Subgroups — C₃×#60582 #10679189

Order 768.

2058 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3126	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×#3112	C₂	1	2	yes	maximal, complemented
7	C₃×#3108	C₂	1	2	yes	maximal, complemented
8	C₃×#3103	C₂	1	2	yes	maximal, complemented
9	C₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₃×#3043	C₂	1	2	yes	maximal, complemented
13	C₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2949	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	#60582	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×SD₁₆	C₂²	1	2	yes	—
22	C₃×#555	—	2	1	no	—
23	C₃×#553	—	2	1	no	—
24	C₃×#553	—	2	1	no	—
25	C₃×#551	—	2	2	no	—
26	C₃×#547	—	2	1	no	—
27	C₃×#546	—	2	2	no	—
28	C₃×#544	C₂²	1	1	yes	characteristic
29	C₃×#542	C₂²	1	2	yes	—
30	C₃×#540	C₂²	1	2	yes	—
31	C₃×#535	C₂²	1	1	yes	characteristic
32	C₃×#532	C₂²	1	2	yes	—
33	C₃×#529	C₂²	1	2	yes	—
34	C₃×#525	C₂²	1	1	yes	characteristic
35	C₂×C₃×#121	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	complemented
43	C₃×#518	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	complemented
47	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
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	complemented
52	C₃×#484	C₂²	1	1	yes	characteristic, complemented
53	C₃×#483	C₂²	1	1	yes	characteristic, complemented
54	C₃×#482	C₂²	1	4	yes	—
55	C₃×#482	C₂²	1	2	yes	complemented
56	C₃×#481	C₂²	1	2	yes	—
57	C₃×#481	C₂²	1	1	yes	characteristic, complemented
58	C₃×#480	C₂²	1	2	yes	—
59	C₃×#480	C₂²	1	1	yes	characteristic, complemented
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×#460	C₂²	1	4	yes	complemented
67	C₃×#460	C₂²	1	4	yes	complemented
68	C₃×#451	C₂²	1	2	yes	complemented
69	C₃×#451	C₂²	1	2	yes	complemented
70	C₃×#448	C₂²	1	2	yes	—
71	C₃×#448	C₂²	1	2	yes	—
72	C₃×#448	C₂²	1	4	yes	—
73	C₃×#448	C₂²	1	2	yes	complemented
74	C₃×#448	C₂²	1	2	yes	complemented
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×SD₁₆	C₂²	1	4	yes	complemented
81	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
82	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
83	C₃×#433	C₂²	1	4	yes	complemented
84	C₃×#432	C₂²	1	2	yes	complemented
85	C₃×#431	C₂²	1	2	yes	complemented
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×#418	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	#3494	C₂×C₃	1	1	yes	characteristic
97	C₂×#519	C₂×C₃	1	1	yes	characteristic, complemented
98	#3126	C₂×C₃	1	4	yes	complemented
99	#3121	C₂×C₃	1	4	yes	complemented
100	#3117	C₂×C₃	1	2	yes	complemented
101	#3112	C₂×C₃	1	2	yes	complemented
102	#3108	C₂×C₃	1	2	yes	complemented
103	#3103	C₂×C₃	1	2	yes	complemented
104	#3094	C₂×C₃	1	1	yes	characteristic, complemented
105	#3091	C₂×C₃	1	1	yes	characteristic, complemented
106	#3082	C₂×C₃	1	2	yes	complemented
107	#3043	C₂×C₃	1	2	yes	complemented
108	#3004	C₂×C₃	1	1	yes	characteristic, complemented
109	C₂×#448	C₂×C₃	1	1	yes	characteristic, complemented
110	#2949	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	2	no	—
114	C₂×C₃×#41	C₂³	1	1	yes	characteristic
115	C₂²×C₃×Q₈	—	2	8	no	—
116	C₂²×C₃×Q₈	—	2	1	no	—
117	C₂²×C₃×Q₈	—	2	1	no	—
118	C₂²×C₃×Q₈	—	2	1	no	—
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	C₂²×C₃×D₄	—	2	1	no	—
123	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
124	C₂³×C₃×C₄	—	2	1	no	—
125	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
126	C₃×#137	—	2	8	no	—
127	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
128	C₂×C₃×SD₁₆	—	2	8	no	—
129	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
132	C₂×C₃×M₁₆	C₂³	1	2	yes	—
133	C₂²×C₃×C₈	C₂³	1	2	yes	—
134	C₃×C₄⋊Q₈	—	2	1	no	—
135	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃×#127	C₂³	1	2	yes	—
137	C₃×#126	—	2	2	no	—
138	C₃×#126	—	2	2	no	—
139	C₃×#125	—	2	1	no	—
140	C₃×#125	C₂³	1	2	yes	—
141	C₃×#124	—	2	2	no	—
142	C₃×#124	—	2	2	no	—
143	C₃×#124	C₂³	1	2	yes	—
144	C₃×#123	—	2	1	no	—
145	C₃×#123	—	2	2	no	—
146	C₃×#123	—	2	2	no	—
147	C₃×#123	—	2	2	no	—
148	C₃×#123	—	2	2	no	—
149	C₃×C₂²⋊Q₈	—	2	2	no	—
150	C₃×C₂²⋊Q₈	—	2	2	no	—
151	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃×#121	—	2	1	no	—
154	C₃×#121	—	2	1	no	—
155	C₃×#121	—	2	2	no	—
156	C₃×#121	—	2	1	no	—
157	C₃×#121	—	2	1	no	—
158	C₃×#121	—	2	2	no	—
159	C₃×#121	—	2	2	no	—
160	C₃×#121	C₂³	1	2	yes	—
161	C₃×#121	C₂³	1	2	yes	—
162	C₃×#121	C₂³	1	1	yes	characteristic
163	C₃×#121	C₂³	1	1	yes	characteristic
164	C₃×#120	—	2	1	no	—
165	C₃×#120	—	2	2	no	—
166	C₃×C₄×Q₈	—	2	2	no	—
167	C₃×C₄×Q₈	—	2	2	no	—
168	C₃×C₄×Q₈	—	2	2	no	—
169	C₃×C₄×Q₈	—	2	2	no	—
170	C₃×C₄×Q₈	—	2	4	no	—
171	C₃×C₄×Q₈	—	2	4	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	C₂³	1	4	yes	—
177	C₃×C₄×Q₈	C₂³	1	4	yes	—
178	C₃×C₄×Q₈	C₂³	1	2	yes	—
179	C₃×C₄×Q₈	C₂³	1	4	yes	—
180	C₃×C₄×Q₈	C₂³	1	4	yes	—
181	C₃×C₄×D₄	—	2	1	no	—
182	C₃×C₄×D₄	—	2	1	no	—
183	C₃×C₄×D₄	—	2	2	no	—
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×C₄×D₄	C₂³	1	2	yes	—
190	C₃×C₄×D₄	C₂³	1	2	yes	—
191	C₃×#117	—	2	1	no	—
192	C₃×#117	—	2	1	no	—
193	C₃×#117	—	2	1	no	—
194	C₃×#117	—	2	4	no	—
195	C₃×#117	—	2	4	no	—
196	C₃×#117	—	2	4	no	—
197	C₃×#117	—	2	4	no	—
198	C₃×#117	—	2	2	no	—
199	C₃×#117	D₄	1	2	yes	—
200	C₃×#117	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
217	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
218	C₂×C₃×C₂²⋊C₄	—	2	2	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×#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	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
250	C₂×#137	C₂²×C₃	1	2	yes	—
251	C₂²×SD₁₆	C₂²×C₃	1	2	yes	—
252	#555	—	2	1	no	—
253	#553	—	2	1	no	—
254	#553	—	2	1	no	—
255	#551	—	2	2	no	—
256	#547	—	2	1	no	—
257	#546	—	2	2	no	—
258	#544	C₂²×C₃	1	1	yes	characteristic
259	#542	C₂²×C₃	1	2	yes	—
260	#540	C₂²×C₃	1	2	yes	—
261	#535	C₂²×C₃	1	1	yes	characteristic
262	#532	C₂²×C₃	1	2	yes	—
263	#529	C₂²×C₃	1	2	yes	—
264	#525	C₂²×C₃	1	1	yes	characteristic
265	C₂×#121	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	2	yes	—
272	#519	C₂²×C₃	1	4	yes	complemented
273	#518	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	complemented
277	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
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	complemented
282	#484	C₂²×C₃	1	1	yes	characteristic, complemented
283	#483	C₂²×C₃	1	1	yes	characteristic, complemented
284	#482	C₂²×C₃	1	4	yes	—
285	#482	C₂²×C₃	1	2	yes	complemented
286	#481	C₂²×C₃	1	2	yes	—
287	#481	C₂²×C₃	1	1	yes	characteristic, complemented
288	#480	C₂²×C₃	1	2	yes	—
289	#480	C₂²×C₃	1	1	yes	characteristic, complemented
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	#460	C₂²×C₃	1	4	yes	complemented
297	#460	C₂²×C₃	1	4	yes	complemented
298	#451	C₂²×C₃	1	2	yes	complemented
299	#451	C₂²×C₃	1	2	yes	complemented
300	#448	C₂²×C₃	1	2	yes	—
301	#448	C₂²×C₃	1	2	yes	—
302	#448	C₂²×C₃	1	4	yes	—
303	#448	C₂²×C₃	1	2	yes	complemented
304	#448	C₂²×C₃	1	2	yes	complemented
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×SD₁₆	C₂²×C₃	1	4	yes	complemented
311	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
312	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
313	#433	C₂²×C₃	1	4	yes	complemented
314	#432	C₂²×C₃	1	2	yes	complemented
315	#431	C₂²×C₃	1	2	yes	complemented
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	#418	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	—	2	1	no	—
327	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
328	C₃×#41	—	2	4	no	—
329	C₃×#41	—	8	4	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	8	no	—
334	C₂×C₃×Q₈	—	2	8	no	—
335	C₂×C₃×Q₈	—	2	2	no	—
336	C₂×C₃×Q₈	—	2	2	no	—
337	C₂×C₃×Q₈	—	2	2	no	—
338	C₂×C₃×Q₈	—	2	2	no	—
339	C₂×C₃×Q₈	—	2	4	no	—
340	C₂×C₃×Q₈	#41	1	8	yes	complemented
341	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
342	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
343	C₂×C₃×D₄	—	2	1	no	—
344	C₂×C₃×D₄	—	2	1	no	—
345	C₂×C₃×D₄	—	2	2	no	—
346	C₂×C₃×D₄	—	2	1	no	—
347	C₂×C₃×D₄	—	2	2	no	—
348	C₂×C₃×D₄	—	2	1	no	—
349	C₂×C₃×D₄	—	2	2	no	—
350	C₂×C₃×D₄	—	2	2	no	—
351	C₂×C₃×D₄	—	2	4	no	—
352	C₂×C₃×D₄	—	8	2	no	—
353	C₂×C₃×D₄	C₂⁴	1	2	yes	—
354	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
355	C₂²×C₃×C₄	—	2	8	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	—	2	4	no	—
360	C₂²×C₃×C₄	—	2	1	no	—
361	C₂²×C₃×C₄	—	2	1	no	—
362	C₂²×C₃×C₄	—	2	1	no	—
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	—	2	2	no	—
365	C₂²×C₃×C₄	—	2	2	no	—
366	C₂²×C₃×C₄	—	2	2	no	—
367	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
368	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
372	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₃×Q₁₆	—	2	8	no	—
376	C₃×SD₁₆	—	2	8	no	—
377	C₃×SD₁₆	—	2	8	no	—
378	C₃×SD₁₆	—	2	8	no	—
379	C₃×M₁₆	—	2	4	no	—
380	C₂×C₃×C₈	—	2	4	no	—
381	C₂×C₃×C₈	C₂⁴	1	2	yes	—
382	C₂×C₃×C₈	C₂⁴	1	4	yes	—
383	C₂×C₃×C₈	C₂⁴	1	2	yes	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	—	2	4	no	—
386	C₃×C₄⋊C₄	—	2	4	no	—
387	C₃×C₄⋊C₄	—	2	4	no	—
388	C₃×C₄⋊C₄	—	2	4	no	—
389	C₃×C₄⋊C₄	—	2	2	no	—
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	—	2	1	no	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	—	2	2	no	—
396	C₃×C₄⋊C₄	—	2	1	no	—
397	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
401	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
404	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	2	no	—
418	C₃×C₂²⋊C₄	—	2	2	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	2	no	—
421	C₃×C₂²⋊C₄	—	2	1	no	—
422	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
425	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₃×C₄²	—	2	4	no	—
427	C₃×C₄²	—	2	4	no	—
428	C₃×C₄²	—	2	4	no	—
429	C₃×C₄²	—	2	4	no	—
430	C₃×C₄²	—	2	2	no	—
431	C₃×C₄²	—	2	2	no	—
432	C₃×C₄²	—	2	2	no	—
433	C₃×C₄²	—	2	1	no	—
434	C₃×C₄²	C₂×D₄	1	2	yes	—
435	C₃×C₄²	C₂×D₄	1	2	yes	—
436	C₃×C₄²	C₂⁴	1	2	yes	—
437	C₃×C₄²	C₂⁴	1	2	yes	—
438	C₂×#41	—	2	2	no	—
439	C₂×#41	C₂³×C₃	1	1	yes	characteristic
440	C₂²×Q₈	—	2	8	no	—
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	—	2	1	no	—
444	C₂²×Q₈	C₂³×C₃	1	2	yes	—
445	C₂²×Q₈	C₂³×C₃	1	2	yes	—
446	C₂²×Q₈	C₂³×C₃	1	2	yes	—
447	C₂²×D₄	—	2	1	no	—
448	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
451	#137	—	2	8	no	—
452	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
453	C₂×SD₁₆	—	2	8	no	—
454	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
455	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
456	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
457	C₂×M₁₆	C₂³×C₃	1	2	yes	—
458	C₂²×C₈	C₂³×C₃	1	2	yes	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
461	#127	C₂³×C₃	1	2	yes	—
462	#126	—	2	2	no	—
463	#126	—	2	2	no	—
464	#125	—	2	1	no	—
465	#125	C₂³×C₃	1	2	yes	—
466	#124	—	2	2	no	—
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	#123	—	2	2	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
477	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	2	no	—
481	#121	—	2	1	no	—
482	#121	—	2	1	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	C₂³×C₃	1	2	yes	—
486	#121	C₂³×C₃	1	2	yes	—
487	#121	C₂³×C₃	1	1	yes	characteristic
488	#121	C₂³×C₃	1	1	yes	characteristic
489	#120	—	2	1	no	—
490	#120	—	2	2	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×Q₈	—	2	4	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
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	4	yes	—
505	C₄×Q₈	C₂³×C₃	1	2	yes	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	C₂³×C₃	1	2	yes	—
514	C₄×D₄	C₂³×C₃	1	2	yes	—
515	C₄×D₄	C₂³×C₃	1	2	yes	—
516	#117	—	2	1	no	—
517	#117	—	2	1	no	—
518	#117	—	2	1	no	—
519	#117	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	—	2	4	no	—
522	#117	—	2	4	no	—
523	#117	—	2	2	no	—
524	#117	C₃×D₄	1	2	yes	—
525	#117	C₃×D₄	1	1	yes	characteristic
526	#117	C₃×D₄	1	1	yes	characteristic
527	#117	C₂³×C₃	1	2	yes	—
528	#117	C₂³×C₃	1	2	yes	—
529	#117	C₂³×C₃	1	1	yes	characteristic
530	#117	C₂³×C₃	1	1	yes	characteristic
531	#117	C₂³×C₃	1	1	yes	characteristic
532	#117	C₂³×C₃	1	2	yes	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₃×D₄	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×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	2	no	—
544	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
545	C₂×C₄²	—	2	2	no	—
546	C₂×C₄²	—	2	2	no	—
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	C₂³×C₃	1	2	yes	—
549	#107	C₂³×C₃	1	2	yes	—
550	#107	C₂³×C₃	1	2	yes	—
551	#107	C₂³×C₃	1	4	yes	—
552	#106	C₂³×C₃	1	2	yes	—
553	#106	C₂³×C₃	1	2	yes	—
554	#106	C₂³×C₃	1	4	yes	—
555	C₄⋊C₈	C₂³×C₃	1	4	yes	—
556	C₄⋊C₈	C₂³×C₃	1	4	yes	—
557	#103	C₂³×C₃	1	4	yes	—
558	#103	C₂³×C₃	1	4	yes	—
559	#103	C₂³×C₃	1	2	yes	—
560	#103	C₂³×C₃	1	2	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	#102	C₂³×C₃	1	4	yes	—
566	#102	C₂³×C₃	1	4	yes	—
567	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
568	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
569	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
571	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
572	#97	C₂³×C₃	1	4	yes	—
573	C₄×C₈	C₂³×C₃	1	4	yes	—
574	C₂³×C₃	—	2	2	no	—
575	C₂³×C₃	—	2	2	no	—
576	C₂³×C₃	—	2	2	no	—
577	C₂³×C₃	—	2	1	no	—
578	C₂³×C₃	—	4	1	no	—
579	C₂³×C₃	—	4	2	no	—
580	C₂³×C₃	—	8	1	no	—
581	C₂³×C₃	—	8	1	no	—
582	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
583	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
584	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
585	C₃×Q₈	—	2	8	no	—
586	C₃×Q₈	—	2	8	no	—
587	C₃×Q₈	—	2	8	no	—
588	C₃×Q₈	—	2	4	no	—
589	C₃×Q₈	—	2	2	no	—
590	C₃×Q₈	—	8	2	no	—
591	C₃×Q₈	C₂×#41	1	8	yes	—
592	C₃×D₄	—	2	4	no	—
593	C₃×D₄	—	2	2	no	—
594	C₃×D₄	—	4	2	no	—
595	C₃×D₄	—	4	4	no	—
596	C₃×D₄	—	4	2	no	—
597	C₃×D₄	—	4	2	no	—
598	C₃×D₄	—	8	2	no	—
599	C₃×D₄	—	8	2	no	—
600	C₃×D₄	—	8	1	no	—
601	C₃×D₄	—	8	2	no	—
602	C₂×C₃×C₄	—	2	8	no	—
603	C₂×C₃×C₄	—	2	8	no	—
604	C₂×C₃×C₄	—	2	8	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	4	no	—
607	C₂×C₃×C₄	—	2	4	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	1	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	—	4	2	no	—
619	C₂×C₃×C₄	—	4	2	no	—
620	C₂×C₃×C₄	—	4	2	no	—
621	C₂×C₃×C₄	—	4	2	no	—
622	C₂×C₃×C₄	—	8	2	no	—
623	C₂×C₃×C₄	—	8	2	no	—
624	C₂×C₃×C₄	—	8	2	no	—
625	C₂×C₃×C₄	—	8	1	no	—
626	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
627	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
628	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
629	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
630	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
632	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
633	C₂×C₃×C₄	C₂×#41	1	4	yes	—
634	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
635	C₃×C₈	—	2	2	no	—
636	C₃×C₈	—	2	2	no	—
637	C₃×C₈	—	2	4	no	—
638	C₂⁴	—	2	1	no	—
639	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
640	#41	—	2	4	no	—
641	#41	—	8	4	no	—
642	C₂×Q₈	—	2	8	no	—
643	C₂×Q₈	—	2	8	no	—
644	C₂×Q₈	—	2	8	no	—
645	C₂×Q₈	—	2	8	no	—
646	C₂×Q₈	—	2	8	no	—
647	C₂×Q₈	—	2	2	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	C₃×#41	1	8	yes	complemented
653	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
654	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	8	2	no	—
665	C₂×D₄	C₂⁴×C₃	1	2	yes	—
666	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
667	C₂²×C₄	—	2	8	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
680	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
681	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
682	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
683	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
687	Q₁₆	—	2	8	no	—
688	SD₁₆	—	2	8	no	—
689	SD₁₆	—	2	8	no	—
690	SD₁₆	—	2	8	no	—
691	M₁₆	—	2	4	no	—
692	C₂×C₈	—	2	4	no	—
693	C₂×C₈	C₂⁴×C₃	1	2	yes	—
694	C₂×C₈	C₂⁴×C₃	1	4	yes	—
695	C₂×C₈	C₂⁴×C₃	1	2	yes	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
710	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
711	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
712	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
713	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
714	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
735	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
736	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
737	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	2	4	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	1	no	—
746	C₄²	C₂×C₃×D₄	1	2	yes	—
747	C₄²	C₂×C₃×D₄	1	2	yes	—
748	C₄²	C₂⁴×C₃	1	2	yes	—
749	C₄²	C₂⁴×C₃	1	2	yes	—
750	C₂²×C₃	—	2	1	no	—
751	C₂²×C₃	—	2	1	no	—
752	C₂²×C₃	—	2	1	no	—
753	C₂²×C₃	—	2	1	no	—
754	C₂²×C₃	—	2	1	no	—
755	C₂²×C₃	—	2	1	no	—
756	C₂²×C₃	—	2	1	no	—
757	C₂²×C₃	—	4	4	no	—
758	C₂²×C₃	—	4	2	no	—
759	C₂²×C₃	—	4	1	no	—
760	C₂²×C₃	—	4	1	no	—
761	C₂²×C₃	—	4	2	no	—
762	C₂²×C₃	—	4	1	no	—
763	C₂²×C₃	—	4	2	no	—
764	C₂²×C₃	—	16	2	no	—
765	C₂²×C₃	#525	1	2	yes	—
766	C₂²×C₃	#577	1	2	yes	—
767	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
768	C₃×C₄	—	2	2	no	—
769	C₃×C₄	—	2	2	no	—
770	C₃×C₄	—	2	8	no	—
771	C₃×C₄	—	2	1	no	—
772	C₃×C₄	—	2	1	no	—
773	C₃×C₄	—	2	2	no	—
774	C₃×C₄	—	2	2	no	—
775	C₃×C₄	—	4	2	no	—
776	C₃×C₄	—	4	1	no	—
777	C₃×C₄	—	4	1	no	—
778	C₃×C₄	—	4	2	no	—
779	C₃×C₄	—	4	2	no	—
780	C₃×C₄	—	4	1	no	—
781	C₃×C₄	#525	1	2	yes	—
782	C₃×C₄	C₂²×#41	1	2	yes	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	1	no	—
790	C₂³	—	8	1	no	—
791	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
792	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
793	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
794	Q₈	—	2	8	no	—
795	Q₈	—	2	8	no	—
796	Q₈	—	2	4	no	—
797	Q₈	—	2	8	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	8	2	no	—
800	Q₈	C₂×C₃×#41	1	8	yes	—
801	D₄	—	2	4	no	—
802	D₄	—	2	2	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	8	2	no	—
808	D₄	—	8	2	no	—
809	D₄	—	8	2	no	—
810	D₄	—	8	1	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	—	8	2	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
836	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
837	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
838	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
839	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
840	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
841	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
842	C₂×C₄	C₂×C₃×#41	1	4	yes	—
843	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
844	C₈	—	2	2	no	—
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₂×C₃	—	2	2	no	—
848	C₂×C₃	—	2	2	no	—
849	C₂×C₃	—	4	1	no	—
850	C₂×C₃	—	8	1	no	—
851	C₂×C₃	—	8	2	no	—
852	C₂×C₃	C₂×#525	1	1	yes	characteristic
853	C₂×C₃	C₂×#577	1	1	yes	characteristic
854	C₂×C₃	#3586	1	1	yes	characteristic
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	16	2	no	—
870	C₂²	C₃×#525	1	2	yes	—
871	C₂²	C₃×#577	1	2	yes	—
872	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
873	C₄	—	2	8	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	C₃×#525	1	2	yes	—
887	C₄	C₂²×C₃×#41	1	2	yes	—
888	C₃	#60582	1	1	yes	characteristic, direct product factor, Sylow
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	2	no	—
893	C₂	—	8	1	no	—
894	C₂	C₂×C₃×#525	1	1	yes	characteristic
895	C₂	C₂×C₃×#577	1	1	yes	characteristic
896	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×#3494	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
2. C₂×C₃×#519	C₂	semidirect
3. C₃×#3126	C₂	semidirect
4. C₃×#3121	C₂	semidirect
5. C₃×#3117	C₂	semidirect
6. C₃×#3112	C₂	semidirect
7. C₃×#3108	C₂	semidirect
8. C₃×#3103	C₂	semidirect
9. C₃×#3094	C₂	semidirect
10. C₃×#3091	C₂	semidirect
11. C₃×#3082	C₂	semidirect
12. C₃×#3043	C₂	semidirect
13. C₃×#3004	C₂	semidirect
14. C₂×C₃×#448	C₂	semidirect
15. C₃×#2949	C₂	semidirect
16. C₃×#2947	C₂	semidirect
17. C₃×#2924	C₂	semidirect
18. #60582	C₃	direct (N × H)
42. C₃×#519	C₂²	semidirect
46. C₂×C₃×C₄×Q₈	C₂²	semidirect
47. C₂×C₃×C₄×Q₈	C₂²	semidirect
51. C₃×#485	C₂²	semidirect
52. C₃×#484	C₂²	semidirect
53. C₃×#483	C₂²	semidirect
55. C₃×#482	C₂²	semidirect
57. C₃×#481	C₂²	semidirect
59. C₃×#480	C₂²	semidirect
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×#460	C₂²	semidirect
67. C₃×#460	C₂²	semidirect
68. C₃×#451	C₂²	semidirect
69. C₃×#451	C₂²	semidirect
73. C₃×#448	C₂²	semidirect
74. C₃×#448	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×SD₁₆	C₂²	semidirect
81. C₃×C₄×SD₁₆	C₂²	semidirect
82. C₃×C₄×SD₁₆	C₂²	semidirect
83. C₃×#433	C₂²	semidirect
84. C₃×#432	C₂²	semidirect
85. C₃×#431	C₂²	semidirect
97. C₂×#519	C₂×C₃	semidirect
98. #3126	C₂×C₃	semidirect
99. #3121	C₂×C₃	semidirect
100. #3117	C₂×C₃	semidirect
101. #3112	C₂×C₃	semidirect
102. #3108	C₂×C₃	semidirect
103. #3103	C₂×C₃	semidirect
104. #3094	C₂×C₃	semidirect
105. #3091	C₂×C₃	semidirect
106. #3082	C₂×C₃	semidirect
107. #3043	C₂×C₃	semidirect
108. #3004	C₂×C₃	semidirect
109. C₂×#448	C₂×C₃	semidirect
110. #2949	C₂×C₃	semidirect
111. #2947	C₂×C₃	semidirect
112. #2924	C₂×C₃	semidirect
272. #519	C₂²×C₃	semidirect
276. C₂×C₄×Q₈	C₂²×C₃	semidirect
277. C₂×C₄×Q₈	C₂²×C₃	semidirect
281. #485	C₂²×C₃	semidirect
282. #484	C₂²×C₃	semidirect
283. #483	C₂²×C₃	semidirect
285. #482	C₂²×C₃	semidirect
287. #481	C₂²×C₃	semidirect
289. #480	C₂²×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. #460	C₂²×C₃	semidirect
297. #460	C₂²×C₃	semidirect
298. #451	C₂²×C₃	semidirect
299. #451	C₂²×C₃	semidirect
303. #448	C₂²×C₃	semidirect
304. #448	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×SD₁₆	C₂²×C₃	semidirect
311. C₄×SD₁₆	C₂²×C₃	semidirect
312. C₄×SD₁₆	C₂²×C₃	semidirect
313. #433	C₂²×C₃	semidirect
314. #432	C₂²×C₃	semidirect
315. #431	C₂²×C₃	semidirect
340. C₂×C₃×Q₈	#41	semidirect
652. C₂×Q₈	C₃×#41	semidirect
888. C₃	#60582	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×#3494	2
C₂×C₃×#519	2
C₃×#3126	2
C₃×#3121	2
C₃×#3117	2
C₃×#3112	2
C₃×#3108	2
C₃×#3103	2
C₃×#3094	2
C₃×#3091	2
C₃×#3082	2
C₃×#3043	2
C₃×#3004	2
C₂×C₃×#448	2
C₃×#2949	2
C₃×#2947	2
C₃×#2924	2
#60582	3

Subgroups — C3×#60582 #10679189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60582 #10679189