Subgroups — C₁₃×#17708 #15704047

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1550	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1549	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1548	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1542	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₁₃×#533	—	2	1	no	—
10	C₁₃×#533	—	2	1	no	—
11	C₁₃×#533	—	2	1	no	—
12	C₁₃×#533	—	2	1	no	—
13	C₁₃×#533	C₄	1	2	yes	—
14	C₁₃×#533	C₄	1	2	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊Q₈	C₄	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
24	C₂×C₁₃×#117	—	2	1	no	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#431	—	2	1	no	—
27	C₁₃×#431	—	2	1	no	—
28	C₁₃×#431	C₂²	1	2	yes	—
29	C₁₃×#431	C₂²	1	2	yes	—
30	C₁₃×#423	—	2	1	no	—
31	C₁₃×#423	—	2	1	no	—
32	C₁₃×#423	C₂²	1	2	yes	—
33	C₁₃×#423	C₂²	1	2	yes	—
34	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
38	C₂×C₄×C₈×C₁₃	—	2	1	no	—
39	C₁₃×#333	C₂²	1	8	yes	complemented
40	C₁₃×#332	C₂²	1	8	yes	complemented
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	4	4	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
56	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
57	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₃×#125	—	2	2	no	—
60	C₁₃×#125	—	2	2	no	—
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×#125	—	2	2	no	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	2	no	—
67	C₁₃×C₂²⋊Q₈	—	2	2	no	—
68	C₁₃×C₂²⋊Q₈	—	2	2	no	—
69	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
70	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	—	2	2	no	—
73	C₄×Q₈×C₁₃	—	2	2	no	—
74	C₄×Q₈×C₁₃	—	2	2	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	2	2	no	—
81	C₁₃×#117	—	2	2	no	—
82	C₁₃×#117	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²×C₁₃	—	2	2	no	—
91	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×C₄⋊C₈	—	2	2	no	—
107	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
108	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊C₈	—	2	2	no	—
110	C₁₃×C₂²⋊C₈	—	2	2	no	—
111	C₄×C₈×C₁₃	—	2	2	no	—
112	C₄×C₈×C₁₃	—	2	2	no	—
113	#17708	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
135	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₁₃×M₁₆	—	4	4	no	—
146	C₁₃×M₁₆	—	4	4	no	—
147	C₂×C₈×C₁₃	—	2	4	no	—
148	C₂×C₈×C₁₃	—	2	4	no	—
149	C₂×C₈×C₁₃	—	4	4	no	—
150	C₂×C₈×C₁₃	—	4	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₄²×C₁₃	—	2	4	no	—
166	C₄²×C₁₃	—	2	4	no	—
167	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
184	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
185	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
186	#1550	C₂×C₁₃	1	4	yes	complemented
187	#1549	C₂×C₁₃	1	2	yes	complemented
188	#1548	C₂×C₁₃	1	2	yes	complemented
189	#1542	C₂×C₁₃	1	4	yes	complemented
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	#103	1	4	yes	—
193	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	Q₈×C₁₃	—	4	4	no	—
197	Q₈×C₁₃	—	4	4	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	Q₈×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	#103	1	4	yes	—
217	C₂×C₄×C₁₃	#103	1	4	yes	—
218	C₂×C₄×C₁₃	#103	1	4	yes	—
219	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
233	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
234	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₁₃	—	4	4	no	—
238	C₈×C₁₃	—	4	4	no	—
239	C₂²×M₁₆	—	2	1	no	—
240	#533	—	2	1	no	—
241	#533	—	2	1	no	—
242	#533	—	2	1	no	—
243	#533	—	2	1	no	—
244	#533	C₄×C₁₃	1	2	yes	—
245	#533	C₄×C₁₃	1	2	yes	—
246	#533	C₂²×C₁₃	1	2	yes	—
247	#533	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#125	—	2	1	no	—
251	C₂×C₂²⋊Q₈	—	2	1	no	—
252	C₂×C₂²⋊Q₈	C₄×C₁₃	1	2	yes	—
253	C₂×C₄×Q₈	—	2	1	no	—
254	C₂×C₄×Q₈	C₄×C₁₃	1	2	yes	—
255	C₂×#117	—	2	1	no	—
256	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
257	#431	—	2	1	no	—
258	#431	—	2	1	no	—
259	#431	C₂²×C₁₃	1	2	yes	—
260	#431	C₂²×C₁₃	1	2	yes	—
261	#423	—	2	1	no	—
262	#423	—	2	1	no	—
263	#423	C₂²×C₁₃	1	2	yes	—
264	#423	C₂²×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₈	—	2	1	no	—
266	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
268	C₂×C₂²⋊C₈	—	2	1	no	—
269	C₂×C₄×C₈	—	2	1	no	—
270	#333	C₂²×C₁₃	1	8	yes	complemented
271	#332	C₂²×C₁₃	1	8	yes	complemented
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	C₂×#103	1	2	yes	—
280	C₂²×C₁₃	C₂×#103	1	2	yes	—
281	C₂²×C₁₃	C₂×#103	1	2	yes	—
282	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	—	4	4	no	—
291	C₄×C₁₃	#413	1	2	yes	—
292	C₄×C₁₃	C₂×#103	1	2	yes	—
293	C₄×C₁₃	C₂×#103	1	2	yes	—
294	C₄×C₁₃	C₂×#103	1	2	yes	—
295	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
296	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
297	C₄×C₁₃	#575	1	2	yes	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	4	4	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
313	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
316	#125	—	2	2	no	—
317	#125	—	2	2	no	—
318	#125	—	2	2	no	—
319	#125	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
327	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
335	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
336	#117	—	2	2	no	—
337	#117	—	2	2	no	—
338	#117	—	2	2	no	—
339	#117	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	—	2	2	no	—
363	C₄⋊C₈	—	2	2	no	—
364	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
365	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
366	C₂²⋊C₈	—	2	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	2	no	—
370	C₂×C₁₃	—	2	2	no	—
371	C₂×C₁₃	—	2	2	no	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
374	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
375	C₂×C₁₃	#2896	1	1	yes	characteristic
376	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
394	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
396	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
397	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
407	M₁₆	—	4	4	no	—
408	M₁₆	—	4	4	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	4	4	no	—
412	C₂×C₈	—	4	4	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₄²	—	2	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
430	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
431	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
433	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
434	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
435	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
436	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
437	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
438	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₁₃	#17708	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	C₁₃×#103	1	4	yes	—
449	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
450	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
451	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
452	Q₈	—	4	4	no	—
453	Q₈	—	4	4	no	—
454	Q₈	—	4	4	no	—
455	Q₈	—	4	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₁₃×#103	1	4	yes	—
473	C₂×C₄	C₁₃×#103	1	4	yes	—
474	C₂×C₄	C₁₃×#103	1	4	yes	—
475	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
477	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
481	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
485	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
486	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
487	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
488	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
489	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₈	—	4	4	no	—
494	C₈	—	4	4	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	C₂×C₁₃×#103	1	2	yes	—
503	C₂²	C₂×C₁₃×#103	1	2	yes	—
504	C₂²	C₂×C₁₃×#103	1	2	yes	—
505	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	4	no	—
514	C₄	C₁₃×#413	1	2	yes	—
515	C₄	C₂×C₁₃×#103	1	2	yes	—
516	C₄	C₂×C₁₃×#103	1	2	yes	—
517	C₄	C₂×C₁₃×#103	1	2	yes	—
518	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
519	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
520	C₄	C₁₃×#575	1	2	yes	—
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	2	2	no	—
524	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
525	C₂	C₂²×C₁₃×#103	1	1	yes	characteristic
526	C₂	C₁₃×#2896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1550	C₂	semidirect
5. C₁₃×#1549	C₂	semidirect
6. C₁₃×#1548	C₂	semidirect
7. C₁₃×#1542	C₂	semidirect
39. C₁₃×#333	C₂²	semidirect
40. C₁₃×#332	C₂²	semidirect
113. #17708	C₁₃	direct (N × H)
186. #1550	C₂×C₁₃	semidirect
187. #1549	C₂×C₁₃	semidirect
188. #1548	C₂×C₁₃	semidirect
189. #1542	C₂×C₁₃	semidirect
270. #333	C₂²×C₁₃	semidirect
271. #332	C₂²×C₁₃	semidirect
445. C₁₃	#17708	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×#533	2
C₂×C₁₃×#431	2
C₂×C₁₃×#423	2
C₁₃×#1550	2
C₁₃×#1549	2
C₁₃×#1548	2
C₁₃×#1542	2
#17708	13

Subgroups — C13×#17708 #15704047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17708 #15704047