Subgroups — C₃×#60589 #10679196

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 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, complemented
2	C₂×C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3124	C₂	1	4	yes	maximal, complemented
4	C₃×#3120	C₂	1	4	yes	maximal, complemented
5	C₃×#3117	C₂	1	2	yes	maximal, complemented
6	C₃×#3110	C₂	1	2	yes	maximal, complemented
7	C₃×#3105	C₂	1	2	yes	maximal, complemented
8	C₃×#3104	C₂	1	2	yes	maximal, complemented
9	C₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3083	C₂	1	2	yes	maximal, complemented
12	C₃×#3046	C₂	1	2	yes	maximal, complemented
13	C₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3002	C₂	1	1	yes	maximal, characteristic
15	C₃×#2951	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	#60589	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×#137	C₂²	1	2	yes	—
21	C₂×C₃×#135	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, complemented
29	C₃×#542	C₂²	1	2	yes	complemented
30	C₃×#541	C₂²	1	2	yes	complemented
31	C₃×#536	C₂²	1	1	yes	characteristic, complemented
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	—	2	2	no	—
37	C₃×#520	—	2	1	no	—
38	C₃×#520	—	2	1	no	—
39	C₃×#520	C₂²	1	2	yes	—
40	C₃×#520	C₂²	1	2	yes	—
41	C₃×#520	C₂²	1	4	yes	—
42	C₃×#520	C₂²	1	1	yes	characteristic, complemented
43	C₃×#519	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
45	C₂×C₃×C₄×D₄	—	2	2	no	—
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₂×C₃×#117	—	2	1	no	—
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
50	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×#484	C₂²	1	2	yes	—
52	C₃×#484	C₂²	1	2	yes	—
53	C₃×#484	C₂²	1	2	yes	—
54	C₃×#484	C₂²	1	4	yes	complemented
55	C₃×#483	C₂²	1	2	yes	complemented
56	C₃×#481	C₂²	1	2	yes	—
57	C₃×#480	C₂²	1	2	yes	complemented
58	C₃×#479	C₂²	1	4	yes	complemented
59	C₃×#478	C₂²	1	4	yes	complemented
60	C₃×#477	C₂²	1	4	yes	complemented
61	C₃×#474	C₂²	1	4	yes	complemented
62	C₃×#464	C₂²	1	4	yes	complemented
63	C₃×#463	C₂²	1	4	yes	complemented
64	C₃×#462	C₂²	1	4	yes	complemented
65	C₃×#461	C₂²	1	4	yes	complemented
66	C₃×#452	C₂²	1	2	yes	—
67	C₃×#452	C₂²	1	4	yes	—
68	C₃×#451	C₂²	1	1	yes	characteristic
69	C₃×#451	C₂²	1	2	yes	—
70	C₃×#450	C₂²	1	1	yes	characteristic
71	C₃×#450	C₂²	1	2	yes	—
72	C₃×#449	C₂²	1	2	yes	—
73	C₃×#448	C₂²	1	1	yes	characteristic
74	C₃×#447	C₂²	1	1	yes	characteristic
75	C₃×#441	C₂²	1	4	yes	complemented
76	C₃×#440	C₂²	1	4	yes	complemented
77	C₃×#440	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×SD₁₆	C₂²	1	4	yes	complemented
82	C₃×C₄×D₈	C₂²	1	4	yes	complemented
83	C₃×#433	C₂²	1	4	yes	complemented
84	C₃×#432	C₂²	1	2	yes	—
85	C₃×#431	C₂²	1	2	yes	—
86	C₃×#428	C₂²	1	2	yes	complemented
87	C₂×C₃×#107	C₂²	1	2	yes	complemented
88	C₃×#424	C₂²	1	2	yes	complemented
89	C₃×#417	C₂²	1	2	yes	—
90	C₃×#417	C₂²	1	2	yes	complemented
91	C₃×#416	C₂²	1	2	yes	—
92	C₂×C₃×#103	C₂²	1	2	yes	complemented
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	complemented
96	#3495	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#520	C₂×C₃	1	1	yes	characteristic, complemented
98	#3124	C₂×C₃	1	4	yes	complemented
99	#3120	C₂×C₃	1	4	yes	complemented
100	#3117	C₂×C₃	1	2	yes	complemented
101	#3110	C₂×C₃	1	2	yes	complemented
102	#3105	C₂×C₃	1	2	yes	complemented
103	#3104	C₂×C₃	1	2	yes	complemented
104	#3092	C₂×C₃	1	1	yes	characteristic, complemented
105	C₂×#484	C₂×C₃	1	1	yes	characteristic, complemented
106	#3083	C₂×C₃	1	2	yes	complemented
107	#3046	C₂×C₃	1	2	yes	complemented
108	#3007	C₂×C₃	1	1	yes	characteristic, complemented
109	#3002	C₂×C₃	1	1	yes	characteristic
110	#2951	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	—	2	8	no	—
114	C₂×C₃×#41	—	2	1	no	—
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	C₂³	1	1	yes	characteristic
117	C₂×C₃×#41	C₂³	1	2	yes	—
118	C₂×C₃×#41	C₂³	1	2	yes	—
119	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
120	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
121	C₂²×C₃×D₄	—	2	1	no	—
122	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
123	C₂³×C₃×C₄	—	2	1	no	—
124	C₂³×C₃×C₄	—	2	1	no	—
125	C₂³×C₃×C₄	—	2	2	no	—
126	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₃×#137	—	2	8	no	—
128	C₃×#135	—	2	8	no	—
129	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
130	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
131	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
134	C₂×C₃×D₈	C₂³	1	2	yes	—
135	C₂×C₃×M₁₆	C₂³	1	2	yes	—
136	C₂²×C₃×C₈	C₂³	1	2	yes	—
137	C₃×C₄⋊Q₈	—	2	1	no	—
138	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃×#126	—	2	2	no	—
141	C₃×#126	—	2	2	no	—
142	C₃×#126	—	2	2	no	—
143	C₃×#126	—	2	2	no	—
144	C₃×#125	—	2	2	no	—
145	C₃×#125	—	2	2	no	—
146	C₃×#125	—	2	1	no	—
147	C₃×#125	—	2	2	no	—
148	C₃×#125	C₂³	1	2	yes	—
149	C₃×#124	—	2	2	no	—
150	C₃×#124	C₂³	1	2	yes	—
151	C₃×#123	—	2	1	no	—
152	C₃×#123	—	2	2	no	—
153	C₃×#123	—	2	2	no	—
154	C₃×#123	—	2	2	no	—
155	C₃×C₂²⋊Q₈	—	2	1	no	—
156	C₃×C₂²⋊Q₈	—	2	1	no	—
157	C₃×C₂²⋊Q₈	—	2	2	no	—
158	C₃×C₂²⋊Q₈	—	2	1	no	—
159	C₃×C₂²⋊Q₈	—	2	1	no	—
160	C₃×C₂²⋊Q₈	—	2	2	no	—
161	C₃×C₂²⋊Q₈	—	2	2	no	—
162	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
163	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
165	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃×#121	C₂³	1	1	yes	characteristic
167	C₃×#121	C₂³	1	1	yes	characteristic
168	C₃×#120	—	2	1	no	—
169	C₃×C₄×Q₈	—	2	1	no	—
170	C₃×C₄×Q₈	—	2	1	no	—
171	C₃×C₄×Q₈	—	2	2	no	—
172	C₃×C₄×Q₈	—	2	2	no	—
173	C₃×C₄×Q₈	—	2	2	no	—
174	C₃×C₄×Q₈	C₂³	1	2	yes	—
175	C₃×C₄×Q₈	C₂³	1	2	yes	—
176	C₃×C₄×Q₈	C₂³	1	2	yes	—
177	C₃×C₄×Q₈	C₂³	1	4	yes	—
178	C₃×C₄×Q₈	C₂³	1	4	yes	—
179	C₃×C₄×D₄	—	2	1	no	—
180	C₃×C₄×D₄	—	2	1	no	—
181	C₃×C₄×D₄	—	2	2	no	—
182	C₃×C₄×D₄	—	2	4	no	—
183	C₃×C₄×D₄	—	2	4	no	—
184	C₃×C₄×D₄	—	2	4	no	—
185	C₃×C₄×D₄	—	2	4	no	—
186	C₃×C₄×D₄	—	2	2	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	—	2	2	no	—
189	C₃×C₄×D₄	C₂³	1	2	yes	—
190	C₃×C₄×D₄	C₂³	1	4	yes	—
191	C₃×C₄×D₄	C₂³	1	4	yes	—
192	C₃×#117	—	2	2	no	—
193	C₃×#117	—	2	2	no	—
194	C₃×#117	—	2	2	no	—
195	C₃×#117	—	2	4	no	—
196	C₃×#117	—	2	1	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	1	yes	characteristic
203	C₃×#117	C₂³	1	1	yes	characteristic
204	C₃×#117	C₂³	1	1	yes	characteristic
205	C₃×#117	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₃×C₄⋊C₄	—	2	2	no	—
208	C₂×C₃×C₄⋊C₄	—	2	1	no	—
209	C₂×C₃×C₄⋊C₄	—	2	1	no	—
210	C₂×C₃×C₄⋊C₄	—	2	1	no	—
211	C₂×C₃×C₄⋊C₄	—	2	2	no	—
212	C₂×C₃×C₄⋊C₄	—	2	4	no	—
213	C₂×C₃×C₄⋊C₄	—	2	2	no	—
214	C₂×C₃×C₄⋊C₄	—	2	1	no	—
215	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
224	C₂×C₃×C₄²	—	2	2	no	—
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₃×#107	C₂³	1	4	yes	—
227	C₃×#107	C₂³	1	4	yes	—
228	C₃×#107	C₂³	1	4	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×#102	C₂³	1	2	yes	—
239	C₃×#102	C₂³	1	2	yes	—
240	C₃×#102	C₂³	1	4	yes	—
241	C₃×#102	C₂³	1	4	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	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
250	C₂×#137	C₂²×C₃	1	2	yes	—
251	C₂×#135	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, complemented
259	#542	C₂²×C₃	1	2	yes	complemented
260	#541	C₂²×C₃	1	2	yes	complemented
261	#536	C₂²×C₃	1	1	yes	characteristic, complemented
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	—	2	2	no	—
267	#520	—	2	1	no	—
268	#520	—	2	1	no	—
269	#520	C₂²×C₃	1	2	yes	—
270	#520	C₂²×C₃	1	4	yes	—
271	#520	C₂²×C₃	1	2	yes	—
272	#520	C₂²×C₃	1	1	yes	characteristic, complemented
273	#519	C₂²×C₃	1	1	yes	characteristic, complemented
274	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
275	C₂×C₄×D₄	—	2	2	no	—
276	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
277	C₂×#117	—	2	1	no	—
278	C₂×#117	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	—	2	1	no	—
280	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
281	#484	C₂²×C₃	1	2	yes	—
282	#484	C₂²×C₃	1	2	yes	—
283	#484	C₂²×C₃	1	2	yes	—
284	#484	C₂²×C₃	1	4	yes	complemented
285	#483	C₂²×C₃	1	2	yes	complemented
286	#481	C₂²×C₃	1	2	yes	—
287	#480	C₂²×C₃	1	2	yes	complemented
288	#479	C₂²×C₃	1	4	yes	complemented
289	#478	C₂²×C₃	1	4	yes	complemented
290	#477	C₂²×C₃	1	4	yes	complemented
291	#474	C₂²×C₃	1	4	yes	complemented
292	#464	C₂²×C₃	1	4	yes	complemented
293	#463	C₂²×C₃	1	4	yes	complemented
294	#462	C₂²×C₃	1	4	yes	complemented
295	#461	C₂²×C₃	1	4	yes	complemented
296	#452	C₂²×C₃	1	2	yes	—
297	#452	C₂²×C₃	1	4	yes	—
298	#451	C₂²×C₃	1	1	yes	characteristic
299	#451	C₂²×C₃	1	2	yes	—
300	#450	C₂²×C₃	1	2	yes	—
301	#450	C₂²×C₃	1	1	yes	characteristic
302	#449	C₂²×C₃	1	2	yes	—
303	#448	C₂²×C₃	1	1	yes	characteristic
304	#447	C₂²×C₃	1	1	yes	characteristic
305	#441	C₂²×C₃	1	4	yes	complemented
306	#440	C₂²×C₃	1	4	yes	complemented
307	#440	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×SD₁₆	C₂²×C₃	1	4	yes	complemented
312	C₄×D₈	C₂²×C₃	1	4	yes	complemented
313	#433	C₂²×C₃	1	4	yes	complemented
314	#432	C₂²×C₃	1	2	yes	—
315	#431	C₂²×C₃	1	2	yes	—
316	#428	C₂²×C₃	1	2	yes	complemented
317	C₂×#107	C₂²×C₃	1	2	yes	complemented
318	#424	C₂²×C₃	1	2	yes	complemented
319	#417	C₂²×C₃	1	2	yes	—
320	#417	C₂²×C₃	1	2	yes	complemented
321	#416	C₂²×C₃	1	2	yes	—
322	C₂×#103	C₂²×C₃	1	2	yes	complemented
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	complemented
326	C₂⁴×C₃	—	2	1	no	—
327	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
328	C₃×#41	—	2	8	no	—
329	C₃×#41	—	2	8	no	—
330	C₃×#41	—	2	4	no	—
331	C₃×#41	—	2	4	no	—
332	C₃×#41	—	2	4	no	—
333	C₃×#41	—	2	4	no	—
334	C₃×#41	#41	1	8	yes	—
335	C₂×C₃×Q₈	—	2	4	no	—
336	C₂×C₃×Q₈	—	2	1	no	—
337	C₂×C₃×Q₈	—	2	1	no	—
338	C₂×C₃×Q₈	—	2	2	no	—
339	C₂×C₃×Q₈	—	2	4	no	—
340	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
341	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
342	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
343	C₂×C₃×D₄	—	2	8	no	—
344	C₂×C₃×D₄	—	2	2	no	—
345	C₂×C₃×D₄	—	2	2	no	—
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	2	1	no	—
348	C₂×C₃×D₄	—	2	1	no	—
349	C₂×C₃×D₄	—	2	1	no	—
350	C₂×C₃×D₄	—	2	1	no	—
351	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×D₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	—	2	8	no	—
354	C₂²×C₃×C₄	—	2	1	no	—
355	C₂²×C₃×C₄	—	2	2	no	—
356	C₂²×C₃×C₄	—	2	2	no	—
357	C₂²×C₃×C₄	—	2	4	no	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	—	2	1	no	—
360	C₂²×C₃×C₄	—	2	1	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	2	2	no	—
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	—	2	4	no	—
365	C₂²×C₃×C₄	—	2	4	no	—
366	C₂²×C₃×C₄	—	2	2	no	—
367	C₂²×C₃×C₄	—	8	4	no	—
368	C₂²×C₃×C₄	—	8	2	no	—
369	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
370	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₃×Q₁₆	—	2	4	no	—
378	C₃×Q₁₆	—	2	8	no	—
379	C₃×SD₁₆	—	2	4	no	—
380	C₃×SD₁₆	—	2	4	no	—
381	C₃×SD₁₆	—	2	8	no	—
382	C₃×D₈	—	2	4	no	—
383	C₃×M₁₆	—	2	4	no	—
384	C₂×C₃×C₈	—	2	4	no	—
385	C₂×C₃×C₈	C₂⁴	1	2	yes	—
386	C₂×C₃×C₈	C₂⁴	1	4	yes	—
387	C₂×C₃×C₈	C₂⁴	1	2	yes	—
388	C₃×C₄⋊C₄	—	2	2	no	—
389	C₃×C₄⋊C₄	—	2	2	no	—
390	C₃×C₄⋊C₄	—	2	4	no	—
391	C₃×C₄⋊C₄	—	2	4	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	—	2	2	no	—
396	C₃×C₄⋊C₄	—	2	2	no	—
397	C₃×C₄⋊C₄	—	2	2	no	—
398	C₃×C₄⋊C₄	—	2	2	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₄⋊C₄	—	2	1	no	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
414	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
416	C₃×C₂²⋊C₄	—	2	2	no	—
417	C₃×C₂²⋊C₄	—	2	2	no	—
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	1	no	—
421	C₃×C₂²⋊C₄	—	2	4	no	—
422	C₃×C₂²⋊C₄	—	2	4	no	—
423	C₃×C₂²⋊C₄	—	2	1	no	—
424	C₃×C₂²⋊C₄	—	2	2	no	—
425	C₃×C₂²⋊C₄	—	2	2	no	—
426	C₃×C₂²⋊C₄	—	2	1	no	—
427	C₃×C₂²⋊C₄	—	2	2	no	—
428	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₃×C₄²	—	2	4	no	—
433	C₃×C₄²	—	2	4	no	—
434	C₃×C₄²	—	2	2	no	—
435	C₃×C₄²	—	2	2	no	—
436	C₃×C₄²	—	2	2	no	—
437	C₃×C₄²	—	2	1	no	—
438	C₃×C₄²	C₂×D₄	1	2	yes	—
439	C₃×C₄²	C₂×D₄	1	2	yes	—
440	C₃×C₄²	C₂⁴	1	2	yes	—
441	C₃×C₄²	C₂⁴	1	2	yes	—
442	C₂×#41	—	2	8	no	—
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	C₂³×C₃	1	2	yes	—
446	C₂×#41	C₂³×C₃	1	1	yes	characteristic
447	C₂×#41	C₂³×C₃	1	2	yes	—
448	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
452	C₂³×C₄	—	2	1	no	—
453	C₂³×C₄	—	2	1	no	—
454	C₂³×C₄	—	2	2	no	—
455	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
456	#137	—	2	8	no	—
457	#135	—	2	8	no	—
458	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
459	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
460	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
461	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
462	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
463	C₂×D₈	C₂³×C₃	1	2	yes	—
464	C₂×M₁₆	C₂³×C₃	1	2	yes	—
465	C₂²×C₈	C₂³×C₃	1	2	yes	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
469	#126	—	2	2	no	—
470	#126	—	2	2	no	—
471	#126	—	2	2	no	—
472	#126	—	2	2	no	—
473	#125	—	2	2	no	—
474	#125	—	2	2	no	—
475	#125	—	2	1	no	—
476	#125	—	2	2	no	—
477	#125	C₂³×C₃	1	2	yes	—
478	#124	—	2	2	no	—
479	#124	C₂³×C₃	1	2	yes	—
480	#123	—	2	1	no	—
481	#123	—	2	2	no	—
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
492	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
493	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
494	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
495	#121	C₂³×C₃	1	1	yes	characteristic
496	#121	C₂³×C₃	1	1	yes	characteristic
497	#120	—	2	1	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	C₂³×C₃	1	4	yes	—
504	C₄×Q₈	C₂³×C₃	1	4	yes	—
505	C₄×Q₈	C₂³×C₃	1	2	yes	—
506	C₄×Q₈	C₂³×C₃	1	2	yes	—
507	C₄×Q₈	C₂³×C₃	1	2	yes	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	C₂³×C₃	1	4	yes	—
519	C₄×D₄	C₂³×C₃	1	4	yes	—
520	C₄×D₄	C₂³×C₃	1	2	yes	—
521	#117	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	—	2	2	no	—
524	#117	—	2	4	no	—
525	#117	—	2	1	no	—
526	#117	—	2	2	no	—
527	#117	—	2	2	no	—
528	#117	C₃×D₄	1	1	yes	characteristic
529	#117	C₃×D₄	1	2	yes	—
530	#117	C₃×D₄	1	1	yes	characteristic
531	#117	C₂³×C₃	1	1	yes	characteristic
532	#117	C₂³×C₃	1	1	yes	characteristic
533	#117	C₂³×C₃	1	1	yes	characteristic
534	#117	C₂³×C₃	1	2	yes	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	2	no	—
541	C₂×C₄⋊C₄	—	2	4	no	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
553	C₂×C₄²	—	2	2	no	—
554	C₂×C₄²	C₂³×C₃	1	2	yes	—
555	#107	C₂³×C₃	1	4	yes	—
556	#107	C₂³×C₃	1	4	yes	—
557	#107	C₂³×C₃	1	4	yes	—
558	#106	C₂³×C₃	1	4	yes	—
559	C₄⋊C₈	C₂³×C₃	1	4	yes	—
560	C₄⋊C₈	C₂³×C₃	1	4	yes	—
561	#103	C₂³×C₃	1	4	yes	—
562	#103	C₂³×C₃	1	4	yes	—
563	#103	C₂³×C₃	1	2	yes	—
564	#103	C₂³×C₃	1	2	yes	—
565	#103	C₂³×C₃	1	4	yes	—
566	#103	C₂³×C₃	1	4	yes	—
567	#102	C₂³×C₃	1	2	yes	—
568	#102	C₂³×C₃	1	2	yes	—
569	#102	C₂³×C₃	1	4	yes	—
570	#102	C₂³×C₃	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
572	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
573	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
576	#97	C₂³×C₃	1	4	yes	—
577	C₄×C₈	C₂³×C₃	1	4	yes	—
578	C₂³×C₃	—	2	4	no	—
579	C₂³×C₃	—	2	2	no	—
580	C₂³×C₃	—	2	2	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	4	1	no	—
584	C₂³×C₃	—	4	2	no	—
585	C₂³×C₃	—	4	2	no	—
586	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
587	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
588	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
589	C₃×Q₈	—	2	4	no	—
590	C₃×Q₈	—	2	2	no	—
591	C₃×Q₈	—	2	4	no	—
592	C₃×Q₈	—	2	2	no	—
593	C₃×Q₈	—	4	2	no	—
594	C₃×Q₈	—	8	2	no	—
595	C₃×Q₈	C₂×#41	1	4	yes	—
596	C₃×D₄	—	2	8	no	—
597	C₃×D₄	—	2	4	no	—
598	C₃×D₄	—	2	8	no	—
599	C₃×D₄	—	2	2	no	—
600	C₃×D₄	—	2	2	no	—
601	C₃×D₄	—	4	2	no	—
602	C₃×D₄	—	4	2	no	—
603	C₃×D₄	—	8	1	no	—
604	C₃×D₄	C₂×#41	1	4	yes	—
605	C₂×C₃×C₄	—	2	4	no	—
606	C₂×C₃×C₄	—	2	8	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	4	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	8	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	4	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	4	2	no	—
622	C₂×C₃×C₄	—	4	4	no	—
623	C₂×C₃×C₄	—	4	2	no	—
624	C₂×C₃×C₄	—	4	2	no	—
625	C₂×C₃×C₄	—	8	2	no	—
626	C₂×C₃×C₄	—	8	4	no	—
627	C₂×C₃×C₄	—	8	4	no	—
628	C₂×C₃×C₄	—	8	1	no	—
629	C₂×C₃×C₄	—	8	2	no	—
630	C₂×C₃×C₄	—	8	2	no	—
631	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
632	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
633	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
634	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
636	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₃×C₄	C₂×#41	1	4	yes	—
639	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
640	C₃×C₈	—	2	2	no	—
641	C₃×C₈	—	2	2	no	—
642	C₃×C₈	—	2	4	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
645	#41	—	2	8	no	—
646	#41	—	2	8	no	—
647	#41	—	2	4	no	—
648	#41	—	2	4	no	—
649	#41	—	2	4	no	—
650	#41	—	2	4	no	—
651	#41	C₃×#41	1	8	yes	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
659	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
660	C₂×D₄	—	2	8	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
669	C₂×D₄	C₂⁴×C₃	1	2	yes	—
670	C₂²×C₄	—	2	8	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	8	4	no	—
685	C₂²×C₄	—	8	2	no	—
686	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
687	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
688	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
689	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
690	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
694	Q₁₆	—	2	4	no	—
695	Q₁₆	—	2	8	no	—
696	SD₁₆	—	2	4	no	—
697	SD₁₆	—	2	4	no	—
698	SD₁₆	—	2	8	no	—
699	D₈	—	2	4	no	—
700	M₁₆	—	2	4	no	—
701	C₂×C₈	—	2	4	no	—
702	C₂×C₈	C₂⁴×C₃	1	2	yes	—
703	C₂×C₈	C₂⁴×C₃	1	4	yes	—
704	C₂×C₈	C₂⁴×C₃	1	2	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
724	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
725	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
726	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
727	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
728	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
746	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
747	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
748	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	1	no	—
755	C₄²	C₂×C₃×D₄	1	2	yes	—
756	C₄²	C₂×C₃×D₄	1	2	yes	—
757	C₄²	C₂⁴×C₃	1	2	yes	—
758	C₄²	C₂⁴×C₃	1	2	yes	—
759	C₂²×C₃	—	2	1	no	—
760	C₂²×C₃	—	2	1	no	—
761	C₂²×C₃	—	2	1	no	—
762	C₂²×C₃	—	2	1	no	—
763	C₂²×C₃	—	2	1	no	—
764	C₂²×C₃	—	2	1	no	—
765	C₂²×C₃	—	2	4	no	—
766	C₂²×C₃	—	2	1	no	—
767	C₂²×C₃	—	4	4	no	—
768	C₂²×C₃	—	4	8	no	—
769	C₂²×C₃	—	4	2	no	—
770	C₂²×C₃	—	4	2	no	—
771	C₂²×C₃	—	4	1	no	—
772	C₂²×C₃	—	4	1	no	—
773	C₂²×C₃	—	4	1	no	—
774	C₂²×C₃	#525	1	2	yes	—
775	C₂²×C₃	#578	1	2	yes	—
776	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	2	no	—
779	C₃×C₄	—	2	1	no	—
780	C₃×C₄	—	2	4	no	—
781	C₃×C₄	—	2	1	no	—
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	—	2	2	no	—
784	C₃×C₄	—	4	4	no	—
785	C₃×C₄	—	4	2	no	—
786	C₃×C₄	—	4	1	no	—
787	C₃×C₄	—	4	1	no	—
788	C₃×C₄	—	4	2	no	—
789	C₃×C₄	—	4	1	no	—
790	C₃×C₄	#525	1	2	yes	—
791	C₃×C₄	C₂²×#41	1	2	yes	—
792	C₂³	—	2	4	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
801	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
802	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	4	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	C₂×C₃×#41	1	4	yes	—
810	D₄	—	2	8	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	8	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	2	no	—
817	D₄	—	8	1	no	—
818	D₄	C₂×C₃×#41	1	4	yes	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	4	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	2	no	—
844	C₂×C₄	—	8	1	no	—
845	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
846	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
847	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
848	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
850	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
851	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
852	C₂×C₄	C₂×C₃×#41	1	4	yes	—
853	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₂×C₃	—	2	2	no	—
858	C₂×C₃	—	2	2	no	—
859	C₂×C₃	—	4	1	no	—
860	C₂×C₃	—	4	4	no	—
861	C₂×C₃	—	8	1	no	—
862	C₂×C₃	C₂×#525	1	1	yes	characteristic
863	C₂×C₃	C₂×#578	1	1	yes	characteristic
864	C₂×C₃	#3585	1	1	yes	characteristic
865	C₂²	—	2	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	4	8	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	C₃×#525	1	2	yes	—
881	C₂²	C₃×#578	1	2	yes	—
882	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	4	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	C₃×#525	1	2	yes	—
897	C₄	C₂²×C₃×#41	1	2	yes	—
898	C₃	#60589	1	1	yes	characteristic, direct product factor, Sylow
899	C₂	—	2	2	no	—
900	C₂	—	2	2	no	—
901	C₂	—	4	1	no	—
902	C₂	—	4	4	no	—
903	C₂	—	8	1	no	—
904	C₂	C₂×C₃×#525	1	1	yes	characteristic
905	C₂	C₂×C₃×#578	1	1	yes	characteristic
906	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3002	C₂
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
1. C₃×#3495	C₂	semidirect
2. C₂×C₃×#520	C₂	semidirect
3. C₃×#3124	C₂	semidirect
4. C₃×#3120	C₂	semidirect
5. C₃×#3117	C₂	semidirect
6. C₃×#3110	C₂	semidirect
7. C₃×#3105	C₂	semidirect
8. C₃×#3104	C₂	semidirect
9. C₃×#3092	C₂	semidirect
10. C₂×C₃×#484	C₂	semidirect
11. C₃×#3083	C₂	semidirect
12. C₃×#3046	C₂	semidirect
13. C₃×#3007	C₂	semidirect
15. C₃×#2951	C₂	semidirect
16. C₃×#2947	C₂	semidirect
17. C₃×#2924	C₂	semidirect
18. #60589	C₃	direct (N × H)
28. C₃×#544	C₂²	semidirect
29. C₃×#542	C₂²	semidirect
30. C₃×#541	C₂²	semidirect
31. C₃×#536	C₂²	semidirect
42. C₃×#520	C₂²	semidirect
43. C₃×#519	C₂²	semidirect
54. C₃×#484	C₂²	semidirect
55. C₃×#483	C₂²	semidirect
57. C₃×#480	C₂²	semidirect
58. C₃×#479	C₂²	semidirect
59. C₃×#478	C₂²	semidirect
60. C₃×#477	C₂²	semidirect
61. C₃×#474	C₂²	semidirect
62. C₃×#464	C₂²	semidirect
63. C₃×#463	C₂²	semidirect
64. C₃×#462	C₂²	semidirect
65. C₃×#461	C₂²	semidirect
75. C₃×#441	C₂²	semidirect
76. C₃×#440	C₂²	semidirect
77. C₃×#440	C₂²	semidirect
78. C₃×#440	C₂²	semidirect
79. C₃×C₄×Q₁₆	C₂²	semidirect
80. C₃×C₄×Q₁₆	C₂²	semidirect
81. C₃×C₄×SD₁₆	C₂²	semidirect
82. C₃×C₄×D₈	C₂²	semidirect
83. C₃×#433	C₂²	semidirect
86. C₃×#428	C₂²	semidirect
87. C₂×C₃×#107	C₂²	semidirect
88. C₃×#424	C₂²	semidirect
90. C₃×#417	C₂²	semidirect
92. C₂×C₃×#103	C₂²	semidirect
95. C₃×#405	C₂²	semidirect
96. #3495	C₂×C₃	semidirect
97. C₂×#520	C₂×C₃	semidirect
98. #3124	C₂×C₃	semidirect
99. #3120	C₂×C₃	semidirect
100. #3117	C₂×C₃	semidirect
101. #3110	C₂×C₃	semidirect
102. #3105	C₂×C₃	semidirect
103. #3104	C₂×C₃	semidirect
104. #3092	C₂×C₃	semidirect
105. C₂×#484	C₂×C₃	semidirect
106. #3083	C₂×C₃	semidirect
107. #3046	C₂×C₃	semidirect
108. #3007	C₂×C₃	semidirect
110. #2951	C₂×C₃	semidirect
111. #2947	C₂×C₃	semidirect
112. #2924	C₂×C₃	semidirect
258. #544	C₂²×C₃	semidirect
259. #542	C₂²×C₃	semidirect
260. #541	C₂²×C₃	semidirect
261. #536	C₂²×C₃	semidirect
272. #520	C₂²×C₃	semidirect
273. #519	C₂²×C₃	semidirect
284. #484	C₂²×C₃	semidirect
285. #483	C₂²×C₃	semidirect
287. #480	C₂²×C₃	semidirect
288. #479	C₂²×C₃	semidirect
289. #478	C₂²×C₃	semidirect
290. #477	C₂²×C₃	semidirect
291. #474	C₂²×C₃	semidirect
292. #464	C₂²×C₃	semidirect
293. #463	C₂²×C₃	semidirect
294. #462	C₂²×C₃	semidirect
295. #461	C₂²×C₃	semidirect
305. #441	C₂²×C₃	semidirect
306. #440	C₂²×C₃	semidirect
307. #440	C₂²×C₃	semidirect
308. #440	C₂²×C₃	semidirect
309. C₄×Q₁₆	C₂²×C₃	semidirect
310. C₄×Q₁₆	C₂²×C₃	semidirect
311. C₄×SD₁₆	C₂²×C₃	semidirect
312. C₄×D₈	C₂²×C₃	semidirect
313. #433	C₂²×C₃	semidirect
316. #428	C₂²×C₃	semidirect
317. C₂×#107	C₂²×C₃	semidirect
318. #424	C₂²×C₃	semidirect
320. #417	C₂²×C₃	semidirect
322. C₂×#103	C₂²×C₃	semidirect
325. #405	C₂²×C₃	semidirect
898. C₃	#60589	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×#520	2
C₃×#3124	2
C₃×#3120	2
C₃×#3117	2
C₃×#3110	2
C₃×#3105	2
C₃×#3104	2
C₃×#3092	2
C₂×C₃×#484	2
C₃×#3083	2
C₃×#3046	2
C₃×#3007	2
C₃×#3002	2
C₃×#2951	2
C₃×#2947	2
C₃×#2924	2
#60589	3

Subgroups — C3×#60589 #10679196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60589 #10679196