Subgroups — C₂×C₁₃×#3373 #15747646

Order 3328.

2134 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3373	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#476	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
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×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	—	2	1	no	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
16	C₁₃×#559	—	2	4	no	—
17	C₁₃×#559	C₂²	1	8	yes	complemented
18	D₄×Q₈×C₁₃	—	2	4	no	—
19	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	—	2	1	no	—
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#489	C₂²	1	16	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	complemented
36	C₁₃×#476	C₂²	1	16	yes	complemented
37	C₁₃×#475	C₂²	1	8	yes	complemented
38	C₁₃×#463	C₂²	1	16	yes	complemented
39	C₁₃×#459	C₂²	1	8	yes	—
40	C₁₃×#446	C₂²	1	8	yes	complemented
41	C₁₃×#442	C₂²	1	16	yes	complemented
42	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#106	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×#103	C₂²	1	2	yes	—
48	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
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	C₂²×Q₈×C₁₃	—	2	8	no	—
56	C₂²×Q₈×C₁₃	—	2	2	no	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	4	8	no	—
59	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	2	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	4	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
70	C₂×C₁₃×D₈	—	2	8	no	—
71	C₂×C₁₃×D₈	C₂³	1	8	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
75	C₁₃×C₄⋊Q₈	—	2	4	no	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
79	C₁₃×#127	—	2	2	no	—
80	C₁₃×#127	C₂³	1	4	yes	—
81	C₁₃×#124	—	2	8	no	—
82	C₁₃×#124	—	2	4	no	—
83	C₁₃×#124	C₂³	1	8	yes	—
84	C₁₃×#123	—	2	16	no	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	—	2	16	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	D₄	1	4	yes	—
89	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	4	no	—
95	C₄×D₄×C₁₃	C₂³	1	4	yes	—
96	C₄×D₄×C₁₃	C₂³	1	8	yes	—
97	C₄×D₄×C₁₃	C₂³	1	8	yes	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
114	C₁₃×#106	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×#103	C₂³	1	4	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	4	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×#3373	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	8	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	4	8	no	—
136	C₂×Q₈×C₁₃	—	4	32	no	—
137	C₂×Q₈×C₁₃	—	4	4	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	4	4	no	—
148	C₂×D₄×C₁₃	—	8	2	no	—
149	C₂×D₄×C₁₃	#41	1	4	yes	—
150	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	8	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	4	8	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	—	8	4	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×SD₁₆	—	2	8	no	—
168	C₁₃×D₈	—	2	16	no	—
169	C₂×C₈×C₁₃	—	2	4	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
173	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	C₂×D₄	1	4	yes	—
193	C₄²×C₁₃	C₂×D₄	1	2	yes	—
194	C₄²×C₁₃	C₂⁴	1	2	yes	—
195	C₄²×C₁₃	C₂⁴	1	4	yes	—
196	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3373	C₂×C₁₃	1	16	yes	direct product factor
199	C₂×#489	C₂×C₁₃	1	2	yes	complemented
200	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#476	C₂×C₁₃	1	2	yes	complemented
203	C₂×#463	C₂×C₁₃	1	2	yes	complemented
204	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
205	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#442	C₂×C₁₃	1	2	yes	complemented
207	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	—	4	4	no	—
215	C₂³×C₁₃	—	4	4	no	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	8	no	—
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	4	16	no	—
221	Q₈×C₁₃	—	4	2	no	—
222	Q₈×C₁₃	—	4	8	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	4	4	no	—
228	D₄×C₁₃	—	4	8	no	—
229	D₄×C₁₃	—	8	4	no	—
230	D₄×C₁₃	C₂×#41	1	4	yes	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	16	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	4	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	8	8	no	—
245	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
252	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
254	C₈×C₁₃	—	2	4	no	—
255	C₈×C₁₃	—	2	2	no	—
256	C₈×C₁₃	—	2	2	no	—
257	C₂³×Q₈	—	2	1	no	—
258	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
260	#559	—	2	4	no	—
261	#559	C₂²×C₁₃	1	8	yes	complemented
262	D₄×Q₈	—	2	4	no	—
263	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
264	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
266	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#124	—	2	1	no	—
268	C₂×#124	C₂²×C₁₃	1	2	yes	—
269	C₂×#123	—	2	2	no	—
270	C₂×C₂²⋊Q₈	—	2	1	no	—
271	C₂×C₂²⋊Q₈	—	2	2	no	—
272	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×C₄×D₄	—	2	1	no	—
275	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
278	#489	C₂²×C₁₃	1	16	yes	complemented
279	#486	C₂²×C₁₃	1	8	yes	complemented
280	#476	C₂²×C₁₃	1	16	yes	complemented
281	#475	C₂²×C₁₃	1	8	yes	complemented
282	#463	C₂²×C₁₃	1	16	yes	complemented
283	#459	C₂²×C₁₃	1	8	yes	—
284	#446	C₂²×C₁₃	1	8	yes	complemented
285	#442	C₂²×C₁₃	1	16	yes	complemented
286	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
287	C₂×#106	C₂²×C₁₃	1	2	yes	—
288	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
291	C₂×#103	C₂²×C₁₃	1	2	yes	—
292	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#102	C₂²×C₁₃	1	2	yes	—
294	C₂×#102	C₂²×C₁₃	1	2	yes	—
295	C₂×#102	C₂²×C₁₃	1	2	yes	—
296	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#97	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	4	8	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	8	8	no	—
307	C₂²×C₁₃	#548	1	2	yes	—
308	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
309	C₂²×C₁₃	#577	1	2	yes	—
310	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	2	4	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	#548	1	2	yes	—
319	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
320	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
321	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
322	C₂²×Q₈	—	2	8	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×Q₈	—	4	8	no	—
326	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	2	no	—
335	C₂×SD₁₆	—	2	4	no	—
336	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
337	C₂×D₈	—	2	8	no	—
338	C₂×D₈	C₂³×C₁₃	1	8	yes	—
339	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
340	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₄⋊Q₈	—	2	4	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
345	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
346	#127	—	2	2	no	—
347	#127	C₂³×C₁₃	1	4	yes	—
348	#124	—	2	8	no	—
349	#124	—	2	4	no	—
350	#124	C₂³×C₁₃	1	8	yes	—
351	#123	—	2	16	no	—
352	C₂²⋊Q₈	—	2	8	no	—
353	C₂²⋊Q₈	—	2	16	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	D₄×C₁₃	1	4	yes	—
356	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
357	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
358	C₄×D₄	—	2	8	no	—
359	C₄×D₄	—	2	4	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	C₂³×C₁₃	1	4	yes	—
363	C₄×D₄	C₂³×C₁₃	1	8	yes	—
364	C₄×D₄	C₂³×C₁₃	1	8	yes	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	#106	C₂³×C₁₃	1	4	yes	—
382	#106	C₂³×C₁₃	1	8	yes	—
383	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
384	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
385	#103	C₂³×C₁₃	1	4	yes	—
386	#103	C₂³×C₁₃	1	8	yes	—
387	#102	C₂³×C₁₃	1	4	yes	—
388	#102	C₂³×C₁₃	1	8	yes	—
389	#102	C₂³×C₁₃	1	8	yes	—
390	#102	C₂³×C₁₃	1	8	yes	—
391	#97	C₂³×C₁₃	1	8	yes	—
392	C₄×C₈	C₂³×C₁₃	1	4	yes	—
393	C₂×C₁₃	—	4	4	no	—
394	C₂×C₁₃	—	8	4	no	—
395	C₂×C₁₃	#3373	1	4	yes	direct product factor
396	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
397	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
399	C₂⁴	—	2	1	no	—
400	C₂⁴	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	8	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	8	no	—
408	C₂×Q₈	—	4	32	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
411	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	8	2	no	—
421	C₂×D₄	C₁₃×#41	1	4	yes	—
422	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
423	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	4	8	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	8	4	no	—
434	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	SD₁₆	—	2	8	no	—
440	D₈	—	2	16	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
445	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
446	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
455	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
456	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
457	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₄²	—	2	4	no	—
464	C₄²	C₂×D₄×C₁₃	1	4	yes	—
465	C₄²	C₂×D₄×C₁₃	1	2	yes	—
466	C₄²	C₂⁴×C₁₃	1	2	yes	—
467	C₄²	C₂⁴×C₁₃	1	4	yes	—
468	C₁₃	C₂×#3373	1	1	yes	characteristic, direct product factor, Sylow
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	Q₈	—	2	8	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	4	16	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	8	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	4	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	8	no	—
490	D₄	—	8	4	no	—
491	D₄	C₂×C₁₃×#41	1	4	yes	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	16	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	8	8	no	—
506	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
512	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
513	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
514	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
515	C₈	—	2	4	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	2	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	8	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	8	8	no	—
526	C₂²	C₁₃×#548	1	2	yes	—
527	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
528	C₂²	C₁₃×#577	1	2	yes	—
529	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₁₃×#548	1	2	yes	—
538	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
539	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
540	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂	—	4	4	no	—
542	C₂	—	8	4	no	—
543	C₂	C₁₃×#3373	1	4	yes	direct product factor
544	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
545	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
546	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#459	C₂
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×#559	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3373	C₂	direct (N × H)
4. C₂×C₁₃×#489	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#475	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
8. C₂×C₁₃×#463	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#442	C₂	semidirect
12. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
17. C₁₃×#559	C₂²	semidirect
19. D₄×Q₈×C₁₃	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#476	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
38. C₁₃×#463	C₂²	semidirect
40. C₁₃×#446	C₂²	semidirect
41. C₁₃×#442	C₂²	semidirect
42. C₄×C₁₃×SD₁₆	C₂²	semidirect
126. C₂×#3373	C₁₃	direct (N × H)
196. C₂×#559	C₂×C₁₃	semidirect
197. C₂×D₄×Q₈	C₂×C₁₃	semidirect
198. #3373	C₂×C₁₃	direct (N × H)
199. C₂×#489	C₂×C₁₃	semidirect
200. C₂×#486	C₂×C₁₃	semidirect
201. C₂×#475	C₂×C₁₃	semidirect
202. C₂×#476	C₂×C₁₃	semidirect
203. C₂×#463	C₂×C₁₃	semidirect
205. C₂×#446	C₂×C₁₃	semidirect
206. C₂×#442	C₂×C₁₃	semidirect
207. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
261. #559	C₂²×C₁₃	semidirect
263. D₄×Q₈	C₂²×C₁₃	semidirect
278. #489	C₂²×C₁₃	semidirect
279. #486	C₂²×C₁₃	semidirect
280. #476	C₂²×C₁₃	semidirect
281. #475	C₂²×C₁₃	semidirect
282. #463	C₂²×C₁₃	semidirect
284. #446	C₂²×C₁₃	semidirect
285. #442	C₂²×C₁₃	semidirect
286. C₄×SD₁₆	C₂²×C₁₃	semidirect
395. C₂×C₁₃	#3373	direct (N × H)
468. C₁₃	C₂×#3373	direct (N × H)
543. C₂	C₁₃×#3373	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×#559	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3373	2
C₂×C₁₃×#489	2
C₂×C₁₃×#486	2
C₂×C₁₃×#475	2
C₂×C₁₃×#476	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3373	13

Subgroups — C2×C13×#3373 #15747646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3373 #15747646