Subgroups — C₃×#60583 #10679190

Order 768.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3127	C₂	1	4	yes	maximal, complemented
4	C₃×#3121	C₂	1	4	yes	maximal, complemented
5	C₃×#3117	C₂	1	2	yes	maximal, complemented
6	C₃×#3113	C₂	1	2	yes	maximal, complemented
7	C₃×#3108	C₂	1	2	yes	maximal, complemented
8	C₃×#3104	C₂	1	2	yes	maximal, complemented
9	C₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3091	C₂	1	1	yes	maximal, characteristic
11	C₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₃×#3044	C₂	1	2	yes	maximal, complemented
13	C₃×#3004	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2950	C₂	1	2	yes	maximal, complemented
16	C₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	#60583	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×#137	C₂²	1	2	yes	—
21	C₂²×C₃×Q₁₆	C₂²	1	2	yes	—
22	C₃×#556	—	2	1	no	—
23	C₃×#554	—	2	1	no	—
24	C₃×#552	—	2	2	no	—
25	C₃×#552	—	2	1	no	—
26	C₃×#552	—	2	1	no	—
27	C₃×#551	—	2	2	no	—
28	C₃×#544	C₂²	1	1	yes	characteristic
29	C₃×#542	C₂²	1	2	yes	—
30	C₃×#541	C₂²	1	2	yes	—
31	C₃×#536	C₂²	1	1	yes	characteristic
32	C₃×#533	C₂²	1	2	yes	—
33	C₃×#529	C₂²	1	2	yes	—
34	C₃×#525	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₃×#520	C₂²	1	1	yes	characteristic
37	C₃×#519	—	2	2	no	—
38	C₃×#519	—	2	1	no	—
39	C₃×#519	—	2	1	no	—
40	C₃×#519	C₂²	1	2	yes	—
41	C₃×#519	C₂²	1	2	yes	—
42	C₃×#519	C₂²	1	4	yes	—
43	C₃×#519	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×Q₈	—	2	1	no	—
45	C₂×C₃×C₄×Q₈	—	2	1	no	—
46	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
47	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
48	C₂×C₃×#117	—	2	2	no	—
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic
50	C₂×C₃×#117	C₂²	1	1	yes	characteristic
51	C₃×#485	C₂²	1	2	yes	—
52	C₃×#485	C₂²	1	4	yes	—
53	C₃×#484	C₂²	1	1	yes	characteristic
54	C₃×#484	C₂²	1	2	yes	—
55	C₃×#483	C₂²	1	1	yes	characteristic
56	C₃×#483	C₂²	1	2	yes	—
57	C₃×#482	C₂²	1	2	yes	—
58	C₃×#481	C₂²	1	1	yes	characteristic
59	C₃×#480	C₂²	1	1	yes	characteristic
60	C₃×#479	C₂²	1	4	yes	complemented
61	C₃×#479	C₂²	1	4	yes	complemented
62	C₃×#477	C₂²	1	4	yes	complemented
63	C₃×#475	C₂²	1	4	yes	complemented
64	C₃×#464	C₂²	1	4	yes	complemented
65	C₃×#464	C₂²	1	4	yes	complemented
66	C₃×#462	C₂²	1	4	yes	complemented
67	C₃×#462	C₂²	1	4	yes	complemented
68	C₃×#451	C₂²	1	2	yes	—
69	C₃×#451	C₂²	1	2	yes	—
70	C₃×#451	C₂²	1	4	yes	—
71	C₃×#451	C₂²	1	2	yes	—
72	C₃×#451	C₂²	1	2	yes	—
73	C₃×#448	C₂²	1	2	yes	—
74	C₃×#448	C₂²	1	2	yes	—
75	C₃×#441	C₂²	1	4	yes	complemented
76	C₃×#441	C₂²	1	4	yes	complemented
77	C₃×#441	C₂²	1	4	yes	complemented
78	C₃×#440	C₂²	1	4	yes	complemented
79	C₃×C₄×Q₁₆	C₂²	1	4	yes	complemented
80	C₃×C₄×Q₁₆	C₂²	1	4	yes	complemented
81	C₃×C₄×Q₁₆	C₂²	1	4	yes	complemented
82	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
83	C₃×#433	C₂²	1	4	yes	—
84	C₃×#432	C₂²	1	2	yes	—
85	C₃×#431	C₂²	1	2	yes	—
86	C₃×#428	C₂²	1	2	yes	—
87	C₃×#427	C₂²	1	2	yes	—
88	C₃×#424	C₂²	1	2	yes	—
89	C₃×#419	C₂²	1	2	yes	—
90	C₃×#419	C₂²	1	2	yes	—
91	C₃×#416	C₂²	1	2	yes	—
92	C₂×C₃×#103	C₂²	1	2	yes	—
93	C₃×#407	C₂²	1	1	yes	characteristic
94	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
95	C₃×#405	C₂²	1	2	yes	—
96	#3495	C₂×C₃	1	1	yes	characteristic
97	C₂×#519	C₂×C₃	1	1	yes	characteristic, complemented
98	#3127	C₂×C₃	1	4	yes	complemented
99	#3121	C₂×C₃	1	4	yes	complemented
100	#3117	C₂×C₃	1	2	yes	complemented
101	#3113	C₂×C₃	1	2	yes	complemented
102	#3108	C₂×C₃	1	2	yes	complemented
103	#3104	C₂×C₃	1	2	yes	complemented
104	#3095	C₂×C₃	1	1	yes	characteristic, complemented
105	#3091	C₂×C₃	1	1	yes	characteristic
106	#3082	C₂×C₃	1	2	yes	complemented
107	#3044	C₂×C₃	1	2	yes	complemented
108	#3004	C₂×C₃	1	1	yes	characteristic
109	C₂×#451	C₂×C₃	1	1	yes	characteristic, complemented
110	#2950	C₂×C₃	1	2	yes	complemented
111	#2947	C₂×C₃	1	2	yes	complemented
112	#2924	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂×C₃×#41	C₂³	1	1	yes	characteristic
114	C₂²×C₃×Q₈	—	2	8	no	—
115	C₂²×C₃×Q₈	—	2	1	no	—
116	C₂²×C₃×Q₈	—	2	1	no	—
117	C₂²×C₃×Q₈	—	2	1	no	—
118	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
119	C₂²×C₃×Q₈	C₂³	1	2	yes	—
120	C₂²×C₃×Q₈	C₂³	1	2	yes	—
121	C₂²×C₃×Q₈	C₂³	1	2	yes	—
122	C₂³×C₃×C₄	—	2	1	no	—
123	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
124	C₃×#137	—	2	8	no	—
125	C₂×C₃×Q₁₆	—	2	8	no	—
126	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
127	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
128	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
129	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₃×M₁₆	C₂³	1	2	yes	—
131	C₂²×C₃×C₈	C₂³	1	2	yes	—
132	C₃×C₄⋊Q₈	—	2	1	no	—
133	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₃×#126	—	2	2	no	—
136	C₃×#126	—	2	2	no	—
137	C₃×#126	—	2	2	no	—
138	C₃×#126	—	2	2	no	—
139	C₃×#125	—	2	2	no	—
140	C₃×#125	—	2	2	no	—
141	C₃×#125	—	2	1	no	—
142	C₃×#125	—	2	2	no	—
143	C₃×#125	C₂³	1	2	yes	—
144	C₃×#124	—	2	2	no	—
145	C₃×#124	C₂³	1	2	yes	—
146	C₃×#123	—	2	1	no	—
147	C₃×#123	—	2	2	no	—
148	C₃×#123	—	2	2	no	—
149	C₃×#123	—	2	2	no	—
150	C₃×C₂²⋊Q₈	—	2	1	no	—
151	C₃×C₂²⋊Q₈	—	2	1	no	—
152	C₃×C₂²⋊Q₈	—	2	2	no	—
153	C₃×C₂²⋊Q₈	—	2	1	no	—
154	C₃×C₂²⋊Q₈	—	2	1	no	—
155	C₃×C₂²⋊Q₈	—	2	2	no	—
156	C₃×C₂²⋊Q₈	—	2	2	no	—
157	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃×#121	C₂³	1	1	yes	characteristic
162	C₃×#121	C₂³	1	1	yes	characteristic
163	C₃×#120	—	2	1	no	—
164	C₃×C₄×Q₈	—	2	2	no	—
165	C₃×C₄×Q₈	—	2	2	no	—
166	C₃×C₄×Q₈	—	2	2	no	—
167	C₃×C₄×Q₈	—	2	4	no	—
168	C₃×C₄×Q₈	—	2	2	no	—
169	C₃×C₄×Q₈	—	2	4	no	—
170	C₃×C₄×Q₈	—	2	1	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	—	2	2	no	—
173	C₃×C₄×Q₈	—	2	2	no	—
174	C₃×C₄×Q₈	—	2	2	no	—
175	C₃×C₄×Q₈	—	2	2	no	—
176	C₃×C₄×Q₈	—	2	2	no	—
177	C₃×C₄×Q₈	C₂³	1	4	yes	—
178	C₃×C₄×Q₈	C₂³	1	4	yes	—
179	C₃×C₄×Q₈	C₂³	1	2	yes	—
180	C₃×C₄×Q₈	C₂³	1	2	yes	—
181	C₃×C₄×Q₈	C₂³	1	2	yes	—
182	C₃×C₄×Q₈	C₂³	1	4	yes	—
183	C₃×C₄×Q₈	C₂³	1	4	yes	—
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	—	2	1	no	—
186	C₃×C₄×D₄	—	2	2	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	C₂³	1	2	yes	—
189	C₃×#117	—	2	1	no	—
190	C₃×#117	—	2	1	no	—
191	C₃×#117	—	2	2	no	—
192	C₃×#117	—	2	1	no	—
193	C₃×#117	—	2	4	no	—
194	C₃×#117	—	2	4	no	—
195	C₃×#117	—	2	4	no	—
196	C₃×#117	—	2	4	no	—
197	C₃×#117	—	2	2	no	—
198	C₃×#117	—	2	2	no	—
199	C₃×#117	D₄	1	1	yes	characteristic
200	C₃×#117	D₄	1	2	yes	—
201	C₃×#117	D₄	1	1	yes	characteristic
202	C₃×#117	C₂³	1	2	yes	—
203	C₃×#117	C₂³	1	1	yes	characteristic
204	C₃×#117	C₂³	1	2	yes	—
205	C₃×#117	C₂³	1	1	yes	characteristic
206	C₃×#117	C₂³	1	1	yes	characteristic
207	C₃×#117	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	—	2	2	no	—
209	C₂×C₃×C₄⋊C₄	—	2	2	no	—
210	C₂×C₃×C₄⋊C₄	—	2	1	no	—
211	C₂×C₃×C₄⋊C₄	—	2	1	no	—
212	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
218	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
220	C₂×C₃×C₄²	—	2	2	no	—
221	C₂×C₃×C₄²	—	2	2	no	—
222	C₂×C₃×C₄²	—	2	1	no	—
223	C₂×C₃×C₄²	C₂³	1	2	yes	—
224	C₃×#107	C₂³	1	2	yes	—
225	C₃×#107	C₂³	1	2	yes	—
226	C₃×#107	C₂³	1	4	yes	—
227	C₃×#106	C₂³	1	2	yes	—
228	C₃×#106	C₂³	1	2	yes	—
229	C₃×#106	C₂³	1	4	yes	—
230	C₃×C₄⋊C₈	C₂³	1	4	yes	—
231	C₃×C₄⋊C₈	C₂³	1	4	yes	—
232	C₃×#103	C₂³	1	4	yes	—
233	C₃×#103	C₂³	1	4	yes	—
234	C₃×#103	C₂³	1	2	yes	—
235	C₃×#103	C₂³	1	2	yes	—
236	C₃×#103	C₂³	1	4	yes	—
237	C₃×#103	C₂³	1	4	yes	—
238	C₃×#103	C₂³	1	4	yes	—
239	C₃×#103	C₂³	1	4	yes	—
240	C₃×#102	C₂³	1	2	yes	—
241	C₃×#102	C₂³	1	2	yes	—
242	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
243	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
244	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₃×#97	C₂³	1	4	yes	—
248	C₃×C₄×C₈	C₂³	1	4	yes	—
249	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
250	C₂×#137	C₂²×C₃	1	2	yes	—
251	C₂²×Q₁₆	C₂²×C₃	1	2	yes	—
252	#556	—	2	1	no	—
253	#554	—	2	1	no	—
254	#552	—	2	2	no	—
255	#552	—	2	1	no	—
256	#552	—	2	1	no	—
257	#551	—	2	2	no	—
258	#544	C₂²×C₃	1	1	yes	characteristic
259	#542	C₂²×C₃	1	2	yes	—
260	#541	C₂²×C₃	1	2	yes	—
261	#536	C₂²×C₃	1	1	yes	characteristic
262	#533	C₂²×C₃	1	2	yes	—
263	#529	C₂²×C₃	1	2	yes	—
264	#525	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	#520	C₂²×C₃	1	1	yes	characteristic
267	#519	—	2	2	no	—
268	#519	—	2	1	no	—
269	#519	—	2	1	no	—
270	#519	C₂²×C₃	1	2	yes	—
271	#519	C₂²×C₃	1	4	yes	—
272	#519	C₂²×C₃	1	2	yes	—
273	#519	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄×Q₈	—	2	1	no	—
275	C₂×C₄×Q₈	—	2	1	no	—
276	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
278	C₂×#117	—	2	2	no	—
279	C₂×#117	C₂²×C₃	1	1	yes	characteristic
280	C₂×#117	C₂²×C₃	1	1	yes	characteristic
281	#485	C₂²×C₃	1	2	yes	—
282	#485	C₂²×C₃	1	4	yes	—
283	#484	C₂²×C₃	1	1	yes	characteristic
284	#484	C₂²×C₃	1	2	yes	—
285	#483	C₂²×C₃	1	1	yes	characteristic
286	#483	C₂²×C₃	1	2	yes	—
287	#482	C₂²×C₃	1	2	yes	—
288	#481	C₂²×C₃	1	1	yes	characteristic
289	#480	C₂²×C₃	1	1	yes	characteristic
290	#479	C₂²×C₃	1	4	yes	complemented
291	#479	C₂²×C₃	1	4	yes	complemented
292	#477	C₂²×C₃	1	4	yes	complemented
293	#475	C₂²×C₃	1	4	yes	complemented
294	#464	C₂²×C₃	1	4	yes	complemented
295	#464	C₂²×C₃	1	4	yes	complemented
296	#462	C₂²×C₃	1	4	yes	complemented
297	#462	C₂²×C₃	1	4	yes	complemented
298	#451	C₂²×C₃	1	2	yes	—
299	#451	C₂²×C₃	1	2	yes	—
300	#451	C₂²×C₃	1	2	yes	—
301	#451	C₂²×C₃	1	4	yes	—
302	#451	C₂²×C₃	1	2	yes	—
303	#448	C₂²×C₃	1	2	yes	—
304	#448	C₂²×C₃	1	2	yes	—
305	#441	C₂²×C₃	1	4	yes	complemented
306	#441	C₂²×C₃	1	4	yes	complemented
307	#441	C₂²×C₃	1	4	yes	complemented
308	#440	C₂²×C₃	1	4	yes	complemented
309	C₄×Q₁₆	C₂²×C₃	1	4	yes	complemented
310	C₄×Q₁₆	C₂²×C₃	1	4	yes	complemented
311	C₄×Q₁₆	C₂²×C₃	1	4	yes	complemented
312	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
313	#433	C₂²×C₃	1	4	yes	—
314	#432	C₂²×C₃	1	2	yes	—
315	#431	C₂²×C₃	1	2	yes	—
316	#428	C₂²×C₃	1	2	yes	—
317	#427	C₂²×C₃	1	2	yes	—
318	#424	C₂²×C₃	1	2	yes	—
319	#419	C₂²×C₃	1	2	yes	—
320	#419	C₂²×C₃	1	2	yes	—
321	#416	C₂²×C₃	1	2	yes	—
322	C₂×#103	C₂²×C₃	1	2	yes	—
323	#407	C₂²×C₃	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
325	#405	C₂²×C₃	1	2	yes	—
326	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
327	C₃×#41	—	2	4	no	—
328	C₂×C₃×Q₈	—	2	8	no	—
329	C₂×C₃×Q₈	—	2	8	no	—
330	C₂×C₃×Q₈	—	2	8	no	—
331	C₂×C₃×Q₈	—	2	8	no	—
332	C₂×C₃×Q₈	—	2	8	no	—
333	C₂×C₃×Q₈	—	2	2	no	—
334	C₂×C₃×Q₈	—	2	2	no	—
335	C₂×C₃×Q₈	—	2	2	no	—
336	C₂×C₃×Q₈	—	2	1	no	—
337	C₂×C₃×Q₈	—	2	2	no	—
338	C₂×C₃×Q₈	—	2	4	no	—
339	C₂×C₃×Q₈	—	2	4	no	—
340	C₂×C₃×Q₈	#41	1	8	yes	—
341	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
342	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
343	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
344	C₂×C₃×D₄	—	2	1	no	—
345	C₂×C₃×D₄	—	2	1	no	—
346	C₂×C₃×D₄	—	2	1	no	—
347	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₃×C₄	—	2	8	no	—
349	C₂²×C₃×C₄	—	2	2	no	—
350	C₂²×C₃×C₄	—	2	2	no	—
351	C₂²×C₃×C₄	—	2	2	no	—
352	C₂²×C₃×C₄	—	2	4	no	—
353	C₂²×C₃×C₄	—	2	1	no	—
354	C₂²×C₃×C₄	—	2	1	no	—
355	C₂²×C₃×C₄	—	2	1	no	—
356	C₂²×C₃×C₄	—	2	1	no	—
357	C₂²×C₃×C₄	—	2	1	no	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
360	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
364	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₃×Q₁₆	—	2	8	no	—
368	C₃×Q₁₆	—	2	8	no	—
369	C₃×Q₁₆	—	2	8	no	—
370	C₃×SD₁₆	—	2	8	no	—
371	C₃×M₁₆	—	2	4	no	—
372	C₂×C₃×C₈	—	2	4	no	—
373	C₂×C₃×C₈	C₂⁴	1	2	yes	—
374	C₂×C₃×C₈	C₂⁴	1	4	yes	—
375	C₂×C₃×C₈	C₂⁴	1	2	yes	—
376	C₃×C₄⋊C₄	—	2	1	no	—
377	C₃×C₄⋊C₄	—	2	4	no	—
378	C₃×C₄⋊C₄	—	2	4	no	—
379	C₃×C₄⋊C₄	—	2	4	no	—
380	C₃×C₄⋊C₄	—	2	4	no	—
381	C₃×C₄⋊C₄	—	2	2	no	—
382	C₃×C₄⋊C₄	—	2	2	no	—
383	C₃×C₄⋊C₄	—	2	2	no	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	—	2	1	no	—
386	C₃×C₄⋊C₄	—	2	2	no	—
387	C₃×C₄⋊C₄	—	2	2	no	—
388	C₃×C₄⋊C₄	—	2	2	no	—
389	C₃×C₄⋊C₄	—	2	2	no	—
390	C₃×C₄⋊C₄	—	2	2	no	—
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	—	2	2	no	—
393	C₃×C₄⋊C₄	—	2	1	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
404	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₃×C₂²⋊C₄	—	2	2	no	—
407	C₃×C₂²⋊C₄	—	2	2	no	—
408	C₃×C₂²⋊C₄	—	2	2	no	—
409	C₃×C₂²⋊C₄	—	2	2	no	—
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	2	2	no	—
415	C₃×C₂²⋊C₄	—	2	2	no	—
416	C₃×C₂²⋊C₄	—	2	1	no	—
417	C₃×C₂²⋊C₄	—	2	2	no	—
418	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
421	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₃×C₄²	—	2	4	no	—
423	C₃×C₄²	—	2	4	no	—
424	C₃×C₄²	—	2	4	no	—
425	C₃×C₄²	—	2	4	no	—
426	C₃×C₄²	—	2	2	no	—
427	C₃×C₄²	—	2	2	no	—
428	C₃×C₄²	—	2	2	no	—
429	C₃×C₄²	—	2	2	no	—
430	C₃×C₄²	—	2	2	no	—
431	C₃×C₄²	—	2	1	no	—
432	C₃×C₄²	C₂×D₄	1	2	yes	—
433	C₃×C₄²	C₂×D₄	1	2	yes	—
434	C₃×C₄²	C₂⁴	1	2	yes	—
435	C₃×C₄²	C₂⁴	1	2	yes	—
436	C₂×#41	C₂³×C₃	1	1	yes	characteristic
437	C₂²×Q₈	—	2	8	no	—
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	—	2	1	no	—
440	C₂²×Q₈	—	2	1	no	—
441	C₂²×Q₈	C₂³×C₃	1	2	yes	—
442	C₂²×Q₈	C₂³×C₃	1	2	yes	—
443	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₃	1	2	yes	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
447	#137	—	2	8	no	—
448	C₂×Q₁₆	—	2	8	no	—
449	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
450	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
451	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
452	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
453	C₂×M₁₆	C₂³×C₃	1	2	yes	—
454	C₂²×C₈	C₂³×C₃	1	2	yes	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
457	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
458	#126	—	2	2	no	—
459	#126	—	2	2	no	—
460	#126	—	2	2	no	—
461	#126	—	2	2	no	—
462	#125	—	2	2	no	—
463	#125	—	2	2	no	—
464	#125	—	2	1	no	—
465	#125	—	2	2	no	—
466	#125	C₂³×C₃	1	2	yes	—
467	#124	—	2	2	no	—
468	#124	C₂³×C₃	1	2	yes	—
469	#123	—	2	1	no	—
470	#123	—	2	2	no	—
471	#123	—	2	2	no	—
472	#123	—	2	2	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
481	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
482	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
483	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
484	#121	C₂³×C₃	1	1	yes	characteristic
485	#121	C₂³×C₃	1	1	yes	characteristic
486	#120	—	2	1	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	4	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	C₂³×C₃	1	4	yes	—
501	C₄×Q₈	C₂³×C₃	1	4	yes	—
502	C₄×Q₈	C₂³×C₃	1	4	yes	—
503	C₄×Q₈	C₂³×C₃	1	4	yes	—
504	C₄×Q₈	C₂³×C₃	1	2	yes	—
505	C₄×Q₈	C₂³×C₃	1	2	yes	—
506	C₄×Q₈	C₂³×C₃	1	2	yes	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	C₂³×C₃	1	2	yes	—
512	#117	—	2	1	no	—
513	#117	—	2	1	no	—
514	#117	—	2	2	no	—
515	#117	—	2	1	no	—
516	#117	—	2	4	no	—
517	#117	—	2	4	no	—
518	#117	—	2	4	no	—
519	#117	—	2	4	no	—
520	#117	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	C₃×D₄	1	1	yes	characteristic
523	#117	C₃×D₄	1	2	yes	—
524	#117	C₃×D₄	1	1	yes	characteristic
525	#117	C₂³×C₃	1	2	yes	—
526	#117	C₂³×C₃	1	2	yes	—
527	#117	C₂³×C₃	1	1	yes	characteristic
528	#117	C₂³×C₃	1	1	yes	characteristic
529	#117	C₂³×C₃	1	1	yes	characteristic
530	#117	C₂³×C₃	1	2	yes	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
543	C₂×C₄²	—	2	2	no	—
544	C₂×C₄²	—	2	2	no	—
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	C₂³×C₃	1	2	yes	—
547	#107	C₂³×C₃	1	2	yes	—
548	#107	C₂³×C₃	1	2	yes	—
549	#107	C₂³×C₃	1	4	yes	—
550	#106	C₂³×C₃	1	2	yes	—
551	#106	C₂³×C₃	1	2	yes	—
552	#106	C₂³×C₃	1	4	yes	—
553	C₄⋊C₈	C₂³×C₃	1	4	yes	—
554	C₄⋊C₈	C₂³×C₃	1	4	yes	—
555	#103	C₂³×C₃	1	4	yes	—
556	#103	C₂³×C₃	1	4	yes	—
557	#103	C₂³×C₃	1	2	yes	—
558	#103	C₂³×C₃	1	2	yes	—
559	#103	C₂³×C₃	1	4	yes	—
560	#103	C₂³×C₃	1	4	yes	—
561	#103	C₂³×C₃	1	4	yes	—
562	#103	C₂³×C₃	1	4	yes	—
563	#102	C₂³×C₃	1	2	yes	—
564	#102	C₂³×C₃	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
566	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
567	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
568	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
570	#97	C₂³×C₃	1	4	yes	—
571	C₄×C₈	C₂³×C₃	1	4	yes	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	2	no	—
574	C₂³×C₃	—	2	1	no	—
575	C₂³×C₃	—	4	1	no	—
576	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
577	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
578	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
579	C₃×Q₈	—	2	8	no	—
580	C₃×Q₈	—	2	8	no	—
581	C₃×Q₈	—	2	8	no	—
582	C₃×Q₈	—	2	4	no	—
583	C₃×Q₈	—	2	4	no	—
584	C₃×Q₈	—	2	2	no	—
585	C₃×Q₈	—	4	2	no	—
586	C₃×Q₈	—	8	2	no	—
587	C₃×Q₈	C₂×#41	1	8	yes	—
588	C₃×D₄	—	2	2	no	—
589	C₃×D₄	—	4	2	no	—
590	C₃×D₄	—	4	2	no	—
591	C₃×D₄	—	8	1	no	—
592	C₂×C₃×C₄	—	2	8	no	—
593	C₂×C₃×C₄	—	2	8	no	—
594	C₂×C₃×C₄	—	2	8	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	4	no	—
597	C₂×C₃×C₄	—	2	4	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	4	2	no	—
610	C₂×C₃×C₄	—	4	2	no	—
611	C₂×C₃×C₄	—	4	2	no	—
612	C₂×C₃×C₄	—	4	2	no	—
613	C₂×C₃×C₄	—	4	2	no	—
614	C₂×C₃×C₄	—	8	2	no	—
615	C₂×C₃×C₄	—	8	1	no	—
616	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
617	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
618	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
619	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
620	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
622	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₃×C₄	C₂×#41	1	4	yes	—
624	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
625	C₃×C₈	—	2	2	no	—
626	C₃×C₈	—	2	2	no	—
627	C₃×C₈	—	2	4	no	—
628	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
629	#41	—	2	4	no	—
630	C₂×Q₈	—	2	8	no	—
631	C₂×Q₈	—	2	8	no	—
632	C₂×Q₈	—	2	8	no	—
633	C₂×Q₈	—	2	8	no	—
634	C₂×Q₈	—	2	8	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	C₃×#41	1	8	yes	—
643	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
644	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
645	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
650	C₂²×C₄	—	2	8	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
662	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
663	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
664	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
665	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
669	Q₁₆	—	2	8	no	—
670	Q₁₆	—	2	8	no	—
671	Q₁₆	—	2	8	no	—
672	SD₁₆	—	2	8	no	—
673	M₁₆	—	2	4	no	—
674	C₂×C₈	—	2	4	no	—
675	C₂×C₈	C₂⁴×C₃	1	2	yes	—
676	C₂×C₈	C₂⁴×C₃	1	4	yes	—
677	C₂×C₈	C₂⁴×C₃	1	2	yes	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
698	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
699	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
700	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
701	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
702	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
721	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
722	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
723	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	C₂×C₃×D₄	1	2	yes	—
735	C₄²	C₂×C₃×D₄	1	2	yes	—
736	C₄²	C₂⁴×C₃	1	2	yes	—
737	C₄²	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₃	—	2	1	no	—
739	C₂²×C₃	—	2	1	no	—
740	C₂²×C₃	—	2	1	no	—
741	C₂²×C₃	—	2	1	no	—
742	C₂²×C₃	—	2	1	no	—
743	C₂²×C₃	—	2	1	no	—
744	C₂²×C₃	—	2	1	no	—
745	C₂²×C₃	—	4	4	no	—
746	C₂²×C₃	—	4	1	no	—
747	C₂²×C₃	—	4	1	no	—
748	C₂²×C₃	—	4	1	no	—
749	C₂²×C₃	#525	1	2	yes	—
750	C₂²×C₃	#578	1	2	yes	—
751	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
752	C₃×C₄	—	2	2	no	—
753	C₃×C₄	—	2	2	no	—
754	C₃×C₄	—	2	8	no	—
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	2	no	—
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	4	2	no	—
760	C₃×C₄	—	4	2	no	—
761	C₃×C₄	—	4	1	no	—
762	C₃×C₄	—	4	1	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	—	4	1	no	—
766	C₃×C₄	#525	1	2	yes	—
767	C₃×C₄	C₂²×#41	1	2	yes	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	1	no	—
772	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
773	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
774	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
775	Q₈	—	2	8	no	—
776	Q₈	—	2	8	no	—
777	Q₈	—	2	4	no	—
778	Q₈	—	2	8	no	—
779	Q₈	—	2	4	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	8	2	no	—
783	Q₈	C₂×C₃×#41	1	8	yes	—
784	D₄	—	2	2	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	2	no	—
787	D₄	—	8	1	no	—
788	C₂×C₄	—	2	8	no	—
789	C₂×C₄	—	2	8	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
813	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
814	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
815	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
816	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
817	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
818	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂×C₃×#41	1	4	yes	—
820	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	—	2	4	no	—
824	C₂×C₃	—	2	2	no	—
825	C₂×C₃	—	2	2	no	—
826	C₂×C₃	—	4	1	no	—
827	C₂×C₃	—	8	1	no	—
828	C₂×C₃	C₂×#525	1	1	yes	characteristic
829	C₂×C₃	C₂×#578	1	1	yes	characteristic
830	C₂×C₃	#3586	1	1	yes	characteristic
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	4	4	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	C₃×#525	1	2	yes	—
843	C₂²	C₃×#578	1	2	yes	—
844	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
845	C₄	—	2	8	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	C₃×#525	1	2	yes	—
860	C₄	C₂²×C₃×#41	1	2	yes	—
861	C₃	#60583	1	1	yes	characteristic, direct product factor, Sylow
862	C₂	—	2	2	no	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	8	1	no	—
866	C₂	C₂×C₃×#525	1	1	yes	characteristic
867	C₂	C₂×C₃×#578	1	1	yes	characteristic
868	C₂	C₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#519	C₂	semidirect
3. C₃×#3127	C₂	semidirect
4. C₃×#3121	C₂	semidirect
5. C₃×#3117	C₂	semidirect
6. C₃×#3113	C₂	semidirect
7. C₃×#3108	C₂	semidirect
8. C₃×#3104	C₂	semidirect
9. C₃×#3095	C₂	semidirect
11. C₃×#3082	C₂	semidirect
12. C₃×#3044	C₂	semidirect
14. C₂×C₃×#451	C₂	semidirect
15. C₃×#2950	C₂	semidirect
16. C₃×#2947	C₂	semidirect
17. C₃×#2924	C₂	semidirect
18. #60583	C₃	direct (N × H)
60. C₃×#479	C₂²	semidirect
61. C₃×#479	C₂²	semidirect
62. C₃×#477	C₂²	semidirect
63. C₃×#475	C₂²	semidirect
64. C₃×#464	C₂²	semidirect
65. C₃×#464	C₂²	semidirect
66. C₃×#462	C₂²	semidirect
67. C₃×#462	C₂²	semidirect
75. C₃×#441	C₂²	semidirect
76. C₃×#441	C₂²	semidirect
77. C₃×#441	C₂²	semidirect
78. C₃×#440	C₂²	semidirect
79. C₃×C₄×Q₁₆	C₂²	semidirect
80. C₃×C₄×Q₁₆	C₂²	semidirect
81. C₃×C₄×Q₁₆	C₂²	semidirect
82. C₃×C₄×SD₁₆	C₂²	semidirect
97. C₂×#519	C₂×C₃	semidirect
98. #3127	C₂×C₃	semidirect
99. #3121	C₂×C₃	semidirect
100. #3117	C₂×C₃	semidirect
101. #3113	C₂×C₃	semidirect
102. #3108	C₂×C₃	semidirect
103. #3104	C₂×C₃	semidirect
104. #3095	C₂×C₃	semidirect
106. #3082	C₂×C₃	semidirect
107. #3044	C₂×C₃	semidirect
109. C₂×#451	C₂×C₃	semidirect
110. #2950	C₂×C₃	semidirect
111. #2947	C₂×C₃	semidirect
112. #2924	C₂×C₃	semidirect
290. #479	C₂²×C₃	semidirect
291. #479	C₂²×C₃	semidirect
292. #477	C₂²×C₃	semidirect
293. #475	C₂²×C₃	semidirect
294. #464	C₂²×C₃	semidirect
295. #464	C₂²×C₃	semidirect
296. #462	C₂²×C₃	semidirect
297. #462	C₂²×C₃	semidirect
305. #441	C₂²×C₃	semidirect
306. #441	C₂²×C₃	semidirect
307. #441	C₂²×C₃	semidirect
308. #440	C₂²×C₃	semidirect
309. C₄×Q₁₆	C₂²×C₃	semidirect
310. C₄×Q₁₆	C₂²×C₃	semidirect
311. C₄×Q₁₆	C₂²×C₃	semidirect
312. C₄×SD₁₆	C₂²×C₃	semidirect
861. C₃	#60583	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3495	2
C₂×C₃×#519	2
C₃×#3127	2
C₃×#3121	2
C₃×#3117	2
C₃×#3113	2
C₃×#3108	2
C₃×#3104	2
C₃×#3095	2
C₃×#3091	2
C₃×#3082	2
C₃×#3044	2
C₃×#3004	2
C₂×C₃×#451	2
C₃×#2950	2
C₃×#2947	2
C₃×#2924	2
#60583	3

Subgroups — C3×#60583 #10679190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60583 #10679190