Subgroups — C₂×C₁₃×#3366 #15747643

Order 3328.

2198 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3366	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#490	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	C₂²	1	8	yes	complemented
18	C₁₃×#550	—	2	4	no	—
19	C₁₃×#550	C₂²	1	8	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#127	C₂²	1	2	yes	—
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×#121	—	2	1	no	—
27	C₂×C₁₃×#121	—	2	2	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₁₃×#490	C₂²	1	16	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	complemented
36	C₁₃×#478	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#459	C₂²	1	16	yes	complemented
39	C₁₃×#459	C₂²	1	8	yes	complemented
40	C₁₃×#446	C₂²	1	8	yes	complemented
41	C₁₃×#442	C₂²	1	16	yes	complemented
42	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#106	C₂²	1	2	yes	—
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₁₃×#102	C₂²	1	2	yes	—
48	C₂×C₁₃×#102	C₂²	1	2	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#41	—	2	8	no	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	2	no	—
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	2	no	—
70	C₂×C₁₃×D₈	—	2	4	no	—
71	C₂×C₁₃×D₈	—	2	8	no	—
72	C₂×C₁₃×D₈	C₂³	1	4	yes	—
73	C₂×C₁₃×D₈	C₂³	1	8	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×#127	—	2	4	no	—
80	C₁₃×#127	—	2	2	no	—
81	C₁₃×#127	C₂³	1	4	yes	—
82	C₁₃×#127	C₂³	1	8	yes	—
83	C₁₃×#125	—	2	4	no	—
84	C₁₃×#125	C₂³	1	8	yes	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	—	2	16	no	—
87	C₁₃×#121	—	2	8	no	—
88	C₁₃×#121	—	2	16	no	—
89	C₄×Q₈×C₁₃	D₄	1	4	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	—	2	4	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	C₂³	1	4	yes	—
96	C₄×D₄×C₁₃	C₂³	1	4	yes	—
97	C₄×D₄×C₁₃	C₂³	1	8	yes	—
98	C₄×D₄×C₁₃	C₂³	1	8	yes	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
103	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
114	C₁₃×#107	C₂³	1	4	yes	—
115	C₁₃×#106	C₂³	1	8	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
118	C₁₃×#102	C₂³	1	4	yes	—
119	C₁₃×#102	C₂³	1	4	yes	—
120	C₁₃×#102	C₂³	1	8	yes	—
121	C₁₃×#102	C₂³	1	8	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₁₃×#102	C₂³	1	8	yes	—
124	C₁₃×#97	C₂³	1	8	yes	—
125	C₄×C₈×C₁₃	C₂³	1	4	yes	—
126	C₂×#3366	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	—	2	2	no	—
129	C₂⁴×C₁₃	—	2	1	no	—
130	C₁₃×#41	—	4	32	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	8	2	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	4	8	no	—
148	C₂×D₄×C₁₃	—	4	4	no	—
149	C₂×D₄×C₁₃	—	8	4	no	—
150	C₂×D₄×C₁₃	—	8	2	no	—
151	C₂×D₄×C₁₃	#41	1	4	yes	complemented
152	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	4	8	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	—	8	4	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₁₃×D₈	—	2	8	no	—
172	C₁₃×D₈	—	2	16	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	4	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
177	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
178	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	8	no	—
194	C₄²×C₁₃	C₂×D₄	1	4	yes	—
195	C₄²×C₁₃	C₂×D₄	1	2	yes	—
196	C₄²×C₁₃	C₂⁴	1	2	yes	—
197	C₄²×C₁₃	C₂⁴	1	4	yes	—
198	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3366	C₂×C₁₃	1	16	yes	direct product factor
201	C₂×#490	C₂×C₁₃	1	2	yes	complemented
202	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#478	C₂×C₁₃	1	2	yes	complemented
204	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#459	C₂×C₁₃	1	2	yes	complemented
207	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#442	C₂×C₁₃	1	2	yes	complemented
209	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	2	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	4	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	4	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₃	—	2	8	no	—
224	Q₈×C₁₃	—	8	4	no	—
225	D₄×C₁₃	—	2	4	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	4	16	no	—
232	D₄×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	8	no	—
235	D₄×C₁₃	—	8	8	no	—
236	D₄×C₁₃	—	8	4	no	—
237	D₄×C₁₃	C₂×#41	1	4	yes	complemented
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	4	16	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	4	8	no	—
249	C₂×C₄×C₁₃	—	4	8	no	—
250	C₂×C₄×C₁₃	—	8	8	no	—
251	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
258	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
259	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
260	C₈×C₁₃	—	2	2	no	—
261	C₈×C₁₃	—	2	4	no	—
262	C₈×C₁₃	—	2	2	no	—
263	C₂²×#41	—	2	1	no	—
264	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
266	#554	—	2	4	no	—
267	#554	C₂²×C₁₃	1	8	yes	complemented
268	#550	—	2	4	no	—
269	#550	C₂²×C₁₃	1	8	yes	complemented
270	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#127	C₂²×C₁₃	1	2	yes	—
273	C₂×#125	C₂²×C₁₃	1	2	yes	—
274	C₂×C₂²⋊Q₈	—	2	1	no	—
275	C₂×C₂²⋊Q₈	—	2	2	no	—
276	C₂×#121	—	2	1	no	—
277	C₂×#121	—	2	2	no	—
278	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
283	C₂²×C₄⋊C₄	—	2	1	no	—
284	#490	C₂²×C₁₃	1	16	yes	complemented
285	#486	C₂²×C₁₃	1	8	yes	complemented
286	#478	C₂²×C₁₃	1	16	yes	complemented
287	#476	C₂²×C₁₃	1	8	yes	complemented
288	#459	C₂²×C₁₃	1	16	yes	complemented
289	#459	C₂²×C₁₃	1	8	yes	complemented
290	#446	C₂²×C₁₃	1	8	yes	complemented
291	#442	C₂²×C₁₃	1	16	yes	complemented
292	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#106	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
296	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#102	C₂²×C₁₃	1	2	yes	—
298	C₂×#102	C₂²×C₁₃	1	2	yes	—
299	C₂×#102	C₂²×C₁₃	1	2	yes	—
300	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#102	C₂²×C₁₃	1	2	yes	—
302	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#97	C₂²×C₁₃	1	2	yes	—
304	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	4	8	no	—
307	C₂²×C₁₃	—	4	2	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	4	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	8	8	no	—
316	C₂²×C₁₃	—	8	4	no	—
317	C₂²×C₁₃	#548	1	2	yes	—
318	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
319	C₂²×C₁₃	#576	1	2	yes	—
320	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	2	4	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	2	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	#548	1	2	yes	—
328	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
329	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
330	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×#41	—	2	8	no	—
332	C₂×#41	—	4	8	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	—	2	2	no	—
346	C₂×D₈	—	2	4	no	—
347	C₂×D₈	—	2	8	no	—
348	C₂×D₈	C₂³×C₁₃	1	4	yes	—
349	C₂×D₈	C₂³×C₁₃	1	8	yes	—
350	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₄⋊Q₈	—	2	2	no	—
354	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
355	#127	—	2	4	no	—
356	#127	—	2	2	no	—
357	#127	C₂³×C₁₃	1	4	yes	—
358	#127	C₂³×C₁₃	1	8	yes	—
359	#125	—	2	4	no	—
360	#125	C₂³×C₁₃	1	8	yes	—
361	C₂²⋊Q₈	—	2	8	no	—
362	C₂²⋊Q₈	—	2	16	no	—
363	#121	—	2	8	no	—
364	#121	—	2	16	no	—
365	C₄×Q₈	D₄×C₁₃	1	4	yes	—
366	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	C₂³×C₁₃	1	4	yes	—
372	C₄×D₄	C₂³×C₁₃	1	8	yes	—
373	C₄×D₄	C₂³×C₁₃	1	4	yes	—
374	C₄×D₄	C₂³×C₁₃	1	8	yes	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	8	no	—
379	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	#107	C₂³×C₁₃	1	4	yes	—
391	#106	C₂³×C₁₃	1	8	yes	—
392	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
393	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
394	#102	C₂³×C₁₃	1	4	yes	—
395	#102	C₂³×C₁₃	1	4	yes	—
396	#102	C₂³×C₁₃	1	8	yes	—
397	#102	C₂³×C₁₃	1	8	yes	—
398	#102	C₂³×C₁₃	1	8	yes	—
399	#102	C₂³×C₁₃	1	8	yes	—
400	#97	C₂³×C₁₃	1	8	yes	—
401	C₄×C₈	C₂³×C₁₃	1	4	yes	—
402	C₂×C₁₃	—	4	4	no	—
403	C₂×C₁₃	—	8	4	no	—
404	C₂×C₁₃	—	8	2	no	—
405	C₂×C₁₃	#3366	1	4	yes	direct product factor
406	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
407	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
409	C₂⁴	—	2	1	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	1	no	—
412	#41	—	4	32	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	8	2	no	—
416	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	4	8	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	8	4	no	—
432	C₂×D₄	—	8	2	no	—
433	C₂×D₄	C₁₃×#41	1	4	yes	complemented
434	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
435	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
436	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	8	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	8	no	—
444	C₂²×C₄	—	4	8	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	8	4	no	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
453	D₈	—	2	8	no	—
454	D₈	—	2	16	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	4	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
459	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
460	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
468	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
469	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
471	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₄²	C₂×D₄×C₁₃	1	4	yes	—
477	C₄²	C₂×D₄×C₁₃	1	2	yes	—
478	C₄²	C₂⁴×C₁₃	1	2	yes	—
479	C₄²	C₂⁴×C₁₃	1	4	yes	—
480	C₁₃	C₂×#3366	1	1	yes	characteristic, direct product factor, Sylow
481	C₂³	—	2	4	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	4	no	—
493	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
494	Q₈	—	2	8	no	—
495	Q₈	—	8	4	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	4	no	—
502	D₄	—	4	16	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	8	no	—
506	D₄	—	8	8	no	—
507	D₄	—	8	4	no	—
508	D₄	C₂×C₁₃×#41	1	4	yes	complemented
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	16	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	8	8	no	—
522	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
523	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
524	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
525	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
528	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
529	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
530	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	4	no	—
533	C₈	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	8	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	8	8	no	—
545	C₂²	—	8	4	no	—
546	C₂²	C₁₃×#548	1	2	yes	—
547	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
548	C₂²	C₁₃×#576	1	2	yes	—
549	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
550	C₄	—	2	4	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	4	no	—
556	C₄	C₁₃×#548	1	2	yes	—
557	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
558	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
559	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
560	C₂	—	4	4	no	—
561	C₂	—	8	4	no	—
562	C₂	—	8	2	no	—
563	C₂	C₁₃×#3366	1	4	yes	direct product factor
564	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
565	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
566	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3366	C₂	direct (N × H)
4. C₂×C₁₃×#490	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#478	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#459	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#442	C₂	semidirect
12. C₂×C₄×C₁₃×D₈	C₂	semidirect
17. C₁₃×#554	C₂²	semidirect
19. C₁₃×#550	C₂²	semidirect
34. C₁₃×#490	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#459	C₂²	semidirect
39. C₁₃×#459	C₂²	semidirect
40. C₁₃×#446	C₂²	semidirect
41. C₁₃×#442	C₂²	semidirect
42. C₄×C₁₃×D₈	C₂²	semidirect
126. C₂×#3366	C₁₃	direct (N × H)
151. C₂×D₄×C₁₃	#41	semidirect
198. C₂×#554	C₂×C₁₃	semidirect
199. C₂×#550	C₂×C₁₃	semidirect
200. #3366	C₂×C₁₃	direct (N × H)
201. C₂×#490	C₂×C₁₃	semidirect
202. C₂×#486	C₂×C₁₃	semidirect
203. C₂×#478	C₂×C₁₃	semidirect
204. C₂×#476	C₂×C₁₃	semidirect
205. C₂×#459	C₂×C₁₃	semidirect
206. C₂×#459	C₂×C₁₃	semidirect
207. C₂×#446	C₂×C₁₃	semidirect
208. C₂×#442	C₂×C₁₃	semidirect
209. C₂×C₄×D₈	C₂×C₁₃	semidirect
237. D₄×C₁₃	C₂×#41	semidirect
267. #554	C₂²×C₁₃	semidirect
269. #550	C₂²×C₁₃	semidirect
284. #490	C₂²×C₁₃	semidirect
285. #486	C₂²×C₁₃	semidirect
286. #478	C₂²×C₁₃	semidirect
287. #476	C₂²×C₁₃	semidirect
288. #459	C₂²×C₁₃	semidirect
289. #459	C₂²×C₁₃	semidirect
290. #446	C₂²×C₁₃	semidirect
291. #442	C₂²×C₁₃	semidirect
292. C₄×D₈	C₂²×C₁₃	semidirect
405. C₂×C₁₃	#3366	direct (N × H)
433. C₂×D₄	C₁₃×#41	semidirect
480. C₁₃	C₂×#3366	direct (N × H)
508. D₄	C₂×C₁₃×#41	semidirect
563. C₂	C₁₃×#3366	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×C₁₃×#554	2
C₂×C₁₃×#550	2
C₁₃×#3366	2
C₂×C₁₃×#490	2
C₂×C₁₃×#486	2
C₂×C₁₃×#478	2
C₂×C₁₃×#476	2
C₂×C₁₃×#459	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×D₈	2
C₂×#3366	13

Subgroups — C2×C13×#3366 #15747643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3366 #15747643