Subgroups — C₁₃×#20885 #15707224

Order 3328.

1358 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1866	C₂	1	8	yes	maximal, complemented
7	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₁₃×#568	—	2	4	no	—
11	C₁₃×#568	—	2	4	no	—
12	C₂×C₁₃×#131	—	2	2	no	—
13	C₂×C₁₃×#131	C₂²	1	4	yes	—
14	C₂²×C₁₃×M₁₆	—	2	2	no	—
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#430	—	2	4	no	—
22	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
23	C₁₃×#424	—	2	2	no	—
24	C₁₃×#424	C₂²	1	4	yes	complemented
25	C₁₃×#423	—	2	2	no	—
26	C₂×C₁₃×#104	—	2	4	no	—
27	C₂×C₁₃×#104	C₂²	1	4	yes	—
28	C₁₃×#419	C₄	1	2	yes	complemented
29	C₁₃×#418	C₄	1	2	yes	complemented
30	C₁₃×#417	C₄	1	4	yes	complemented
31	C₁₃×#416	C₂²	1	4	yes	—
32	C₁₃×#339	C₂²	1	4	yes	complemented
33	C₁₃×#336	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#41	—	2	1	no	—
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
39	C₂×C₁₃×#41	D₄	1	4	yes	—
40	C₂×C₁₃×#41	Q₈	1	4	yes	—
41	C₂×C₁₃×#41	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#131	—	2	16	no	—
49	C₁₃×#131	—	2	8	no	—
50	C₁₃×#131	—	2	8	no	—
51	C₂×C₁₃×M₁₆	—	2	16	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	4	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
65	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	—	2	4	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×#117	—	2	1	no	—
75	C₁₃×#117	—	2	1	no	—
76	C₁₃×#117	C₂×C₄	1	2	yes	—
77	C₁₃×#117	C₂³	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₁₃×#108	—	2	8	no	—
86	C₁₃×C₄⋊C₈	—	2	8	no	—
87	C₁₃×#104	—	2	8	no	—
88	C₁₃×#103	C₂×C₄	1	8	yes	complemented
89	C₁₃×#102	C₂×C₄	1	8	yes	complemented
90	#20885	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	1	no	—
92	C₂⁴×C₁₃	#41	1	1	yes	characteristic
93	C₁₃×#41	—	2	4	no	—
94	C₁₃×#41	—	2	4	no	—
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	2	4	no	—
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	2	2	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	C₄⋊C₄	1	8	yes	—
101	C₁₃×#41	C₂×D₄	1	4	yes	—
102	C₁₃×#41	C₂×Q₈	1	4	yes	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
106	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	4	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
114	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	4	4	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×M₁₆	—	2	16	no	—
135	C₁₃×M₁₆	—	2	4	no	—
136	C₁₃×M₁₆	—	2	4	no	—
137	C₁₃×M₁₆	—	2	4	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	—	2	2	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	4	2	no	—
144	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₁₃	—	2	16	no	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	4	2	no	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
155	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	4	2	no	—
165	C₂×#568	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic
169	#2896	C₂×C₁₃	1	1	yes	characteristic
170	#1866	C₂×C₁₃	1	8	yes	complemented
171	C₂×#339	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	4	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	8	2	no	—
177	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
178	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
179	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
180	C₂³×C₁₃	#123	1	2	yes	—
181	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
185	D₄×C₁₃	—	2	4	no	—
186	D₄×C₁₃	—	2	4	no	—
187	D₄×C₁₃	—	2	8	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	4	no	—
190	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	8	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	8	2	no	—
202	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	#120	1	2	yes	—
209	C₂×C₄×C₁₃	#120	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄×C₁₃	#123	1	2	yes	—
214	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₈×C₁₃	—	2	4	no	—
221	C₈×C₁₃	—	2	4	no	—
222	C₈×C₁₃	—	2	4	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
225	#568	—	2	4	no	—
226	#568	—	2	4	no	—
227	C₂×#131	—	2	2	no	—
228	C₂×#131	C₂²×C₁₃	1	4	yes	—
229	C₂²×M₁₆	—	2	2	no	—
230	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
236	#430	—	2	4	no	—
237	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
238	#424	—	2	2	no	—
239	#424	C₂²×C₁₃	1	4	yes	complemented
240	#423	—	2	2	no	—
241	C₂×#104	—	2	4	no	—
242	C₂×#104	C₂²×C₁₃	1	4	yes	—
243	#419	C₄×C₁₃	1	2	yes	complemented
244	#418	C₄×C₁₃	1	2	yes	complemented
245	#417	C₄×C₁₃	1	4	yes	complemented
246	#416	C₂²×C₁₃	1	4	yes	—
247	#339	C₂²×C₁₃	1	4	yes	complemented
248	#336	C₂²×C₁₃	1	4	yes	complemented
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	2	4	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	8	4	no	—
257	C₂²×C₁₃	#385	1	2	yes	—
258	C₂²×C₁₃	#385	1	2	yes	—
259	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
261	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
262	C₄×C₁₃	—	2	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	#385	1	2	yes	—
266	C₄×C₁₃	#385	1	2	yes	—
267	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
270	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×#41	—	2	1	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	1	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
276	C₂×#41	D₄×C₁₃	1	4	yes	—
277	C₂×#41	Q₈×C₁₃	1	4	yes	—
278	C₂×#41	C₂³×C₁₃	1	2	yes	—
279	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
285	#131	—	2	16	no	—
286	#131	—	2	8	no	—
287	#131	—	2	8	no	—
288	C₂×M₁₆	—	2	16	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	4	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
300	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
301	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
302	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
303	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
304	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
305	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	4	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
311	#117	—	2	1	no	—
312	#117	—	2	1	no	—
313	#117	C₂×C₄×C₁₃	1	2	yes	—
314	#117	C₂³×C₁₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	#108	—	2	8	no	—
323	C₄⋊C₈	—	2	8	no	—
324	#104	—	2	8	no	—
325	#103	C₂×C₄×C₁₃	1	8	yes	complemented
326	#102	C₂×C₄×C₁₃	1	8	yes	complemented
327	C₂×C₁₃	—	2	1	no	—
328	C₂×C₁₃	—	2	2	no	—
329	C₂×C₁₃	—	2	1	no	—
330	C₂×C₁₃	—	2	2	no	—
331	C₂×C₁₃	—	4	4	no	—
332	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
333	C₂×C₁₃	#2956	1	2	yes	—
334	C₂⁴	—	2	1	no	—
335	C₂⁴	C₁₃×#41	1	1	yes	characteristic
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	2	4	no	—
339	#41	—	2	4	no	—
340	#41	—	2	4	no	—
341	#41	—	2	2	no	—
342	#41	—	2	2	no	—
343	#41	C₁₃×C₄⋊C₄	1	8	yes	—
344	#41	C₂×D₄×C₁₃	1	4	yes	—
345	#41	C₂×Q₈×C₁₃	1	4	yes	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	C₁₃×C₄⋊C₄	1	4	yes	—
349	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
357	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
374	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
375	C₂²×C₄	C₁₃×#41	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	M₁₆	—	2	16	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	—	2	4	no	—
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	4	2	no	—
387	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
388	C₂×C₈	—	2	16	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
398	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	2	no	—
408	C₁₃	#20885	1	1	yes	characteristic, direct product factor, Sylow
409	C₂³	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	8	2	no	—
413	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
414	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
415	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
416	C₂³	C₁₃×#123	1	2	yes	—
417	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	2	2	no	—
420	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
421	D₄	—	2	8	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	4	no	—
425	D₄	—	2	2	no	—
426	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	8	2	no	—
438	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
439	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
440	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
441	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
442	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
443	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
444	C₂×C₄	C₁₃×#120	1	2	yes	—
445	C₂×C₄	C₁₃×#120	1	2	yes	—
446	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
447	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
448	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
449	C₂×C₄	C₁₃×#123	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₈	—	2	4	no	—
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	C₁₃×#385	1	2	yes	—
469	C₂²	C₁₃×#385	1	2	yes	—
470	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
471	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
472	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
473	C₄	—	2	4	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	C₁₃×#385	1	2	yes	—
477	C₄	C₁₃×#385	1	2	yes	—
478	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
479	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
480	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
481	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	2	1	no	—
486	C₂	—	4	4	no	—
487	C₂	C₂×C₁₃×#385	1	1	yes	characteristic
488	C₂	C₁₃×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#430	C₂	semidirect
3. C₁₃×#2905	C₂	semidirect
6. C₁₃×#1866	C₂	semidirect
7. C₂×C₁₃×#339	C₂	semidirect
8. C₁₃×#1728	C₂	semidirect
22. C₂×C₁₃×#108	C₂²	semidirect
24. C₁₃×#424	C₂²	semidirect
28. C₁₃×#419	C₄	semidirect
29. C₁₃×#418	C₄	semidirect
30. C₁₃×#417	C₄	semidirect
32. C₁₃×#339	C₂²	semidirect
33. C₁₃×#336	C₂²	semidirect
88. C₁₃×#103	C₂×C₄	semidirect
89. C₁₃×#102	C₂×C₄	semidirect
90. #20885	C₁₃	direct (N × H)
166. C₂×#430	C₂×C₁₃	semidirect
167. #2905	C₂×C₁₃	semidirect
170. #1866	C₂×C₁₃	semidirect
171. C₂×#339	C₂×C₁₃	semidirect
172. #1728	C₂×C₁₃	semidirect
237. C₂×#108	C₂²×C₁₃	semidirect
239. #424	C₂²×C₁₃	semidirect
243. #419	C₄×C₁₃	semidirect
244. #418	C₄×C₁₃	semidirect
245. #417	C₄×C₁₃	semidirect
247. #339	C₂²×C₁₃	semidirect
248. #336	C₂²×C₁₃	semidirect
325. #103	C₂×C₄×C₁₃	semidirect
326. #102	C₂×C₄×C₁₃	semidirect
408. C₁₃	#20885	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×#568	2
C₂×C₁₃×#430	2
C₁₃×#2905	2
C₂²×C₁₃×#104	2
C₁₃×#2896	2
C₁₃×#1866	2
C₂×C₁₃×#339	2
C₁₃×#1728	2
#20885	13

Subgroups — C13×#20885 #15707224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20885 #15707224