Subgroups — C₃×#60429 #10679036

Order 768.

2730 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#577	C₂	1	2	yes	maximal, complemented
2	C₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3046	C₂	1	6	yes	maximal, complemented
5	C₃×#3042	C₂	1	6	yes	maximal, complemented
6	C₃×#3039	C₂	1	3	yes	maximal, complemented
7	C₃×#3036	C₂	1	3	yes	maximal, complemented
8	C₃×#3035	C₂	1	3	yes	maximal, complemented
9	C₂×C₃×#461	C₂	1	3	yes	maximal, complemented
10	C₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2898	C₂	1	2	yes	maximal, complemented
12	#60429	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₃×#577	—	2	16	no	—
16	C₂×C₃×#137	C₂²	1	6	yes	—
17	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	6	yes	—
18	C₂×C₃×#135	C₂²	1	6	yes	—
19	C₂²×C₃×SD₁₆	C₂²	1	6	yes	—
20	C₂×C₃×#131	C₂²	1	2	yes	—
21	C₃×D₄×Q₈	—	2	1	no	—
22	C₃×D₄×Q₈	—	2	1	no	—
23	C₃×#547	—	2	3	no	—
24	C₃×#547	—	2	3	no	—
25	C₃×#536	C₂²	1	6	yes	complemented
26	C₃×#532	C₂²	1	3	yes	complemented
27	C₂×C₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
28	C₃×#520	—	2	1	no	—
29	C₃×#520	C₂²	1	3	yes	—
30	C₃×#520	C₂²	1	1	yes	characteristic
31	C₃×#518	—	2	3	no	—
32	C₃×#518	C₂²	1	3	yes	—
33	C₃×C₄×#41	—	2	1	no	—
34	C₃×C₄×#41	C₂²	1	3	yes	—
35	C₃×C₄×#41	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	—	2	3	no	—
37	C₂×C₃×C₄×D₄	C₂²	1	3	yes	—
38	C₃×#464	C₂²	1	6	yes	complemented
39	C₃×#463	C₂²	1	6	yes	complemented
40	C₃×#463	C₂²	1	12	yes	complemented
41	C₃×#462	C₂²	1	3	yes	complemented
42	C₃×#462	C₂²	1	6	yes	complemented
43	C₃×#461	C₂²	1	3	yes	complemented
44	C₃×#461	C₂²	1	6	yes	complemented
45	C₃×#461	C₂²	1	12	yes	complemented
46	C₃×#461	C₂²	1	6	yes	complemented
47	C₃×#460	C₂²	1	1	yes	characteristic, complemented
48	C₃×#459	C₂²	1	3	yes	complemented
49	C₃×#424	C₂²	1	6	yes	complemented
50	C₃×#423	C₂²	1	3	yes	complemented
51	C₂×C₃×C₄⋊C₈	C₂²	1	3	yes	complemented
52	C₃×#419	C₂²	1	6	yes	complemented
53	C₃×#417	C₂²	1	6	yes	complemented
54	C₃×#416	C₂²	1	6	yes	complemented
55	C₂×C₃×#103	C₂²	1	6	yes	complemented
56	C₂×#577	C₂×C₃	1	2	yes	complemented
57	#3499	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
59	#3046	C₂×C₃	1	6	yes	complemented
60	#3042	C₂×C₃	1	6	yes	complemented
61	#3039	C₂×C₃	1	3	yes	complemented
62	#3036	C₂×C₃	1	3	yes	complemented
63	#3035	C₂×C₃	1	3	yes	complemented
64	C₂×#461	C₂×C₃	1	3	yes	complemented
65	#2906	C₂×C₃	1	1	yes	characteristic, complemented
66	#2898	C₂×C₃	1	2	yes	complemented
67	C₃×2₋¹⁺⁴	—	2	8	no	—
68	C₃×2₋¹⁺⁴	—	2	8	no	—
69	C₃×H(5,𝔽₂)	—	2	4	no	—
70	C₃×H(5,𝔽₂)	D₄	1	8	yes	complemented
71	C₂×C₃×#41	—	2	1	no	—
72	C₂×C₃×#41	—	2	6	no	—
73	C₂×C₃×#41	C₂³	1	6	yes	—
74	C₂×C₃×#41	C₂³	1	3	yes	—
75	C₂×C₃×#41	C₂³	1	1	yes	characteristic
76	C₂²×C₃×Q₈	—	2	2	no	—
77	C₂²×C₃×Q₈	C₂³	1	6	yes	—
78	C₂²×C₃×D₄	—	2	3	no	—
79	C₂²×C₃×D₄	C₂³	1	3	yes	—
80	C₂³×C₃×C₄	—	2	3	no	—
81	C₃×#137	—	2	24	no	—
82	C₃×AGL(1,ℤ/8)	—	2	24	no	—
83	C₃×#135	—	2	24	no	—
84	C₂×C₃×Q₁₆	C₂³	1	6	yes	—
85	C₂×C₃×SD₁₆	—	2	24	no	—
86	C₂×C₃×SD₁₆	C₂³	1	6	yes	—
87	C₂×C₃×SD₁₆	C₂³	1	12	yes	—
88	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
89	C₂×C₃×D₈	C₂³	1	6	yes	—
90	C₃×#131	—	2	8	no	—
91	C₂×C₃×M₁₆	C₂³	1	6	yes	—
92	C₂²×C₃×C₈	C₂³	1	6	yes	—
93	C₃×C₄⋊Q₈	—	2	3	no	—
94	C₃×C₄⋊Q₈	—	2	3	no	—
95	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
96	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
97	C₃×#127	C₂³	1	1	yes	characteristic
98	C₃×#124	C₂³	1	6	yes	—
99	C₃×#123	—	2	12	no	—
100	C₃×C₂²⋊Q₈	—	2	6	no	—
101	C₃×C₂²⋊Q₈	—	2	6	no	—
102	C₃×#121	—	2	3	no	—
103	C₃×#121	—	2	3	no	—
104	C₃×C₄×Q₈	—	2	1	no	—
105	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
106	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
107	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
108	C₃×C₄×Q₈	C₂³	1	3	yes	—
109	C₃×C₄×D₄	—	2	3	no	—
110	C₃×C₄×D₄	—	2	3	no	—
111	C₃×C₄×D₄	—	2	3	no	—
112	C₃×C₄×D₄	—	2	3	no	—
113	C₃×C₄×D₄	—	2	3	no	—
114	C₃×C₄×D₄	—	2	6	no	—
115	C₃×C₄×D₄	—	2	3	no	—
116	C₃×C₄×D₄	—	2	3	no	—
117	C₃×C₄×D₄	—	2	3	no	—
118	C₃×C₄×D₄	—	2	3	no	—
119	C₃×C₄×D₄	D₄	1	3	yes	—
120	C₃×C₄×D₄	D₄	1	3	yes	—
121	C₃×C₄×D₄	C₂³	1	3	yes	—
122	C₃×C₄×D₄	C₂³	1	6	yes	—
123	C₃×C₄×D₄	C₂³	1	3	yes	—
124	C₃×#117	—	2	3	no	—
125	C₃×#117	—	2	3	no	—
126	C₃×#117	C₂³	1	3	yes	—
127	C₃×#117	C₂³	1	3	yes	—
128	C₂×C₃×C₄⋊C₄	—	2	3	no	—
129	C₂×C₃×C₄⋊C₄	—	2	3	no	—
130	C₂×C₃×C₄⋊C₄	—	2	3	no	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
132	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
133	C₂×C₃×C₂²⋊C₄	—	2	6	no	—
134	C₂×C₃×C₄²	—	2	3	no	—
135	C₂×C₃×C₄²	C₂³	1	3	yes	—
136	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
137	C₃×C₄⋊C₈	C₂³	1	3	yes	—
138	C₃×C₄⋊C₈	C₂³	1	6	yes	—
139	C₃×C₄⋊C₈	C₂³	1	6	yes	—
140	C₃×#103	C₂³	1	6	yes	—
141	C₃×#103	C₂³	1	12	yes	—
142	C₃×#103	C₂³	1	6	yes	—
143	C₃×#102	C₂³	1	2	yes	—
144	C₃×#102	C₂³	1	6	yes	—
145	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	—
146	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
147	#577	—	2	16	no	—
148	C₂×#137	C₂²×C₃	1	6	yes	—
149	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	6	yes	—
150	C₂×#135	C₂²×C₃	1	6	yes	—
151	C₂²×SD₁₆	C₂²×C₃	1	6	yes	—
152	C₂×#131	C₂²×C₃	1	2	yes	—
153	D₄×Q₈	—	2	1	no	—
154	D₄×Q₈	—	2	1	no	—
155	#547	—	2	3	no	—
156	#547	—	2	3	no	—
157	#536	C₂²×C₃	1	6	yes	complemented
158	#532	C₂²×C₃	1	3	yes	complemented
159	C₂×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
160	#520	—	2	1	no	—
161	#520	C₂²×C₃	1	3	yes	—
162	#520	C₂²×C₃	1	1	yes	characteristic
163	#518	—	2	3	no	—
164	#518	C₂²×C₃	1	3	yes	—
165	C₄×#41	—	2	1	no	—
166	C₄×#41	C₂²×C₃	1	3	yes	—
167	C₄×#41	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₄×D₄	—	2	3	no	—
169	C₂×C₄×D₄	C₂²×C₃	1	3	yes	—
170	#464	C₂²×C₃	1	6	yes	complemented
171	#463	C₂²×C₃	1	6	yes	complemented
172	#463	C₂²×C₃	1	12	yes	complemented
173	#462	C₂²×C₃	1	3	yes	complemented
174	#462	C₂²×C₃	1	6	yes	complemented
175	#461	C₂²×C₃	1	3	yes	complemented
176	#461	C₂²×C₃	1	6	yes	complemented
177	#461	C₂²×C₃	1	12	yes	complemented
178	#461	C₂²×C₃	1	6	yes	complemented
179	#460	C₂²×C₃	1	1	yes	characteristic, complemented
180	#459	C₂²×C₃	1	3	yes	complemented
181	#424	C₂²×C₃	1	6	yes	complemented
182	#423	C₂²×C₃	1	3	yes	complemented
183	C₂×C₄⋊C₈	C₂²×C₃	1	3	yes	complemented
184	#419	C₂²×C₃	1	6	yes	complemented
185	#417	C₂²×C₃	1	6	yes	complemented
186	#416	C₂²×C₃	1	6	yes	complemented
187	C₂×#103	C₂²×C₃	1	6	yes	complemented
188	C₂⁴×C₃	—	2	3	no	—
189	C₃×#41	—	2	8	no	—
190	C₃×#41	—	2	6	no	—
191	C₃×#41	—	2	12	no	—
192	C₃×#41	—	2	12	no	—
193	C₃×#41	—	4	24	no	—
194	C₃×#41	C₂×D₄	1	12	yes	—
195	C₃×#41	C₂×D₄	1	4	yes	—
196	C₃×#41	#41	1	4	yes	—
197	C₂×C₃×Q₈	—	2	6	no	—
198	C₂×C₃×Q₈	—	2	12	no	—
199	C₂×C₃×Q₈	—	2	12	no	—
200	C₂×C₃×Q₈	—	4	8	no	—
201	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
203	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
204	C₂×C₃×D₄	—	2	3	no	—
205	C₂×C₃×D₄	—	2	24	no	—
206	C₂×C₃×D₄	—	2	6	no	—
207	C₂×C₃×D₄	—	2	3	no	—
208	C₂×C₃×D₄	—	2	1	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	6	no	—
211	C₂×C₃×D₄	C₂×D₄	1	12	yes	—
212	C₂×C₃×D₄	C₂×D₄	1	3	yes	—
213	C₂×C₃×D₄	C₂⁴	1	2	yes	—
214	C₂×C₃×D₄	C₂⁴	1	3	yes	—
215	C₂²×C₃×C₄	—	2	3	no	—
216	C₂²×C₃×C₄	—	2	6	no	—
217	C₂²×C₃×C₄	—	2	3	no	—
218	C₂²×C₃×C₄	—	2	3	no	—
219	C₂²×C₃×C₄	—	2	6	no	—
220	C₂²×C₃×C₄	—	2	3	no	—
221	C₂²×C₃×C₄	—	2	6	no	—
222	C₂²×C₃×C₄	—	8	6	no	—
223	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
224	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
225	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
226	C₃×Q₁₆	—	2	12	no	—
227	C₃×SD₁₆	—	2	4	no	—
228	C₃×SD₁₆	—	2	12	no	—
229	C₃×SD₁₆	—	2	24	no	—
230	C₃×D₈	—	2	12	no	—
231	C₃×M₁₆	—	2	12	no	—
232	C₂×C₃×C₈	—	2	12	no	—
233	C₂×C₃×C₈	C₂⁴	1	2	yes	—
234	C₂×C₃×C₈	C₂⁴	1	6	yes	—
235	C₃×C₄⋊C₄	—	2	3	no	—
236	C₃×C₄⋊C₄	—	2	3	no	—
237	C₃×C₄⋊C₄	—	2	3	no	—
238	C₃×C₄⋊C₄	—	2	3	no	—
239	C₃×C₄⋊C₄	—	2	6	no	—
240	C₃×C₄⋊C₄	—	2	6	no	—
241	C₃×C₄⋊C₄	—	2	1	no	—
242	C₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
243	C₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
244	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
245	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
246	C₃×C₂²⋊C₄	—	2	3	no	—
247	C₃×C₂²⋊C₄	—	2	3	no	—
248	C₃×C₂²⋊C₄	—	2	6	no	—
249	C₃×C₂²⋊C₄	—	2	3	no	—
250	C₃×C₂²⋊C₄	—	2	6	no	—
251	C₃×C₂²⋊C₄	—	2	6	no	—
252	C₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	—	2	3	no	—
255	C₃×C₄²	—	2	3	no	—
256	C₃×C₄²	C₂×D₄	1	3	yes	—
257	C₃×C₄²	C₂×D₄	1	3	yes	—
258	C₃×C₄²	C₂⁴	1	1	yes	characteristic
259	C₃×C₄²	C₂⁴	1	3	yes	—
260	2₋¹⁺⁴	—	2	8	no	—
261	2₋¹⁺⁴	—	2	8	no	—
262	H(5,𝔽₂)	—	2	4	no	—
263	H(5,𝔽₂)	C₃×D₄	1	8	yes	complemented
264	C₂×#41	—	2	1	no	—
265	C₂×#41	—	2	6	no	—
266	C₂×#41	C₂³×C₃	1	6	yes	—
267	C₂×#41	C₂³×C₃	1	3	yes	—
268	C₂×#41	C₂³×C₃	1	1	yes	characteristic
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	C₂³×C₃	1	6	yes	—
271	C₂²×D₄	—	2	3	no	—
272	C₂²×D₄	C₂³×C₃	1	3	yes	—
273	C₂³×C₄	—	2	3	no	—
274	#137	—	2	24	no	—
275	AGL(1,ℤ/8)	—	2	24	no	—
276	#135	—	2	24	no	—
277	C₂×Q₁₆	C₂³×C₃	1	6	yes	—
278	C₂×SD₁₆	—	2	24	no	—
279	C₂×SD₁₆	C₂³×C₃	1	6	yes	—
280	C₂×SD₁₆	C₂³×C₃	1	12	yes	—
281	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
282	C₂×D₈	C₂³×C₃	1	6	yes	—
283	#131	—	2	8	no	—
284	C₂×M₁₆	C₂³×C₃	1	6	yes	—
285	C₂²×C₈	C₂³×C₃	1	6	yes	—
286	C₄⋊Q₈	—	2	3	no	—
287	C₄⋊Q₈	—	2	3	no	—
288	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
289	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
290	#127	C₂³×C₃	1	1	yes	characteristic
291	#124	C₂³×C₃	1	6	yes	—
292	#123	—	2	12	no	—
293	C₂²⋊Q₈	—	2	6	no	—
294	C₂²⋊Q₈	—	2	6	no	—
295	#121	—	2	3	no	—
296	#121	—	2	3	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
299	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
300	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
301	C₄×Q₈	C₂³×C₃	1	3	yes	—
302	C₄×D₄	—	2	3	no	—
303	C₄×D₄	—	2	3	no	—
304	C₄×D₄	—	2	3	no	—
305	C₄×D₄	—	2	3	no	—
306	C₄×D₄	—	2	3	no	—
307	C₄×D₄	—	2	6	no	—
308	C₄×D₄	—	2	3	no	—
309	C₄×D₄	—	2	3	no	—
310	C₄×D₄	—	2	3	no	—
311	C₄×D₄	—	2	3	no	—
312	C₄×D₄	C₃×D₄	1	3	yes	—
313	C₄×D₄	C₃×D₄	1	3	yes	—
314	C₄×D₄	C₂³×C₃	1	3	yes	—
315	C₄×D₄	C₂³×C₃	1	6	yes	—
316	C₄×D₄	C₂³×C₃	1	3	yes	—
317	#117	—	2	3	no	—
318	#117	—	2	3	no	—
319	#117	C₂³×C₃	1	3	yes	—
320	#117	C₂³×C₃	1	3	yes	—
321	C₂×C₄⋊C₄	—	2	3	no	—
322	C₂×C₄⋊C₄	—	2	3	no	—
323	C₂×C₄⋊C₄	—	2	3	no	—
324	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
325	C₂×C₂²⋊C₄	—	2	3	no	—
326	C₂×C₂²⋊C₄	—	2	6	no	—
327	C₂×C₄²	—	2	3	no	—
328	C₂×C₄²	C₂³×C₃	1	3	yes	—
329	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₃	1	3	yes	—
331	C₄⋊C₈	C₂³×C₃	1	6	yes	—
332	C₄⋊C₈	C₂³×C₃	1	6	yes	—
333	#103	C₂³×C₃	1	6	yes	—
334	#103	C₂³×C₃	1	12	yes	—
335	#103	C₂³×C₃	1	6	yes	—
336	#102	C₂³×C₃	1	2	yes	—
337	#102	C₂³×C₃	1	6	yes	—
338	C₂³×C₃	—	2	3	no	—
339	C₂³×C₃	—	2	12	no	—
340	C₂³×C₃	—	2	2	no	—
341	C₂³×C₃	—	8	3	no	—
342	C₂³×C₃	—	8	3	no	—
343	C₂³×C₃	C₂²×D₄	1	3	yes	—
344	C₃×Q₈	—	2	1	no	—
345	C₃×Q₈	—	2	6	no	—
346	C₃×Q₈	—	2	6	no	—
347	C₃×Q₈	—	4	12	no	—
348	C₃×Q₈	#121	1	4	yes	—
349	C₃×Q₈	C₂²×D₄	1	2	yes	—
350	C₃×D₄	—	2	12	no	—
351	C₃×D₄	—	2	12	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	3	no	—
354	C₃×D₄	—	2	2	no	—
355	C₃×D₄	—	4	2	no	—
356	C₃×D₄	—	4	12	no	—
357	C₃×D₄	—	4	2	no	—
358	C₃×D₄	#121	1	12	yes	—
359	C₃×D₄	C₂²×D₄	1	6	yes	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	12	no	—
362	C₂×C₃×C₄	—	2	6	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	3	no	—
365	C₂×C₃×C₄	—	2	6	no	—
366	C₂×C₃×C₄	—	4	3	no	—
367	C₂×C₃×C₄	—	4	12	no	—
368	C₂×C₃×C₄	—	4	12	no	—
369	C₂×C₃×C₄	—	4	6	no	—
370	C₂×C₃×C₄	—	8	3	no	—
371	C₂×C₃×C₄	—	8	6	no	—
372	C₂×C₃×C₄	—	8	3	no	—
373	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
374	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
376	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
377	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
378	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×#41	1	6	yes	—
380	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
381	C₃×C₈	—	2	2	no	—
382	C₃×C₈	—	2	6	no	—
383	C₂⁴	—	2	3	no	—
384	#41	—	2	8	no	—
385	#41	—	2	6	no	—
386	#41	—	2	12	no	—
387	#41	—	2	12	no	—
388	#41	—	4	24	no	—
389	#41	C₂×C₃×D₄	1	12	yes	—
390	#41	C₂×C₃×D₄	1	4	yes	—
391	#41	C₃×#41	1	4	yes	—
392	C₂×Q₈	—	2	6	no	—
393	C₂×Q₈	—	2	12	no	—
394	C₂×Q₈	—	2	12	no	—
395	C₂×Q₈	—	4	8	no	—
396	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
397	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
398	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
399	C₂×D₄	—	2	3	no	—
400	C₂×D₄	—	2	24	no	—
401	C₂×D₄	—	2	6	no	—
402	C₂×D₄	—	2	3	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	6	no	—
406	C₂×D₄	C₂×C₃×D₄	1	12	yes	—
407	C₂×D₄	C₂×C₃×D₄	1	3	yes	—
408	C₂×D₄	C₂⁴×C₃	1	2	yes	—
409	C₂×D₄	C₂⁴×C₃	1	3	yes	—
410	C₂²×C₄	—	2	3	no	—
411	C₂²×C₄	—	2	6	no	—
412	C₂²×C₄	—	2	3	no	—
413	C₂²×C₄	—	2	3	no	—
414	C₂²×C₄	—	2	6	no	—
415	C₂²×C₄	—	2	3	no	—
416	C₂²×C₄	—	2	6	no	—
417	C₂²×C₄	—	8	6	no	—
418	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
419	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
420	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
421	Q₁₆	—	2	12	no	—
422	SD₁₆	—	2	4	no	—
423	SD₁₆	—	2	12	no	—
424	SD₁₆	—	2	24	no	—
425	D₈	—	2	12	no	—
426	M₁₆	—	2	12	no	—
427	C₂×C₈	—	2	12	no	—
428	C₂×C₈	C₂⁴×C₃	1	2	yes	—
429	C₂×C₈	C₂⁴×C₃	1	6	yes	—
430	C₄⋊C₄	—	2	3	no	—
431	C₄⋊C₄	—	2	3	no	—
432	C₄⋊C₄	—	2	3	no	—
433	C₄⋊C₄	—	2	3	no	—
434	C₄⋊C₄	—	2	6	no	—
435	C₄⋊C₄	—	2	6	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂×C₃×D₄	1	3	yes	—
438	C₄⋊C₄	C₂×C₃×D₄	1	3	yes	—
439	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
440	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
441	C₂²⋊C₄	—	2	3	no	—
442	C₂²⋊C₄	—	2	3	no	—
443	C₂²⋊C₄	—	2	6	no	—
444	C₂²⋊C₄	—	2	3	no	—
445	C₂²⋊C₄	—	2	6	no	—
446	C₂²⋊C₄	—	2	6	no	—
447	C₂²⋊C₄	C₂×C₃×D₄	1	6	yes	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	3	no	—
450	C₄²	—	2	3	no	—
451	C₄²	C₂×C₃×D₄	1	3	yes	—
452	C₄²	C₂×C₃×D₄	1	3	yes	—
453	C₄²	C₂⁴×C₃	1	1	yes	characteristic
454	C₄²	C₂⁴×C₃	1	3	yes	—
455	C₂²×C₃	—	2	3	no	—
456	C₂²×C₃	—	2	3	no	—
457	C₂²×C₃	—	2	6	no	—
458	C₂²×C₃	—	4	3	no	—
459	C₂²×C₃	—	4	3	no	—
460	C₂²×C₃	—	4	2	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	4	2	no	—
463	C₂²×C₃	—	8	12	no	—
464	C₂²×C₃	C₂×#121	1	6	yes	—
465	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
466	C₃×C₄	—	2	1	no	—
467	C₃×C₄	—	2	3	no	—
468	C₃×C₄	—	2	2	no	—
469	C₃×C₄	—	2	3	no	—
470	C₃×C₄	—	4	1	no	—
471	C₃×C₄	—	4	6	no	—
472	C₃×C₄	—	4	3	no	—
473	C₃×C₄	C₂×#121	1	6	yes	—
474	C₃×C₄	#577	1	2	yes	complemented
475	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
476	C₃×C₄	C₂²×#41	1	1	yes	characteristic
477	C₂³	—	2	3	no	—
478	C₂³	—	2	12	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	8	3	no	—
481	C₂³	—	8	3	no	—
482	C₂³	C₂²×C₃×D₄	1	3	yes	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	6	no	—
485	Q₈	—	2	6	no	—
486	Q₈	—	4	12	no	—
487	Q₈	C₃×#121	1	4	yes	—
488	Q₈	C₂²×C₃×D₄	1	2	yes	—
489	D₄	—	2	12	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	3	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	12	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	12	no	—
496	D₄	—	4	2	no	—
497	D₄	C₃×#121	1	12	yes	—
498	D₄	C₂²×C₃×D₄	1	6	yes	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	6	no	—
501	C₂×C₄	—	2	12	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	3	no	—
504	C₂×C₄	—	2	6	no	—
505	C₂×C₄	—	4	3	no	—
506	C₂×C₄	—	4	12	no	—
507	C₂×C₄	—	4	6	no	—
508	C₂×C₄	—	4	12	no	—
509	C₂×C₄	—	8	6	no	—
510	C₂×C₄	—	8	3	no	—
511	C₂×C₄	—	8	3	no	—
512	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
513	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
515	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×C₃×D₄	1	6	yes	—
517	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
518	C₂×C₄	C₂×C₃×#41	1	6	yes	—
519	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	6	no	—
522	C₂×C₃	—	2	6	no	—
523	C₂×C₃	—	4	6	no	—
524	C₂×C₃	—	8	2	no	—
525	C₂×C₃	C₂²×#121	1	1	yes	characteristic
526	C₂×C₃	C₂×#577	1	1	yes	characteristic
527	C₂×C₃	#3586	1	1	yes	characteristic
528	C₂²	—	2	3	no	—
529	C₂²	—	2	3	no	—
530	C₂²	—	2	6	no	—
531	C₂²	—	4	3	no	—
532	C₂²	—	4	3	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	12	no	—
537	C₂²	C₂×C₃×#121	1	6	yes	—
538	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	3	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	3	no	—
543	C₄	—	4	6	no	—
544	C₄	—	4	3	no	—
545	C₄	—	4	1	no	—
546	C₄	C₂×C₃×#121	1	6	yes	—
547	C₄	C₃×#577	1	2	yes	complemented
548	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
549	C₄	C₂²×C₃×#41	1	1	yes	characteristic
550	C₃	#60429	1	1	yes	characteristic, direct product factor, Sylow
551	C₂	—	2	6	no	—
552	C₂	—	4	6	no	—
553	C₂	—	8	2	no	—
554	C₂	C₂²×C₃×#121	1	1	yes	characteristic
555	C₂	C₂×C₃×#577	1	1	yes	characteristic
556	C₂	C₃×#3586	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. C₂×C₃×#577	C₂	semidirect
2. C₃×#3499	C₂	semidirect
3. C₃×C₄×H(5,𝔽₂)	C₂	semidirect
4. C₃×#3046	C₂	semidirect
5. C₃×#3042	C₂	semidirect
6. C₃×#3039	C₂	semidirect
7. C₃×#3036	C₂	semidirect
8. C₃×#3035	C₂	semidirect
9. C₂×C₃×#461	C₂	semidirect
10. C₃×#2906	C₂	semidirect
11. C₃×#2898	C₂	semidirect
12. #60429	C₃	direct (N × H)
25. C₃×#536	C₂²	semidirect
26. C₃×#532	C₂²	semidirect
27. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
38. C₃×#464	C₂²	semidirect
39. C₃×#463	C₂²	semidirect
40. C₃×#463	C₂²	semidirect
41. C₃×#462	C₂²	semidirect
42. C₃×#462	C₂²	semidirect
43. C₃×#461	C₂²	semidirect
44. C₃×#461	C₂²	semidirect
45. C₃×#461	C₂²	semidirect
46. C₃×#461	C₂²	semidirect
47. C₃×#460	C₂²	semidirect
48. C₃×#459	C₂²	semidirect
49. C₃×#424	C₂²	semidirect
50. C₃×#423	C₂²	semidirect
51. C₂×C₃×C₄⋊C₈	C₂²	semidirect
52. C₃×#419	C₂²	semidirect
53. C₃×#417	C₂²	semidirect
54. C₃×#416	C₂²	semidirect
55. C₂×C₃×#103	C₂²	semidirect
56. C₂×#577	C₂×C₃	semidirect
57. #3499	C₂×C₃	semidirect
58. C₄×H(5,𝔽₂)	C₂×C₃	semidirect
59. #3046	C₂×C₃	semidirect
60. #3042	C₂×C₃	semidirect
61. #3039	C₂×C₃	semidirect
62. #3036	C₂×C₃	semidirect
63. #3035	C₂×C₃	semidirect
64. C₂×#461	C₂×C₃	semidirect
65. #2906	C₂×C₃	semidirect
66. #2898	C₂×C₃	semidirect
70. C₃×H(5,𝔽₂)	D₄	semidirect
157. #536	C₂²×C₃	semidirect
158. #532	C₂²×C₃	semidirect
159. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
170. #464	C₂²×C₃	semidirect
171. #463	C₂²×C₃	semidirect
172. #463	C₂²×C₃	semidirect
173. #462	C₂²×C₃	semidirect
174. #462	C₂²×C₃	semidirect
175. #461	C₂²×C₃	semidirect
176. #461	C₂²×C₃	semidirect
177. #461	C₂²×C₃	semidirect
178. #461	C₂²×C₃	semidirect
179. #460	C₂²×C₃	semidirect
180. #459	C₂²×C₃	semidirect
181. #424	C₂²×C₃	semidirect
182. #423	C₂²×C₃	semidirect
183. C₂×C₄⋊C₈	C₂²×C₃	semidirect
184. #419	C₂²×C₃	semidirect
185. #417	C₂²×C₃	semidirect
186. #416	C₂²×C₃	semidirect
187. C₂×#103	C₂²×C₃	semidirect
263. H(5,𝔽₂)	C₃×D₄	semidirect
474. C₃×C₄	#577	semidirect
547. C₄	C₃×#577	semidirect
550. C₃	#60429	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#577	2
C₃×#3499	2
C₃×C₄×H(5,𝔽₂)	2
C₃×#3046	2
C₃×#3042	2
C₃×#3039	2
C₃×#3036	2
C₃×#3035	2
C₂×C₃×#461	2
C₃×#2906	2
C₃×#2898	2
#60429	3

Subgroups — C3×#60429 #10679036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60429 #10679036