Subgroups — C₃×#61797 #10680404

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3348	C₂	1	4	yes	maximal, complemented
4	C₃×#3347	C₂	1	4	yes	maximal, complemented
5	C₃×#3318	C₂	1	4	yes	maximal, complemented
6	C₃×#3310	C₂	1	4	yes	maximal, complemented
7	C₃×#3234	C₂	1	2	yes	maximal, complemented
8	C₃×#3198	C₂	1	4	yes	maximal, complemented
9	C₃×#3115	C₂	1	2	yes	maximal, complemented
10	C₃×#3096	C₂	1	4	yes	maximal, complemented
11	C₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
12	#61797	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×H(3,𝔽₄)	—	2	2	no	—
14	C₃×#555	—	2	1	no	—
15	C₃×#555	C₂²	1	4	yes	—
16	C₃×#553	—	2	4	no	—
17	C₃×#553	C₂²	1	4	yes	complemented
18	C₃×#552	C₂²	1	4	yes	complemented
19	C₃×D₄²	—	2	1	no	—
20	C₃×D₄²	C₂²	1	4	yes	—
21	C₃×#541	—	2	1	no	—
22	C₃×#540	—	2	1	no	—
23	C₃×#537	C₂²	1	2	yes	complemented
24	C₃×#535	—	2	4	no	—
25	C₃×#535	C₂²	1	4	yes	—
26	C₃×#532	C₂²	1	2	yes	—
27	C₃×#532	C₂²	1	1	yes	characteristic
28	C₃×#529	—	2	2	no	—
29	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
30	C₃×#520	C₂²	1	2	yes	complemented
31	C₃×C₄×#41	C₂²	1	1	yes	characteristic, complemented
32	C₃×#501	C₂²	1	4	yes	complemented
33	C₃×#490	C₂²	1	4	yes	—
34	C₃×#485	C₂²	1	4	yes	complemented
35	C₃×#482	C₂²	1	4	yes	complemented
36	C₃×#482	C₂²	1	4	yes	complemented
37	C₃×#482	C₂²	1	4	yes	complemented
38	C₃×#482	C₂²	1	4	yes	complemented
39	C₃×#481	C₂²	1	4	yes	complemented
40	C₃×#481	C₂²	1	4	yes	complemented
41	C₃×#480	C₂²	1	4	yes	complemented
42	C₃×#480	C₂²	1	4	yes	complemented
43	C₃×#478	C₂²	1	4	yes	complemented
44	C₃×#478	C₂²	1	4	yes	complemented
45	C₃×#475	C₂²	1	2	yes	complemented
46	C₃×#474	C₂²	1	2	yes	complemented
47	C₃×#469	C₂²	1	4	yes	complemented
48	C₃×#468	C₂²	1	4	yes	complemented
49	C₃×#466	C₂²	1	4	yes	complemented
50	C₃×#465	C₂²	1	4	yes	complemented
51	C₃×#460	C₂²	1	2	yes	—
52	C₃×#459	C₂²	1	2	yes	—
53	C₃×#450	C₂²	1	4	yes	complemented
54	C₃×#449	C₂²	1	4	yes	complemented
55	C₃×#447	C₂²	1	4	yes	complemented
56	C₃×#442	C₂²	1	4	yes	complemented
57	C₃×#440	C₂²	1	4	yes	complemented
58	C₃×#435	C₂²	1	4	yes	complemented
59	C₃×#435	C₂²	1	4	yes	complemented
60	C₃×#432	C₂²	1	2	yes	complemented
61	C₃×#428	C₂²	1	4	yes	complemented
62	C₃×#427	C₂²	1	4	yes	complemented
63	C₃×#418	C₂²	1	4	yes	complemented
64	C₂×C₃×#102	C₂²	1	4	yes	complemented
65	C₃×#408	C₂²	1	4	yes	complemented
66	#3549	C₂×C₃	1	1	yes	characteristic, complemented
67	#3512	C₂×C₃	1	1	yes	characteristic, complemented
68	#3348	C₂×C₃	1	4	yes	complemented
69	#3347	C₂×C₃	1	4	yes	complemented
70	#3318	C₂×C₃	1	4	yes	complemented
71	#3310	C₂×C₃	1	4	yes	complemented
72	#3234	C₂×C₃	1	2	yes	complemented
73	#3198	C₂×C₃	1	4	yes	complemented
74	#3115	C₂×C₃	1	2	yes	complemented
75	#3096	C₂×C₃	1	4	yes	complemented
76	#2980	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×C₃×#41	—	2	2	no	—
78	C₂×C₃×#41	C₂³	1	1	yes	characteristic
79	C₂×C₃×#41	C₂³	1	2	yes	—
80	C₂²×C₃×D₄	—	2	4	no	—
81	C₂²×C₃×D₄	C₂³	1	4	yes	—
82	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
83	C₂×C₃×D₈	C₂³	1	4	yes	—
84	C₂×C₃×M₁₆	C₂³	1	4	yes	—
85	C₂²×C₃×C₈	C₂³	1	4	yes	—
86	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₃×#127	—	2	4	no	—
89	C₃×#127	D₄	1	1	yes	characteristic
90	C₃×#127	C₂³	1	2	yes	—
91	C₃×#126	—	2	4	no	—
92	C₃×#126	—	2	4	no	—
93	C₃×#125	—	2	4	no	—
94	C₃×#125	—	2	1	no	—
95	C₃×#125	—	2	1	no	—
96	C₃×#125	C₂³	1	4	yes	—
97	C₃×#124	—	2	4	no	—
98	C₃×#124	—	2	4	no	—
99	C₃×#124	—	2	4	no	—
100	C₃×#124	—	2	2	no	—
101	C₃×#124	D₄	1	2	yes	—
102	C₃×#123	—	2	4	no	—
103	C₃×#123	—	2	4	no	—
104	C₃×C₂²⋊Q₈	—	2	2	no	—
105	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
106	C₃×#121	—	2	2	no	—
107	C₃×#121	—	2	4	no	—
108	C₃×#121	—	2	4	no	—
109	C₃×#121	—	2	4	no	—
110	C₃×#121	—	2	2	no	—
111	C₃×#121	—	2	4	no	—
112	C₃×#121	D₄	1	4	yes	—
113	C₃×#121	C₂³	1	4	yes	—
114	C₃×#121	C₂³	1	4	yes	—
115	C₃×#121	C₂³	1	4	yes	—
116	C₃×#121	C₂³	1	4	yes	—
117	C₃×#120	—	2	4	no	—
118	C₃×#120	—	2	4	no	—
119	C₃×#120	—	2	4	no	—
120	C₃×#120	—	2	4	no	—
121	C₃×C₄×Q₈	—	2	2	no	—
122	C₃×C₄×Q₈	C₂³	1	2	yes	—
123	C₃×C₄×D₄	—	2	2	no	—
124	C₃×C₄×D₄	—	2	4	no	—
125	C₃×C₄×D₄	—	2	2	no	—
126	C₃×C₄×D₄	—	2	4	no	—
127	C₃×C₄×D₄	—	2	2	no	—
128	C₃×C₄×D₄	C₂³	1	4	yes	—
129	C₃×C₄×D₄	C₂³	1	2	yes	—
130	C₃×C₄×D₄	C₂³	1	4	yes	—
131	C₃×#117	—	2	4	no	—
132	C₃×#117	—	2	4	no	—
133	C₃×#117	—	2	1	no	—
134	C₃×#117	C₂³	1	4	yes	—
135	C₃×#117	C₂³	1	4	yes	—
136	C₃×#117	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	—	2	2	no	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄²	—	2	1	no	—
141	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
142	C₃×#107	C₂³	1	4	yes	—
143	C₃×#107	C₂³	1	4	yes	—
144	C₃×#107	C₂³	1	4	yes	—
145	C₃×#106	C₂³	1	4	yes	—
146	C₃×#106	C₂³	1	4	yes	—
147	C₃×#106	C₂³	1	4	yes	—
148	C₃×C₄⋊C₈	C₂³	1	2	yes	—
149	C₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₃×#103	C₂³	1	4	yes	—
151	C₃×#102	C₂³	1	4	yes	—
152	C₃×#102	C₂³	1	4	yes	—
153	C₃×#102	C₂³	1	4	yes	—
154	C₃×#102	C₂³	1	4	yes	—
155	C₃×#102	C₂³	1	4	yes	—
156	C₃×#102	C₂³	1	4	yes	—
157	C₃×#102	C₂³	1	4	yes	—
158	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
161	C₃×#97	C₂³	1	4	yes	—
162	H(3,𝔽₄)	—	2	2	no	—
163	#555	—	2	1	no	—
164	#555	C₂²×C₃	1	4	yes	—
165	#553	—	2	4	no	—
166	#553	C₂²×C₃	1	4	yes	complemented
167	#552	C₂²×C₃	1	4	yes	complemented
168	D₄²	—	2	1	no	—
169	D₄²	C₂²×C₃	1	4	yes	—
170	#541	—	2	1	no	—
171	#540	—	2	1	no	—
172	#537	C₂²×C₃	1	2	yes	complemented
173	#535	—	2	4	no	—
174	#535	C₂²×C₃	1	4	yes	—
175	#532	C₂²×C₃	1	2	yes	—
176	#532	C₂²×C₃	1	1	yes	characteristic
177	#529	—	2	2	no	—
178	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
179	#520	C₂²×C₃	1	2	yes	complemented
180	C₄×#41	C₂²×C₃	1	1	yes	characteristic, complemented
181	#501	C₂²×C₃	1	4	yes	complemented
182	#490	C₂²×C₃	1	4	yes	—
183	#485	C₂²×C₃	1	4	yes	complemented
184	#482	C₂²×C₃	1	4	yes	complemented
185	#482	C₂²×C₃	1	4	yes	complemented
186	#482	C₂²×C₃	1	4	yes	complemented
187	#482	C₂²×C₃	1	4	yes	complemented
188	#481	C₂²×C₃	1	4	yes	complemented
189	#481	C₂²×C₃	1	4	yes	complemented
190	#480	C₂²×C₃	1	4	yes	complemented
191	#480	C₂²×C₃	1	4	yes	complemented
192	#478	C₂²×C₃	1	4	yes	complemented
193	#478	C₂²×C₃	1	4	yes	complemented
194	#475	C₂²×C₃	1	2	yes	complemented
195	#474	C₂²×C₃	1	2	yes	complemented
196	#469	C₂²×C₃	1	4	yes	complemented
197	#468	C₂²×C₃	1	4	yes	complemented
198	#466	C₂²×C₃	1	4	yes	complemented
199	#465	C₂²×C₃	1	4	yes	complemented
200	#460	C₂²×C₃	1	2	yes	—
201	#459	C₂²×C₃	1	2	yes	—
202	#450	C₂²×C₃	1	4	yes	complemented
203	#449	C₂²×C₃	1	4	yes	complemented
204	#447	C₂²×C₃	1	4	yes	complemented
205	#442	C₂²×C₃	1	4	yes	complemented
206	#440	C₂²×C₃	1	4	yes	complemented
207	#435	C₂²×C₃	1	4	yes	complemented
208	#435	C₂²×C₃	1	4	yes	complemented
209	#432	C₂²×C₃	1	2	yes	complemented
210	#428	C₂²×C₃	1	4	yes	complemented
211	#427	C₂²×C₃	1	4	yes	complemented
212	#418	C₂²×C₃	1	4	yes	complemented
213	C₂×#102	C₂²×C₃	1	4	yes	complemented
214	#408	C₂²×C₃	1	4	yes	complemented
215	C₂⁴×C₃	—	2	4	no	—
216	C₃×#41	—	4	2	no	—
217	C₃×#41	—	4	2	no	—
218	C₃×#41	—	4	2	no	—
219	C₃×#41	—	8	4	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
222	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
223	C₂×C₃×D₄	—	2	1	no	—
224	C₂×C₃×D₄	—	2	4	no	—
225	C₂×C₃×D₄	—	2	4	no	—
226	C₂×C₃×D₄	—	2	4	no	—
227	C₂×C₃×D₄	—	2	4	no	—
228	C₂×C₃×D₄	—	2	2	no	—
229	C₂×C₃×D₄	—	2	2	no	—
230	C₂×C₃×D₄	—	2	4	no	—
231	C₂×C₃×D₄	—	4	4	no	—
232	C₂×C₃×D₄	—	4	4	no	—
233	C₂×C₃×D₄	—	8	8	no	—
234	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
235	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
236	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
237	C₂×C₃×D₄	C₂⁴	1	4	yes	—
238	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	4	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	—	2	2	no	—
244	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
245	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
247	C₃×SD₁₆	—	4	4	no	—
248	C₃×D₈	—	4	4	no	—
249	C₃×M₁₆	—	4	4	no	—
250	C₂×C₃×C₈	—	4	4	no	—
251	C₂×C₃×C₈	C₂⁴	1	4	yes	—
252	C₂×C₃×C₈	C₂⁴	1	4	yes	—
253	C₃×C₄⋊C₄	—	2	4	no	—
254	C₃×C₄⋊C₄	—	2	4	no	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	4	no	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	2	4	no	—
260	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
261	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
263	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
264	C₃×C₂²⋊C₄	—	2	4	no	—
265	C₃×C₂²⋊C₄	—	2	1	no	—
266	C₃×C₂²⋊C₄	—	2	4	no	—
267	C₃×C₂²⋊C₄	—	2	4	no	—
268	C₃×C₂²⋊C₄	—	2	2	no	—
269	C₃×C₂²⋊C₄	—	2	4	no	—
270	C₃×C₂²⋊C₄	—	2	4	no	—
271	C₃×C₂²⋊C₄	—	2	4	no	—
272	C₃×C₂²⋊C₄	—	2	4	no	—
273	C₃×C₂²⋊C₄	—	2	4	no	—
274	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
275	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
276	C₃×C₄²	—	2	2	no	—
277	C₃×C₄²	—	2	1	no	—
278	C₃×C₄²	—	2	4	no	—
279	C₃×C₄²	—	2	4	no	—
280	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
281	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
282	C₃×C₄²	C₂⁴	1	2	yes	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	C₂³×C₃	1	1	yes	characteristic
285	C₂×#41	C₂³×C₃	1	2	yes	—
286	C₂²×D₄	—	2	4	no	—
287	C₂²×D₄	C₂³×C₃	1	4	yes	—
288	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
289	C₂×D₈	C₂³×C₃	1	4	yes	—
290	C₂×M₁₆	C₂³×C₃	1	4	yes	—
291	C₂²×C₈	C₂³×C₃	1	4	yes	—
292	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
293	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
294	#127	—	2	4	no	—
295	#127	C₃×D₄	1	1	yes	characteristic
296	#127	C₂³×C₃	1	2	yes	—
297	#126	—	2	4	no	—
298	#126	—	2	4	no	—
299	#125	—	2	4	no	—
300	#125	—	2	1	no	—
301	#125	—	2	1	no	—
302	#125	C₂³×C₃	1	4	yes	—
303	#124	—	2	4	no	—
304	#124	—	2	4	no	—
305	#124	—	2	4	no	—
306	#124	—	2	2	no	—
307	#124	C₃×D₄	1	2	yes	—
308	#123	—	2	4	no	—
309	#123	—	2	4	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
312	#121	—	2	2	no	—
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	2	no	—
317	#121	—	2	4	no	—
318	#121	C₃×D₄	1	4	yes	—
319	#121	C₂³×C₃	1	4	yes	—
320	#121	C₂³×C₃	1	4	yes	—
321	#121	C₂³×C₃	1	4	yes	—
322	#121	C₂³×C₃	1	4	yes	—
323	#120	—	2	4	no	—
324	#120	—	2	4	no	—
325	#120	—	2	4	no	—
326	#120	—	2	4	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	C₂³×C₃	1	2	yes	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	C₂³×C₃	1	2	yes	—
335	C₄×D₄	C₂³×C₃	1	4	yes	—
336	C₄×D₄	C₂³×C₃	1	4	yes	—
337	#117	—	2	4	no	—
338	#117	—	2	4	no	—
339	#117	—	2	1	no	—
340	#117	C₂³×C₃	1	1	yes	characteristic
341	#117	C₂³×C₃	1	4	yes	—
342	#117	C₂³×C₃	1	4	yes	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
348	#107	C₂³×C₃	1	4	yes	—
349	#107	C₂³×C₃	1	4	yes	—
350	#107	C₂³×C₃	1	4	yes	—
351	#106	C₂³×C₃	1	4	yes	—
352	#106	C₂³×C₃	1	4	yes	—
353	#106	C₂³×C₃	1	4	yes	—
354	C₄⋊C₈	C₂³×C₃	1	2	yes	—
355	C₄⋊C₈	C₂³×C₃	1	2	yes	—
356	#103	C₂³×C₃	1	4	yes	—
357	#102	C₂³×C₃	1	4	yes	—
358	#102	C₂³×C₃	1	4	yes	—
359	#102	C₂³×C₃	1	4	yes	—
360	#102	C₂³×C₃	1	4	yes	—
361	#102	C₂³×C₃	1	4	yes	—
362	#102	C₂³×C₃	1	4	yes	—
363	#102	C₂³×C₃	1	4	yes	—
364	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
365	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
366	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
367	#97	C₂³×C₃	1	4	yes	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	—	2	4	no	—
370	C₂³×C₃	—	8	4	no	—
371	C₂³×C₃	—	8	4	no	—
372	C₂³×C₃	—	8	4	no	—
373	C₂³×C₃	C₂²×D₄	1	4	yes	—
374	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
375	C₃×Q₈	—	2	2	no	—
376	C₃×Q₈	—	4	2	no	—
377	C₃×Q₈	—	8	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	2	4	no	—
380	C₃×D₄	—	2	4	no	—
381	C₃×D₄	—	4	4	no	—
382	C₃×D₄	—	4	2	no	—
383	C₃×D₄	—	4	4	no	—
384	C₃×D₄	—	4	4	no	—
385	C₃×D₄	—	4	2	no	—
386	C₃×D₄	—	8	4	no	—
387	C₃×D₄	—	8	2	no	—
388	C₃×D₄	—	8	4	no	—
389	C₃×D₄	—	8	4	no	—
390	C₃×D₄	—	8	4	no	—
391	C₃×D₄	—	8	4	no	—
392	C₂×C₃×C₄	—	2	4	no	—
393	C₂×C₃×C₄	—	2	4	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	4	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	4	no	—
399	C₂×C₃×C₄	—	4	2	no	—
400	C₂×C₃×C₄	—	4	8	no	—
401	C₂×C₃×C₄	—	4	2	no	—
402	C₂×C₃×C₄	—	8	2	no	—
403	C₂×C₃×C₄	—	8	4	no	—
404	C₂×C₃×C₄	—	8	2	no	—
405	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
406	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
408	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
409	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
410	C₃×C₈	—	2	4	no	—
411	C₃×C₈	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	#41	—	4	2	no	—
416	#41	—	8	4	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
419	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	8	8	no	—
431	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
432	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
433	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
434	C₂×D₄	C₂⁴×C₃	1	4	yes	—
435	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
444	SD₁₆	—	4	4	no	—
445	D₈	—	4	4	no	—
446	M₁₆	—	4	4	no	—
447	C₂×C₈	—	4	4	no	—
448	C₂×C₈	C₂⁴×C₃	1	4	yes	—
449	C₂×C₈	C₂⁴×C₃	1	4	yes	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
458	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
459	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
460	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
472	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	4	no	—
477	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
478	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
479	C₄²	C₂⁴×C₃	1	2	yes	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	4	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	4	no	—
485	C₂²×C₃	—	4	4	no	—
486	C₂²×C₃	—	4	2	no	—
487	C₂²×C₃	—	4	4	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	4	no	—
490	C₂²×C₃	—	16	8	no	—
491	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
492	C₃×C₄	—	2	2	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	2	4	no	—
496	C₃×C₄	—	4	4	no	—
497	C₃×C₄	—	4	2	no	—
498	C₃×C₄	—	4	4	no	—
499	C₃×C₄	—	4	1	no	—
500	C₃×C₄	#585	1	2	yes	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	8	4	no	—
504	C₂³	—	8	4	no	—
505	C₂³	—	8	4	no	—
506	C₂³	C₂²×C₃×D₄	1	4	yes	—
507	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
508	Q₈	—	2	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	8	2	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	2	no	—
519	D₄	—	8	4	no	—
520	D₄	—	8	2	no	—
521	D₄	—	8	4	no	—
522	D₄	—	8	4	no	—
523	D₄	—	8	4	no	—
524	D₄	—	8	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	4	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
539	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
540	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
541	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
542	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
543	C₈	—	2	4	no	—
544	C₈	—	2	4	no	—
545	C₂×C₃	—	4	1	no	—
546	C₂×C₃	—	4	4	no	—
547	C₂×C₃	—	8	1	no	—
548	C₂×C₃	—	8	4	no	—
549	C₂×C₃	#3485	1	1	yes	characteristic
550	C₂×C₃	#3585	1	2	yes	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	16	8	no	—
562	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
563	C₄	—	2	1	no	—
564	C₄	—	2	4	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	4	no	—
571	C₄	C₃×#585	1	2	yes	—
572	C₃	#61797	1	1	yes	characteristic, direct product factor, Sylow
573	C₂	—	4	4	no	—
574	C₂	—	4	1	no	—
575	C₂	—	8	4	no	—
576	C₂	—	8	1	no	—
577	C₂	C₃×#3485	1	1	yes	characteristic
578	C₂	C₃×#3585	1	2	yes	—

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3549	C₂	semidirect
2. C₃×#3512	C₂	semidirect
3. C₃×#3348	C₂	semidirect
4. C₃×#3347	C₂	semidirect
5. C₃×#3318	C₂	semidirect
6. C₃×#3310	C₂	semidirect
7. C₃×#3234	C₂	semidirect
8. C₃×#3198	C₂	semidirect
9. C₃×#3115	C₂	semidirect
10. C₃×#3096	C₂	semidirect
11. C₃×#2980	C₂	semidirect
12. #61797	C₃	direct (N × H)
17. C₃×#553	C₂²	semidirect
18. C₃×#552	C₂²	semidirect
23. C₃×#537	C₂²	semidirect
29. C₂×C₃×#125	C₂²	semidirect
30. C₃×#520	C₂²	semidirect
31. C₃×C₄×#41	C₂²	semidirect
32. C₃×#501	C₂²	semidirect
34. C₃×#485	C₂²	semidirect
35. C₃×#482	C₂²	semidirect
36. C₃×#482	C₂²	semidirect
37. C₃×#482	C₂²	semidirect
38. C₃×#482	C₂²	semidirect
39. C₃×#481	C₂²	semidirect
40. C₃×#481	C₂²	semidirect
41. C₃×#480	C₂²	semidirect
42. C₃×#480	C₂²	semidirect
43. C₃×#478	C₂²	semidirect
44. C₃×#478	C₂²	semidirect
45. C₃×#475	C₂²	semidirect
46. C₃×#474	C₂²	semidirect
47. C₃×#469	C₂²	semidirect
48. C₃×#468	C₂²	semidirect
49. C₃×#466	C₂²	semidirect
50. C₃×#465	C₂²	semidirect
53. C₃×#450	C₂²	semidirect
54. C₃×#449	C₂²	semidirect
55. C₃×#447	C₂²	semidirect
56. C₃×#442	C₂²	semidirect
57. C₃×#440	C₂²	semidirect
58. C₃×#435	C₂²	semidirect
59. C₃×#435	C₂²	semidirect
60. C₃×#432	C₂²	semidirect
61. C₃×#428	C₂²	semidirect
62. C₃×#427	C₂²	semidirect
63. C₃×#418	C₂²	semidirect
64. C₂×C₃×#102	C₂²	semidirect
65. C₃×#408	C₂²	semidirect
66. #3549	C₂×C₃	semidirect
67. #3512	C₂×C₃	semidirect
68. #3348	C₂×C₃	semidirect
69. #3347	C₂×C₃	semidirect
70. #3318	C₂×C₃	semidirect
71. #3310	C₂×C₃	semidirect
72. #3234	C₂×C₃	semidirect
73. #3198	C₂×C₃	semidirect
74. #3115	C₂×C₃	semidirect
75. #3096	C₂×C₃	semidirect
76. #2980	C₂×C₃	semidirect
166. #553	C₂²×C₃	semidirect
167. #552	C₂²×C₃	semidirect
172. #537	C₂²×C₃	semidirect
178. C₂×#125	C₂²×C₃	semidirect
179. #520	C₂²×C₃	semidirect
180. C₄×#41	C₂²×C₃	semidirect
181. #501	C₂²×C₃	semidirect
183. #485	C₂²×C₃	semidirect
184. #482	C₂²×C₃	semidirect
185. #482	C₂²×C₃	semidirect
186. #482	C₂²×C₃	semidirect
187. #482	C₂²×C₃	semidirect
188. #481	C₂²×C₃	semidirect
189. #481	C₂²×C₃	semidirect
190. #480	C₂²×C₃	semidirect
191. #480	C₂²×C₃	semidirect
192. #478	C₂²×C₃	semidirect
193. #478	C₂²×C₃	semidirect
194. #475	C₂²×C₃	semidirect
195. #474	C₂²×C₃	semidirect
196. #469	C₂²×C₃	semidirect
197. #468	C₂²×C₃	semidirect
198. #466	C₂²×C₃	semidirect
199. #465	C₂²×C₃	semidirect
202. #450	C₂²×C₃	semidirect
203. #449	C₂²×C₃	semidirect
204. #447	C₂²×C₃	semidirect
205. #442	C₂²×C₃	semidirect
206. #440	C₂²×C₃	semidirect
207. #435	C₂²×C₃	semidirect
208. #435	C₂²×C₃	semidirect
209. #432	C₂²×C₃	semidirect
210. #428	C₂²×C₃	semidirect
211. #427	C₂²×C₃	semidirect
212. #418	C₂²×C₃	semidirect
213. C₂×#102	C₂²×C₃	semidirect
214. #408	C₂²×C₃	semidirect
572. C₃	#61797	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×#3549	2
C₃×#3512	2
C₃×#3348	2
C₃×#3347	2
C₃×#3318	2
C₃×#3310	2
C₃×#3234	2
C₃×#3198	2
C₃×#3115	2
C₃×#3096	2
C₃×#2980	2
#61797	3

Subgroups — C3×#61797 #10680404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61797 #10680404