Subgroups — C₃×#60782 #10679389

Order 768.

2208 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3212	C₂	1	4	yes	maximal, complemented
4	C₃×#3211	C₂	1	4	yes	maximal, complemented
5	C₃×#3210	C₂	1	2	yes	maximal, complemented
6	C₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3207	C₂	1	2	yes	maximal, complemented
9	C₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3147	C₂	1	2	yes	maximal, complemented
12	C₃×#3131	C₂	1	2	yes	maximal, complemented
13	C₃×#3035	C₂	1	4	yes	maximal, complemented
14	C₃×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	#60782	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃×#41	C₂²	1	2	yes	—
18	C₂×C₃×#135	C₂²	1	8	yes	complemented
19	C₃×#533	C₂²	1	1	yes	characteristic
20	C₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₃×#533	C₂²	1	1	yes	characteristic, complemented
22	C₃×#532	—	2	1	no	—
23	C₃×#532	—	2	1	no	—
24	C₃×#532	—	2	1	no	—
25	C₃×#532	—	2	1	no	—
26	C₃×#532	C₂²	1	2	yes	—
27	C₃×#532	C₂²	1	2	yes	—
28	C₃×#532	C₂²	1	2	yes	—
29	C₃×#532	C₂²	1	2	yes	—
30	C₃×#532	C₂²	1	1	yes	characteristic
31	C₃×#532	C₂²	1	1	yes	characteristic, complemented
32	C₃×#532	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×#127	C₂²	1	1	yes	characteristic
35	C₃×#529	—	2	1	no	—
36	C₃×#529	—	2	1	no	—
37	C₃×#529	—	2	1	no	—
38	C₃×#529	—	2	1	no	—
39	C₃×#529	C₂²	1	2	yes	—
40	C₃×#529	C₂²	1	2	yes	complemented
41	C₂×C₃×#124	C₂²	1	2	yes	—
42	C₃×#525	—	2	1	no	—
43	C₃×#525	—	2	1	no	—
44	C₃×#525	C₂²	1	2	yes	—
45	C₂×C₃×#121	—	2	1	no	—
46	C₂×C₃×#121	—	2	1	no	—
47	C₃×C₄×#41	—	2	1	no	—
48	C₃×C₄×#41	—	2	1	no	—
49	C₃×C₄×#41	C₂²	1	2	yes	complemented
50	C₂×C₃×C₄×D₄	—	2	1	no	—
51	C₂×C₃×C₄×D₄	—	2	1	no	—
52	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
53	C₃×#495	C₂²	1	8	yes	complemented
54	C₃×#494	C₂²	1	2	yes	complemented
55	C₃×#493	C₂²	1	2	yes	complemented
56	C₃×#492	C₂²	1	2	yes	complemented
57	C₃×#492	C₂²	1	2	yes	complemented
58	C₃×#488	C₂²	1	8	yes	complemented
59	C₃×#487	C₂²	1	2	yes	complemented
60	C₃×#487	C₂²	1	2	yes	complemented
61	C₃×#486	C₂²	1	2	yes	complemented
62	C₃×#486	C₂²	1	2	yes	complemented
63	C₃×#464	C₂²	1	8	yes	complemented
64	C₃×#463	C₂²	1	8	yes	complemented
65	C₃×#462	C₂²	1	4	yes	complemented
66	C₃×#461	C₂²	1	4	yes	complemented
67	C₃×#460	C₂²	1	4	yes	complemented
68	C₃×#459	C₂²	1	4	yes	complemented
69	C₃×#452	C₂²	1	8	yes	complemented
70	C₃×#451	C₂²	1	4	yes	—
71	C₃×#450	C₂²	1	4	yes	—
72	C₃×#449	C₂²	1	8	yes	complemented
73	C₃×#448	C₂²	1	4	yes	—
74	C₃×#447	C₂²	1	4	yes	—
75	C₃×#431	C₂²	1	1	yes	characteristic
76	C₃×#431	C₂²	1	1	yes	characteristic
77	C₃×#431	C₂²	1	2	yes	—
78	C₃×#431	C₂²	1	2	yes	complemented
79	C₃×#431	C₂²	1	2	yes	complemented
80	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
81	C₃×#416	C₂²	1	8	yes	complemented
82	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
83	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
84	#3444	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#532	C₂×C₃	1	1	yes	characteristic, complemented
86	#3212	C₂×C₃	1	4	yes	complemented
87	#3211	C₂×C₃	1	4	yes	complemented
88	#3210	C₂×C₃	1	2	yes	complemented
89	#3209	C₂×C₃	1	1	yes	characteristic, complemented
90	#3208	C₂×C₃	1	1	yes	characteristic, complemented
91	#3207	C₂×C₃	1	2	yes	complemented
92	#3206	C₂×C₃	1	1	yes	characteristic, complemented
93	#3205	C₂×C₃	1	1	yes	characteristic, complemented
94	#3147	C₂×C₃	1	2	yes	complemented
95	#3131	C₂×C₃	1	2	yes	complemented
96	#3035	C₂×C₃	1	4	yes	complemented
97	#3002	C₂×C₃	1	4	yes	complemented
98	C₂×#431	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×C₃×#41	—	2	2	no	—
100	C₂×C₃×#41	—	2	2	no	—
101	C₂×C₃×#41	—	2	1	no	—
102	C₂×C₃×#41	—	2	1	no	—
103	C₂×C₃×#41	—	4	8	no	—
104	C₂×C₃×#41	C₂³	1	2	yes	—
105	C₂×C₃×#41	C₂³	1	4	yes	—
106	C₂×C₃×#41	C₂³	1	4	yes	—
107	C₂²×C₃×Q₈	C₂³	1	2	yes	—
108	C₂²×C₃×D₄	—	2	2	no	—
109	C₂²×C₃×D₄	—	2	1	no	—
110	C₂²×C₃×D₄	—	2	1	no	—
111	C₂²×C₃×D₄	C₂³	1	2	yes	—
112	C₂³×C₃×C₄	—	2	2	no	—
113	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
114	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₃×#135	—	4	16	no	—
117	C₂×C₃×Q₁₆	C₂³	1	8	yes	—
118	C₂×C₃×SD₁₆	C₂³	1	8	yes	—
119	C₂×C₃×SD₁₆	C₂³	1	8	yes	—
120	C₂×C₃×D₈	C₂³	1	8	yes	—
121	C₂²×C₃×C₈	C₂³	1	4	yes	—
122	C₃×C₄⋊Q₈	—	2	1	no	—
123	C₃×C₄⋊Q₈	—	2	1	no	—
124	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₃×#127	—	2	1	no	—
130	C₃×#127	—	2	1	no	—
131	C₃×#127	C₂³	1	2	yes	—
132	C₃×#127	C₂³	1	2	yes	—
133	C₃×#127	C₂³	1	1	yes	characteristic
134	C₃×#126	—	2	2	no	—
135	C₃×#126	—	2	2	no	—
136	C₃×#125	—	2	1	no	—
137	C₃×#125	—	2	1	no	—
138	C₃×#125	C₂³	1	2	yes	—
139	C₃×#124	—	2	2	no	—
140	C₃×#124	—	2	2	no	—
141	C₃×#124	—	2	1	no	—
142	C₃×#124	—	2	1	no	—
143	C₃×#124	C₂³	1	4	yes	—
144	C₃×#124	C₂³	1	4	yes	—
145	C₃×#124	C₂³	1	2	yes	—
146	C₃×#123	—	2	2	no	—
147	C₃×#123	—	2	2	no	—
148	C₃×#123	—	2	2	no	—
149	C₃×C₂²⋊Q₈	—	2	1	no	—
150	C₃×C₂²⋊Q₈	—	2	1	no	—
151	C₃×C₂²⋊Q₈	—	2	1	no	—
152	C₃×C₂²⋊Q₈	—	2	1	no	—
153	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₃×#121	—	2	2	no	—
156	C₃×#121	—	2	2	no	—
157	C₃×#121	—	2	2	no	—
158	C₃×#121	—	2	2	no	—
159	C₃×#121	—	2	2	no	—
160	C₃×#121	—	2	2	no	—
161	C₃×#121	—	2	2	no	—
162	C₃×#121	—	2	2	no	—
163	C₃×#121	—	2	1	no	—
164	C₃×#121	—	2	1	no	—
165	C₃×#121	—	2	1	no	—
166	C₃×#121	—	2	1	no	—
167	C₃×#121	C₂³	1	2	yes	—
168	C₃×#121	C₂³	1	2	yes	—
169	C₃×#120	—	2	2	no	—
170	C₃×C₄×Q₈	—	2	1	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	2	1	no	—
174	C₃×C₄×Q₈	C₂³	1	2	yes	—
175	C₃×C₄×Q₈	C₂³	1	2	yes	—
176	C₃×C₄×D₄	—	2	2	no	—
177	C₃×C₄×D₄	—	2	2	no	—
178	C₃×C₄×D₄	—	2	2	no	—
179	C₃×C₄×D₄	—	2	2	no	—
180	C₃×C₄×D₄	—	2	2	no	—
181	C₃×C₄×D₄	—	2	2	no	—
182	C₃×C₄×D₄	—	2	2	no	—
183	C₃×C₄×D₄	—	2	2	no	—
184	C₃×C₄×D₄	—	2	2	no	—
185	C₃×C₄×D₄	—	2	2	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	—	2	2	no	—
190	C₃×C₄×D₄	—	2	1	no	—
191	C₃×C₄×D₄	—	2	1	no	—
192	C₃×C₄×D₄	—	2	1	no	—
193	C₃×C₄×D₄	—	2	1	no	—
194	C₃×C₄×D₄	C₂³	1	2	yes	—
195	C₃×C₄×D₄	C₂³	1	2	yes	—
196	C₃×#117	—	2	1	no	—
197	C₃×#117	—	2	1	no	—
198	C₃×#117	—	2	2	no	—
199	C₃×#117	—	2	2	no	—
200	C₃×#117	—	2	2	no	—
201	C₃×#117	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₃×C₄⋊C₄	—	2	1	no	—
204	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₃×C₄²	—	2	2	no	—
207	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
208	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
209	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
210	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
211	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
212	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
213	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₃×C₄⋊C₈	C₂³	1	2	yes	—
221	C₃×C₄⋊C₈	C₂³	1	4	yes	—
222	C₃×#103	C₂³	1	8	yes	—
223	C₃×#103	C₂³	1	8	yes	—
224	C₃×#102	C₂³	1	8	yes	—
225	C₃×#102	C₂³	1	8	yes	—
226	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃×C₄×C₈	C₂³	1	2	yes	—
230	C₃×C₄×C₈	C₂³	1	2	yes	—
231	C₃×C₄×C₈	C₂³	1	4	yes	—
232	C₂²×#41	C₂²×C₃	1	2	yes	—
233	C₂×#135	C₂²×C₃	1	8	yes	complemented
234	#533	C₂²×C₃	1	1	yes	characteristic
235	#533	C₂²×C₃	1	1	yes	characteristic, complemented
236	#533	C₂²×C₃	1	1	yes	characteristic, complemented
237	#532	—	2	1	no	—
238	#532	—	2	1	no	—
239	#532	—	2	1	no	—
240	#532	—	2	1	no	—
241	#532	C₂²×C₃	1	2	yes	—
242	#532	C₂²×C₃	1	2	yes	—
243	#532	C₂²×C₃	1	2	yes	—
244	#532	C₂²×C₃	1	2	yes	—
245	#532	C₂²×C₃	1	1	yes	characteristic
246	#532	C₂²×C₃	1	1	yes	characteristic, complemented
247	#532	C₂²×C₃	1	1	yes	characteristic, complemented
248	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
249	C₂×#127	C₂²×C₃	1	1	yes	characteristic
250	#529	—	2	1	no	—
251	#529	—	2	1	no	—
252	#529	—	2	1	no	—
253	#529	—	2	1	no	—
254	#529	C₂²×C₃	1	2	yes	—
255	#529	C₂²×C₃	1	2	yes	complemented
256	C₂×#124	C₂²×C₃	1	2	yes	—
257	#525	—	2	1	no	—
258	#525	—	2	1	no	—
259	#525	C₂²×C₃	1	2	yes	—
260	C₂×#121	—	2	1	no	—
261	C₂×#121	—	2	1	no	—
262	C₄×#41	—	2	1	no	—
263	C₄×#41	—	2	1	no	—
264	C₄×#41	C₂²×C₃	1	2	yes	complemented
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
268	#495	C₂²×C₃	1	8	yes	complemented
269	#494	C₂²×C₃	1	2	yes	complemented
270	#493	C₂²×C₃	1	2	yes	complemented
271	#492	C₂²×C₃	1	2	yes	complemented
272	#492	C₂²×C₃	1	2	yes	complemented
273	#488	C₂²×C₃	1	8	yes	complemented
274	#487	C₂²×C₃	1	2	yes	complemented
275	#487	C₂²×C₃	1	2	yes	complemented
276	#486	C₂²×C₃	1	2	yes	complemented
277	#486	C₂²×C₃	1	2	yes	complemented
278	#464	C₂²×C₃	1	8	yes	complemented
279	#463	C₂²×C₃	1	8	yes	complemented
280	#462	C₂²×C₃	1	4	yes	complemented
281	#461	C₂²×C₃	1	4	yes	complemented
282	#460	C₂²×C₃	1	4	yes	complemented
283	#459	C₂²×C₃	1	4	yes	complemented
284	#452	C₂²×C₃	1	8	yes	complemented
285	#451	C₂²×C₃	1	4	yes	—
286	#450	C₂²×C₃	1	4	yes	—
287	#449	C₂²×C₃	1	8	yes	complemented
288	#448	C₂²×C₃	1	4	yes	—
289	#447	C₂²×C₃	1	4	yes	—
290	#431	C₂²×C₃	1	1	yes	characteristic
291	#431	C₂²×C₃	1	1	yes	characteristic
292	#431	C₂²×C₃	1	2	yes	—
293	#431	C₂²×C₃	1	2	yes	complemented
294	#431	C₂²×C₃	1	2	yes	complemented
295	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
296	#416	C₂²×C₃	1	8	yes	complemented
297	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
298	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
299	C₂⁴×C₃	—	2	2	no	—
300	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
301	C₃×#41	—	2	8	no	—
302	C₃×#41	—	2	16	no	—
303	C₃×#41	—	4	8	no	—
304	C₃×#41	—	4	4	no	—
305	C₃×#41	—	4	8	no	—
306	C₃×#41	—	4	8	no	—
307	C₃×#41	—	4	4	no	—
308	C₂×C₃×Q₈	—	2	1	no	—
309	C₂×C₃×Q₈	—	2	1	no	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	—	4	4	no	—
312	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
313	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
314	C₂×C₃×D₄	—	2	2	no	—
315	C₂×C₃×D₄	—	2	2	no	—
316	C₂×C₃×D₄	—	2	2	no	—
317	C₂×C₃×D₄	—	2	4	no	—
318	C₂×C₃×D₄	—	2	4	no	—
319	C₂×C₃×D₄	—	2	1	no	—
320	C₂×C₃×D₄	—	2	1	no	—
321	C₂×C₃×D₄	—	2	2	no	—
322	C₂×C₃×D₄	—	2	2	no	—
323	C₂×C₃×D₄	—	2	2	no	—
324	C₂×C₃×D₄	—	2	2	no	—
325	C₂×C₃×D₄	—	2	2	no	—
326	C₂×C₃×D₄	—	4	4	no	—
327	C₂×C₃×D₄	—	4	4	no	—
328	C₂×C₃×D₄	—	4	8	no	—
329	C₂×C₃×D₄	—	4	4	no	—
330	C₂×C₃×D₄	C₂⁴	1	4	yes	—
331	C₂×C₃×D₄	C₂⁴	1	2	yes	—
332	C₂²×C₃×C₄	—	2	4	no	—
333	C₂²×C₃×C₄	—	2	4	no	—
334	C₂²×C₃×C₄	—	2	2	no	—
335	C₂²×C₃×C₄	—	2	2	no	—
336	C₂²×C₃×C₄	—	2	2	no	—
337	C₂²×C₃×C₄	—	2	4	no	—
338	C₂²×C₃×C₄	—	2	2	no	—
339	C₂²×C₃×C₄	—	2	4	no	—
340	C₂²×C₃×C₄	—	4	2	no	—
341	C₂²×C₃×C₄	—	4	8	no	—
342	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
360	C₃×Q₁₆	—	4	8	no	—
361	C₃×SD₁₆	—	4	8	no	—
362	C₃×SD₁₆	—	4	8	no	—
363	C₃×D₈	—	4	8	no	—
364	C₂×C₃×C₈	—	2	8	no	—
365	C₂×C₃×C₈	C₂⁴	1	4	yes	—
366	C₂×C₃×C₈	C₂⁴	1	4	yes	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	2	2	no	—
369	C₃×C₄⋊C₄	—	2	2	no	—
370	C₃×C₄⋊C₄	—	2	2	no	—
371	C₃×C₄⋊C₄	—	2	1	no	—
372	C₃×C₄⋊C₄	—	2	1	no	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	2	1	no	—
375	C₃×C₄⋊C₄	—	2	2	no	—
376	C₃×C₄⋊C₄	—	2	2	no	—
377	C₃×C₄⋊C₄	—	2	2	no	—
378	C₃×C₄⋊C₄	—	2	2	no	—
379	C₃×C₄⋊C₄	—	2	2	no	—
380	C₃×C₄⋊C₄	—	2	2	no	—
381	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
382	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
383	C₃×C₂²⋊C₄	—	2	2	no	—
384	C₃×C₂²⋊C₄	—	2	2	no	—
385	C₃×C₂²⋊C₄	—	2	2	no	—
386	C₃×C₂²⋊C₄	—	2	4	no	—
387	C₃×C₂²⋊C₄	—	2	4	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	2	4	no	—
390	C₃×C₂²⋊C₄	—	2	2	no	—
391	C₃×C₂²⋊C₄	—	2	2	no	—
392	C₃×C₂²⋊C₄	—	2	2	no	—
393	C₃×C₂²⋊C₄	—	2	2	no	—
394	C₃×C₂²⋊C₄	—	2	2	no	—
395	C₃×C₂²⋊C₄	—	2	2	no	—
396	C₃×C₄²	—	2	2	no	—
397	C₃×C₄²	—	2	2	no	—
398	C₃×C₄²	—	2	2	no	—
399	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
400	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
401	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
402	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
403	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
404	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
405	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
406	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
407	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
408	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
409	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
410	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
411	C₃×C₄²	C₂⁴	1	1	yes	characteristic
412	C₃×C₄²	C₂⁴	1	1	yes	characteristic
413	C₃×C₄²	C₂⁴	1	1	yes	characteristic
414	C₃×C₄²	C₂⁴	1	1	yes	characteristic
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	2	no	—
419	C₂×#41	—	4	8	no	—
420	C₂×#41	C₂³×C₃	1	2	yes	—
421	C₂×#41	C₂³×C₃	1	4	yes	—
422	C₂×#41	C₂³×C₃	1	4	yes	—
423	C₂²×Q₈	C₂³×C₃	1	2	yes	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	C₂³×C₃	1	2	yes	—
428	C₂³×C₄	—	2	2	no	—
429	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
430	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
432	#135	—	4	16	no	—
433	C₂×Q₁₆	C₂³×C₃	1	8	yes	—
434	C₂×SD₁₆	C₂³×C₃	1	8	yes	—
435	C₂×SD₁₆	C₂³×C₃	1	8	yes	—
436	C₂×D₈	C₂³×C₃	1	8	yes	—
437	C₂²×C₈	C₂³×C₃	1	4	yes	—
438	C₄⋊Q₈	—	2	1	no	—
439	C₄⋊Q₈	—	2	1	no	—
440	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
441	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
442	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
443	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
444	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
445	#127	—	2	1	no	—
446	#127	—	2	1	no	—
447	#127	C₂³×C₃	1	2	yes	—
448	#127	C₂³×C₃	1	2	yes	—
449	#127	C₂³×C₃	1	1	yes	characteristic
450	#126	—	2	2	no	—
451	#126	—	2	2	no	—
452	#125	—	2	1	no	—
453	#125	—	2	1	no	—
454	#125	C₂³×C₃	1	2	yes	—
455	#124	—	2	2	no	—
456	#124	—	2	2	no	—
457	#124	—	2	1	no	—
458	#124	—	2	1	no	—
459	#124	C₂³×C₃	1	4	yes	—
460	#124	C₂³×C₃	1	4	yes	—
461	#124	C₂³×C₃	1	2	yes	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
470	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	2	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	—	2	1	no	—
483	#121	C₂³×C₃	1	2	yes	—
484	#121	C₂³×C₃	1	2	yes	—
485	#120	—	2	2	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×Q₈	C₂³×C₃	1	2	yes	—
491	C₄×Q₈	C₂³×C₃	1	2	yes	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	C₂³×C₃	1	2	yes	—
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	2	no	—
516	#117	—	2	2	no	—
517	#117	C₂³×C₃	1	2	yes	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	2	no	—
521	C₂×C₂²⋊C₄	—	2	2	no	—
522	C₂×C₄²	—	2	2	no	—
523	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
524	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
525	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
526	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
527	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
528	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
535	C₄⋊C₈	C₂³×C₃	1	2	yes	—
536	C₄⋊C₈	C₂³×C₃	1	2	yes	—
537	C₄⋊C₈	C₂³×C₃	1	4	yes	—
538	#103	C₂³×C₃	1	8	yes	—
539	#103	C₂³×C₃	1	8	yes	—
540	#102	C₂³×C₃	1	8	yes	—
541	#102	C₂³×C₃	1	8	yes	—
542	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
543	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
544	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
545	C₄×C₈	C₂³×C₃	1	2	yes	—
546	C₄×C₈	C₂³×C₃	1	2	yes	—
547	C₄×C₈	C₂³×C₃	1	4	yes	—
548	C₂³×C₃	—	2	2	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	4	no	—
552	C₂³×C₃	—	4	1	no	—
553	C₂³×C₃	—	4	4	no	—
554	C₂³×C₃	—	4	4	no	—
555	C₂³×C₃	—	4	4	no	—
556	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
557	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
558	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
559	C₃×Q₈	—	2	4	no	—
560	C₃×Q₈	—	2	8	no	—
561	C₃×Q₈	—	4	4	no	—
562	C₃×Q₈	—	4	2	no	—
563	C₃×Q₈	—	4	2	no	—
564	C₃×D₄	—	2	4	no	—
565	C₃×D₄	—	2	8	no	—
566	C₃×D₄	—	4	4	no	—
567	C₃×D₄	—	4	4	no	—
568	C₃×D₄	—	4	8	no	—
569	C₃×D₄	—	4	4	no	—
570	C₃×D₄	—	4	8	no	—
571	C₃×D₄	—	4	4	no	—
572	C₃×D₄	—	4	4	no	—
573	C₃×D₄	—	4	4	no	—
574	C₃×D₄	—	4	4	no	—
575	C₃×D₄	—	4	2	no	—
576	C₃×D₄	—	4	4	no	—
577	C₃×D₄	—	4	2	no	—
578	C₂×C₃×C₄	—	2	2	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	2	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	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	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	2	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	4	no	—
595	C₂×C₃×C₄	—	4	1	no	—
596	C₂×C₃×C₄	—	4	1	no	—
597	C₂×C₃×C₄	—	4	1	no	—
598	C₂×C₃×C₄	—	4	8	no	—
599	C₂×C₃×C₄	—	4	4	no	—
600	C₂×C₃×C₄	—	4	4	no	—
601	C₂×C₃×C₄	—	4	8	no	—
602	C₂×C₃×C₄	—	4	4	no	—
603	C₂×C₃×C₄	—	4	4	no	—
604	C₂×C₃×C₄	#135	1	4	yes	complemented
605	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
615	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
616	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
617	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
618	C₃×C₈	—	2	4	no	—
619	C₃×C₈	—	2	4	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
622	#41	—	2	8	no	—
623	#41	—	2	16	no	—
624	#41	—	4	8	no	—
625	#41	—	4	8	no	—
626	#41	—	4	8	no	—
627	#41	—	4	4	no	—
628	#41	—	4	4	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	4	4	no	—
633	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
634	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	4	4	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	8	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	C₂⁴×C₃	1	4	yes	—
652	C₂×D₄	C₂⁴×C₃	1	2	yes	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	8	no	—
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	1	yes	characteristic
666	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
667	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
668	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
669	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
673	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
674	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
681	Q₁₆	—	4	8	no	—
682	SD₁₆	—	4	8	no	—
683	SD₁₆	—	4	8	no	—
684	D₈	—	4	8	no	—
685	C₂×C₈	—	2	8	no	—
686	C₂×C₈	C₂⁴×C₃	1	4	yes	—
687	C₂×C₈	C₂⁴×C₃	1	4	yes	—
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	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
721	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
722	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
723	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
724	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
725	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
726	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
727	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
728	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
729	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
730	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
731	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
732	C₄²	C₂⁴×C₃	1	1	yes	characteristic
733	C₄²	C₂⁴×C₃	1	1	yes	characteristic
734	C₄²	C₂⁴×C₃	1	1	yes	characteristic
735	C₄²	C₂⁴×C₃	1	1	yes	characteristic
736	C₂²×C₃	—	2	1	no	—
737	C₂²×C₃	—	2	1	no	—
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	—	4	4	no	—
744	C₂²×C₃	—	4	4	no	—
745	C₂²×C₃	—	4	2	no	—
746	C₂²×C₃	—	4	2	no	—
747	C₂²×C₃	—	4	4	no	—
748	C₂²×C₃	—	4	2	no	—
749	C₂²×C₃	—	4	4	no	—
750	C₂²×C₃	—	8	8	no	—
751	C₂²×C₃	#535	1	2	yes	—
752	C₂²×C₃	C₂×#135	1	2	yes	—
753	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
754	C₃×C₄	—	2	1	no	—
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	1	no	—
759	C₃×C₄	—	2	1	no	—
760	C₃×C₄	—	2	1	no	—
761	C₃×C₄	—	4	4	no	—
762	C₃×C₄	—	4	2	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	#535	1	2	yes	—
766	C₃×C₄	C₂×#135	1	2	yes	—
767	C₃×C₄	C₂×#135	1	2	yes	—
768	C₃×C₄	#575	1	2	yes	—
769	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	4	no	—
774	C₂³	—	4	1	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	4	no	—
778	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
779	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
780	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
781	Q₈	—	2	4	no	—
782	Q₈	—	2	8	no	—
783	Q₈	—	4	4	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	2	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	8	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	8	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	8	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	8	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	C₃×#135	1	4	yes	complemented
827	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
828	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
830	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
832	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
833	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
835	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
837	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
838	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
839	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
840	C₈	—	2	4	no	—
841	C₈	—	2	4	no	—
842	C₂×C₃	—	2	2	no	—
843	C₂×C₃	—	2	2	no	—
844	C₂×C₃	—	4	1	no	—
845	C₂×C₃	—	8	2	no	—
846	C₂×C₃	—	8	4	no	—
847	C₂×C₃	C₂×#535	1	1	yes	characteristic
848	C₂×C₃	C₂²×#135	1	1	yes	characteristic
849	C₂×C₃	C₂×#575	1	1	yes	characteristic
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	4	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	8	8	no	—
865	C₂²	C₃×#535	1	2	yes	—
866	C₂²	C₂×C₃×#135	1	2	yes	—
867	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	4	4	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	C₃×#535	1	2	yes	—
880	C₄	C₂×C₃×#135	1	2	yes	—
881	C₄	C₂×C₃×#135	1	2	yes	—
882	C₄	C₃×#575	1	2	yes	—
883	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
884	C₃	#60782	1	1	yes	characteristic, direct product factor, Sylow
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	4	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×C₃×#535	1	1	yes	characteristic
891	C₂	C₂²×C₃×#135	1	1	yes	characteristic
892	C₂	C₂×C₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3444	C₂	semidirect
2. C₂×C₃×#532	C₂	semidirect
3. C₃×#3212	C₂	semidirect
4. C₃×#3211	C₂	semidirect
5. C₃×#3210	C₂	semidirect
6. C₃×#3209	C₂	semidirect
7. C₃×#3208	C₂	semidirect
8. C₃×#3207	C₂	semidirect
9. C₃×#3206	C₂	semidirect
10. C₃×#3205	C₂	semidirect
11. C₃×#3147	C₂	semidirect
12. C₃×#3131	C₂	semidirect
13. C₃×#3035	C₂	semidirect
14. C₃×#3002	C₂	semidirect
15. C₂×C₃×#431	C₂	semidirect
16. #60782	C₃	direct (N × H)
18. C₂×C₃×#135	C₂²	semidirect
20. C₃×#533	C₂²	semidirect
21. C₃×#533	C₂²	semidirect
31. C₃×#532	C₂²	semidirect
32. C₃×#532	C₂²	semidirect
40. C₃×#529	C₂²	semidirect
49. C₃×C₄×#41	C₂²	semidirect
53. C₃×#495	C₂²	semidirect
54. C₃×#494	C₂²	semidirect
55. C₃×#493	C₂²	semidirect
56. C₃×#492	C₂²	semidirect
57. C₃×#492	C₂²	semidirect
58. C₃×#488	C₂²	semidirect
59. C₃×#487	C₂²	semidirect
60. C₃×#487	C₂²	semidirect
61. C₃×#486	C₂²	semidirect
62. C₃×#486	C₂²	semidirect
63. C₃×#464	C₂²	semidirect
64. C₃×#463	C₂²	semidirect
65. C₃×#462	C₂²	semidirect
66. C₃×#461	C₂²	semidirect
67. C₃×#460	C₂²	semidirect
68. C₃×#459	C₂²	semidirect
69. C₃×#452	C₂²	semidirect
72. C₃×#449	C₂²	semidirect
78. C₃×#431	C₂²	semidirect
79. C₃×#431	C₂²	semidirect
80. C₂×C₃×C₄⋊C₈	C₂²	semidirect
81. C₃×#416	C₂²	semidirect
83. C₂×C₃×C₄×C₈	C₂²	semidirect
84. #3444	C₂×C₃	semidirect
85. C₂×#532	C₂×C₃	semidirect
86. #3212	C₂×C₃	semidirect
87. #3211	C₂×C₃	semidirect
88. #3210	C₂×C₃	semidirect
89. #3209	C₂×C₃	semidirect
90. #3208	C₂×C₃	semidirect
91. #3207	C₂×C₃	semidirect
92. #3206	C₂×C₃	semidirect
93. #3205	C₂×C₃	semidirect
94. #3147	C₂×C₃	semidirect
95. #3131	C₂×C₃	semidirect
96. #3035	C₂×C₃	semidirect
97. #3002	C₂×C₃	semidirect
98. C₂×#431	C₂×C₃	semidirect
233. C₂×#135	C₂²×C₃	semidirect
235. #533	C₂²×C₃	semidirect
236. #533	C₂²×C₃	semidirect
246. #532	C₂²×C₃	semidirect
247. #532	C₂²×C₃	semidirect
255. #529	C₂²×C₃	semidirect
264. C₄×#41	C₂²×C₃	semidirect
268. #495	C₂²×C₃	semidirect
269. #494	C₂²×C₃	semidirect
270. #493	C₂²×C₃	semidirect
271. #492	C₂²×C₃	semidirect
272. #492	C₂²×C₃	semidirect
273. #488	C₂²×C₃	semidirect
274. #487	C₂²×C₃	semidirect
275. #487	C₂²×C₃	semidirect
276. #486	C₂²×C₃	semidirect
277. #486	C₂²×C₃	semidirect
278. #464	C₂²×C₃	semidirect
279. #463	C₂²×C₃	semidirect
280. #462	C₂²×C₃	semidirect
281. #461	C₂²×C₃	semidirect
282. #460	C₂²×C₃	semidirect
283. #459	C₂²×C₃	semidirect
284. #452	C₂²×C₃	semidirect
287. #449	C₂²×C₃	semidirect
293. #431	C₂²×C₃	semidirect
294. #431	C₂²×C₃	semidirect
295. C₂×C₄⋊C₈	C₂²×C₃	semidirect
296. #416	C₂²×C₃	semidirect
298. C₂×C₄×C₈	C₂²×C₃	semidirect
604. C₂×C₃×C₄	#135	semidirect
826. C₂×C₄	C₃×#135	semidirect
884. C₃	#60782	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×#3444	2
C₂×C₃×#532	2
C₃×#3212	2
C₃×#3211	2
C₃×#3210	2
C₃×#3209	2
C₃×#3208	2
C₃×#3207	2
C₃×#3206	2
C₃×#3205	2
C₃×#3147	2
C₃×#3131	2
C₃×#3035	2
C₃×#3002	2
C₂×C₃×#431	2
#60782	3

Subgroups — C3×#60782 #10679389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60782 #10679389