	yes	maximal, complemented
8	C₃×#2679	C₂	1	2	yes	maximal, complemented
9	C₃×#2662	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2613	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2610	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2603	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2476	C₂	1	2	yes	maximal, complemented
17	C₃×#2472	C₂	1	2	yes	maximal, complemented
18	C₃×#2424	C₂	1	2	yes	maximal, complemented
19	C₃×#2418	C₂	1	2	yes	maximal, complemented
20	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2404	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
24	#41989	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
27	C₃×#551	—	2	8	no	—
28	C₃×#546	—	2	8	no	—
29	C₂×C₃×#126	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#126	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#123	C₂²	1	1	yes	characteristic
34	C₂×C₃×#123	C₂²	1	1	yes	characteristic
35	C₂×C₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₃×#123	C₂²	1	2	yes	complemented
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	C₂²	1	2	yes	—
43	C₂×C₃×#121	C₂²	1	2	yes	—
44	C₂×C₃×#120	C₂²	1	2	yes	—
45	C₂×C₃×#120	C₂²	1	1	yes	characteristic
46	C₂×C₃×#120	C₂²	1	2	yes	—
47	C₂×C₃×#120	C₂²	1	2	yes	—
48	C₂×C₃×#120	C₂²	1	2	yes	complemented
49	C₂×C₃×#120	C₂²	1	2	yes	complemented
50	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
54	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
58	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₃×#399	C₂²	1	2	yes	complemented
60	C₃×#398	C₂²	1	1	yes	characteristic, complemented
61	C₃×#398	C₂²	1	1	yes	characteristic, complemented
62	C₃×#398	C₂²	1	2	yes	complemented
63	C₃×#397	C₂²	1	1	yes	characteristic, complemented
64	C₃×#397	C₂²	1	1	yes	characteristic, complemented
65	C₃×#397	C₂²	1	2	yes	complemented
66	C₃×#397	C₂²	1	2	yes	complemented
67	C₃×#396	C₂²	1	2	yes	complemented
68	C₃×#396	C₂²	1	2	yes	complemented
69	C₃×#396	C₂²	1	2	yes	complemented
70	C₃×#395	C₂²	1	1	yes	characteristic, complemented
71	C₃×#395	C₂²	1	1	yes	characteristic, complemented
72	C₃×#394	C₂²	1	2	yes	—
73	C₃×#394	C₂²	1	2	yes	—
74	C₃×#394	C₂²	1	1	yes	characteristic, complemented
75	C₃×#394	C₂²	1	1	yes	characteristic, complemented
76	C₃×#394	C₂²	1	2	yes	complemented
77	C₃×#394	C₂²	1	2	yes	complemented
78	C₃×#394	C₂²	1	2	yes	complemented
79	C₃×#394	C₂²	1	2	yes	complemented
80	C₃×#394	C₂²	1	2	yes	complemented
81	C₃×#394	C₂²	1	1	yes	characteristic, complemented
82	C₃×#394	C₂²	1	2	yes	complemented
83	C₃×#394	C₂²	1	2	yes	complemented
84	C₃×#394	C₂²	1	2	yes	complemented
85	C₃×#394	C₂²	1	2	yes	complemented
86	C₃×#394	C₂²	1	1	yes	characteristic, complemented
87	C₃×#393	C₂²	1	1	yes	characteristic, complemented
88	C₃×#393	C₂²	1	1	yes	characteristic, complemented
89	C₃×#393	C₂²	1	2	yes	complemented
90	C₃×#392	C₂²	1	1	yes	characteristic
91	C₃×#392	C₂²	1	1	yes	characteristic
92	C₃×#392	C₂²	1	1	yes	characteristic
93	C₃×#392	C₂²	1	1	yes	characteristic
94	C₃×#392	C₂²	1	2	yes	—
95	C₃×#390	C₂²	1	2	yes	—
96	C₃×#390	C₂²	1	2	yes	complemented
97	C₃×#390	C₂²	1	2	yes	complemented
98	C₃×#390	C₂²	1	2	yes	complemented
99	C₃×#390	C₂²	1	2	yes	complemented
100	C₃×#389	C₂²	1	2	yes	complemented
101	C₃×#388	C₂²	1	2	yes	complemented
102	C₃×#388	C₂²	1	2	yes	complemented
103	C₃×#388	C₂²	1	2	yes	complemented
104	C₃×#388	C₂²	1	2	yes	complemented
105	C₃×#388	C₂²	1	2	yes	complemented
106	C₃×#388	C₂²	1	2	yes	complemented
107	C₃×#387	C₂²	1	2	yes	complemented
108	C₃×#386	C₂²	1	2	yes	complemented
109	C₃×#386	C₂²	1	2	yes	complemented
110	C₃×#386	C₂²	1	2	yes	complemented
111	C₃×#386	C₂²	1	2	yes	complemented
112	C₃×#386	C₂²	1	2	yes	complemented
113	C₃×#386	C₂²	1	2	yes	complemented
114	C₃×#385	C₂²	1	2	yes	complemented
115	C₃×#385	C₂²	1	2	yes	complemented
116	C₃×#381	C₂²	1	1	yes	characteristic, complemented
117	C₃×#381	C₂²	1	1	yes	characteristic, complemented
118	C₃×#380	C₂²	1	1	yes	characteristic, complemented
119	C₃×#380	C₂²	1	2	yes	complemented
120	C₃×#380	C₂²	1	1	yes	characteristic, complemented
121	C₃×#379	C₂²	1	2	yes	complemented
122	C₃×#379	C₂²	1	2	yes	complemented
123	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
124	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
125	C₃×#376	C₂²	1	1	yes	characteristic, complemented
126	C₂×#551	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
128	#2816	C₂×C₃	1	1	yes	characteristic, complemented
129	#2814	C₂×C₃	1	1	yes	characteristic, complemented
130	#2705	C₂×C₃	1	2	yes	complemented
131	#2697	C₂×C₃	1	2	yes	complemented
132	#2681	C₂×C₃	1	2	yes	complemented
133	#2679	C₂×C₃	1	2	yes	complemented
134	#2662	C₂×C₃	1	1	yes	characteristic, complemented
135	#2638	C₂×C₃	1	1	yes	characteristic, complemented
136	#2617	C₂×C₃	1	1	yes	characteristic, complemented
137	#2616	C₂×C₃	1	1	yes	characteristic, complemented
138	#2613	C₂×C₃	1	1	yes	characteristic, complemented
139	#2610	C₂×C₃	1	1	yes	characteristic, complemented
140	#2603	C₂×C₃	1	1	yes	characteristic, complemented
141	#2476	C₂×C₃	1	2	yes	complemented
142	#2472	C₂×C₃	1	2	yes	complemented
143	#2424	C₂×C₃	1	2	yes	complemented
144	#2418	C₂×C₃	1	2	yes	complemented
145	#2408	C₂×C₃	1	1	yes	characteristic, complemented
146	#2404	C₂×C₃	1	1	yes	characteristic, complemented
147	#2392	C₂×C₃	1	1	yes	characteristic, complemented
148	#2319	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	2	yes	—
150	C₂⁵×C₃	C₂³	1	1	yes	characteristic
151	C₂×C₃×#41	—	2	4	no	—
152	C₂×C₃×#41	—	4	4	no	—
153	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	—	2	4	no	—
156	C₂²×C₃×D₄	—	4	4	no	—
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂³	1	2	yes	—
164	C₂²×C₃×D₄	C₂³	1	2	yes	—
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂³	1	2	yes	—
168	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
169	C₂³×C₃×C₄	C₂³	1	2	yes	—
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	2	yes	—
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
174	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
175	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
176	C₃×#126	—	2	4	no	—
177	C₃×#126	—	2	4	no	—
178	C₃×#124	—	2	4	no	—
179	C₃×#124	—	2	4	no	—
180	C₃×#123	—	2	4	no	—
181	C₃×#123	—	2	4	no	—
182	C₃×#123	—	2	8	no	—
183	C₃×#123	—	2	4	no	—
184	C₃×C₂²⋊Q₈	—	2	4	no	—
185	C₃×C₂²⋊Q₈	—	2	4	no	—
186	C₃×C₂²⋊Q₈	—	2	4	no	—
187	C₃×C₂²⋊Q₈	—	4	4	no	—
188	C₃×#121	—	2	4	no	—
189	C₃×#121	—	2	8	no	—
190	C₃×#121	—	4	4	no	—
191	C₃×#120	—	2	8	no	—
192	C₃×#120	—	2	4	no	—
193	C₃×#120	—	4	4	no	—
194	C₃×#120	—	4	4	no	—
195	C₃×#120	—	4	4	no	—
196	C₃×#120	—	4	4	no	—
197	C₃×C₄×D₄	—	2	4	no	—
198	C₃×C₄×D₄	—	2	4	no	—
199	C₃×C₄×D₄	—	4	4	no	—
200	C₃×C₄×D₄	D₄	1	8	yes	complemented
201	C₃×#117	—	2	4	no	—
202	C₃×#117	—	2	4	no	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
221	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
222	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
254	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
256	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
257	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
258	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
259	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
260	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
263	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
264	C₂×C₃×C₄²	C₂³	1	2	yes	—
265	C₂×C₃×C₄²	C₂³	1	2	yes	—
266	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	1	yes	characteristic
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	1	yes	characteristic
273	C₃×#95	C₂³	1	1	yes	characteristic
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
283	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
284	#551	—	2	8	no	—
285	#546	—	2	8	no	—
286	C₂×#126	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₂×#126	C₂²×C₃	1	1	yes	characteristic, complemented
288	C₂×#124	C₂²×C₃	1	1	yes	characteristic
289	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
290	C₂×#123	C₂²×C₃	1	1	yes	characteristic
291	C₂×#123	C₂²×C₃	1	1	yes	characteristic
292	C₂×#123	C₂²×C₃	1	1	yes	characteristic
293	C₂×#123	C₂²×C₃	1	2	yes	complemented
294	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
298	C₂×#121	C₂²×C₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₃	1	2	yes	—
300	C₂×#121	C₂²×C₃	1	2	yes	—
301	C₂×#120	C₂²×C₃	1	1	yes	characteristic
302	C₂×#120	C₂²×C₃	1	2	yes	—
303	C₂×#120	C₂²×C₃	1	2	yes	—
304	C₂×#120	C₂²×C₃	1	2	yes	—
305	C₂×#120	C₂²×C₃	1	2	yes	complemented
306	C₂×#120	C₂²×C₃	1	2	yes	complemented
307	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
311	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
315	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
316	#399	C₂²×C₃	1	2	yes	complemented
317	#398	C₂²×C₃	1	1	yes	characteristic, complemented
318	#398	C₂²×C₃	1	1	yes	characteristic, complemented
319	#398	C₂²×C₃	1	2	yes	complemented
320	#397	C₂²×C₃	1	1	yes	characteristic, complemented
321	#397	C₂²×C₃	1	1	yes	characteristic, complemented
322	#397	C₂²×C₃	1	2	yes	complemented
323	#397	C₂²×C₃	1	2	yes	complemented
324	#396	C₂²×C₃	1	2	yes	complemented
325	#396	C₂²×C₃	1	2	yes	complemented
326	#396	C₂²×C₃	1	2	yes	complemented
327	#395	C₂²×C₃	1	1	yes	characteristic, complemented
328	#395	C₂²×C₃	1	1	yes	characteristic, complemented
329	#394	C₂²×C₃	1	2	yes	—
330	#394	C₂²×C₃	1	2	yes	—
331	#394	C₂²×C₃	1	1	yes	characteristic, complemented
332	#394	C₂²×C₃	1	1	yes	characteristic, complemented
333	#394	C₂²×C₃	1	2	yes	complemented
334	#394	C₂²×C₃	1	2	yes	complemented
335	#394	C₂²×C₃	1	1	yes	characteristic, complemented
336	#394	C₂²×C₃	1	1	yes	characteristic, complemented
337	#394	C₂²×C₃	1	2	yes	complemented
338	#394	C₂²×C₃	1	2	yes	complemented
339	#394	C₂²×C₃	1	2	yes	complemented
340	#394	C₂²×C₃	1	2	yes	complemented
341	#394	C₂²×C₃	1	2	yes	complemented
342	#394	C₂²×C₃	1	2	yes	complemented
343	#394	C₂²×C₃	1	2	yes	complemented
344	#393	C₂²×C₃	1	2	yes	complemented
345	#393	C₂²×C₃	1	1	yes	characteristic, complemented
346	#393	C₂²×C₃	1	1	yes	characteristic, complemented
347	#392	C₂²×C₃	1	1	yes	characteristic
348	#392	C₂²×C₃	1	1	yes	characteristic
349	#392	C₂²×C₃	1	1	yes	characteristic
350	#392	C₂²×C₃	1	2	yes	—
351	#392	C₂²×C₃	1	1	yes	characteristic
352	#390	C₂²×C₃	1	2	yes	—
353	#390	C₂²×C₃	1	2	yes	complemented
354	#390	C₂²×C₃	1	2	yes	complemented
355	#390	C₂²×C₃	1	2	yes	complemented
356	#390	C₂²×C₃	1	2	yes	complemented
357	#389	C₂²×C₃	1	2	yes	complemented
358	#388	C₂²×C₃	1	2	yes	complemented
359	#388	C₂²×C₃	1	2	yes	complemented
360	#388	C₂²×C₃	1	2	yes	complemented
361	#388	C₂²×C₃	1	2	yes	complemented
362	#388	C₂²×C₃	1	2	yes	complemented
363	#388	C₂²×C₃	1	2	yes	complemented
364	#387	C₂²×C₃	1	2	yes	complemented
365	#386	C₂²×C₃	1	2	yes	complemented
366	#386	C₂²×C₃	1	2	yes	complemented
367	#386	C₂²×C₃	1	2	yes	complemented
368	#386	C₂²×C₃	1	2	yes	complemented
369	#386	C₂²×C₃	1	2	yes	complemented
370	#386	C₂²×C₃	1	2	yes	complemented
371	#385	C₂²×C₃	1	2	yes	complemented
372	#385	C₂²×C₃	1	2	yes	complemented
373	#381	C₂²×C₃	1	1	yes	characteristic, complemented
374	#381	C₂²×C₃	1	1	yes	characteristic, complemented
375	#380	C₂²×C₃	1	1	yes	characteristic, complemented
376	#380	C₂²×C₃	1	1	yes	characteristic, complemented
377	#380	C₂²×C₃	1	2	yes	complemented
378	#379	C₂²×C₃	1	2	yes	complemented
379	#379	C₂²×C₃	1	2	yes	complemented
380	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
381	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
382	#376	C₂²×C₃	1	1	yes	characteristic, complemented
383	C₂⁴×C₃	—	2	2	no	—
384	C₂⁴×C₃	—	2	4	no	—
385	C₂⁴×C₃	—	2	2	no	—
386	C₂⁴×C₃	—	2	4	no	—
387	C₂⁴×C₃	—	4	2	no	—
388	C₂⁴×C₃	—	4	2	no	—
389	C₂⁴×C₃	—	4	1	no	—
390	C₂⁴×C₃	—	4	2	no	—
391	C₂⁴×C₃	—	4	2	no	—
392	C₂⁴×C₃	—	4	2	no	—
393	C₂⁴×C₃	—	4	2	no	—
394	C₂⁴×C₃	—	4	2	no	—
395	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
396	C₂⁴×C₃	C₂⁴	1	2	yes	—
397	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
398	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
399	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
400	C₂⁴×C₃	C₂⁴	1	2	yes	—
401	C₃×#41	—	4	16	no	—
402	C₂×C₃×Q₈	—	2	2	no	—
403	C₂×C₃×Q₈	—	2	2	no	—
404	C₂×C₃×Q₈	—	4	2	no	—
405	C₂×C₃×Q₈	—	4	2	no	—
406	C₂×C₃×D₄	—	2	4	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	2	4	no	—
409	C₂×C₃×D₄	—	2	4	no	—
410	C₂×C₃×D₄	—	2	2	no	—
411	C₂×C₃×D₄	—	2	4	no	—
412	C₂×C₃×D₄	—	2	4	no	—
413	C₂×C₃×D₄	—	2	4	no	—
414	C₂×C₃×D₄	—	2	4	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	4	no	—
417	C₂×C₃×D₄	—	2	4	no	—
418	C₂×C₃×D₄	—	2	2	no	—
419	C₂×C₃×D₄	—	2	4	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	4	2	no	—
422	C₂×C₃×D₄	—	4	2	no	—
423	C₂×C₃×D₄	—	4	2	no	—
424	C₂×C₃×D₄	—	4	2	no	—
425	C₂×C₃×D₄	—	4	1	no	—
426	C₂×C₃×D₄	—	4	2	no	—
427	C₂×C₃×D₄	—	4	2	no	—
428	C₂×C₃×D₄	—	4	2	no	—
429	C₂×C₃×D₄	—	4	2	no	—
430	C₂×C₃×D₄	—	4	2	no	—
431	C₂×C₃×D₄	—	4	2	no	—
432	C₂×C₃×D₄	—	4	2	no	—
433	C₂×C₃×D₄	—	4	2	no	—
434	C₂×C₃×D₄	—	4	2	no	—
435	C₂×C₃×D₄	—	4	2	no	—
436	C₂×C₃×D₄	—	4	2	no	—
437	C₂×C₃×D₄	—	4	16	no	—
438	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
439	C₂²×C₃×C₄	—	2	2	no	—
440	C₂²×C₃×C₄	—	2	2	no	—
441	C₂²×C₃×C₄	—	2	4	no	—
442	C₂²×C₃×C₄	—	2	2	no	—
443	C₂²×C₃×C₄	—	2	4	no	—
444	C₂²×C₃×C₄	—	2	4	no	—
445	C₂²×C₃×C₄	—	2	2	no	—
446	C₂²×C₃×C₄	—	4	1	no	—
447	C₂²×C₃×C₄	—	4	2	no	—
448	C₂²×C₃×C₄	—	4	2	no	—
449	C₂²×C₃×C₄	—	4	2	no	—
450	C₂²×C₃×C₄	—	4	2	no	—
451	C₂²×C₃×C₄	—	4	2	no	—
452	C₂²×C₃×C₄	—	4	2	no	—
453	C₂²×C₃×C₄	—	4	2	no	—
454	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
455	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
456	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
457	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
459	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
460	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
461	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
463	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
464	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
466	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
467	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
468	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
469	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
473	C₃×C₄⋊C₄	—	2	2	no	—
474	C₃×C₄⋊C₄	—	2	2	no	—
475	C₃×C₄⋊C₄	—	2	2	no	—
476	C₃×C₄⋊C₄	—	2	2	no	—
477	C₃×C₄⋊C₄	—	2	2	no	—
478	C₃×C₄⋊C₄	—	2	2	no	—
479	C₃×C₄⋊C₄	—	2	4	no	—
480	C₃×C₄⋊C₄	—	2	2	no	—
481	C₃×C₄⋊C₄	—	2	2	no	—
482	C₃×C₄⋊C₄	—	4	2	no	—
483	C₃×C₄⋊C₄	—	4	2	no	—
484	C₃×C₄⋊C₄	—	4	2	no	—
485	C₃×C₄⋊C₄	—	4	2	no	—
486	C₃×C₄⋊C₄	—	4	2	no	—
487	C₃×C₄⋊C₄	—	4	2	no	—
488	C₃×C₄⋊C₄	—	4	2	no	—
489	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
490	C₃×C₂²⋊C₄	—	2	4	no	—
491	C₃×C₂²⋊C₄	—	2	2	no	—
492	C₃×C₂²⋊C₄	—	2	2	no	—
493	C₃×C₂²⋊C₄	—	2	2	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	2	4	no	—
496	C₃×C₂²⋊C₄	—	2	4	no	—
497	C₃×C₂²⋊C₄	—	2	4	no	—
498	C₃×C₂²⋊C₄	—	2	2	no	—
499	C₃×C₂²⋊C₄	—	2	4	no	—
500	C₃×C₂²⋊C₄	—	2	4	no	—
501	C₃×C₂²⋊C₄	—	2	2	no	—
502	C₃×C₂²⋊C₄	—	2	2	no	—
503	C₃×C₂²⋊C₄	—	2	2	no	—
504	C₃×C₂²⋊C₄	—	2	2	no	—
505	C₃×C₂²⋊C₄	—	2	2	no	—
506	C₃×C₂²⋊C₄	—	2	2	no	—
507	C₃×C₂²⋊C₄	—	2	4	no	—
508	C₃×C₂²⋊C₄	—	2	4	no	—
509	C₃×C₂²⋊C₄	—	2	2	no	—
510	C₃×C₂²⋊C₄	—	4	2	no	—
511	C₃×C₂²⋊C₄	—	4	2	no	—
512	C₃×C₂²⋊C₄	—	4	2	no	—
513	C₃×C₂²⋊C₄	—	4	2	no	—
514	C₃×C₂²⋊C₄	—	4	2	no	—
515	C₃×C₂²⋊C₄	—	4	2	no	—
516	C₃×C₂²⋊C₄	—	4	2	no	—
517	C₃×C₂²⋊C₄	—	4	2	no	—
518	C₃×C₂²⋊C₄	—	4	2	no	—
519	C₃×C₂²⋊C₄	—	4	2	no	—
520	C₃×C₂²⋊C₄	—	4	2	no	—
521	C₃×C₂²⋊C₄	—	4	2	no	—
522	C₃×C₂²⋊C₄	—	4	2	no	—
523	C₃×C₂²⋊C₄	—	4	2	no	—
524	C₃×C₂²⋊C₄	—	4	2	no	—
525	C₃×C₂²⋊C₄	—	4	2	no	—
526	C₃×C₂²⋊C₄	—	4	2	no	—
527	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
528	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
529	C₃×C₄²	—	2	2	no	—
530	C₃×C₄²	—	2	2	no	—
531	C₃×C₄²	—	4	2	no	—
532	C₃×C₄²	—	4	2	no	—
533	C₃×C₄²	C₂×D₄	1	4	yes	—
534	C₂⁵	C₂³×C₃	1	1	yes	characteristic
535	C₂⁵	C₂³×C₃	1	2	yes	—
536	C₂×#41	—	2	4	no	—
537	C₂×#41	—	4	4	no	—
538	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
540	C₂²×D₄	—	2	4	no	—
541	C₂²×D₄	—	4	4	no	—
542	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₃	1	2	yes	—
545	C₂²×D₄	C₂³×C₃	1	2	yes	—
546	C₂²×D₄	C₂³×C₃	1	2	yes	—
547	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₃	1	2	yes	—
549	C₂²×D₄	C₂³×C₃	1	2	yes	—
550	C₂²×D₄	C₂³×C₃	1	2	yes	—
551	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃	1	2	yes	—
553	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₃	1	2	yes	—
556	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₃	1	2	yes	—
559	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
561	#126	—	2	4	no	—
562	#126	—	2	4	no	—
563	#124	—	2	4	no	—
564	#124	—	2	4	no	—
565	#123	—	2	4	no	—
566	#123	—	2	4	no	—
567	#123	—	2	8	no	—
568	#123	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	4	4	no	—
573	#121	—	2	4	no	—
574	#121	—	2	8	no	—
575	#121	—	4	4	no	—
576	#120	—	2	8	no	—
577	#120	—	2	4	no	—
578	#120	—	4	4	no	—
579	#120	—	4	4	no	—
580	#120	—	4	4	no	—
581	#120	—	4	4	no	—
582	C₄×D₄	—	2	4	no	—
583	C₄×D₄	—	2	4	no	—
584	C₄×D₄	—	4	4	no	—
585	C₄×D₄	C₃×D₄	1	8	yes	complemented
586	#117	—	2	4	no	—
587	#117	—	2	4	no	—
588	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	—	2	4	no	—
606	C₂×C₂²⋊C₄	—	2	8	no	—
607	C₂×C₂²⋊C₄	—	2	4	no	—
608	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₃	1	2	yes	—
651	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
652	#95	C₂³×C₃	1	1	yes	characteristic
653	#95	C₂³×C₃	1	1	yes	characteristic
654	#95	C₂³×C₃	1	2	yes	—
655	#95	C₂³×C₃	1	2	yes	—
656	#95	C₂³×C₃	1	2	yes	—
657	#95	C₂³×C₃	1	1	yes	characteristic
658	#95	C₂³×C₃	1	1	yes	characteristic
659	#95	C₂³×C₃	1	2	yes	—
660	#95	C₂³×C₃	1	2	yes	—
661	#95	C₂³×C₃	1	2	yes	—
662	#95	C₂³×C₃	1	2	yes	—
663	#95	C₂³×C₃	1	2	yes	—
664	#95	C₂³×C₃	1	2	yes	—
665	#95	C₂³×C₃	1	2	yes	—
666	#95	C₂³×C₃	1	2	yes	—
667	C₂³×C₃	—	2	1	no	—
668	C₂³×C₃	—	2	2	no	—
669	C₂³×C₃	—	2	2	no	—
670	C₂³×C₃	—	2	1	no	—
671	C₂³×C₃	—	2	1	no	—
672	C₂³×C₃	—	2	2	no	—
673	C₂³×C₃	—	2	2	no	—
674	C₂³×C₃	—	2	2	no	—
675	C₂³×C₃	—	2	2	no	—
676	C₂³×C₃	—	2	2	no	—
677	C₂³×C₃	—	2	2	no	—
678	C₂³×C₃	—	2	2	no	—
679	C₂³×C₃	—	2	1	no	—
680	C₂³×C₃	—	2	2	no	—
681	C₂³×C₃	—	2	1	no	—
682	C₂³×C₃	—	2	2	no	—
683	C₂³×C₃	—	2	2	no	—
684	C₂³×C₃	—	2	1	no	—
685	C₂³×C₃	—	2	1	no	—
686	C₂³×C₃	—	2	2	no	—
687	C₂³×C₃	—	2	1	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	2	no	—
690	C₂³×C₃	—	2	2	no	—
691	C₂³×C₃	—	2	2	no	—
692	C₂³×C₃	—	2	2	no	—
693	C₂³×C₃	—	2	2	no	—
694	C₂³×C₃	—	2	2	no	—
695	C₂³×C₃	—	2	2	no	—
696	C₂³×C₃	—	2	1	no	—
697	C₂³×C₃	—	4	8	no	—
698	C₂³×C₃	—	4	4	no	—
699	C₂³×C₃	—	4	4	no	—
700	C₂³×C₃	—	4	8	no	—
701	C₂³×C₃	—	8	2	no	—
702	C₂³×C₃	—	8	4	no	—
703	C₂³×C₃	—	8	4	no	—
704	C₂³×C₃	—	8	4	no	—
705	C₂³×C₃	—	8	4	no	—
706	C₂³×C₃	—	8	4	no	—
707	C₂³×C₃	—	8	4	no	—
708	C₂³×C₃	—	8	4	no	—
709	C₂³×C₃	C₂²×D₄	1	2	yes	—
710	C₂³×C₃	C₂²×D₄	1	2	yes	—
711	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
712	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
713	C₂³×C₃	C₂⁵	1	1	yes	characteristic
714	C₃×Q₈	—	4	4	no	—
715	C₃×Q₈	—	8	2	no	—
716	C₃×D₄	—	2	8	no	—
717	C₃×D₄	—	4	4	no	—
718	C₃×D₄	—	4	8	no	—
719	C₃×D₄	—	4	4	no	—
720	C₃×D₄	—	4	4	no	—
721	C₃×D₄	—	4	8	no	—
722	C₃×D₄	—	4	8	no	—
723	C₃×D₄	—	8	2	no	—
724	C₃×D₄	—	8	4	no	—
725	C₃×D₄	—	8	4	no	—
726	C₃×D₄	—	8	4	no	—
727	C₃×D₄	—	8	4	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	2	2	no	—
730	C₂×C₃×C₄	—	2	2	no	—
731	C₂×C₃×C₄	—	2	2	no	—
732	C₂×C₃×C₄	—	2	2	no	—
733	C₂×C₃×C₄	—	2	1	no	—
734	C₂×C₃×C₄	—	2	1	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	1	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	2	2	no	—
740	C₂×C₃×C₄	—	2	1	no	—
741	C₂×C₃×C₄	—	2	2	no	—
742	C₂×C₃×C₄	—	2	2	no	—
743	C₂×C₃×C₄	—	2	2	no	—
744	C₂×C₃×C₄	—	2	2	no	—
745	C₂×C₃×C₄	—	2	2	no	—
746	C₂×C₃×C₄	—	2	2	no	—
747	C₂×C₃×C₄	—	2	2	no	—
748	C₂×C₃×C₄	—	2	2	no	—
749	C₂×C₃×C₄	—	2	1	no	—
750	C₂×C₃×C₄	—	2	2	no	—
751	C₂×C₃×C₄	—	2	2	no	—
752	C₂×C₃×C₄	—	2	2	no	—
753	C₂×C₃×C₄	—	2	1	no	—
754	C₂×C₃×C₄	—	2	2	no	—
755	C₂×C₃×C₄	—	2	2	no	—
756	C₂×C₃×C₄	—	2	2	no	—
757	C₂×C₃×C₄	—	2	2	no	—
758	C₂×C₃×C₄	—	2	2	no	—
759	C₂×C₃×C₄	—	2	2	no	—
760	C₂×C₃×C₄	—	2	1	no	—
761	C₂×C₃×C₄	—	2	2	no	—
762	C₂×C₃×C₄	—	2	2	no	—
763	C₂×C₃×C₄	—	2	2	no	—
764	C₂×C₃×C₄	—	2	1	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	4	4	no	—
767	C₂×C₃×C₄	—	4	4	no	—
768	C₂×C₃×C₄	—	4	4	no	—
769	C₂×C₃×C₄	—	4	8	no	—
770	C₂×C₃×C₄	—	4	4	no	—
771	C₂×C₃×C₄	—	8	2	no	—
772	C₂×C₃×C₄	—	8	4	no	—
773	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
774	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
775	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
776	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
777	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
778	C₂⁴	—	2	2	no	—
779	C₂⁴	—	2	4	no	—
780	C₂⁴	—	2	2	no	—
781	C₂⁴	—	2	4	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	1	no	—
786	C₂⁴	—	4	2	no	—
787	C₂⁴	—	4	2	no	—
788	C₂⁴	—	4	2	no	—
789	C₂⁴	—	4	2	no	—
790	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
791	C₂⁴	C₂⁴×C₃	1	2	yes	—
792	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
793	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
794	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
795	C₂⁴	C₂⁴×C₃	1	2	yes	—
796	#41	—	4	16	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	16	no	—
833	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
850	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
851	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	2	no	—
882	C₄⋊C₄	—	4	2	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
923	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	4	2	no	—
927	C₄²	—	4	2	no	—
928	C₄²	C₂×C₃×D₄	1	4	yes	—
929	C₂²×C₃	—	2	2	no	—
930	C₂²×C₃	—	2	2	no	—
931	C₂²×C₃	—	2	4	no	—
932	C₂²×C₃	—	2	2	no	—
933	C₂²×C₃	—	2	2	no	—
934	C₂²×C₃	—	2	2	no	—
935	C₂²×C₃	—	2	2	no	—
936	C₂²×C₃	—	2	2	no	—
937	C₂²×C₃	—	2	4	no	—
938	C₂²×C₃	—	2	4	no	—
939	C₂²×C₃	—	2	4	no	—
940	C₂²×C₃	—	4	1	no	—
941	C₂²×C₃	—	4	2	no	—
942	C₂²×C₃	—	4	1	no	—
943	C₂²×C₃	—	4	2	no	—
944	C₂²×C₃	—	4	2	no	—
945	C₂²×C₃	—	4	2	no	—
946	C₂²×C₃	—	4	2	no	—
947	C₂²×C₃	—	4	2	no	—
948	C₂²×C₃	—	4	2	no	—
949	C₂²×C₃	—	4	2	no	—
950	C₂²×C₃	—	4	2	no	—
951	C₂²×C₃	—	4	1	no	—
952	C₂²×C₃	—	4	2	no	—
953	C₂²×C₃	—	4	2	no	—
954	C₂²×C₃	—	4	1	no	—
955	C₂²×C₃	—	4	2	no	—
956	C₂²×C₃	—	4	1	no	—
957	C₂²×C₃	—	4	2	no	—
958	C₂²×C₃	—	4	2	no	—
959	C₂²×C₃	—	4	2	no	—
960	C₂²×C₃	—	4	2	no	—
961	C₂²×C₃	—	4	2	no	—
962	C₂²×C₃	—	4	2	no	—
963	C₂²×C₃	—	8	8	no	—
964	C₂²×C₃	—	8	16	no	—
965	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
966	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
967	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
968	C₂²×C₃	#585	1	2	yes	—
969	C₂²×C₃	#585	1	1	yes	characteristic
970	C₃×C₄	—	2	2	no	—
971	C₃×C₄	—	2	2	no	—
972	C₃×C₄	—	2	2	no	—
973	C₃×C₄	—	2	2	no	—
974	C₃×C₄	—	2	2	no	—
975	C₃×C₄	—	4	1	no	—
976	C₃×C₄	—	4	1	no	—
977	C₃×C₄	—	4	2	no	—
978	C₃×C₄	—	4	1	no	—
979	C₃×C₄	—	4	1	no	—
980	C₃×C₄	—	4	1	no	—
981	C₃×C₄	—	4	2	no	—
982	C₃×C₄	—	4	1	no	—
983	C₃×C₄	—	4	2	no	—
984	C₃×C₄	—	4	2	no	—
985	C₃×C₄	—	4	2	no	—
986	C₃×C₄	—	4	2	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	4	8	no	—
1018	C₂³	—	4	4	no	—
1019	C₂³	—	4	4	no	—
1020	C₂³	—	4	8	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	—	8	4	no	—
1023	C₂³	—	8	4	no	—
1024	C₂³	—	8	4	no	—
1025	C₂³	—	8	4	no	—
1026	C₂³	—	8	4	no	—
1027	C₂³	—	8	4	no	—
1028	C₂³	—	8	4	no	—
1029	C₂³	C₂²×C₃×D₄	1	2	yes	—
1030	C₂³	C₂²×C₃×D₄	1	2	yes	—
1031	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
1032	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1033	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1034	Q₈	—	4	4	no	—
1035	Q₈	—	8	2	no	—
1036	D₄	—	2	8	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	8	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	8	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	8	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	4	no	—
1045	D₄	—	8	4	no	—
1046	D₄	—	8	4	no	—
1047	D₄	—	8	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	4	no	—
1088	C₂×C₄	—	4	8	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	4	no	—
1093	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1094	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1095	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1096	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1097	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1098	C₂×C₃	—	4	2	no	—
1099	C₂×C₃	—	4	4	no	—
1100	C₂×C₃	—	4	2	no	—
1101	C₂×C₃	—	4	2	no	—
1102	C₂×C₃	—	8	2	no	—
1103	C₂×C₃	—	8	1	no	—
1104	C₂×C₃	#3449	1	1	yes	characteristic
1105	C₂×C₃	#3484	1	1	yes	characteristic
1106	C₂×C₃	#3488	1	1	yes	characteristic
1107	C₂×C₃	#3534	1	2	yes	—
1108	C₂×C₃	#3545	1	2	yes	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	4	no	—
1118	C₂²	—	2	4	no	—
1119	C₂²	—	2	4	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	8	16	no	—
1144	C₂²	—	8	8	no	—
1145	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1146	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1147	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1148	C₂²	C₃×#585	1	2	yes	—
1149	C₂²	C₃×#585	1	1	yes	characteristic
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₃	#41989	1	1	yes	characteristic, direct product factor, Sylow
1168	C₂	—	4	2	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	4	4	no	—
1171	C₂	—	4	2	no	—
1172	C₂	—	8	2	no	—
1173	C₂	—	8	1	no	—
1174	C₂	C₃×#3449	1	1	yes	characteristic
1175	C₂	C₃×#3484	1	1	yes	characteristic
1176	C₂	C₃×#3488	1	1	yes	characteristic
1177	C₂	C₃×#3534	1	2	yes	—
1178	C₂	C₃×#3545	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#551	C₂	semidirect
2. C₂×C₃×#546	C₂	semidirect
3. C₃×#2816	C₂	semidirect
4. C₃×#2814	C₂	semidirect
5. C₃×#2705	C₂	semidirect
6. C₃×#2697	C₂	semidirect
7. C₃×#2681	C₂	semidirect
8. C₃×#2679	C₂	semidirect
9. C₃×#2662	C₂	semidirect
10. C₃×#2638	C₂	semidirect
11. C₃×#2617	C₂	semidirect
12. C₃×#2616	C₂	semidirect
13. C₃×#2613	C₂	semidirect
14. C₃×#2610	C₂	semidirect
15. C₃×#2603	C₂	semidirect
16. C₃×#2476	C₂	semidirect
17. C₃×#2472	C₂	semidirect
18. C₃×#2424	C₂	semidirect
19. C₃×#2418	C₂	semidirect
20. C₃×#2408	C₂	semidirect
21. C₃×#2404	C₂	semidirect
22. C₃×#2392	C₂	semidirect
23. C₃×#2319	C₂	semidirect
24. #41989	C₃	direct (N × H)
26. C₂³×C₃×D₄	C₂²	semidirect
29. C₂×C₃×#126	C₂²	semidirect
30. C₂×C₃×#126	C₂²	semidirect
32. C₂×C₃×#124	C₂²	semidirect
36. C₂×C₃×#123	C₂²	semidirect
37. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₃×#120	C₂²	semidirect
49. C₂×C₃×#120	C₂²	semidirect
52. C₂×C₃×C₄×D₄	C₂²	semidirect
53. C₂×C₃×C₄×D₄	C₂²	semidirect
54. C₂×C₃×#117	C₂²	semidirect
55. C₂×C₃×#117	C₂²	semidirect
56. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
57. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
58. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
59. C₃×#399	C₂²	semidirect
60. C₃×#398	C₂²	semidirect
61. C₃×#398	C₂²	semidirect
62. C₃×#398	C₂²	semidirect
63. C₃×#397	C₂²	semidirect
64. C₃×#397	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
66. C₃×#397	C₂²	semidirect
67. C₃×#396	C₂²	semidirect
68. C₃×#396	C₂²	semidirect
69. C₃×#396	C₂²	semidirect
70. C₃×#395	C₂²	semidirect
71. C₃×#395	C₂²	semidirect
74. C₃×#394	C₂²	semidirect
75. C₃×#394	C₂²	semidirect
76. C₃×#394	C₂²	semidirect
77. C₃×#394	C₂²	semidirect
78. C₃×#394	C₂²	semidirect
79. C₃×#394	C₂²	semidirect
80. C₃×#394	C₂²	semidirect
81. C₃×#394	C₂²	semidirect
82. C₃×#394	C₂²	semidirect
83. C₃×#394	C₂²	semidirect
84. C₃×#394	C₂²	semidirect
85. C₃×#394	C₂²	semidirect
86. C₃×#394	C₂²	semidirect
87. C₃×#393	C₂²	semidirect
88. C₃×#393	C₂²	semidirect
89. C₃×#393	C₂²	semidirect
96. C₃×#390	C₂²	semidirect
97. C₃×#390	C₂²	semidirect
98. C₃×#390	C₂²	semidirect
99. C₃×#390	C₂²	semidirect
100. C₃×#389	C₂²	semidirect
101. C₃×#388	C₂²	semidirect
102. C₃×#388	C₂²	semidirect
103. C₃×#388	C₂²	semidirect
104. C₃×#388	C₂²	semidirect
105. C₃×#388	C₂²	semidirect
106. C₃×#388	C₂²	semidirect
107. C₃×#387	C₂²	semidirect
108. C₃×#386	C₂²	semidirect
109. C₃×#386	C₂²	semidirect
110. C₃×#386	C₂²	semidirect
111. C₃×#386	C₂²	semidirect
112. C₃×#386	C₂²	semidirect
113. C₃×#386	C₂²	semidirect
114. C₃×#385	C₂²	semidirect
115. C₃×#385	C₂²	semidirect
116. C₃×#381	C₂²	semidirect
117. C₃×#381	C₂²	semidirect
118. C₃×#380	C₂²	semidirect
119. C₃×#380	C₂²	semidirect
120. C₃×#380	C₂²	semidirect
121. C₃×#379	C₂²	semidirect
122. C₃×#379	C₂²	semidirect
123. C₃×C₄×C₄⋊C₄	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₃×#376	C₂²	semidirect
126. C₂×#551	C₂×C₃	semidirect
127. C₂×#546	C₂×C₃	semidirect
128. #2816	C₂×C₃	semidirect
129. #2814	C₂×C₃	semidirect
130. #2705	C₂×C₃	semidirect
131. #2697	C₂×C₃	semidirect
132. #2681	C₂×C₃	semidirect
133. #2679	C₂×C₃	semidirect
134. #2662	C₂×C₃	semidirect
135. #2638	C₂×C₃	semidirect
136. #2617	C₂×C₃	semidirect
137. #2616	C₂×C₃	semidirect
138. #2613	C₂×C₃	semidirect
139. #2610	C₂×C₃	semidirect
140. #2603	C₂×C₃	semidirect
141. #2476	C₂×C₃	semidirect
142. #2472	C₂×C₃	semidirect
143. #2424	C₂×C₃	semidirect
144. #2418	C₂×C₃	semidirect
145. #2408	C₂×C₃	semidirect
146. #2404	C₂×C₃	semidirect
147. #2392	C₂×C₃	semidirect
148. #2319	C₂×C₃	semidirect
200. C₃×C₄×D₄	D₄	semidirect
283. C₂³×D₄	C₂²×C₃	semidirect
286. C₂×#126	C₂²×C₃	semidirect
287. C₂×#126	C₂²×C₃	semidirect
289. C₂×#124	C₂²×C₃	semidirect
293. C₂×#123	C₂²×C₃	semidirect
294. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
296. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
297. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
305. C₂×#120	C₂²×C₃	semidirect
306. C₂×#120	C₂²×C₃	semidirect
309. C₂×C₄×D₄	C₂²×C₃	semidirect
310. C₂×C₄×D₄	C₂²×C₃	semidirect
311. C₂×#117	C₂²×C₃	semidirect
312. C₂×#117	C₂²×C₃	semidirect
313. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
314. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
315. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
316. #399	C₂²×C₃	semidirect
317. #398	C₂²×C₃	semidirect
318. #398	C₂²×C₃	semidirect
319. #398	C₂²×C₃	semidirect
320. #397	C₂²×C₃	semidirect
321. #397	C₂²×C₃	semidirect
322. #397	C₂²×C₃	semidirect
323. #397	C₂²×C₃	semidirect
324. #396	C₂²×C₃	semidirect
325. #396	C₂²×C₃	semidirect
326. #396	C₂²×C₃	semidirect
327. #395	C₂²×C₃	semidirect
328. #395	C₂²×C₃	semidirect
331. #394	C₂²×C₃	semidirect
332. #394	C₂²×C₃	semidirect
333. #394	C₂²×C₃	semidirect
334. #394	C₂²×C₃	semidirect
335. #394	C₂²×C₃	semidirect
336. #394	C₂²×C₃	semidirect
337. #394	C₂²×C₃	semidirect
338. #394	C₂²×C₃	semidirect
339. #394	C₂²×C₃	semidirect
340. #394	C₂²×C₃	semidirect
341. #394	C₂²×C₃	semidirect
342. #394	C₂²×C₃	semidirect
343. #394	C₂²×C₃	semidirect
344. #393	C₂²×C₃	semidirect
345. #393	C₂²×C₃	semidirect
346. #393	C₂²×C₃	semidirect
353. #390	C₂²×C₃	semidirect
354. #390	C₂²×C₃	semidirect
355. #390	C₂²×C₃	semidirect
356. #390	C₂²×C₃	semidirect
357. #389	C₂²×C₃	semidirect
358. #388	C₂²×C₃	semidirect
359. #388	C₂²×C₃	semidirect
360. #388	C₂²×C₃	semidirect
361. #388	C₂²×C₃	semidirect
362. #388	C₂²×C₃	semidirect
363. #388	C₂²×C₃	semidirect
364. #387	C₂²×C₃	semidirect
365. #386	C₂²×C₃	semidirect
366. #386	C₂²×C₃	semidirect
367. #386	C₂²×C₃	semidirect
368. #386	C₂²×C₃	semidirect
369. #386	C₂²×C₃	semidirect
370. #386	C₂²×C₃	semidirect
371. #385	C₂²×C₃	semidirect
372. #385	C₂²×C₃	semidirect
373. #381	C₂²×C₃	semidirect
374. #381	C₂²×C₃	semidirect
375. #380	C₂²×C₃	semidirect
376. #380	C₂²×C₃	semidirect
377. #380	C₂²×C₃	semidirect
378. #379	C₂²×C₃	semidirect
379. #379	C₂²×C₃	semidirect
380. C₄×C₄⋊C₄	C₂²×C₃	semidirect
381. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
382. #376	C₂²×C₃	semidirect
585. C₄×D₄	C₃×D₄	semidirect
1167. C₃	#41989	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×#551	2
C₂×C₃×#546	2
C₃×#2816	2
C₃×#2814	2
C₃×#2705	2
C₃×#2697	2
C₃×#2681	2
C₃×#2679	2
C₃×#2662	2
C₃×#2638	2
C₃×#2617	2
C₃×#2616	2
C₃×#2613	2
C₃×#2610	2
C₃×#2603	2
C₃×#2476	2
C₃×#2472	2
C₃×#2424	2
C₃×#2418	2
C₃×#2408	2
C₃×#2404	2
C₃×#2392	2
C₃×#2319	2
#41989	3

Subgroups — C3×#41989 #10660596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41989 #10660596