Subgroups — C₃×#60546 #10679153

Order 768.

2172 conjugacy classes of subgroups.

The subgroup lattice has 1018 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×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3117	C₂	1	2	yes	maximal, complemented
4	C₃×#3116	C₂	1	2	yes	maximal, complemented
5	C₃×#3115	C₂	1	2	yes	maximal, complemented
6	C₃×#3114	C₂	1	2	yes	maximal, complemented
7	C₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3111	C₂	1	4	yes	maximal, complemented
10	C₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3091	C₂	1	2	yes	maximal, complemented
13	C₃×#3076	C₂	1	2	yes	maximal, complemented
14	C₃×#3035	C₂	1	2	yes	maximal, complemented
15	C₃×#3002	C₂	1	2	yes	maximal, complemented
16	C₃×#2943	C₂	1	4	yes	maximal, complemented
17	C₂×C₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
18	#60546	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×#135	C₂²	1	4	yes	—
21	C₃×#533	C₂²	1	1	yes	characteristic
22	C₃×#533	C₂²	1	1	yes	characteristic, complemented
23	C₃×#533	C₂²	1	1	yes	characteristic, complemented
24	C₃×#532	C₂²	1	1	yes	characteristic
25	C₃×#532	C₂²	1	1	yes	characteristic, complemented
26	C₃×#532	C₂²	1	1	yes	characteristic, complemented
27	C₃×#529	—	2	1	no	—
28	C₃×#529	—	2	1	no	—
29	C₃×#529	—	2	1	no	—
30	C₃×#529	—	2	1	no	—
31	C₃×#529	C₂²	1	2	yes	—
32	C₃×#529	C₂²	1	2	yes	complemented
33	C₃×#525	—	2	1	no	—
34	C₃×#525	—	2	1	no	—
35	C₃×#525	C₂²	1	2	yes	—
36	C₃×C₄×#41	—	2	1	no	—
37	C₃×C₄×#41	—	2	1	no	—
38	C₃×C₄×#41	—	2	1	no	—
39	C₃×C₄×#41	—	2	1	no	—
40	C₃×C₄×#41	—	2	1	no	—
41	C₃×C₄×#41	—	2	1	no	—
42	C₃×C₄×#41	C₂²	1	2	yes	—
43	C₃×C₄×#41	C₂²	1	2	yes	—
44	C₃×C₄×#41	C₂²	1	2	yes	—
45	C₃×C₄×#41	C₂²	1	2	yes	—
46	C₃×C₄×#41	C₂²	1	2	yes	complemented
47	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	—	2	1	no	—
50	C₂×C₃×C₄×D₄	—	2	1	no	—
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₃×#117	—	2	1	no	—
54	C₂×C₃×#117	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₄²	—	2	1	no	—
56	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
57	C₃×#485	C₂²	1	4	yes	complemented
58	C₃×#484	C₂²	1	2	yes	—
59	C₃×#483	C₂²	1	2	yes	—
60	C₃×#482	C₂²	1	4	yes	complemented
61	C₃×#481	C₂²	1	2	yes	—
62	C₃×#480	C₂²	1	2	yes	—
63	C₃×#479	C₂²	1	4	yes	complemented
64	C₃×#478	C₂²	1	4	yes	complemented
65	C₃×#477	C₂²	1	2	yes	complemented
66	C₃×#476	C₂²	1	2	yes	complemented
67	C₃×#475	C₂²	1	2	yes	complemented
68	C₃×#474	C₂²	1	2	yes	complemented
69	C₃×#464	C₂²	1	4	yes	complemented
70	C₃×#463	C₂²	1	4	yes	complemented
71	C₃×#462	C₂²	1	2	yes	complemented
72	C₃×#461	C₂²	1	2	yes	complemented
73	C₃×#460	C₂²	1	2	yes	complemented
74	C₃×#459	C₂²	1	2	yes	complemented
75	C₃×#452	C₂²	1	4	yes	—
76	C₃×#451	C₂²	1	2	yes	—
77	C₃×#450	C₂²	1	2	yes	—
78	C₃×#449	C₂²	1	4	yes	—
79	C₃×#448	C₂²	1	2	yes	—
80	C₃×#447	C₂²	1	2	yes	—
81	C₃×#442	C₂²	1	4	yes	complemented
82	C₃×#442	C₂²	1	4	yes	complemented
83	C₃×#441	C₂²	1	4	yes	complemented
84	C₃×#441	C₂²	1	4	yes	complemented
85	C₃×#440	C₂²	1	4	yes	complemented
86	C₃×#440	C₂²	1	4	yes	complemented
87	C₃×#440	C₂²	1	4	yes	complemented
88	C₃×#440	C₂²	1	4	yes	complemented
89	C₃×#432	C₂²	1	1	yes	characteristic
90	C₃×#432	C₂²	1	1	yes	characteristic
91	C₃×#432	C₂²	1	2	yes	—
92	C₃×#432	C₂²	1	2	yes	complemented
93	C₃×#432	C₂²	1	2	yes	complemented
94	C₃×#427	C₂²	1	4	yes	complemented
95	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
96	C₃×#416	C₂²	1	4	yes	—
97	C₃×#416	C₂²	1	4	yes	complemented
98	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
99	C₂×C₃×#97	C₂²	1	2	yes	complemented
100	#3444	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
102	#3117	C₂×C₃	1	2	yes	complemented
103	#3116	C₂×C₃	1	2	yes	complemented
104	#3115	C₂×C₃	1	2	yes	complemented
105	#3114	C₂×C₃	1	2	yes	complemented
106	#3113	C₂×C₃	1	1	yes	characteristic, complemented
107	#3112	C₂×C₃	1	1	yes	characteristic, complemented
108	#3111	C₂×C₃	1	4	yes	complemented
109	#3110	C₂×C₃	1	1	yes	characteristic, complemented
110	#3109	C₂×C₃	1	1	yes	characteristic, complemented
111	#3091	C₂×C₃	1	2	yes	complemented
112	#3076	C₂×C₃	1	2	yes	complemented
113	#3035	C₂×C₃	1	2	yes	complemented
114	#3002	C₂×C₃	1	2	yes	complemented
115	#2943	C₂×C₃	1	4	yes	complemented
116	C₂×#432	C₂×C₃	1	1	yes	characteristic, complemented
117	C₂×C₃×#41	—	2	8	no	—
118	C₂×C₃×#41	—	2	1	no	—
119	C₂×C₃×#41	—	2	1	no	—
120	C₂×C₃×#41	—	2	1	no	—
121	C₂×C₃×#41	—	2	1	no	—
122	C₂×C₃×#41	C₂³	1	2	yes	—
123	C₂×C₃×#41	C₂³	1	2	yes	—
124	C₂×C₃×#41	C₂³	1	2	yes	—
125	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₃×D₄	—	2	1	no	—
127	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
128	C₂³×C₃×C₄	—	2	1	no	—
129	C₂³×C₃×C₄	—	2	1	no	—
130	C₂³×C₃×C₄	—	2	1	no	—
131	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
132	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
133	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
134	C₃×#135	—	2	16	no	—
135	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
136	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
137	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
138	C₂×C₃×D₈	C₂³	1	4	yes	—
139	C₂²×C₃×C₈	C₂³	1	4	yes	—
140	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃×#127	C₂³	1	1	yes	characteristic
144	C₃×#126	—	2	2	no	—
145	C₃×#126	—	2	2	no	—
146	C₃×#125	—	2	1	no	—
147	C₃×#125	—	2	1	no	—
148	C₃×#125	C₂³	1	2	yes	—
149	C₃×#124	—	2	1	no	—
150	C₃×#124	—	2	1	no	—
151	C₃×#124	C₂³	1	2	yes	—
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	1	no	—
158	C₃×C₂²⋊Q₈	—	2	1	no	—
159	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₃×#121	—	2	1	no	—
162	C₃×#121	—	2	1	no	—
163	C₃×#121	—	2	1	no	—
164	C₃×#121	—	2	1	no	—
165	C₃×#121	C₂³	1	2	yes	—
166	C₃×#121	C₂³	1	2	yes	—
167	C₃×#120	—	2	2	no	—
168	C₃×C₄×Q₈	—	2	1	no	—
169	C₃×C₄×Q₈	—	2	1	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	—	2	1	no	—
175	C₃×C₄×Q₈	—	2	1	no	—
176	C₃×C₄×Q₈	C₂³	1	2	yes	—
177	C₃×C₄×Q₈	C₂³	1	2	yes	—
178	C₃×C₄×Q₈	C₂³	1	2	yes	—
179	C₃×C₄×Q₈	C₂³	1	2	yes	—
180	C₃×C₄×Q₈	C₂³	1	2	yes	—
181	C₃×C₄×Q₈	C₂³	1	2	yes	—
182	C₃×C₄×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	2	no	—
191	C₃×C₄×D₄	—	2	2	no	—
192	C₃×C₄×D₄	—	2	2	no	—
193	C₃×C₄×D₄	—	2	2	no	—
194	C₃×C₄×D₄	—	2	2	no	—
195	C₃×C₄×D₄	—	2	2	no	—
196	C₃×C₄×D₄	—	2	1	no	—
197	C₃×C₄×D₄	—	2	1	no	—
198	C₃×C₄×D₄	—	2	1	no	—
199	C₃×C₄×D₄	—	2	1	no	—
200	C₃×C₄×D₄	—	2	1	no	—
201	C₃×C₄×D₄	—	2	1	no	—
202	C₃×C₄×D₄	—	2	1	no	—
203	C₃×C₄×D₄	—	2	1	no	—
204	C₃×C₄×D₄	C₂³	1	2	yes	—
205	C₃×C₄×D₄	C₂³	1	2	yes	—
206	C₃×C₄×D₄	C₂³	1	2	yes	—
207	C₃×C₄×D₄	C₂³	1	2	yes	—
208	C₃×C₄×D₄	C₂³	1	2	yes	—
209	C₃×C₄×D₄	C₂³	1	2	yes	—
210	C₃×#117	—	2	1	no	—
211	C₃×#117	—	2	1	no	—
212	C₃×#117	—	2	1	no	—
213	C₃×#117	—	2	1	no	—
214	C₃×#117	—	2	2	no	—
215	C₃×#117	—	2	2	no	—
216	C₃×#117	—	2	2	no	—
217	C₃×#117	—	2	2	no	—
218	C₃×#117	—	2	2	no	—
219	C₃×#117	—	2	2	no	—
220	C₃×#117	—	2	2	no	—
221	C₃×#117	C₂³	1	2	yes	—
222	C₃×#117	C₂³	1	2	yes	—
223	C₃×#117	C₂³	1	2	yes	—
224	C₂×C₃×C₄⋊C₄	—	2	1	no	—
225	C₂×C₃×C₄⋊C₄	—	2	1	no	—
226	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₃×C₄²	—	2	1	no	—
232	C₂×C₃×C₄²	—	2	1	no	—
233	C₂×C₃×C₄²	—	2	1	no	—
234	C₂×C₃×C₄²	—	2	2	no	—
235	C₂×C₃×C₄²	—	2	2	no	—
236	C₂×C₃×C₄²	—	2	2	no	—
237	C₂×C₃×C₄²	—	2	2	no	—
238	C₂×C₃×C₄²	—	2	2	no	—
239	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
240	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
241	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
242	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
243	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
244	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
250	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₃×#107	C₂³	1	4	yes	—
252	C₃×#107	C₂³	1	4	yes	—
253	C₃×#106	C₂³	1	4	yes	—
254	C₃×#106	C₂³	1	4	yes	—
255	C₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃×C₄⋊C₈	C₂³	1	4	yes	—
258	C₃×#103	C₂³	1	4	yes	—
259	C₃×#103	C₂³	1	4	yes	—
260	C₃×#103	C₂³	1	4	yes	—
261	C₃×#103	C₂³	1	4	yes	—
262	C₃×#102	C₂³	1	4	yes	—
263	C₃×#102	C₂³	1	4	yes	—
264	C₃×#102	C₂³	1	4	yes	—
265	C₃×#102	C₂³	1	4	yes	—
266	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
269	C₃×#97	C₂³	1	2	yes	—
270	C₃×#97	C₂³	1	4	yes	—
271	C₃×#97	C₂³	1	2	yes	—
272	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
273	C₂×#135	C₂²×C₃	1	4	yes	—
274	#533	C₂²×C₃	1	1	yes	characteristic
275	#533	C₂²×C₃	1	1	yes	characteristic, complemented
276	#533	C₂²×C₃	1	1	yes	characteristic, complemented
277	#532	C₂²×C₃	1	1	yes	characteristic
278	#532	C₂²×C₃	1	1	yes	characteristic, complemented
279	#532	C₂²×C₃	1	1	yes	characteristic, complemented
280	#529	—	2	1	no	—
281	#529	—	2	1	no	—
282	#529	—	2	1	no	—
283	#529	—	2	1	no	—
284	#529	C₂²×C₃	1	2	yes	—
285	#529	C₂²×C₃	1	2	yes	complemented
286	#525	—	2	1	no	—
287	#525	—	2	1	no	—
288	#525	C₂²×C₃	1	2	yes	—
289	C₄×#41	—	2	1	no	—
290	C₄×#41	—	2	1	no	—
291	C₄×#41	—	2	1	no	—
292	C₄×#41	—	2	1	no	—
293	C₄×#41	—	2	1	no	—
294	C₄×#41	—	2	1	no	—
295	C₄×#41	C₂²×C₃	1	2	yes	—
296	C₄×#41	C₂²×C₃	1	2	yes	—
297	C₄×#41	C₂²×C₃	1	2	yes	—
298	C₄×#41	C₂²×C₃	1	2	yes	—
299	C₄×#41	C₂²×C₃	1	2	yes	complemented
300	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
306	C₂×#117	—	2	1	no	—
307	C₂×#117	C₂²×C₃	1	1	yes	characteristic
308	C₂²×C₄²	—	2	1	no	—
309	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
310	#485	C₂²×C₃	1	4	yes	complemented
311	#484	C₂²×C₃	1	2	yes	—
312	#483	C₂²×C₃	1	2	yes	—
313	#482	C₂²×C₃	1	4	yes	complemented
314	#481	C₂²×C₃	1	2	yes	—
315	#480	C₂²×C₃	1	2	yes	—
316	#479	C₂²×C₃	1	4	yes	complemented
317	#478	C₂²×C₃	1	4	yes	complemented
318	#477	C₂²×C₃	1	2	yes	complemented
319	#476	C₂²×C₃	1	2	yes	complemented
320	#475	C₂²×C₃	1	2	yes	complemented
321	#474	C₂²×C₃	1	2	yes	complemented
322	#464	C₂²×C₃	1	4	yes	complemented
323	#463	C₂²×C₃	1	4	yes	complemented
324	#462	C₂²×C₃	1	2	yes	complemented
325	#461	C₂²×C₃	1	2	yes	complemented
326	#460	C₂²×C₃	1	2	yes	complemented
327	#459	C₂²×C₃	1	2	yes	complemented
328	#452	C₂²×C₃	1	4	yes	—
329	#451	C₂²×C₃	1	2	yes	—
330	#450	C₂²×C₃	1	2	yes	—
331	#449	C₂²×C₃	1	4	yes	—
332	#448	C₂²×C₃	1	2	yes	—
333	#447	C₂²×C₃	1	2	yes	—
334	#442	C₂²×C₃	1	4	yes	complemented
335	#442	C₂²×C₃	1	4	yes	complemented
336	#441	C₂²×C₃	1	4	yes	complemented
337	#441	C₂²×C₃	1	4	yes	complemented
338	#440	C₂²×C₃	1	4	yes	complemented
339	#440	C₂²×C₃	1	4	yes	complemented
340	#440	C₂²×C₃	1	4	yes	complemented
341	#440	C₂²×C₃	1	4	yes	complemented
342	#432	C₂²×C₃	1	1	yes	characteristic
343	#432	C₂²×C₃	1	1	yes	characteristic
344	#432	C₂²×C₃	1	2	yes	—
345	#432	C₂²×C₃	1	2	yes	complemented
346	#432	C₂²×C₃	1	2	yes	complemented
347	#427	C₂²×C₃	1	4	yes	complemented
348	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
349	#416	C₂²×C₃	1	4	yes	—
350	#416	C₂²×C₃	1	4	yes	complemented
351	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
352	C₂×#97	C₂²×C₃	1	2	yes	complemented
353	C₂⁴×C₃	—	2	1	no	—
354	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
355	C₃×#41	—	2	8	no	—
356	C₃×#41	—	2	8	no	—
357	C₃×#41	—	2	4	no	—
358	C₃×#41	—	2	4	no	—
359	C₃×#41	—	2	4	no	—
360	C₃×#41	—	2	8	no	—
361	C₃×#41	—	4	4	no	—
362	C₃×#41	—	4	4	no	—
363	C₃×#41	#41	1	8	yes	complemented
364	C₂×C₃×Q₈	—	2	4	no	—
365	C₂×C₃×Q₈	—	2	1	no	—
366	C₂×C₃×Q₈	—	2	1	no	—
367	C₂×C₃×Q₈	—	2	1	no	—
368	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
369	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
370	C₂×C₃×D₄	—	2	8	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	2	2	no	—
373	C₂×C₃×D₄	—	2	4	no	—
374	C₂×C₃×D₄	—	2	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	—	2	2	no	—
377	C₂×C₃×D₄	—	2	1	no	—
378	C₂×C₃×D₄	—	2	1	no	—
379	C₂×C₃×D₄	—	2	1	no	—
380	C₂×C₃×D₄	C₂⁴	1	2	yes	—
381	C₂×C₃×D₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	—	2	8	no	—
383	C₂²×C₃×C₄	—	2	1	no	—
384	C₂²×C₃×C₄	—	2	2	no	—
385	C₂²×C₃×C₄	—	2	2	no	—
386	C₂²×C₃×C₄	—	2	4	no	—
387	C₂²×C₃×C₄	—	2	1	no	—
388	C₂²×C₃×C₄	—	2	1	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	2	2	no	—
391	C₂²×C₃×C₄	—	2	2	no	—
392	C₂²×C₃×C₄	—	2	2	no	—
393	C₂²×C₃×C₄	—	2	2	no	—
394	C₂²×C₃×C₄	—	2	2	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	4	2	no	—
397	C₂²×C₃×C₄	—	4	2	no	—
398	C₂²×C₃×C₄	—	4	4	no	—
399	C₂²×C₃×C₄	—	4	4	no	—
400	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₃×Q₁₆	—	2	8	no	—
419	C₃×SD₁₆	—	2	8	no	—
420	C₃×SD₁₆	—	2	8	no	—
421	C₃×D₈	—	2	8	no	—
422	C₂×C₃×C₈	—	2	8	no	—
423	C₂×C₃×C₈	C₂⁴	1	4	yes	—
424	C₂×C₃×C₈	C₂⁴	1	4	yes	—
425	C₃×C₄⋊C₄	—	2	2	no	—
426	C₃×C₄⋊C₄	—	2	2	no	—
427	C₃×C₄⋊C₄	—	2	2	no	—
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	2	1	no	—
430	C₃×C₄⋊C₄	—	2	1	no	—
431	C₃×C₄⋊C₄	—	2	1	no	—
432	C₃×C₄⋊C₄	—	2	1	no	—
433	C₃×C₄⋊C₄	—	2	1	no	—
434	C₃×C₄⋊C₄	—	2	1	no	—
435	C₃×C₄⋊C₄	—	2	2	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	2	2	no	—
440	C₃×C₄⋊C₄	—	2	2	no	—
441	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
442	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
444	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₃×C₂²⋊C₄	—	2	2	no	—
446	C₃×C₂²⋊C₄	—	2	2	no	—
447	C₃×C₂²⋊C₄	—	2	2	no	—
448	C₃×C₂²⋊C₄	—	2	2	no	—
449	C₃×C₂²⋊C₄	—	2	2	no	—
450	C₃×C₂²⋊C₄	—	2	2	no	—
451	C₃×C₂²⋊C₄	—	2	2	no	—
452	C₃×C₂²⋊C₄	—	2	2	no	—
453	C₃×C₂²⋊C₄	—	2	2	no	—
454	C₃×C₂²⋊C₄	—	2	2	no	—
455	C₃×C₂²⋊C₄	—	2	2	no	—
456	C₃×C₂²⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	2	2	no	—
459	C₃×C₂²⋊C₄	—	2	2	no	—
460	C₃×C₄²	—	2	2	no	—
461	C₃×C₄²	—	2	2	no	—
462	C₃×C₄²	—	2	2	no	—
463	C₃×C₄²	—	2	2	no	—
464	C₃×C₄²	—	2	2	no	—
465	C₃×C₄²	—	2	2	no	—
466	C₃×C₄²	—	2	2	no	—
467	C₃×C₄²	—	2	2	no	—
468	C₃×C₄²	—	2	2	no	—
469	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
470	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
471	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
472	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
473	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
474	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
475	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
476	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
477	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
478	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
479	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
480	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
481	C₃×C₄²	C₂⁴	1	1	yes	characteristic
482	C₃×C₄²	C₂⁴	1	1	yes	characteristic
483	C₃×C₄²	C₂⁴	1	1	yes	characteristic
484	C₃×C₄²	C₂⁴	1	1	yes	characteristic
485	C₂×#41	—	2	8	no	—
486	C₂×#41	—	2	1	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	1	no	—
489	C₂×#41	—	2	1	no	—
490	C₂×#41	C₂³×C₃	1	2	yes	—
491	C₂×#41	C₂³×C₃	1	2	yes	—
492	C₂×#41	C₂³×C₃	1	2	yes	—
493	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
500	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
502	#135	—	2	16	no	—
503	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
504	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
505	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
506	C₂×D₈	C₂³×C₃	1	4	yes	—
507	C₂²×C₈	C₂³×C₃	1	4	yes	—
508	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
511	#127	C₂³×C₃	1	1	yes	characteristic
512	#126	—	2	2	no	—
513	#126	—	2	2	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	C₂³×C₃	1	2	yes	—
517	#124	—	2	1	no	—
518	#124	—	2	1	no	—
519	#124	C₂³×C₃	1	2	yes	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
528	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	C₂³×C₃	1	2	yes	—
534	#121	C₂³×C₃	1	2	yes	—
535	#120	—	2	2	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	C₂³×C₃	1	2	yes	—
545	C₄×Q₈	C₂³×C₃	1	2	yes	—
546	C₄×Q₈	C₂³×C₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₃	1	2	yes	—
549	C₄×Q₈	C₂³×C₃	1	2	yes	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	C₂³×C₃	1	2	yes	—
573	C₄×D₄	C₂³×C₃	1	2	yes	—
574	C₄×D₄	C₂³×C₃	1	2	yes	—
575	C₄×D₄	C₂³×C₃	1	2	yes	—
576	C₄×D₄	C₂³×C₃	1	2	yes	—
577	C₄×D₄	C₂³×C₃	1	2	yes	—
578	#117	—	2	1	no	—
579	#117	—	2	1	no	—
580	#117	—	2	1	no	—
581	#117	—	2	1	no	—
582	#117	—	2	2	no	—
583	#117	—	2	2	no	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	C₂³×C₃	1	2	yes	—
590	#117	C₂³×C₃	1	2	yes	—
591	#117	C₂³×C₃	1	2	yes	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₄²	—	2	1	no	—
600	C₂×C₄²	—	2	1	no	—
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	—	2	2	no	—
603	C₂×C₄²	—	2	2	no	—
604	C₂×C₄²	—	2	2	no	—
605	C₂×C₄²	—	2	2	no	—
606	C₂×C₄²	—	2	2	no	—
607	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
608	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
609	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
610	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
611	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
612	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
619	#107	C₂³×C₃	1	4	yes	—
620	#107	C₂³×C₃	1	4	yes	—
621	#106	C₂³×C₃	1	4	yes	—
622	#106	C₂³×C₃	1	4	yes	—
623	C₄⋊C₈	C₂³×C₃	1	2	yes	—
624	C₄⋊C₈	C₂³×C₃	1	2	yes	—
625	C₄⋊C₈	C₂³×C₃	1	4	yes	—
626	#103	C₂³×C₃	1	4	yes	—
627	#103	C₂³×C₃	1	4	yes	—
628	#103	C₂³×C₃	1	4	yes	—
629	#103	C₂³×C₃	1	4	yes	—
630	#102	C₂³×C₃	1	4	yes	—
631	#102	C₂³×C₃	1	4	yes	—
632	#102	C₂³×C₃	1	4	yes	—
633	#102	C₂³×C₃	1	4	yes	—
634	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
635	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
636	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
637	#97	C₂³×C₃	1	2	yes	—
638	#97	C₂³×C₃	1	4	yes	—
639	#97	C₂³×C₃	1	2	yes	—
640	C₂³×C₃	—	2	4	no	—
641	C₂³×C₃	—	2	2	no	—
642	C₂³×C₃	—	2	2	no	—
643	C₂³×C₃	—	2	2	no	—
644	C₂³×C₃	—	2	2	no	—
645	C₂³×C₃	—	4	1	no	—
646	C₂³×C₃	—	4	2	no	—
647	C₂³×C₃	—	4	2	no	—
648	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
649	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
650	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
651	C₃×Q₈	—	2	4	no	—
652	C₃×Q₈	—	2	2	no	—
653	C₃×Q₈	—	2	4	no	—
654	C₃×Q₈	—	4	2	no	—
655	C₃×Q₈	—	4	2	no	—
656	C₃×Q₈	C₂×#41	1	4	yes	—
657	C₃×D₄	—	2	8	no	—
658	C₃×D₄	—	2	4	no	—
659	C₃×D₄	—	2	8	no	—
660	C₃×D₄	—	2	2	no	—
661	C₃×D₄	—	2	4	no	—
662	C₃×D₄	—	4	2	no	—
663	C₃×D₄	—	4	4	no	—
664	C₃×D₄	—	4	4	no	—
665	C₃×D₄	—	4	4	no	—
666	C₃×D₄	—	4	2	no	—
667	C₃×D₄	C₂×#41	1	4	yes	—
668	C₂×C₃×C₄	—	2	4	no	—
669	C₂×C₃×C₄	—	2	8	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	8	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	2	2	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	4	1	no	—
688	C₂×C₃×C₄	—	4	1	no	—
689	C₂×C₃×C₄	—	4	1	no	—
690	C₂×C₃×C₄	—	4	1	no	—
691	C₂×C₃×C₄	—	4	1	no	—
692	C₂×C₃×C₄	—	4	1	no	—
693	C₂×C₃×C₄	—	4	1	no	—
694	C₂×C₃×C₄	—	4	4	no	—
695	C₂×C₃×C₄	—	4	4	no	—
696	C₂×C₃×C₄	—	4	4	no	—
697	C₂×C₃×C₄	—	4	4	no	—
698	C₂×C₃×C₄	—	4	4	no	—
699	C₂×C₃×C₄	—	4	2	no	—
700	C₂×C₃×C₄	—	4	2	no	—
701	C₂×C₃×C₄	—	4	4	no	—
702	C₂×C₃×C₄	—	4	4	no	—
703	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
704	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
705	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
706	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
707	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
708	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
709	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
710	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
712	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
713	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
714	C₂×C₃×C₄	C₂×#41	1	4	yes	—
715	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
716	C₃×C₈	—	2	4	no	—
717	C₃×C₈	—	2	4	no	—
718	C₂⁴	—	2	1	no	—
719	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
720	#41	—	2	8	no	—
721	#41	—	2	8	no	—
722	#41	—	2	4	no	—
723	#41	—	2	4	no	—
724	#41	—	2	4	no	—
725	#41	—	2	8	no	—
726	#41	—	4	4	no	—
727	#41	—	4	4	no	—
728	#41	C₃×#41	1	8	yes	complemented
729	C₂×Q₈	—	2	4	no	—
730	C₂×Q₈	—	2	1	no	—
731	C₂×Q₈	—	2	1	no	—
732	C₂×Q₈	—	2	1	no	—
733	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
734	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
735	C₂×D₄	—	2	8	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	C₂⁴×C₃	1	2	yes	—
746	C₂×D₄	C₂⁴×C₃	1	2	yes	—
747	C₂²×C₄	—	2	8	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	4	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
766	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
767	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
768	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
769	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
770	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
771	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
772	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
773	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
774	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
775	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
776	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
777	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
778	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
779	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
783	Q₁₆	—	2	8	no	—
784	SD₁₆	—	2	8	no	—
785	SD₁₆	—	2	8	no	—
786	D₈	—	2	8	no	—
787	C₂×C₈	—	2	8	no	—
788	C₂×C₈	C₂⁴×C₃	1	4	yes	—
789	C₂×C₈	C₂⁴×C₃	1	4	yes	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
835	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
836	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
837	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
838	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
839	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
840	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
841	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
842	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
843	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
844	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
845	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
846	C₄²	C₂⁴×C₃	1	1	yes	characteristic
847	C₄²	C₂⁴×C₃	1	1	yes	characteristic
848	C₄²	C₂⁴×C₃	1	1	yes	characteristic
849	C₄²	C₂⁴×C₃	1	1	yes	characteristic
850	C₂²×C₃	—	2	1	no	—
851	C₂²×C₃	—	2	1	no	—
852	C₂²×C₃	—	2	1	no	—
853	C₂²×C₃	—	2	1	no	—
854	C₂²×C₃	—	2	1	no	—
855	C₂²×C₃	—	2	4	no	—
856	C₂²×C₃	—	2	1	no	—
857	C₂²×C₃	—	2	1	no	—
858	C₂²×C₃	—	4	4	no	—
859	C₂²×C₃	—	4	8	no	—
860	C₂²×C₃	—	4	2	no	—
861	C₂²×C₃	—	4	2	no	—
862	C₂²×C₃	—	4	2	no	—
863	C₂²×C₃	—	4	2	no	—
864	C₂²×C₃	—	4	2	no	—
865	C₂²×C₃	#525	1	2	yes	—
866	C₂²×C₃	#575	1	2	yes	—
867	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
868	C₃×C₄	—	2	1	no	—
869	C₃×C₄	—	2	4	no	—
870	C₃×C₄	—	2	1	no	—
871	C₃×C₄	—	2	1	no	—
872	C₃×C₄	—	2	1	no	—
873	C₃×C₄	—	2	1	no	—
874	C₃×C₄	—	2	1	no	—
875	C₃×C₄	—	2	1	no	—
876	C₃×C₄	—	2	1	no	—
877	C₃×C₄	—	2	1	no	—
878	C₃×C₄	—	4	2	no	—
879	C₃×C₄	—	4	2	no	—
880	C₃×C₄	—	4	2	no	—
881	C₃×C₄	—	4	2	no	—
882	C₃×C₄	—	4	2	no	—
883	C₃×C₄	#525	1	2	yes	—
884	C₃×C₄	#575	1	2	yes	—
885	C₃×C₄	C₂²×#41	1	2	yes	—
886	C₂³	—	2	4	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	4	1	no	—
892	C₂³	—	4	2	no	—
893	C₂³	—	4	2	no	—
894	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
895	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
896	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
897	Q₈	—	2	4	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	4	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	4	2	no	—
902	Q₈	C₂×C₃×#41	1	4	yes	—
903	D₄	—	2	8	no	—
904	D₄	—	2	4	no	—
905	D₄	—	2	8	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	4	no	—
908	D₄	—	4	2	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	2	no	—
913	D₄	C₂×C₃×#41	1	4	yes	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	8	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	1	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	—	4	4	no	—
945	C₂×C₄	—	4	2	no	—
946	C₂×C₄	—	4	2	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
950	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
951	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
952	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
953	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
954	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
955	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
956	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
957	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
958	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
959	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
960	C₂×C₄	C₂×C₃×#41	1	4	yes	—
961	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
962	C₈	—	2	4	no	—
963	C₈	—	2	4	no	—
964	C₂×C₃	—	2	2	no	—
965	C₂×C₃	—	2	2	no	—
966	C₂×C₃	—	4	1	no	—
967	C₂×C₃	—	4	4	no	—
968	C₂×C₃	—	8	2	no	—
969	C₂×C₃	C₂×#525	1	1	yes	characteristic
970	C₂×C₃	C₂×#575	1	1	yes	characteristic
971	C₂×C₃	C₂×#575	1	1	yes	characteristic
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	4	4	no	—
981	C₂²	—	4	8	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	C₃×#525	1	2	yes	—
988	C₂²	C₃×#575	1	2	yes	—
989	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
990	C₄	—	2	1	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	C₃×#525	1	2	yes	—
1006	C₄	C₃×#575	1	2	yes	—
1007	C₄	C₂²×C₃×#41	1	2	yes	—
1008	C₃	#60546	1	1	yes	characteristic, direct product factor, Sylow
1009	C₂	—	2	2	no	—
1010	C₂	—	2	2	no	—
1011	C₂	—	4	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₂×C₃×#525	1	1	yes	characteristic
1015	C₂	C₂×C₃×#575	1	1	yes	characteristic
1016	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×C₄×#41	C₂	semidirect
3. C₃×#3117	C₂	semidirect
4. C₃×#3116	C₂	semidirect
5. C₃×#3115	C₂	semidirect
6. C₃×#3114	C₂	semidirect
7. C₃×#3113	C₂	semidirect
8. C₃×#3112	C₂	semidirect
9. C₃×#3111	C₂	semidirect
10. C₃×#3110	C₂	semidirect
11. C₃×#3109	C₂	semidirect
12. C₃×#3091	C₂	semidirect
13. C₃×#3076	C₂	semidirect
14. C₃×#3035	C₂	semidirect
15. C₃×#3002	C₂	semidirect
16. C₃×#2943	C₂	semidirect
17. C₂×C₃×#432	C₂	semidirect
18. #60546	C₃	direct (N × H)
22. C₃×#533	C₂²	semidirect
23. C₃×#533	C₂²	semidirect
25. C₃×#532	C₂²	semidirect
26. C₃×#532	C₂²	semidirect
32. C₃×#529	C₂²	semidirect
46. C₃×C₄×#41	C₂²	semidirect
57. C₃×#485	C₂²	semidirect
60. C₃×#482	C₂²	semidirect
63. C₃×#479	C₂²	semidirect
64. C₃×#478	C₂²	semidirect
65. C₃×#477	C₂²	semidirect
66. C₃×#476	C₂²	semidirect
67. C₃×#475	C₂²	semidirect
68. C₃×#474	C₂²	semidirect
69. C₃×#464	C₂²	semidirect
70. C₃×#463	C₂²	semidirect
71. C₃×#462	C₂²	semidirect
72. C₃×#461	C₂²	semidirect
73. C₃×#460	C₂²	semidirect
74. C₃×#459	C₂²	semidirect
81. C₃×#442	C₂²	semidirect
82. C₃×#442	C₂²	semidirect
83. C₃×#441	C₂²	semidirect
84. C₃×#441	C₂²	semidirect
85. C₃×#440	C₂²	semidirect
86. C₃×#440	C₂²	semidirect
87. C₃×#440	C₂²	semidirect
88. C₃×#440	C₂²	semidirect
92. C₃×#432	C₂²	semidirect
93. C₃×#432	C₂²	semidirect
94. C₃×#427	C₂²	semidirect
95. C₂×C₃×C₄⋊C₈	C₂²	semidirect
97. C₃×#416	C₂²	semidirect
99. C₂×C₃×#97	C₂²	semidirect
100. #3444	C₂×C₃	semidirect
101. C₂×C₄×#41	C₂×C₃	semidirect
102. #3117	C₂×C₃	semidirect
103. #3116	C₂×C₃	semidirect
104. #3115	C₂×C₃	semidirect
105. #3114	C₂×C₃	semidirect
106. #3113	C₂×C₃	semidirect
107. #3112	C₂×C₃	semidirect
108. #3111	C₂×C₃	semidirect
109. #3110	C₂×C₃	semidirect
110. #3109	C₂×C₃	semidirect
111. #3091	C₂×C₃	semidirect
112. #3076	C₂×C₃	semidirect
113. #3035	C₂×C₃	semidirect
114. #3002	C₂×C₃	semidirect
115. #2943	C₂×C₃	semidirect
116. C₂×#432	C₂×C₃	semidirect
275. #533	C₂²×C₃	semidirect
276. #533	C₂²×C₃	semidirect
278. #532	C₂²×C₃	semidirect
279. #532	C₂²×C₃	semidirect
285. #529	C₂²×C₃	semidirect
299. C₄×#41	C₂²×C₃	semidirect
310. #485	C₂²×C₃	semidirect
313. #482	C₂²×C₃	semidirect
316. #479	C₂²×C₃	semidirect
317. #478	C₂²×C₃	semidirect
318. #477	C₂²×C₃	semidirect
319. #476	C₂²×C₃	semidirect
320. #475	C₂²×C₃	semidirect
321. #474	C₂²×C₃	semidirect
322. #464	C₂²×C₃	semidirect
323. #463	C₂²×C₃	semidirect
324. #462	C₂²×C₃	semidirect
325. #461	C₂²×C₃	semidirect
326. #460	C₂²×C₃	semidirect
327. #459	C₂²×C₃	semidirect
334. #442	C₂²×C₃	semidirect
335. #442	C₂²×C₃	semidirect
336. #441	C₂²×C₃	semidirect
337. #441	C₂²×C₃	semidirect
338. #440	C₂²×C₃	semidirect
339. #440	C₂²×C₃	semidirect
340. #440	C₂²×C₃	semidirect
341. #440	C₂²×C₃	semidirect
345. #432	C₂²×C₃	semidirect
346. #432	C₂²×C₃	semidirect
347. #427	C₂²×C₃	semidirect
348. C₂×C₄⋊C₈	C₂²×C₃	semidirect
350. #416	C₂²×C₃	semidirect
352. C₂×#97	C₂²×C₃	semidirect
363. C₃×#41	#41	semidirect
728. #41	C₃×#41	semidirect
1008. C₃	#60546	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×C₄×#41	2
C₃×#3117	2
C₃×#3116	2
C₃×#3115	2
C₃×#3114	2
C₃×#3113	2
C₃×#3112	2
C₃×#3111	2
C₃×#3110	2
C₃×#3109	2
C₃×#3091	2
C₃×#3076	2
C₃×#3035	2
C₃×#3002	2
C₃×#2943	2
C₂×C₃×#432	2
#60546	3

Subgroups — C3×#60546 #10679153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60546 #10679153