Subgroups — C₃×#61835 #10680442

Order 768.

1800 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3389	C₂	1	4	yes	maximal, complemented
4	C₃×#3385	C₂	1	2	yes	maximal, complemented
5	C₃×#3380	C₂	1	2	yes	maximal, complemented
6	C₃×#3370	C₂	1	4	yes	maximal, complemented
7	C₃×#3366	C₂	1	2	yes	maximal, complemented
8	C₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3234	C₂	1	2	yes	maximal, complemented
11	C₃×#3232	C₂	1	2	yes	maximal, complemented
12	C₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3114	C₂	1	2	yes	maximal, complemented
14	C₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3100	C₂	1	2	yes	maximal, complemented
17	C₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	#61835	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#559	C₂²	1	1	yes	characteristic, complemented
20	C₃×#559	C₂²	1	2	yes	complemented
21	C₃×Q₈²	C₂²	1	1	yes	characteristic, complemented
22	C₃×#554	—	2	1	no	—
23	C₃×#554	—	2	1	no	—
24	C₃×#554	—	2	2	no	—
25	C₃×#554	C₂²	1	2	yes	—
26	C₃×#554	C₂²	1	4	yes	—
27	C₃×#554	C₂²	1	2	yes	—
28	C₃×#554	C₂²	1	2	yes	complemented
29	C₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃×#550	C₂²	1	1	yes	characteristic, complemented
31	C₃×#548	—	2	1	no	—
32	C₃×#547	—	2	1	no	—
33	C₃×#547	—	2	2	no	—
34	C₃×#542	—	2	2	no	—
35	C₃×#542	—	2	1	no	—
36	C₃×#532	C₂²	1	1	yes	characteristic
37	C₃×#532	C₂²	1	2	yes	—
38	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₃×#529	C₂²	1	2	yes	—
40	C₃×#529	C₂²	1	1	yes	characteristic
41	C₂×C₃×#125	C₂²	1	2	yes	—
42	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
44	C₃×#520	—	2	1	no	—
45	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
49	C₃×#501	C₂²	1	4	yes	complemented
50	C₃×#501	C₂²	1	2	yes	complemented
51	C₃×#500	C₂²	1	2	yes	complemented
52	C₃×#499	C₂²	1	4	yes	complemented
53	C₃×#490	C₂²	1	4	yes	complemented
54	C₃×#489	C₂²	1	2	yes	complemented
55	C₃×#488	C₂²	1	4	yes	complemented
56	C₃×#486	C₂²	1	2	yes	complemented
57	C₃×#484	C₂²	1	1	yes	characteristic
58	C₃×#483	C₂²	1	2	yes	—
59	C₃×#481	C₂²	1	2	yes	—
60	C₃×#481	C₂²	1	1	yes	characteristic
61	C₃×#480	C₂²	1	2	yes	—
62	C₃×#480	C₂²	1	2	yes	—
63	C₃×#480	C₂²	1	2	yes	—
64	C₃×#479	C₂²	1	4	yes	complemented
65	C₃×#478	C₂²	1	2	yes	—
66	C₃×#478	C₂²	1	4	yes	—
67	C₃×#478	C₂²	1	4	yes	complemented
68	C₃×#478	C₂²	1	4	yes	complemented
69	C₃×#478	C₂²	1	4	yes	complemented
70	C₃×#477	C₂²	1	2	yes	complemented
71	C₃×#476	C₂²	1	2	yes	—
72	C₃×#476	C₂²	1	2	yes	complemented
73	C₃×#474	C₂²	1	4	yes	—
74	C₃×#474	C₂²	1	4	yes	complemented
75	C₃×#463	C₂²	1	2	yes	—
76	C₃×#463	C₂²	1	4	yes	—
77	C₃×#459	C₂²	1	4	yes	—
78	C₃×#459	C₂²	1	2	yes	—
79	C₃×#450	C₂²	1	1	yes	characteristic
80	C₃×#447	C₂²	1	1	yes	characteristic
81	C₃×#447	C₂²	1	2	yes	—
82	C₃×#446	C₂²	1	2	yes	complemented
83	C₃×#446	C₂²	1	4	yes	complemented
84	C₃×C₈×Q₈	C₂²	1	2	yes	complemented
85	C₃×#442	C₂²	1	4	yes	—
86	C₃×#442	C₂²	1	4	yes	—
87	C₃×#440	C₂²	1	4	yes	—
88	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
89	C₃×C₄×D₈	C₂²	1	4	yes	—
90	C₃×C₄×D₈	C₂²	1	4	yes	—
91	C₃×C₄×D₈	C₂²	1	2	yes	—
92	C₃×#432	C₂²	1	2	yes	—
93	C₃×#432	C₂²	1	1	yes	characteristic
94	C₃×#431	C₂²	1	1	yes	characteristic
95	C₃×#431	C₂²	1	2	yes	—
96	#3522	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#554	C₂×C₃	1	1	yes	characteristic, complemented
98	#3389	C₂×C₃	1	4	yes	complemented
99	#3385	C₂×C₃	1	2	yes	complemented
100	#3380	C₂×C₃	1	2	yes	complemented
101	#3370	C₂×C₃	1	4	yes	complemented
102	#3366	C₂×C₃	1	2	yes	complemented
103	#3361	C₂×C₃	1	2	yes	complemented
104	#3238	C₂×C₃	1	1	yes	characteristic, complemented
105	#3234	C₂×C₃	1	2	yes	complemented
106	#3232	C₂×C₃	1	2	yes	complemented
107	#3226	C₂×C₃	1	1	yes	characteristic, complemented
108	#3114	C₂×C₃	1	2	yes	complemented
109	#3109	C₂×C₃	1	1	yes	characteristic, complemented
110	#3105	C₂×C₃	1	1	yes	characteristic, complemented
111	#3100	C₂×C₃	1	2	yes	complemented
112	#2984	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂×C₃×#41	—	2	1	no	—
114	C₂×C₃×#41	—	2	1	no	—
115	C₂×C₃×#41	—	2	2	no	—
116	C₂²×C₃×Q₈	—	2	1	no	—
117	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
118	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
119	C₂³×C₃×C₄	—	2	1	no	—
120	C₂³×C₃×C₄	—	2	2	no	—
121	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
122	C₂×C₃×D₈	C₂³	1	2	yes	—
123	C₂×C₃×D₈	C₂³	1	4	yes	—
124	C₃×C₄⋊Q₈	—	2	1	no	—
125	C₃×C₄⋊Q₈	—	2	2	no	—
126	C₃×C₄⋊Q₈	—	2	1	no	—
127	C₃×C₄⋊Q₈	—	2	1	no	—
128	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₃×#127	C₂³	1	1	yes	characteristic
133	C₃×#127	C₂³	1	2	yes	—
134	C₃×#126	—	2	2	no	—
135	C₃×#126	—	2	1	no	—
136	C₃×#125	—	2	2	no	—
137	C₃×#125	—	2	2	no	—
138	C₃×#125	C₂³	1	4	yes	—
139	C₃×#125	C₂³	1	4	yes	—
140	C₃×#125	C₂³	1	2	yes	—
141	C₃×#125	C₂³	1	1	yes	characteristic
142	C₃×#124	—	2	1	no	—
143	C₃×#124	—	2	2	no	—
144	C₃×#124	—	2	2	no	—
145	C₃×#124	—	2	1	no	—
146	C₃×#124	C₂³	1	2	yes	—
147	C₃×#124	C₂³	1	1	yes	characteristic
148	C₃×#123	—	2	1	no	—
149	C₃×#123	—	2	2	no	—
150	C₃×#123	—	2	2	no	—
151	C₃×#123	—	2	2	no	—
152	C₃×#123	—	2	2	no	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	2	no	—
155	C₃×C₂²⋊Q₈	—	2	4	no	—
156	C₃×C₂²⋊Q₈	—	2	1	no	—
157	C₃×C₂²⋊Q₈	—	2	2	no	—
158	C₃×C₂²⋊Q₈	—	2	4	no	—
159	C₃×C₂²⋊Q₈	—	2	4	no	—
160	C₃×C₂²⋊Q₈	—	2	4	no	—
161	C₃×C₂²⋊Q₈	—	2	4	no	—
162	C₃×C₂²⋊Q₈	—	2	2	no	—
163	C₃×C₂²⋊Q₈	—	2	2	no	—
164	C₃×C₂²⋊Q₈	—	2	2	no	—
165	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃×#121	—	2	1	no	—
167	C₃×#121	—	2	2	no	—
168	C₃×#121	—	2	1	no	—
169	C₃×#121	—	2	2	no	—
170	C₃×#121	C₂³	1	1	yes	characteristic
171	C₃×#121	C₂³	1	2	yes	—
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
174	C₃×C₄×Q₈	D₄	1	2	yes	—
175	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
176	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
177	C₃×C₄×Q₈	C₂³	1	2	yes	—
178	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
179	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
180	C₃×C₄×Q₈	C₂³	1	2	yes	—
181	C₃×C₄×D₄	—	2	1	no	—
182	C₃×C₄×D₄	—	2	2	no	—
183	C₃×C₄×D₄	—	2	1	no	—
184	C₃×C₄×D₄	—	2	2	no	—
185	C₃×C₄×D₄	—	2	2	no	—
186	C₃×C₄×D₄	—	2	1	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	—	2	1	no	—
189	C₃×C₄×D₄	—	2	2	no	—
190	C₃×C₄×D₄	—	2	1	no	—
191	C₃×C₄×D₄	C₂³	1	2	yes	—
192	C₃×C₄×D₄	C₂³	1	2	yes	—
193	C₃×C₄×D₄	C₂³	1	2	yes	—
194	C₃×C₄×D₄	C₂³	1	4	yes	—
195	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
196	C₃×C₄×D₄	C₂³	1	2	yes	—
197	C₃×C₄×D₄	C₂³	1	4	yes	—
198	C₃×C₄×D₄	C₂³	1	2	yes	—
199	C₃×C₄×D₄	C₂³	1	2	yes	—
200	C₃×#117	—	2	2	no	—
201	C₃×#117	—	2	1	no	—
202	C₂×C₃×C₄⋊C₄	—	2	2	no	—
203	C₂×C₃×C₄⋊C₄	—	2	1	no	—
204	C₂×C₃×C₄⋊C₄	—	2	2	no	—
205	C₂×C₃×C₄⋊C₄	—	2	2	no	—
206	C₂×C₃×C₄⋊C₄	—	2	2	no	—
207	C₂×C₃×C₄⋊C₄	—	2	4	no	—
208	C₂×C₃×C₄⋊C₄	—	2	1	no	—
209	C₂×C₃×C₄⋊C₄	—	2	2	no	—
210	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₃×#107	C₂³	1	4	yes	—
219	C₃×#107	C₂³	1	4	yes	—
220	C₃×#107	C₂³	1	2	yes	—
221	C₃×#107	C₂³	1	4	yes	—
222	C₃×#106	C₂³	1	2	yes	—
223	C₃×#106	C₂³	1	4	yes	—
224	C₃×#106	C₂³	1	4	yes	—
225	C₃×C₄⋊C₈	C₂³	1	4	yes	—
226	C₃×C₄⋊C₈	C₂³	1	2	yes	—
227	C₃×C₄⋊C₈	C₂³	1	2	yes	—
228	C₃×C₄⋊C₈	C₂³	1	4	yes	—
229	C₃×#103	C₂³	1	2	yes	—
230	C₃×#103	C₂³	1	4	yes	—
231	C₃×#102	C₂³	1	2	yes	—
232	C₃×#102	C₂³	1	4	yes	—
233	C₃×#102	C₂³	1	2	yes	—
234	C₃×#102	C₂³	1	4	yes	—
235	C₃×#102	C₂³	1	4	yes	—
236	C₃×#102	C₂³	1	2	yes	—
237	C₃×#102	C₂³	1	4	yes	—
238	C₃×#102	C₂³	1	4	yes	—
239	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
240	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
242	C₃×#97	C₂³	1	4	yes	—
243	C₃×#97	C₂³	1	2	yes	—
244	C₃×C₄×C₈	C₂³	1	4	yes	—
245	C₃×C₄×C₈	C₂³	1	2	yes	—
246	#559	C₂²×C₃	1	1	yes	characteristic, complemented
247	#559	C₂²×C₃	1	2	yes	complemented
248	Q₈²	C₂²×C₃	1	1	yes	characteristic, complemented
249	#554	—	2	1	no	—
250	#554	—	2	1	no	—
251	#554	—	2	2	no	—
252	#554	C₂²×C₃	1	2	yes	—
253	#554	C₂²×C₃	1	2	yes	—
254	#554	C₂²×C₃	1	4	yes	—
255	#554	C₂²×C₃	1	1	yes	characteristic, complemented
256	#554	C₂²×C₃	1	2	yes	complemented
257	#550	C₂²×C₃	1	1	yes	characteristic, complemented
258	#548	—	2	1	no	—
259	#547	—	2	1	no	—
260	#547	—	2	2	no	—
261	#542	—	2	2	no	—
262	#542	—	2	1	no	—
263	#532	C₂²×C₃	1	2	yes	—
264	#532	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	#529	C₂²×C₃	1	1	yes	characteristic
267	#529	C₂²×C₃	1	2	yes	—
268	C₂×#125	C₂²×C₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	—	2	1	no	—
270	C₂×C₂²⋊Q₈	—	2	2	no	—
271	#520	—	2	1	no	—
272	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	—	2	1	no	—
276	#501	C₂²×C₃	1	4	yes	complemented
277	#501	C₂²×C₃	1	2	yes	complemented
278	#500	C₂²×C₃	1	2	yes	complemented
279	#499	C₂²×C₃	1	4	yes	complemented
280	#490	C₂²×C₃	1	4	yes	complemented
281	#489	C₂²×C₃	1	2	yes	complemented
282	#488	C₂²×C₃	1	4	yes	complemented
283	#486	C₂²×C₃	1	2	yes	complemented
284	#484	C₂²×C₃	1	1	yes	characteristic
285	#483	C₂²×C₃	1	2	yes	—
286	#481	C₂²×C₃	1	1	yes	characteristic
287	#481	C₂²×C₃	1	2	yes	—
288	#480	C₂²×C₃	1	2	yes	—
289	#480	C₂²×C₃	1	2	yes	—
290	#480	C₂²×C₃	1	2	yes	—
291	#479	C₂²×C₃	1	4	yes	complemented
292	#478	C₂²×C₃	1	2	yes	—
293	#478	C₂²×C₃	1	4	yes	—
294	#478	C₂²×C₃	1	4	yes	complemented
295	#478	C₂²×C₃	1	4	yes	complemented
296	#478	C₂²×C₃	1	4	yes	complemented
297	#477	C₂²×C₃	1	2	yes	complemented
298	#476	C₂²×C₃	1	2	yes	—
299	#476	C₂²×C₃	1	2	yes	complemented
300	#474	C₂²×C₃	1	4	yes	—
301	#474	C₂²×C₃	1	4	yes	complemented
302	#463	C₂²×C₃	1	2	yes	—
303	#463	C₂²×C₃	1	4	yes	—
304	#459	C₂²×C₃	1	4	yes	—
305	#459	C₂²×C₃	1	2	yes	—
306	#450	C₂²×C₃	1	1	yes	characteristic
307	#447	C₂²×C₃	1	1	yes	characteristic
308	#447	C₂²×C₃	1	2	yes	—
309	#446	C₂²×C₃	1	2	yes	complemented
310	#446	C₂²×C₃	1	4	yes	complemented
311	C₈×Q₈	C₂²×C₃	1	2	yes	complemented
312	#442	C₂²×C₃	1	4	yes	—
313	#442	C₂²×C₃	1	4	yes	—
314	#440	C₂²×C₃	1	4	yes	—
315	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
316	C₄×D₈	C₂²×C₃	1	4	yes	—
317	C₄×D₈	C₂²×C₃	1	4	yes	—
318	C₄×D₈	C₂²×C₃	1	2	yes	—
319	#432	C₂²×C₃	1	1	yes	characteristic
320	#432	C₂²×C₃	1	2	yes	—
321	#431	C₂²×C₃	1	2	yes	—
322	#431	C₂²×C₃	1	1	yes	characteristic
323	C₂⁴×C₃	—	2	1	no	—
324	C₃×#41	—	4	4	no	—
325	C₃×#41	—	8	4	no	—
326	C₃×#41	—	8	2	no	—
327	C₂×C₃×Q₈	—	2	2	no	—
328	C₂×C₃×Q₈	—	2	2	no	—
329	C₂×C₃×Q₈	—	2	1	no	—
330	C₂×C₃×Q₈	—	2	2	no	—
331	C₂×C₃×Q₈	—	4	2	no	—
332	C₂×C₃×Q₈	—	8	2	no	—
333	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
334	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
335	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
336	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
337	C₂×C₃×D₄	—	2	4	no	—
338	C₂×C₃×D₄	—	2	1	no	—
339	C₂×C₃×D₄	—	2	2	no	—
340	C₂×C₃×D₄	—	2	1	no	—
341	C₂×C₃×D₄	—	2	2	no	—
342	C₂×C₃×D₄	—	2	1	no	—
343	C₂×C₃×D₄	—	2	1	no	—
344	C₂×C₃×D₄	—	2	2	no	—
345	C₂×C₃×D₄	C₂⁴	1	2	yes	—
346	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
347	C₂×C₃×D₄	C₂⁴	1	2	yes	—
348	C₂²×C₃×C₄	—	2	1	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	2	no	—
353	C₂²×C₃×C₄	—	2	1	no	—
354	C₂²×C₃×C₄	—	2	4	no	—
355	C₂²×C₃×C₄	—	2	4	no	—
356	C₂²×C₃×C₄	—	2	2	no	—
357	C₂²×C₃×C₄	—	2	2	no	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	—	4	4	no	—
360	C₂²×C₃×C₄	—	8	4	no	—
361	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
363	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₃×SD₁₆	—	2	4	no	—
367	C₃×D₈	—	2	4	no	—
368	C₃×D₈	—	2	8	no	—
369	C₂×C₃×C₈	C₂⁴	1	2	yes	—
370	C₂×C₃×C₈	C₂⁴	1	2	yes	—
371	C₂×C₃×C₈	C₂⁴	1	4	yes	—
372	C₃×C₄⋊C₄	—	2	4	no	—
373	C₃×C₄⋊C₄	—	2	4	no	—
374	C₃×C₄⋊C₄	—	2	2	no	—
375	C₃×C₄⋊C₄	—	2	2	no	—
376	C₃×C₄⋊C₄	—	2	1	no	—
377	C₃×C₄⋊C₄	—	2	2	no	—
378	C₃×C₄⋊C₄	—	2	2	no	—
379	C₃×C₄⋊C₄	—	2	1	no	—
380	C₃×C₄⋊C₄	—	2	4	no	—
381	C₃×C₄⋊C₄	—	2	4	no	—
382	C₃×C₄⋊C₄	—	2	1	no	—
383	C₃×C₄⋊C₄	—	2	2	no	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	—	2	2	no	—
386	C₃×C₄⋊C₄	—	2	1	no	—
387	C₃×C₄⋊C₄	—	2	1	no	—
388	C₃×C₄⋊C₄	—	2	2	no	—
389	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
397	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
398	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
399	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₃×C₂²⋊C₄	—	2	1	no	—
402	C₃×C₂²⋊C₄	—	2	2	no	—
403	C₃×C₂²⋊C₄	—	2	2	no	—
404	C₃×C₂²⋊C₄	—	2	4	no	—
405	C₃×C₂²⋊C₄	—	2	4	no	—
406	C₃×C₂²⋊C₄	—	2	2	no	—
407	C₃×C₂²⋊C₄	—	2	1	no	—
408	C₃×C₂²⋊C₄	—	2	1	no	—
409	C₃×C₂²⋊C₄	—	2	2	no	—
410	C₃×C₂²⋊C₄	—	2	2	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	2	no	—
414	C₃×C₂²⋊C₄	—	2	2	no	—
415	C₃×C₂²⋊C₄	—	2	2	no	—
416	C₃×C₂²⋊C₄	—	2	2	no	—
417	C₃×C₄²	—	2	2	no	—
418	C₃×C₄²	—	2	1	no	—
419	C₃×C₄²	C₂×D₄	1	2	yes	—
420	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
421	C₃×C₄²	C₂×D₄	1	2	yes	—
422	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
423	C₃×C₄²	C₂⁴	1	2	yes	—
424	C₃×C₄²	C₂⁴	1	1	yes	characteristic
425	C₃×C₄²	C₂⁴	1	1	yes	characteristic
426	C₃×C₄²	C₂⁴	1	2	yes	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	2	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	—	2	2	no	—
435	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
436	C₂×D₈	C₂³×C₃	1	2	yes	—
437	C₂×D₈	C₂³×C₃	1	4	yes	—
438	C₄⋊Q₈	—	2	1	no	—
439	C₄⋊Q₈	—	2	2	no	—
440	C₄⋊Q₈	—	2	1	no	—
441	C₄⋊Q₈	—	2	1	no	—
442	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
443	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
444	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
445	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
446	#127	C₂³×C₃	1	1	yes	characteristic
447	#127	C₂³×C₃	1	2	yes	—
448	#126	—	2	2	no	—
449	#126	—	2	1	no	—
450	#125	—	2	2	no	—
451	#125	—	2	2	no	—
452	#125	C₂³×C₃	1	4	yes	—
453	#125	C₂³×C₃	1	4	yes	—
454	#125	C₂³×C₃	1	2	yes	—
455	#125	C₂³×C₃	1	1	yes	characteristic
456	#124	—	2	1	no	—
457	#124	—	2	2	no	—
458	#124	—	2	2	no	—
459	#124	—	2	1	no	—
460	#124	C₂³×C₃	1	2	yes	—
461	#124	C₂³×C₃	1	1	yes	characteristic
462	#123	—	2	1	no	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	#123	—	2	2	no	—
466	#123	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	4	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	4	no	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
480	#121	—	2	1	no	—
481	#121	—	2	2	no	—
482	#121	—	2	1	no	—
483	#121	—	2	2	no	—
484	#121	C₂³×C₃	1	1	yes	characteristic
485	#121	C₂³×C₃	1	2	yes	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
488	C₄×Q₈	C₃×D₄	1	2	yes	—
489	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
490	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
491	C₄×Q₈	C₂³×C₃	1	2	yes	—
492	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
493	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
494	C₄×Q₈	C₂³×C₃	1	2	yes	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	1	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	C₂³×C₃	1	4	yes	—
506	C₄×D₄	C₂³×C₃	1	2	yes	—
507	C₄×D₄	C₂³×C₃	1	4	yes	—
508	C₄×D₄	C₂³×C₃	1	2	yes	—
509	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
510	C₄×D₄	C₂³×C₃	1	2	yes	—
511	C₄×D₄	C₂³×C₃	1	2	yes	—
512	C₄×D₄	C₂³×C₃	1	2	yes	—
513	C₄×D₄	C₂³×C₃	1	2	yes	—
514	#117	—	2	2	no	—
515	#117	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	2	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	2	no	—
524	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₄²	C₂³×C₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	#107	C₂³×C₃	1	4	yes	—
533	#107	C₂³×C₃	1	4	yes	—
534	#107	C₂³×C₃	1	2	yes	—
535	#107	C₂³×C₃	1	4	yes	—
536	#106	C₂³×C₃	1	2	yes	—
537	#106	C₂³×C₃	1	4	yes	—
538	#106	C₂³×C₃	1	4	yes	—
539	C₄⋊C₈	C₂³×C₃	1	4	yes	—
540	C₄⋊C₈	C₂³×C₃	1	2	yes	—
541	C₄⋊C₈	C₂³×C₃	1	2	yes	—
542	C₄⋊C₈	C₂³×C₃	1	4	yes	—
543	#103	C₂³×C₃	1	2	yes	—
544	#103	C₂³×C₃	1	4	yes	—
545	#102	C₂³×C₃	1	2	yes	—
546	#102	C₂³×C₃	1	4	yes	—
547	#102	C₂³×C₃	1	2	yes	—
548	#102	C₂³×C₃	1	4	yes	—
549	#102	C₂³×C₃	1	4	yes	—
550	#102	C₂³×C₃	1	2	yes	—
551	#102	C₂³×C₃	1	4	yes	—
552	#102	C₂³×C₃	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
554	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
556	#97	C₂³×C₃	1	4	yes	—
557	#97	C₂³×C₃	1	2	yes	—
558	C₄×C₈	C₂³×C₃	1	4	yes	—
559	C₄×C₈	C₂³×C₃	1	2	yes	—
560	C₂³×C₃	—	2	4	no	—
561	C₂³×C₃	—	2	2	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	—	4	2	no	—
565	C₂³×C₃	—	4	2	no	—
566	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
567	C₃×Q₈	—	2	2	no	—
568	C₃×Q₈	—	2	2	no	—
569	C₃×Q₈	—	2	2	no	—
570	C₃×Q₈	—	4	2	no	—
571	C₃×Q₈	—	8	2	no	—
572	C₃×Q₈	—	8	2	no	—
573	C₃×Q₈	—	8	2	no	—
574	C₃×Q₈	—	8	1	no	—
575	C₃×D₄	—	2	4	no	—
576	C₃×D₄	—	2	2	no	—
577	C₃×D₄	—	2	2	no	—
578	C₃×D₄	—	2	4	no	—
579	C₃×D₄	—	4	4	no	—
580	C₃×D₄	—	4	2	no	—
581	C₃×D₄	—	4	4	no	—
582	C₃×D₄	—	4	2	no	—
583	C₃×D₄	—	8	2	no	—
584	C₃×D₄	—	8	1	no	—
585	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
586	C₂×C₃×C₄	—	2	4	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	4	no	—
596	C₂×C₃×C₄	—	4	2	no	—
597	C₂×C₃×C₄	—	4	4	no	—
598	C₂×C₃×C₄	—	4	4	no	—
599	C₂×C₃×C₄	—	4	2	no	—
600	C₂×C₃×C₄	—	4	4	no	—
601	C₂×C₃×C₄	—	4	4	no	—
602	C₂×C₃×C₄	—	4	2	no	—
603	C₂×C₃×C₄	—	8	4	no	—
604	C₂×C₃×C₄	—	8	4	no	—
605	C₂×C₃×C₄	—	8	2	no	—
606	C₂×C₃×C₄	—	8	2	no	—
607	C₂×C₃×C₄	—	8	2	no	—
608	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
609	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
611	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
614	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
615	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
616	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
618	C₃×C₈	—	2	2	no	—
619	C₃×C₈	—	2	4	no	—
620	C₃×C₈	—	2	2	no	—
621	C₂⁴	—	2	1	no	—
622	#41	—	4	4	no	—
623	#41	—	8	4	no	—
624	#41	—	8	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	8	2	no	—
631	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
632	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
633	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	C₂⁴×C₃	1	2	yes	—
644	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
645	C₂×D₄	C₂⁴×C₃	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	8	4	no	—
659	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
660	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
661	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
662	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
664	SD₁₆	—	2	4	no	—
665	D₈	—	2	4	no	—
666	D₈	—	2	8	no	—
667	C₂×C₈	C₂⁴×C₃	1	2	yes	—
668	C₂×C₈	C₂⁴×C₃	1	2	yes	—
669	C₂×C₈	C₂⁴×C₃	1	4	yes	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
688	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
689	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
690	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
691	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
692	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
693	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
696	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	1	no	—
717	C₄²	C₂×C₃×D₄	1	2	yes	—
718	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
719	C₄²	C₂×C₃×D₄	1	2	yes	—
720	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
721	C₄²	C₂⁴×C₃	1	2	yes	—
722	C₄²	C₂⁴×C₃	1	1	yes	characteristic
723	C₄²	C₂⁴×C₃	1	1	yes	characteristic
724	C₄²	C₂⁴×C₃	1	2	yes	—
725	C₂²×C₃	—	2	1	no	—
726	C₂²×C₃	—	2	1	no	—
727	C₂²×C₃	—	2	4	no	—
728	C₂²×C₃	—	4	8	no	—
729	C₂²×C₃	—	4	2	no	—
730	C₂²×C₃	—	4	2	no	—
731	C₂²×C₃	—	4	2	no	—
732	C₂²×C₃	—	4	1	no	—
733	C₂²×C₃	—	4	2	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	1	no	—
736	C₂²×C₃	—	4	2	no	—
737	C₂²×C₃	#576	1	2	yes	—
738	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
739	C₃×C₄	—	2	1	no	—
740	C₃×C₄	—	2	1	no	—
741	C₃×C₄	—	2	2	no	—
742	C₃×C₄	—	2	2	no	—
743	C₃×C₄	—	2	2	no	—
744	C₃×C₄	—	2	2	no	—
745	C₃×C₄	—	2	1	no	—
746	C₃×C₄	—	2	1	no	—
747	C₃×C₄	—	4	1	no	—
748	C₃×C₄	—	4	1	no	—
749	C₃×C₄	—	4	2	no	—
750	C₃×C₄	—	4	4	no	—
751	C₃×C₄	—	4	1	no	—
752	C₃×C₄	—	4	2	no	—
753	C₃×C₄	#575	1	2	yes	—
754	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	8	2	no	—
767	Q₈	—	8	2	no	—
768	Q₈	—	8	2	no	—
769	Q₈	—	8	1	no	—
770	D₄	—	2	4	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	2	4	no	—
774	D₄	—	4	4	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	2	no	—
778	D₄	—	8	2	no	—
779	D₄	—	8	1	no	—
780	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
804	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
805	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
806	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
807	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
808	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
809	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
810	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
811	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
813	C₈	—	2	2	no	—
814	C₈	—	2	4	no	—
815	C₈	—	2	2	no	—
816	C₂×C₃	—	2	2	no	—
817	C₂×C₃	—	4	4	no	—
818	C₂×C₃	—	8	2	no	—
819	C₂×C₃	—	8	1	no	—
820	C₂×C₃	#3486	1	1	yes	characteristic
821	C₂×C₃	C₂×#575	1	1	yes	characteristic
822	C₂×C₃	C₂×#576	1	1	yes	characteristic
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	4	8	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	C₃×#576	1	2	yes	—
836	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
837	C₄	—	2	1	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	C₃×#575	1	2	yes	—
852	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
853	C₃	#61835	1	1	yes	characteristic, direct product factor, Sylow
854	C₂	—	2	2	no	—
855	C₂	—	4	4	no	—
856	C₂	—	8	2	no	—
857	C₂	—	8	1	no	—
858	C₂	C₃×#3486	1	1	yes	characteristic
859	C₂	C₂×C₃×#575	1	1	yes	characteristic
860	C₂	C₂×C₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3522	C₂	semidirect
2. C₂×C₃×#554	C₂	semidirect
3. C₃×#3389	C₂	semidirect
4. C₃×#3385	C₂	semidirect
5. C₃×#3380	C₂	semidirect
6. C₃×#3370	C₂	semidirect
7. C₃×#3366	C₂	semidirect
8. C₃×#3361	C₂	semidirect
9. C₃×#3238	C₂	semidirect
10. C₃×#3234	C₂	semidirect
11. C₃×#3232	C₂	semidirect
12. C₃×#3226	C₂	semidirect
13. C₃×#3114	C₂	semidirect
14. C₃×#3109	C₂	semidirect
15. C₃×#3105	C₂	semidirect
16. C₃×#3100	C₂	semidirect
17. C₃×#2984	C₂	semidirect
18. #61835	C₃	direct (N × H)
19. C₃×#559	C₂²	semidirect
20. C₃×#559	C₂²	semidirect
21. C₃×Q₈²	C₂²	semidirect
28. C₃×#554	C₂²	semidirect
29. C₃×#554	C₂²	semidirect
30. C₃×#550	C₂²	semidirect
49. C₃×#501	C₂²	semidirect
50. C₃×#501	C₂²	semidirect
51. C₃×#500	C₂²	semidirect
52. C₃×#499	C₂²	semidirect
53. C₃×#490	C₂²	semidirect
54. C₃×#489	C₂²	semidirect
55. C₃×#488	C₂²	semidirect
56. C₃×#486	C₂²	semidirect
64. C₃×#479	C₂²	semidirect
67. C₃×#478	C₂²	semidirect
68. C₃×#478	C₂²	semidirect
69. C₃×#478	C₂²	semidirect
70. C₃×#477	C₂²	semidirect
72. C₃×#476	C₂²	semidirect
74. C₃×#474	C₂²	semidirect
82. C₃×#446	C₂²	semidirect
83. C₃×#446	C₂²	semidirect
84. C₃×C₈×Q₈	C₂²	semidirect
96. #3522	C₂×C₃	semidirect
97. C₂×#554	C₂×C₃	semidirect
98. #3389	C₂×C₃	semidirect
99. #3385	C₂×C₃	semidirect
100. #3380	C₂×C₃	semidirect
101. #3370	C₂×C₃	semidirect
102. #3366	C₂×C₃	semidirect
103. #3361	C₂×C₃	semidirect
104. #3238	C₂×C₃	semidirect
105. #3234	C₂×C₃	semidirect
106. #3232	C₂×C₃	semidirect
107. #3226	C₂×C₃	semidirect
108. #3114	C₂×C₃	semidirect
109. #3109	C₂×C₃	semidirect
110. #3105	C₂×C₃	semidirect
111. #3100	C₂×C₃	semidirect
112. #2984	C₂×C₃	semidirect
246. #559	C₂²×C₃	semidirect
247. #559	C₂²×C₃	semidirect
248. Q₈²	C₂²×C₃	semidirect
255. #554	C₂²×C₃	semidirect
256. #554	C₂²×C₃	semidirect
257. #550	C₂²×C₃	semidirect
276. #501	C₂²×C₃	semidirect
277. #501	C₂²×C₃	semidirect
278. #500	C₂²×C₃	semidirect
279. #499	C₂²×C₃	semidirect
280. #490	C₂²×C₃	semidirect
281. #489	C₂²×C₃	semidirect
282. #488	C₂²×C₃	semidirect
283. #486	C₂²×C₃	semidirect
291. #479	C₂²×C₃	semidirect
294. #478	C₂²×C₃	semidirect
295. #478	C₂²×C₃	semidirect
296. #478	C₂²×C₃	semidirect
297. #477	C₂²×C₃	semidirect
299. #476	C₂²×C₃	semidirect
301. #474	C₂²×C₃	semidirect
309. #446	C₂²×C₃	semidirect
310. #446	C₂²×C₃	semidirect
311. C₈×Q₈	C₂²×C₃	semidirect
853. C₃	#61835	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×#3522	2
C₂×C₃×#554	2
C₃×#3389	2
C₃×#3385	2
C₃×#3380	2
C₃×#3370	2
C₃×#3366	2
C₃×#3361	2
C₃×#3238	2
C₃×#3234	2
C₃×#3232	2
C₃×#3226	2
C₃×#3114	2
C₃×#3109	2
C₃×#3105	2
C₃×#3100	2
C₃×#2984	2
#61835	3

Subgroups — C3×#61835 #10680442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61835 #10680442