Subgroups — C₂×C₁₃×#3361 #15747637

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 540 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×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3361	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#478	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×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
15	C₁₃×#559	—	2	4	no	—
16	C₁₃×#559	C₂²	1	8	yes	complemented
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	—	2	2	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₁₃×#488	C₂²	1	16	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	complemented
36	C₁₃×#478	C₂²	1	16	yes	complemented
37	C₁₃×#477	C₂²	1	8	yes	complemented
38	C₁₃×#463	C₂²	1	16	yes	complemented
39	C₁₃×#459	C₂²	1	8	yes	—
40	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₄×C₁₃×D₈	C₂²	1	16	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	2	yes	—
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	—	2	2	no	—
65	C₂×C₁₃×SD₁₆	—	2	4	no	—
66	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
67	C₂×C₁₃×D₈	—	2	8	no	—
68	C₂×C₁₃×D₈	C₂³	1	8	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₁₃×#127	—	2	2	no	—
75	C₁₃×#127	C₂³	1	4	yes	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	C₂³	1	8	yes	—
78	C₁₃×#124	—	2	8	no	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#124	C₂³	1	8	yes	—
81	C₁₃×#123	—	2	16	no	—
82	C₁₃×C₂²⋊Q₈	—	2	8	no	—
83	C₁₃×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	D₄	1	4	yes	—
86	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
87	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	4	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	4	no	—
92	C₄×D₄×C₁₃	C₂³	1	8	yes	—
93	C₄×D₄×C₁₃	C₂³	1	8	yes	—
94	C₄×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#107	C₂³	1	8	yes	—
114	C₁₃×#106	C₂³	1	4	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#103	C₂³	1	4	yes	—
118	C₁₃×#103	C₂³	1	8	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	C₄×C₈×C₁₃	C₂³	1	8	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	C₂×#3361	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	8	2	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
135	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	4	4	no	—
144	C₂×D₄×C₁₃	—	8	2	no	—
145	C₂×D₄×C₁₃	#41	1	4	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	8	no	—
154	C₂²×C₄×C₁₃	—	2	8	no	—
155	C₂²×C₄×C₁₃	—	4	4	no	—
156	C₂²×C₄×C₁₃	—	8	4	no	—
157	C₂²×C₄×C₁₃	—	8	4	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×SD₁₆	—	2	8	no	—
164	C₁₃×D₈	—	2	16	no	—
165	C₂×C₈×C₁₃	—	2	4	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
171	C₁₃×C₄⋊C₄	—	2	8	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₄²×C₁₃	—	2	4	no	—
189	C₄²×C₁₃	C₂×D₄	1	4	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂⁴	1	4	yes	—
192	C₄²×C₁₃	C₂⁴	1	2	yes	—
193	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#3361	C₂×C₁₃	1	16	yes	direct product factor
196	C₂×#488	C₂×C₁₃	1	2	yes	complemented
197	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#478	C₂×C₁₃	1	2	yes	complemented
200	C₂×#463	C₂×C₁₃	1	2	yes	complemented
201	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
202	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	4	no	—
211	C₂³×C₁₃	—	4	4	no	—
212	C₂³×C₁₃	—	4	4	no	—
213	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₁₃	—	2	8	no	—
215	Q₈×C₁₃	—	2	2	no	—
216	Q₈×C₁₃	—	2	2	no	—
217	Q₈×C₁₃	—	4	2	no	—
218	Q₈×C₁₃	—	8	4	no	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	—	2	4	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	4	4	no	—
224	D₄×C₁₃	—	4	8	no	—
225	D₄×C₁₃	—	8	4	no	—
226	D₄×C₁₃	C₂×#41	1	4	yes	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	8	no	—
239	C₂×C₄×C₁₃	—	8	8	no	—
240	C₂×C₄×C₁₃	—	8	8	no	—
241	C₂×C₄×C₁₃	#135	1	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
248	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
250	C₈×C₁₃	—	2	4	no	—
251	C₈×C₁₃	—	2	2	no	—
252	C₈×C₁₃	—	2	2	no	—
253	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
255	#559	—	2	4	no	—
256	#559	C₂²×C₁₃	1	8	yes	complemented
257	#554	—	2	4	no	—
258	#554	C₂²×C₁₃	1	8	yes	complemented
259	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#125	C₂²×C₁₃	1	2	yes	—
262	C₂×#124	—	2	1	no	—
263	C₂×#124	C₂²×C₁₃	1	2	yes	—
264	C₂×#123	—	2	2	no	—
265	C₂×C₂²⋊Q₈	—	2	1	no	—
266	C₂×C₂²⋊Q₈	—	2	2	no	—
267	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄×D₄	—	2	1	no	—
270	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
272	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	—	2	1	no	—
274	#488	C₂²×C₁₃	1	16	yes	complemented
275	#486	C₂²×C₁₃	1	8	yes	complemented
276	#478	C₂²×C₁₃	1	16	yes	complemented
277	#477	C₂²×C₁₃	1	8	yes	complemented
278	#463	C₂²×C₁₃	1	16	yes	complemented
279	#459	C₂²×C₁₃	1	8	yes	—
280	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
281	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
282	C₄×D₈	C₂²×C₁₃	1	16	yes	complemented
283	C₂×#107	C₂²×C₁₃	1	2	yes	—
284	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#103	C₂²×C₁₃	1	2	yes	—
288	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₁₃	1	2	yes	—
290	C₂×#102	C₂²×C₁₃	1	2	yes	—
291	C₂×#102	C₂²×C₁₃	1	2	yes	—
292	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	4	8	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	4	no	—
301	C₂²×C₁₃	—	4	4	no	—
302	C₂²×C₁₃	—	8	8	no	—
303	C₂²×C₁₃	#548	1	2	yes	—
304	C₂²×C₁₃	C₂×#135	1	2	yes	—
305	C₂²×C₁₃	#576	1	2	yes	—
306	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	#548	1	2	yes	—
315	C₄×C₁₃	C₂×#135	1	4	yes	—
316	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
324	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	—	2	2	no	—
328	C₂×SD₁₆	—	2	4	no	—
329	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
330	C₂×D₈	—	2	8	no	—
331	C₂×D₈	C₂³×C₁₃	1	8	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
333	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
337	#127	—	2	2	no	—
338	#127	C₂³×C₁₃	1	4	yes	—
339	#125	—	2	4	no	—
340	#125	C₂³×C₁₃	1	8	yes	—
341	#124	—	2	8	no	—
342	#124	—	2	4	no	—
343	#124	C₂³×C₁₃	1	8	yes	—
344	#123	—	2	16	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	16	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	D₄×C₁₃	1	4	yes	—
349	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
350	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	C₂³×C₁₃	1	8	yes	—
356	C₄×D₄	C₂³×C₁₃	1	4	yes	—
357	C₄×D₄	C₂³×C₁₃	1	8	yes	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	8	no	—
363	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	#107	C₂³×C₁₃	1	8	yes	—
377	#106	C₂³×C₁₃	1	4	yes	—
378	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
380	#103	C₂³×C₁₃	1	4	yes	—
381	#103	C₂³×C₁₃	1	8	yes	—
382	#102	C₂³×C₁₃	1	4	yes	—
383	#102	C₂³×C₁₃	1	8	yes	—
384	#102	C₂³×C₁₃	1	8	yes	—
385	#102	C₂³×C₁₃	1	8	yes	—
386	C₄×C₈	C₂³×C₁₃	1	8	yes	—
387	C₄×C₈	C₂³×C₁₃	1	4	yes	—
388	C₂×C₁₃	—	4	4	no	—
389	C₂×C₁₃	—	8	4	no	—
390	C₂×C₁₃	#3361	1	4	yes	direct product factor
391	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
392	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
393	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	2	2	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	8	2	no	—
402	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
403	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	8	2	no	—
413	C₂×D₄	C₁₃×#41	1	4	yes	—
414	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
415	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	8	4	no	—
425	C₂²×C₄	—	8	4	no	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
431	SD₁₆	—	2	8	no	—
432	D₈	—	2	16	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
437	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
438	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
447	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
448	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
449	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
450	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₄²	—	2	4	no	—
457	C₄²	C₂×D₄×C₁₃	1	4	yes	—
458	C₄²	C₂×D₄×C₁₃	1	2	yes	—
459	C₄²	C₂⁴×C₁₃	1	4	yes	—
460	C₄²	C₂⁴×C₁₃	1	2	yes	—
461	C₁₃	C₂×#3361	1	1	yes	characteristic, direct product factor, Sylow
462	C₂³	—	2	4	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	Q₈	—	2	8	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	8	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	8	no	—
482	D₄	—	8	4	no	—
483	D₄	C₂×C₁₃×#41	1	4	yes	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	8	8	no	—
497	C₂×C₄	—	8	8	no	—
498	C₂×C₄	C₁₃×#135	1	4	yes	—
499	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
505	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
506	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
507	C₈	—	2	4	no	—
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	8	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	8	8	no	—
518	C₂²	C₁₃×#548	1	2	yes	—
519	C₂²	C₂×C₁₃×#135	1	2	yes	—
520	C₂²	C₁₃×#576	1	2	yes	—
521	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
522	C₄	—	2	4	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	2	no	—
529	C₄	C₁₃×#548	1	2	yes	—
530	C₄	C₂×C₁₃×#135	1	4	yes	—
531	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
532	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂	—	4	4	no	—
534	C₂	—	8	4	no	—
535	C₂	C₁₃×#3361	1	4	yes	direct product factor
536	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
537	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
538	C₂	C₂×C₁₃×#576	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×C₁₃×#554	C₂	semidirect
3. C₁₃×#3361	C₂	direct (N × H)
4. C₂×C₁₃×#488	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#477	C₂	semidirect
7. C₂×C₁₃×#478	C₂	semidirect
8. C₂×C₁₃×#463	C₂	semidirect
10. C₂×C₈×Q₈×C₁₃	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₄×C₁₃×D₈	C₂	semidirect
16. C₁₃×#559	C₂²	semidirect
18. C₁₃×#554	C₂²	semidirect
34. C₁₃×#488	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#477	C₂²	semidirect
38. C₁₃×#463	C₂²	semidirect
40. C₈×Q₈×C₁₃	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₄×C₁₃×D₈	C₂²	semidirect
125. C₂×#3361	C₁₃	direct (N × H)
193. C₂×#559	C₂×C₁₃	semidirect
194. C₂×#554	C₂×C₁₃	semidirect
195. #3361	C₂×C₁₃	direct (N × H)
196. C₂×#488	C₂×C₁₃	semidirect
197. C₂×#486	C₂×C₁₃	semidirect
198. C₂×#477	C₂×C₁₃	semidirect
199. C₂×#478	C₂×C₁₃	semidirect
200. C₂×#463	C₂×C₁₃	semidirect
202. C₂×C₈×Q₈	C₂×C₁₃	semidirect
203. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
204. C₂×C₄×D₈	C₂×C₁₃	semidirect
256. #559	C₂²×C₁₃	semidirect
258. #554	C₂²×C₁₃	semidirect
274. #488	C₂²×C₁₃	semidirect
275. #486	C₂²×C₁₃	semidirect
276. #478	C₂²×C₁₃	semidirect
277. #477	C₂²×C₁₃	semidirect
278. #463	C₂²×C₁₃	semidirect
280. C₈×Q₈	C₂²×C₁₃	semidirect
281. C₄×SD₁₆	C₂²×C₁₃	semidirect
282. C₄×D₈	C₂²×C₁₃	semidirect
390. C₂×C₁₃	#3361	direct (N × H)
461. C₁₃	C₂×#3361	direct (N × H)
535. C₂	C₁₃×#3361	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×C₁₃×#554	2
C₁₃×#3361	2
C₂×C₁₃×#488	2
C₂×C₁₃×#486	2
C₂×C₁₃×#477	2
C₂×C₁₃×#478	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂×#3361	13

Subgroups — C2×C13×#3361 #15747637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3361 #15747637