Subgroups — C₃×#60597 #10679204

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3125	C₂	1	4	yes	maximal, complemented
4	C₃×#3118	C₂	1	4	yes	maximal, complemented
5	C₃×#3116	C₂	1	2	yes	maximal, complemented
6	C₃×#3109	C₂	1	2	yes	maximal, complemented
7	C₃×#3106	C₂	1	2	yes	maximal, complemented
8	C₃×#3101	C₂	1	2	yes	maximal, complemented
9	C₃×#3099	C₂	1	2	yes	maximal, complemented
10	C₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₃×#2952	C₂	1	2	yes	maximal, complemented
16	C₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	#60597	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₃×#135	C₂²	1	2	yes	—
22	C₃×#556	—	2	1	no	—
23	C₃×#555	—	2	1	no	—
24	C₃×#554	—	2	1	no	—
25	C₃×#553	—	2	2	no	—
26	C₃×#548	—	2	2	no	—
27	C₃×#547	—	2	1	no	—
28	C₃×#542	C₂²	1	4	yes	complemented
29	C₃×#537	C₂²	1	2	yes	—
30	C₃×#533	C₂²	1	2	yes	complemented
31	C₃×#532	C₂²	1	1	yes	characteristic, complemented
32	C₃×#532	C₂²	1	2	yes	complemented
33	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#520	—	2	1	no	—
35	C₃×#520	C₂²	1	1	yes	characteristic
36	C₃×#520	C₂²	1	2	yes	—
37	C₃×#520	C₂²	1	1	yes	characteristic
38	C₃×#520	C₂²	1	2	yes	complemented
39	C₃×#518	—	2	1	no	—
40	C₃×#518	—	2	2	no	—
41	C₃×#518	C₂²	1	1	yes	characteristic
42	C₃×#518	C₂²	1	2	yes	—
43	C₃×C₄×#41	—	2	1	no	—
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic
45	C₃×C₄×#41	C₂²	1	2	yes	—
46	C₃×C₄×#41	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×D₄	—	2	2	no	—
48	C₂×C₃×C₄×D₄	—	2	1	no	—
49	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
51	C₃×#485	C₂²	1	4	yes	complemented
52	C₃×#483	C₂²	1	4	yes	complemented
53	C₃×#482	C₂²	1	4	yes	complemented
54	C₃×#481	C₂²	1	4	yes	complemented
55	C₃×#477	C₂²	1	2	yes	complemented
56	C₃×#476	C₂²	1	2	yes	complemented
57	C₃×#476	C₂²	1	2	yes	complemented
58	C₃×#476	C₂²	1	4	yes	complemented
59	C₃×#476	C₂²	1	2	yes	complemented
60	C₃×#475	C₂²	1	2	yes	complemented
61	C₃×#474	C₂²	1	2	yes	complemented
62	C₃×#464	C₂²	1	2	yes	complemented
63	C₃×#463	C₂²	1	2	yes	complemented
64	C₃×#463	C₂²	1	4	yes	complemented
65	C₃×#462	C₂²	1	1	yes	characteristic, complemented
66	C₃×#461	C₂²	1	1	yes	characteristic, complemented
67	C₃×#461	C₂²	1	2	yes	complemented
68	C₃×#460	C₂²	1	1	yes	characteristic, complemented
69	C₃×#459	C₂²	1	1	yes	characteristic, complemented
70	C₃×#459	C₂²	1	2	yes	complemented
71	C₃×#452	C₂²	1	4	yes	—
72	C₃×#450	C₂²	1	4	yes	—
73	C₃×#449	C₂²	1	4	yes	—
74	C₃×#447	C₂²	1	4	yes	—
75	C₃×#442	C₂²	1	4	yes	complemented
76	C₃×#442	C₂²	1	4	yes	complemented
77	C₃×#441	C₂²	1	4	yes	complemented
78	C₃×#440	C₂²	1	4	yes	complemented
79	C₃×C₄×SD₁₆	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×D₈	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	complemented
87	C₂×C₃×#106	C₂²	1	2	yes	complemented
88	C₃×#423	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
90	C₃×#417	C₂²	1	2	yes	—
91	C₃×#417	C₂²	1	2	yes	complemented
92	C₃×#416	C₂²	1	2	yes	complemented
93	C₂×C₃×#102	C₂²	1	2	yes	—
94	C₃×#408	C₂²	1	2	yes	—
95	C₃×#405	C₂²	1	2	yes	complemented
96	#3511	C₂×C₃	1	1	yes	characteristic, complemented
97	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
98	#3125	C₂×C₃	1	4	yes	complemented
99	#3118	C₂×C₃	1	4	yes	complemented
100	#3116	C₂×C₃	1	2	yes	complemented
101	#3109	C₂×C₃	1	2	yes	complemented
102	#3106	C₂×C₃	1	2	yes	complemented
103	#3101	C₂×C₃	1	2	yes	complemented
104	#3099	C₂×C₃	1	2	yes	complemented
105	#3079	C₂×C₃	1	1	yes	characteristic, complemented
106	C₂×#476	C₂×C₃	1	1	yes	characteristic, complemented
107	#3036	C₂×C₃	1	1	yes	characteristic, complemented
108	#3035	C₂×C₃	1	1	yes	characteristic, complemented
109	#3012	C₂×C₃	1	2	yes	complemented
110	#2952	C₂×C₃	1	2	yes	complemented
111	#2946	C₂×C₃	1	2	yes	complemented
112	#2925	C₂×C₃	1	1	yes	characteristic, complemented
113	C₃×H(5,𝔽₂)	—	2	4	no	—
114	C₃×H(5,𝔽₂)	—	2	4	no	—
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	—	2	2	no	—
117	C₂×C₃×#41	C₂³	1	2	yes	—
118	C₂×C₃×#41	C₂³	1	2	yes	—
119	C₂×C₃×#41	C₂³	1	1	yes	characteristic
120	C₂×C₃×#41	C₂³	1	1	yes	characteristic
121	C₂²×C₃×Q₈	—	2	1	no	—
122	C₂²×C₃×D₄	—	2	2	no	—
123	C₂²×C₃×D₄	—	2	1	no	—
124	C₂²×C₃×D₄	C₂³	1	2	yes	—
125	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
126	C₂³×C₃×C₄	—	2	1	no	—
127	C₂³×C₃×C₄	—	2	2	no	—
128	C₃×AGL(1,ℤ/8)	—	2	8	no	—
129	C₃×#135	—	2	8	no	—
130	C₂×C₃×Q₁₆	C₂³	1	2	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×D₈	C₂³	1	4	yes	—
136	C₂×C₃×M₁₆	C₂³	1	2	yes	—
137	C₂²×C₃×C₈	C₂³	1	2	yes	—
138	C₃×C₄⋊Q₈	—	2	1	no	—
139	C₃×C₄⋊Q₈	—	2	1	no	—
140	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₃×#127	C₂³	1	1	yes	characteristic
144	C₃×#126	—	2	4	no	—
145	C₃×#125	—	2	2	no	—
146	C₃×#124	—	2	4	no	—
147	C₃×#124	—	2	2	no	—
148	C₃×#124	C₂³	1	2	yes	—
149	C₃×#123	—	2	4	no	—
150	C₃×C₂²⋊Q₈	—	2	2	no	—
151	C₃×C₂²⋊Q₈	—	2	2	no	—
152	C₃×C₂²⋊Q₈	—	2	4	no	—
153	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₃×#121	—	2	2	no	—
155	C₃×#121	—	2	4	no	—
156	C₃×#121	—	2	1	no	—
157	C₃×#121	—	2	1	no	—
158	C₃×#121	—	2	2	no	—
159	C₃×#121	C₂³	1	4	yes	—
160	C₃×C₄×Q₈	—	2	1	no	—
161	C₃×C₄×Q₈	—	2	2	no	—
162	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
163	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
164	C₃×C₄×Q₈	C₂³	1	4	yes	—
165	C₃×C₄×Q₈	C₂³	1	2	yes	—
166	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
167	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
168	C₃×C₄×D₄	—	2	2	no	—
169	C₃×C₄×D₄	—	2	1	no	—
170	C₃×C₄×D₄	—	2	1	no	—
171	C₃×C₄×D₄	—	2	2	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	—	2	2	no	—
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	—	2	2	no	—
176	C₃×C₄×D₄	—	2	1	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	4	no	—
182	C₃×C₄×D₄	—	2	2	no	—
183	C₃×C₄×D₄	—	2	1	no	—
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	—	2	2	no	—
186	C₃×C₄×D₄	—	2	1	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	—	2	1	no	—
189	C₃×C₄×D₄	D₄	1	2	yes	—
190	C₃×C₄×D₄	D₄	1	1	yes	characteristic
191	C₃×C₄×D₄	D₄	1	1	yes	characteristic
192	C₃×C₄×D₄	D₄	1	2	yes	—
193	C₃×C₄×D₄	C₂³	1	2	yes	—
194	C₃×C₄×D₄	C₂³	1	4	yes	—
195	C₃×C₄×D₄	C₂³	1	2	yes	—
196	C₃×C₄×D₄	C₂³	1	2	yes	—
197	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
198	C₃×C₄×D₄	C₂³	1	2	yes	—
199	C₃×C₄×D₄	C₂³	1	2	yes	—
200	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
201	C₃×#117	—	2	2	no	—
202	C₃×#117	—	2	1	no	—
203	C₃×#117	—	2	2	no	—
204	C₃×#117	—	2	2	no	—
205	C₃×#117	—	2	1	no	—
206	C₃×#117	—	2	2	no	—
207	C₃×#117	C₂³	1	1	yes	characteristic
208	C₃×#117	C₂³	1	2	yes	—
209	C₃×#117	C₂³	1	1	yes	characteristic
210	C₃×#117	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	—	2	1	no	—
212	C₂×C₃×C₄⋊C₄	—	2	1	no	—
213	C₂×C₃×C₄⋊C₄	—	2	2	no	—
214	C₂×C₃×C₄⋊C₄	—	2	2	no	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
222	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₃×C₄²	—	2	2	no	—
224	C₂×C₃×C₄²	—	2	1	no	—
225	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₄²	C₂³	1	2	yes	—
227	C₃×#107	C₂³	1	4	yes	—
228	C₃×#106	C₂³	1	4	yes	—
229	C₃×#106	C₂³	1	4	yes	—
230	C₃×#106	C₂³	1	4	yes	—
231	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
232	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
233	C₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₃×#103	C₂³	1	2	yes	—
237	C₃×#103	C₂³	1	2	yes	—
238	C₃×#103	C₂³	1	4	yes	—
239	C₃×#103	C₂³	1	4	yes	—
240	C₃×#102	C₂³	1	4	yes	—
241	C₃×#102	C₂³	1	4	yes	—
242	C₃×#102	C₂³	1	2	yes	—
243	C₃×#102	C₂³	1	2	yes	—
244	C₃×#102	C₂³	1	4	yes	—
245	C₃×#102	C₂³	1	4	yes	—
246	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
248	C₃×#97	C₂³	1	4	yes	—
249	C₃×C₄×C₈	C₂³	1	4	yes	—
250	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
251	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
252	C₂×#135	C₂²×C₃	1	2	yes	—
253	#556	—	2	1	no	—
254	#555	—	2	1	no	—
255	#554	—	2	1	no	—
256	#553	—	2	2	no	—
257	#548	—	2	2	no	—
258	#547	—	2	1	no	—
259	#542	C₂²×C₃	1	4	yes	complemented
260	#537	C₂²×C₃	1	2	yes	—
261	#533	C₂²×C₃	1	2	yes	complemented
262	#532	C₂²×C₃	1	1	yes	characteristic, complemented
263	#532	C₂²×C₃	1	2	yes	complemented
264	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
265	#520	—	2	1	no	—
266	#520	C₂²×C₃	1	2	yes	—
267	#520	C₂²×C₃	1	1	yes	characteristic
268	#520	C₂²×C₃	1	1	yes	characteristic
269	#520	C₂²×C₃	1	2	yes	complemented
270	#518	—	2	1	no	—
271	#518	—	2	2	no	—
272	#518	C₂²×C₃	1	2	yes	—
273	#518	C₂²×C₃	1	1	yes	characteristic
274	C₄×#41	—	2	1	no	—
275	C₄×#41	C₂²×C₃	1	1	yes	characteristic
276	C₄×#41	C₂²×C₃	1	2	yes	—
277	C₄×#41	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₄×D₄	—	2	2	no	—
279	C₂×C₄×D₄	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
281	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
282	#485	C₂²×C₃	1	4	yes	complemented
283	#483	C₂²×C₃	1	4	yes	complemented
284	#482	C₂²×C₃	1	4	yes	complemented
285	#481	C₂²×C₃	1	4	yes	complemented
286	#477	C₂²×C₃	1	2	yes	complemented
287	#476	C₂²×C₃	1	2	yes	complemented
288	#476	C₂²×C₃	1	2	yes	complemented
289	#476	C₂²×C₃	1	2	yes	complemented
290	#476	C₂²×C₃	1	4	yes	complemented
291	#475	C₂²×C₃	1	2	yes	complemented
292	#474	C₂²×C₃	1	2	yes	complemented
293	#464	C₂²×C₃	1	2	yes	complemented
294	#463	C₂²×C₃	1	2	yes	complemented
295	#463	C₂²×C₃	1	4	yes	complemented
296	#462	C₂²×C₃	1	1	yes	characteristic, complemented
297	#461	C₂²×C₃	1	1	yes	characteristic, complemented
298	#461	C₂²×C₃	1	2	yes	complemented
299	#460	C₂²×C₃	1	1	yes	characteristic, complemented
300	#459	C₂²×C₃	1	2	yes	complemented
301	#459	C₂²×C₃	1	1	yes	characteristic, complemented
302	#452	C₂²×C₃	1	4	yes	—
303	#450	C₂²×C₃	1	4	yes	—
304	#449	C₂²×C₃	1	4	yes	—
305	#447	C₂²×C₃	1	4	yes	—
306	#442	C₂²×C₃	1	4	yes	complemented
307	#442	C₂²×C₃	1	4	yes	complemented
308	#441	C₂²×C₃	1	4	yes	complemented
309	#440	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	C₄×D₈	C₂²×C₃	1	4	yes	complemented
314	#433	C₂²×C₃	1	4	yes	complemented
315	#432	C₂²×C₃	1	2	yes	complemented
316	#431	C₂²×C₃	1	2	yes	complemented
317	#428	C₂²×C₃	1	2	yes	complemented
318	C₂×#106	C₂²×C₃	1	2	yes	complemented
319	#423	C₂²×C₃	1	1	yes	characteristic, complemented
320	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
321	#417	C₂²×C₃	1	2	yes	—
322	#417	C₂²×C₃	1	2	yes	complemented
323	#416	C₂²×C₃	1	2	yes	complemented
324	C₂×#102	C₂²×C₃	1	2	yes	—
325	#408	C₂²×C₃	1	2	yes	—
326	#405	C₂²×C₃	1	2	yes	complemented
327	C₂⁴×C₃	—	2	2	no	—
328	C₂⁴×C₃	—	2	1	no	—
329	C₃×#41	—	2	8	no	—
330	C₃×#41	—	2	4	no	—
331	C₃×#41	—	2	4	no	—
332	C₃×#41	—	2	2	no	—
333	C₃×#41	—	2	2	no	—
334	C₃×#41	—	2	2	no	—
335	C₃×#41	—	2	4	no	—
336	C₃×#41	—	2	4	no	—
337	C₃×#41	—	8	4	no	—
338	C₃×#41	#41	1	4	yes	complemented
339	C₂×C₃×Q₈	—	2	2	no	—
340	C₂×C₃×Q₈	—	2	2	no	—
341	C₂×C₃×Q₈	—	8	2	no	—
342	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
343	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
344	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
345	C₂×C₃×D₄	—	2	16	no	—
346	C₂×C₃×D₄	—	2	8	no	—
347	C₂×C₃×D₄	—	2	2	no	—
348	C₂×C₃×D₄	—	2	1	no	—
349	C₂×C₃×D₄	—	2	4	no	—
350	C₂×C₃×D₄	—	2	4	no	—
351	C₂×C₃×D₄	—	2	2	no	—
352	C₂×C₃×D₄	—	2	4	no	—
353	C₂×C₃×D₄	—	2	2	no	—
354	C₂×C₃×D₄	—	2	1	no	—
355	C₂×C₃×D₄	—	2	1	no	—
356	C₂×C₃×D₄	—	2	1	no	—
357	C₂×C₃×D₄	—	2	2	no	—
358	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
359	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
360	C₂×C₃×D₄	#41	1	4	yes	complemented
361	C₂×C₃×D₄	C₂⁴	1	2	yes	—
362	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×D₄	C₂⁴	1	2	yes	—
364	C₂²×C₃×C₄	—	2	2	no	—
365	C₂²×C₃×C₄	—	2	1	no	—
366	C₂²×C₃×C₄	—	2	2	no	—
367	C₂²×C₃×C₄	—	2	1	no	—
368	C₂²×C₃×C₄	—	2	2	no	—
369	C₂²×C₃×C₄	—	2	2	no	—
370	C₂²×C₃×C₄	—	2	1	no	—
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	1	no	—
373	C₂²×C₃×C₄	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	4	no	—
378	C₂²×C₃×C₄	—	8	2	no	—
379	C₂²×C₃×C₄	—	8	4	no	—
380	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
382	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₃×Q₁₆	—	2	4	no	—
387	C₃×SD₁₆	—	2	4	no	—
388	C₃×SD₁₆	—	2	4	no	—
389	C₃×SD₁₆	—	2	8	no	—
390	C₃×D₈	—	2	4	no	—
391	C₃×D₈	—	2	8	no	—
392	C₃×M₁₆	—	2	4	no	—
393	C₂×C₃×C₈	—	2	4	no	—
394	C₂×C₃×C₈	C₂⁴	1	2	yes	—
395	C₂×C₃×C₈	C₂⁴	1	4	yes	—
396	C₂×C₃×C₈	C₂⁴	1	2	yes	—
397	C₃×C₄⋊C₄	—	2	2	no	—
398	C₃×C₄⋊C₄	—	2	1	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	2	1	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	2	no	—
403	C₃×C₄⋊C₄	—	2	4	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	2	1	no	—
406	C₃×C₄⋊C₄	—	2	1	no	—
407	C₃×C₄⋊C₄	—	2	1	no	—
408	C₃×C₄⋊C₄	—	2	4	no	—
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	C₂×D₄	1	2	yes	—
413	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
414	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₃×C₂²⋊C₄	—	2	2	no	—
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	4	no	—
420	C₃×C₂²⋊C₄	—	2	2	no	—
421	C₃×C₂²⋊C₄	—	2	1	no	—
422	C₃×C₂²⋊C₄	—	2	2	no	—
423	C₃×C₂²⋊C₄	—	2	2	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	4	no	—
428	C₃×C₂²⋊C₄	—	2	4	no	—
429	C₃×C₂²⋊C₄	—	2	2	no	—
430	C₃×C₂²⋊C₄	—	2	2	no	—
431	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₃×C₄²	—	2	1	no	—
435	C₃×C₄²	—	2	1	no	—
436	C₃×C₄²	—	2	2	no	—
437	C₃×C₄²	—	2	2	no	—
438	C₃×C₄²	—	2	1	no	—
439	C₃×C₄²	—	2	4	no	—
440	C₃×C₄²	C₂×D₄	1	2	yes	—
441	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
442	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
443	C₃×C₄²	C₂×D₄	1	2	yes	—
444	C₃×C₄²	C₂⁴	1	2	yes	—
445	C₃×C₄²	C₂⁴	1	1	yes	characteristic
446	C₃×C₄²	C₂⁴	1	1	yes	characteristic
447	H(5,𝔽₂)	—	2	4	no	—
448	H(5,𝔽₂)	—	2	4	no	—
449	C₂×#41	—	2	1	no	—
450	C₂×#41	—	2	2	no	—
451	C₂×#41	C₂³×C₃	1	2	yes	—
452	C₂×#41	C₂³×C₃	1	2	yes	—
453	C₂×#41	C₂³×C₃	1	1	yes	characteristic
454	C₂×#41	C₂³×C₃	1	1	yes	characteristic
455	C₂²×Q₈	—	2	1	no	—
456	C₂²×D₄	—	2	2	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	C₂³×C₃	1	2	yes	—
459	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	2	no	—
462	AGL(1,ℤ/8)	—	2	8	no	—
463	#135	—	2	8	no	—
464	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
465	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
466	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
467	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
468	C₂×D₈	C₂³×C₃	1	2	yes	—
469	C₂×D₈	C₂³×C₃	1	4	yes	—
470	C₂×M₁₆	C₂³×C₃	1	2	yes	—
471	C₂²×C₈	C₂³×C₃	1	2	yes	—
472	C₄⋊Q₈	—	2	1	no	—
473	C₄⋊Q₈	—	2	1	no	—
474	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
476	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
477	#127	C₂³×C₃	1	1	yes	characteristic
478	#126	—	2	4	no	—
479	#125	—	2	2	no	—
480	#124	—	2	4	no	—
481	#124	—	2	2	no	—
482	#124	C₂³×C₃	1	2	yes	—
483	#123	—	2	4	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
488	#121	—	2	2	no	—
489	#121	—	2	4	no	—
490	#121	—	2	1	no	—
491	#121	—	2	1	no	—
492	#121	—	2	2	no	—
493	#121	C₂³×C₃	1	4	yes	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
497	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
498	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
499	C₄×Q₈	C₂³×C₃	1	2	yes	—
500	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
501	C₄×Q₈	C₂³×C₃	1	4	yes	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	C₃×D₄	1	2	yes	—
524	C₄×D₄	C₃×D₄	1	1	yes	characteristic
525	C₄×D₄	C₃×D₄	1	1	yes	characteristic
526	C₄×D₄	C₃×D₄	1	2	yes	—
527	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
528	C₄×D₄	C₂³×C₃	1	2	yes	—
529	C₄×D₄	C₂³×C₃	1	2	yes	—
530	C₄×D₄	C₂³×C₃	1	2	yes	—
531	C₄×D₄	C₂³×C₃	1	2	yes	—
532	C₄×D₄	C₂³×C₃	1	2	yes	—
533	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
534	C₄×D₄	C₂³×C₃	1	4	yes	—
535	#117	—	2	2	no	—
536	#117	—	2	1	no	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	#117	—	2	1	no	—
540	#117	—	2	2	no	—
541	#117	C₂³×C₃	1	1	yes	characteristic
542	#117	C₂³×C₃	1	2	yes	—
543	#117	C₂³×C₃	1	1	yes	characteristic
544	#117	C₂³×C₃	1	2	yes	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	2	no	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₂²⋊C₄	—	2	2	no	—
556	C₂×C₂²⋊C₄	—	2	2	no	—
557	C₂×C₄²	—	2	2	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃	1	2	yes	—
561	#107	C₂³×C₃	1	4	yes	—
562	#106	C₂³×C₃	1	4	yes	—
563	#106	C₂³×C₃	1	4	yes	—
564	#106	C₂³×C₃	1	4	yes	—
565	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
567	C₄⋊C₈	C₂³×C₃	1	2	yes	—
568	C₄⋊C₈	C₂³×C₃	1	2	yes	—
569	C₄⋊C₈	C₂³×C₃	1	2	yes	—
570	#103	C₂³×C₃	1	2	yes	—
571	#103	C₂³×C₃	1	2	yes	—
572	#103	C₂³×C₃	1	4	yes	—
573	#103	C₂³×C₃	1	4	yes	—
574	#102	C₂³×C₃	1	4	yes	—
575	#102	C₂³×C₃	1	4	yes	—
576	#102	C₂³×C₃	1	2	yes	—
577	#102	C₂³×C₃	1	2	yes	—
578	#102	C₂³×C₃	1	4	yes	—
579	#102	C₂³×C₃	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
582	#97	C₂³×C₃	1	4	yes	—
583	C₄×C₈	C₂³×C₃	1	4	yes	—
584	C₂³×C₃	—	2	8	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	1	no	—
587	C₂³×C₃	—	2	4	no	—
588	C₂³×C₃	—	2	2	no	—
589	C₂³×C₃	—	8	1	no	—
590	C₂³×C₃	—	8	2	no	—
591	C₂³×C₃	—	8	1	no	—
592	C₂³×C₃	—	8	2	no	—
593	C₂³×C₃	C₂²×D₄	1	2	yes	—
594	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
595	C₃×Q₈	—	2	2	no	—
596	C₃×Q₈	—	2	1	no	—
597	C₃×Q₈	—	2	2	no	—
598	C₃×Q₈	—	2	2	no	—
599	C₃×Q₈	—	4	4	no	—
600	C₃×Q₈	—	8	2	no	—
601	C₃×Q₈	C₂×#41	1	2	yes	—
602	C₃×D₄	—	2	8	no	—
603	C₃×D₄	—	2	8	no	—
604	C₃×D₄	—	2	4	no	—
605	C₃×D₄	—	2	4	no	—
606	C₃×D₄	—	2	2	no	—
607	C₃×D₄	—	2	4	no	—
608	C₃×D₄	—	2	2	no	—
609	C₃×D₄	—	2	1	no	—
610	C₃×D₄	—	2	2	no	—
611	C₃×D₄	—	2	2	no	—
612	C₃×D₄	—	4	2	no	—
613	C₃×D₄	—	4	4	no	—
614	C₃×D₄	—	4	2	no	—
615	C₃×D₄	—	8	4	no	—
616	C₃×D₄	C₂×#41	1	2	yes	—
617	C₃×D₄	C₂×#41	1	4	yes	—
618	C₂×C₃×C₄	—	2	8	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	4	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	4	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	4	no	—
630	C₂×C₃×C₄	—	4	1	no	—
631	C₂×C₃×C₄	—	4	2	no	—
632	C₂×C₃×C₄	—	4	4	no	—
633	C₂×C₃×C₄	—	4	4	no	—
634	C₂×C₃×C₄	—	4	2	no	—
635	C₂×C₃×C₄	—	8	2	no	—
636	C₂×C₃×C₄	—	8	1	no	—
637	C₂×C₃×C₄	—	8	2	no	—
638	C₂×C₃×C₄	—	8	2	no	—
639	C₂×C₃×C₄	—	8	2	no	—
640	C₂×C₃×C₄	—	8	4	no	—
641	C₂×C₃×C₄	—	8	1	no	—
642	C₂×C₃×C₄	—	8	2	no	—
643	C₂×C₃×C₄	—	8	2	no	—
644	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
645	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
646	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
648	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₃×C₄	C₂×#41	1	2	yes	—
653	C₂×C₃×C₄	C₂×#41	1	2	yes	—
654	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
655	C₃×C₈	—	2	2	no	—
656	C₃×C₈	—	2	2	no	—
657	C₃×C₈	—	2	4	no	—
658	C₂⁴	—	2	2	no	—
659	C₂⁴	—	2	1	no	—
660	#41	—	2	8	no	—
661	#41	—	2	4	no	—
662	#41	—	2	4	no	—
663	#41	—	2	2	no	—
664	#41	—	2	2	no	—
665	#41	—	2	2	no	—
666	#41	—	2	4	no	—
667	#41	—	2	4	no	—
668	#41	—	8	4	no	—
669	#41	C₃×#41	1	4	yes	complemented
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	8	2	no	—
673	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
674	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
676	C₂×D₄	—	2	16	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
690	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
691	C₂×D₄	C₃×#41	1	4	yes	complemented
692	C₂×D₄	C₂⁴×C₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
694	C₂×D₄	C₂⁴×C₃	1	2	yes	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	8	2	no	—
710	C₂²×C₄	—	8	4	no	—
711	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
712	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
713	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
717	Q₁₆	—	2	4	no	—
718	SD₁₆	—	2	4	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	2	8	no	—
721	D₈	—	2	4	no	—
722	D₈	—	2	8	no	—
723	M₁₆	—	2	4	no	—
724	C₂×C₈	—	2	4	no	—
725	C₂×C₈	C₂⁴×C₃	1	2	yes	—
726	C₂×C₈	C₂⁴×C₃	1	4	yes	—
727	C₂×C₈	C₂⁴×C₃	1	2	yes	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
741	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
742	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
743	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
763	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
764	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	1	no	—
770	C₄²	—	2	4	no	—
771	C₄²	C₂×C₃×D₄	1	2	yes	—
772	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
773	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
774	C₄²	C₂×C₃×D₄	1	2	yes	—
775	C₄²	C₂⁴×C₃	1	2	yes	—
776	C₄²	C₂⁴×C₃	1	1	yes	characteristic
777	C₄²	C₂⁴×C₃	1	1	yes	characteristic
778	C₂²×C₃	—	2	1	no	—
779	C₂²×C₃	—	2	1	no	—
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	4	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	2	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	1	no	—
787	C₂²×C₃	—	4	2	no	—
788	C₂²×C₃	—	4	1	no	—
789	C₂²×C₃	—	4	2	no	—
790	C₂²×C₃	—	4	2	no	—
791	C₂²×C₃	—	4	2	no	—
792	C₂²×C₃	—	8	4	no	—
793	C₂²×C₃	—	8	8	no	—
794	C₂²×C₃	#525	1	2	yes	—
795	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
796	C₃×C₄	—	2	1	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	1	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	2	1	no	—
803	C₃×C₄	—	4	1	no	—
804	C₃×C₄	—	4	4	no	—
805	C₃×C₄	—	4	2	no	—
806	C₃×C₄	—	4	2	no	—
807	C₃×C₄	—	4	1	no	—
808	C₃×C₄	#525	1	2	yes	—
809	C₃×C₄	#577	1	2	yes	—
810	C₃×C₄	C₂²×#41	1	1	yes	characteristic
811	C₃×C₄	C₂²×#41	1	1	yes	characteristic
812	C₂³	—	2	8	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	8	1	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	1	no	—
820	C₂³	—	8	2	no	—
821	C₂³	C₂²×C₃×D₄	1	2	yes	—
822	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
823	Q₈	—	2	1	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	8	2	no	—
829	Q₈	C₂×C₃×#41	1	2	yes	—
830	D₄	—	2	8	no	—
831	D₄	—	2	8	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	2	no	—
843	D₄	—	8	4	no	—
844	D₄	C₂×C₃×#41	1	2	yes	—
845	D₄	C₂×C₃×#41	1	4	yes	—
846	C₂×C₄	—	2	8	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	4	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	1	no	—
869	C₂×C₄	—	8	1	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
873	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
874	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
875	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
876	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
877	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
878	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
879	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂×C₃×#41	1	2	yes	—
881	C₂×C₄	C₂×C₃×#41	1	2	yes	—
882	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₈	—	2	4	no	—
886	C₂×C₃	—	2	2	no	—
887	C₂×C₃	—	4	2	no	—
888	C₂×C₃	—	4	4	no	—
889	C₂×C₃	—	4	2	no	—
890	C₂×C₃	—	8	2	no	—
891	C₂×C₃	C₂×#525	1	1	yes	characteristic
892	C₂×C₃	C₂×#577	1	1	yes	characteristic
893	C₂×C₃	#3585	1	1	yes	characteristic
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	8	4	no	—
909	C₂²	—	8	8	no	—
910	C₂²	C₃×#525	1	2	yes	—
911	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	4	no	—
924	C₄	C₃×#525	1	2	yes	—
925	C₄	C₃×#577	1	2	yes	—
926	C₄	C₂²×C₃×#41	1	1	yes	characteristic
927	C₄	C₂²×C₃×#41	1	1	yes	characteristic
928	C₃	#60597	1	1	yes	characteristic, direct product factor, Sylow
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×C₃×#525	1	1	yes	characteristic
935	C₂	C₂×C₃×#577	1	1	yes	characteristic
936	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3511	C₂	semidirect
2. C₃×C₄×H(5,𝔽₂)	C₂	semidirect
3. C₃×#3125	C₂	semidirect
4. C₃×#3118	C₂	semidirect
5. C₃×#3116	C₂	semidirect
6. C₃×#3109	C₂	semidirect
7. C₃×#3106	C₂	semidirect
8. C₃×#3101	C₂	semidirect
9. C₃×#3099	C₂	semidirect
10. C₃×#3079	C₂	semidirect
11. C₂×C₃×#476	C₂	semidirect
12. C₃×#3036	C₂	semidirect
13. C₃×#3035	C₂	semidirect
14. C₃×#3012	C₂	semidirect
15. C₃×#2952	C₂	semidirect
16. C₃×#2946	C₂	semidirect
17. C₃×#2925	C₂	semidirect
18. #60597	C₃	direct (N × H)
28. C₃×#542	C₂²	semidirect
30. C₃×#533	C₂²	semidirect
31. C₃×#532	C₂²	semidirect
32. C₃×#532	C₂²	semidirect
33. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
38. C₃×#520	C₂²	semidirect
51. C₃×#485	C₂²	semidirect
52. C₃×#483	C₂²	semidirect
53. C₃×#482	C₂²	semidirect
54. C₃×#481	C₂²	semidirect
55. C₃×#477	C₂²	semidirect
56. C₃×#476	C₂²	semidirect
57. C₃×#476	C₂²	semidirect
58. C₃×#476	C₂²	semidirect
59. C₃×#476	C₂²	semidirect
60. C₃×#475	C₂²	semidirect
61. C₃×#474	C₂²	semidirect
62. C₃×#464	C₂²	semidirect
63. C₃×#463	C₂²	semidirect
64. C₃×#463	C₂²	semidirect
65. C₃×#462	C₂²	semidirect
66. C₃×#461	C₂²	semidirect
67. C₃×#461	C₂²	semidirect
68. C₃×#460	C₂²	semidirect
69. C₃×#459	C₂²	semidirect
70. C₃×#459	C₂²	semidirect
75. C₃×#442	C₂²	semidirect
76. C₃×#442	C₂²	semidirect
77. C₃×#441	C₂²	semidirect
78. C₃×#440	C₂²	semidirect
79. C₃×C₄×SD₁₆	C₂²	semidirect
80. C₃×C₄×SD₁₆	C₂²	semidirect
81. C₃×C₄×SD₁₆	C₂²	semidirect
82. C₃×C₄×D₈	C₂²	semidirect
83. C₃×#433	C₂²	semidirect
84. C₃×#432	C₂²	semidirect
85. C₃×#431	C₂²	semidirect
86. C₃×#428	C₂²	semidirect
87. C₂×C₃×#106	C₂²	semidirect
88. C₃×#423	C₂²	semidirect
89. C₂×C₃×C₄⋊C₈	C₂²	semidirect
91. C₃×#417	C₂²	semidirect
92. C₃×#416	C₂²	semidirect
95. C₃×#405	C₂²	semidirect
96. #3511	C₂×C₃	semidirect
97. C₄×H(5,𝔽₂)	C₂×C₃	semidirect
98. #3125	C₂×C₃	semidirect
99. #3118	C₂×C₃	semidirect
100. #3116	C₂×C₃	semidirect
101. #3109	C₂×C₃	semidirect
102. #3106	C₂×C₃	semidirect
103. #3101	C₂×C₃	semidirect
104. #3099	C₂×C₃	semidirect
105. #3079	C₂×C₃	semidirect
106. C₂×#476	C₂×C₃	semidirect
107. #3036	C₂×C₃	semidirect
108. #3035	C₂×C₃	semidirect
109. #3012	C₂×C₃	semidirect
110. #2952	C₂×C₃	semidirect
111. #2946	C₂×C₃	semidirect
112. #2925	C₂×C₃	semidirect
259. #542	C₂²×C₃	semidirect
261. #533	C₂²×C₃	semidirect
262. #532	C₂²×C₃	semidirect
263. #532	C₂²×C₃	semidirect
264. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
269. #520	C₂²×C₃	semidirect
282. #485	C₂²×C₃	semidirect
283. #483	C₂²×C₃	semidirect
284. #482	C₂²×C₃	semidirect
285. #481	C₂²×C₃	semidirect
286. #477	C₂²×C₃	semidirect
287. #476	C₂²×C₃	semidirect
288. #476	C₂²×C₃	semidirect
289. #476	C₂²×C₃	semidirect
290. #476	C₂²×C₃	semidirect
291. #475	C₂²×C₃	semidirect
292. #474	C₂²×C₃	semidirect
293. #464	C₂²×C₃	semidirect
294. #463	C₂²×C₃	semidirect
295. #463	C₂²×C₃	semidirect
296. #462	C₂²×C₃	semidirect
297. #461	C₂²×C₃	semidirect
298. #461	C₂²×C₃	semidirect
299. #460	C₂²×C₃	semidirect
300. #459	C₂²×C₃	semidirect
301. #459	C₂²×C₃	semidirect
306. #442	C₂²×C₃	semidirect
307. #442	C₂²×C₃	semidirect
308. #441	C₂²×C₃	semidirect
309. #440	C₂²×C₃	semidirect
310. C₄×SD₁₆	C₂²×C₃	semidirect
311. C₄×SD₁₆	C₂²×C₃	semidirect
312. C₄×SD₁₆	C₂²×C₃	semidirect
313. C₄×D₈	C₂²×C₃	semidirect
314. #433	C₂²×C₃	semidirect
315. #432	C₂²×C₃	semidirect
316. #431	C₂²×C₃	semidirect
317. #428	C₂²×C₃	semidirect
318. C₂×#106	C₂²×C₃	semidirect
319. #423	C₂²×C₃	semidirect
320. C₂×C₄⋊C₈	C₂²×C₃	semidirect
322. #417	C₂²×C₃	semidirect
323. #416	C₂²×C₃	semidirect
326. #405	C₂²×C₃	semidirect
338. C₃×#41	#41	semidirect
360. C₂×C₃×D₄	#41	semidirect
669. #41	C₃×#41	semidirect
691. C₂×D₄	C₃×#41	semidirect
928. C₃	#60597	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×#3511	2
C₃×C₄×H(5,𝔽₂)	2
C₃×#3125	2
C₃×#3118	2
C₃×#3116	2
C₃×#3109	2
C₃×#3106	2
C₃×#3101	2
C₃×#3099	2
C₃×#3079	2
C₂×C₃×#476	2
C₃×#3036	2
C₃×#3035	2
C₃×#3012	2
C₃×#2952	2
C₃×#2946	2
C₃×#2925	2
#60597	3

Subgroups — C3×#60597 #10679204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60597 #10679204