Subgroups — C₁₃×#20884 #15707223

Order 3328.

1342 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#421	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	C₁₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#131	—	2	4	no	—
11	C₂×C₁₃×#131	—	2	4	no	—
12	C₂×C₁₃×#131	—	2	2	no	—
13	C₂×C₁₃×#131	C₂²	1	4	yes	—
14	C₂²×C₁₃×M₁₆	—	2	1	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	C₂³×C₈×C₁₃	—	2	1	no	—
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₁₃×#430	—	2	4	no	—
23	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
24	C₁₃×#424	—	2	1	no	—
25	C₁₃×#424	—	2	1	no	—
26	C₁₃×#424	C₂²	1	4	yes	complemented
27	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
28	C₁₃×#421	—	2	4	no	—
29	C₂×C₁₃×#104	C₂²	1	4	yes	—
30	C₁₃×#419	C₄	1	2	yes	complemented
31	C₁₃×#418	C₄	1	2	yes	complemented
32	C₁₃×#417	C₄	1	4	yes	complemented
33	C₁₃×#416	C₂²	1	4	yes	—
34	C₁₃×#339	C₂²	1	4	yes	complemented
35	C₁₃×#336	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×#41	D₄	1	4	yes	—
42	C₂×C₁₃×#41	Q₈	1	4	yes	—
43	C₂×C₁₃×#41	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#131	—	2	16	no	—
50	C₁₃×#131	—	2	8	no	—
51	C₁₃×#131	—	2	8	no	—
52	C₂×C₁₃×M₁₆	—	2	8	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	4	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃	—	2	8	no	—
67	C₂²×C₈×C₁₃	—	2	1	no	—
68	C₂²×C₈×C₁₃	—	2	2	no	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	4	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	D₄	1	2	yes	—
73	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#117	—	2	1	no	—
78	C₁₃×#117	—	2	1	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	2	2	no	—
81	C₁₃×#117	C₂×C₄	1	2	yes	—
82	C₁₃×#117	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₁₃×#108	—	2	8	no	—
90	C₁₃×C₄⋊C₈	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	4	no	—
92	C₁₃×#104	—	2	8	no	—
93	C₁₃×#103	C₂×C₄	1	8	yes	—
94	C₁₃×#102	C₂×C₄	1	8	yes	—
95	#20884	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	2	1	no	—
97	C₂⁴×C₁₃	#41	1	1	yes	characteristic
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	2	4	no	—
100	C₁₃×#41	—	2	4	no	—
101	C₁₃×#41	—	2	4	no	—
102	C₁₃×#41	—	2	4	no	—
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	—	2	2	no	—
105	C₁₃×#41	C₄⋊C₄	1	8	yes	—
106	C₁₃×#41	C₂×D₄	1	4	yes	—
107	C₁₃×#41	C₂×Q₈	1	4	yes	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	4	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
119	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
134	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×M₁₆	—	2	16	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	2	2	no	—
144	C₁₃×M₁₆	—	4	2	no	—
145	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₁₃	—	2	16	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	4	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	4	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	4	2	no	—
158	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
159	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	2	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic
172	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#421	C₂×C₁₃	1	1	yes	characteristic
175	#2896	C₂×C₁₃	1	1	yes	characteristic
176	#1866	C₂×C₁₃	1	8	yes	complemented
177	#1733	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	—	4	4	no	—
183	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
186	C₂³×C₁₃	#123	1	2	yes	—
187	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	4	no	—
190	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
191	D₄×C₁₃	—	2	4	no	—
192	D₄×C₁₃	—	2	4	no	—
193	D₄×C₁₃	—	2	8	no	—
194	D₄×C₁₃	—	2	2	no	—
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	4	4	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	#120	1	2	yes	—
213	C₂×C₄×C₁₃	#120	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
215	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
216	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
217	C₂×C₄×C₁₃	#123	1	2	yes	—
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₈×C₁₃	—	2	4	no	—
225	C₈×C₁₃	—	2	2	no	—
226	C₈×C₁₃	—	2	4	no	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	4	2	no	—
229	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#131	—	2	4	no	—
231	C₂×#131	—	2	4	no	—
232	C₂×#131	—	2	2	no	—
233	C₂×#131	C₂²×C₁₃	1	4	yes	—
234	C₂²×M₁₆	—	2	1	no	—
235	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
238	C₂³×C₈	—	2	1	no	—
239	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
242	#430	—	2	4	no	—
243	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
244	#424	—	2	1	no	—
245	#424	—	2	1	no	—
246	#424	C₂²×C₁₃	1	4	yes	complemented
247	C₂×C₄⋊C₈	—	2	2	no	—
248	#421	—	2	4	no	—
249	C₂×#104	C₂²×C₁₃	1	4	yes	—
250	#419	C₄×C₁₃	1	2	yes	complemented
251	#418	C₄×C₁₃	1	2	yes	complemented
252	#417	C₄×C₁₃	1	4	yes	complemented
253	#416	C₂²×C₁₃	1	4	yes	—
254	#339	C₂²×C₁₃	1	4	yes	complemented
255	#336	C₂²×C₁₃	1	4	yes	complemented
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	2	2	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	8	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	#385	1	2	yes	—
265	C₂²×C₁₃	#385	1	2	yes	—
266	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	—	8	2	no	—
272	C₄×C₁₃	#385	1	2	yes	—
273	C₄×C₁₃	#385	1	2	yes	—
274	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
275	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
276	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
277	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	1	no	—
280	C₂×#41	—	2	1	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
283	C₂×#41	D₄×C₁₃	1	4	yes	—
284	C₂×#41	Q₈×C₁₃	1	4	yes	—
285	C₂×#41	C₂³×C₁₃	1	2	yes	—
286	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
291	#131	—	2	16	no	—
292	#131	—	2	8	no	—
293	#131	—	2	8	no	—
294	C₂×M₁₆	—	2	8	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	4	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
304	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
305	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
306	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
307	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
308	C₂²×C₈	—	2	8	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	4	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₈	D₄×C₁₃	1	2	yes	—
317	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
319	#117	—	2	1	no	—
320	#117	—	2	1	no	—
321	#117	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	C₂×C₄×C₁₃	1	2	yes	—
324	#117	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
331	#108	—	2	8	no	—
332	C₄⋊C₈	—	2	4	no	—
333	C₄⋊C₈	—	2	4	no	—
334	#104	—	2	8	no	—
335	#103	C₂×C₄×C₁₃	1	8	yes	—
336	#102	C₂×C₄×C₁₃	1	8	yes	—
337	C₂×C₁₃	—	2	1	no	—
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	2	1	no	—
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	—	4	4	no	—
342	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
343	C₂×C₁₃	#2955	1	2	yes	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	C₁₃×#41	1	1	yes	characteristic
346	#41	—	2	4	no	—
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	2	2	no	—
352	#41	—	2	2	no	—
353	#41	C₁₃×C₄⋊C₄	1	8	yes	—
354	#41	C₂×D₄×C₁₃	1	4	yes	—
355	#41	C₂×Q₈×C₁₃	1	4	yes	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₁₃×C₄⋊C₄	1	4	yes	—
359	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
367	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
382	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
383	C₂²×C₄	C₁₃×#41	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	M₁₆	—	2	16	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
394	C₂×C₈	—	2	16	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
407	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
408	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₁₃	#20884	1	1	yes	characteristic, direct product factor, Sylow
420	C₂³	—	2	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	4	no	—
424	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
425	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
426	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
427	C₂³	C₁₃×#123	1	2	yes	—
428	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	2	2	no	—
431	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
432	D₄	—	2	8	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	2	no	—
437	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
448	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
449	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
452	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
453	C₂×C₄	C₁₃×#120	1	2	yes	—
454	C₂×C₄	C₁₃×#120	1	2	yes	—
455	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
456	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
457	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
458	C₂×C₄	C₁₃×#123	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
465	C₈	—	2	4	no	—
466	C₈	—	2	2	no	—
467	C₈	—	2	4	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	C₁₃×#385	1	2	yes	—
479	C₂²	C₁₃×#385	1	2	yes	—
480	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
481	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
483	C₄	—	2	4	no	—
484	C₄	—	4	4	no	—
485	C₄	—	8	2	no	—
486	C₄	C₁₃×#385	1	2	yes	—
487	C₄	C₁₃×#385	1	2	yes	—
488	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
489	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
490	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
491	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
492	C₂	—	2	1	no	—
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	4	no	—
497	C₂	C₂×C₁₃×#385	1	1	yes	characteristic
498	C₂	C₁₃×#2955	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 ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#430	C₂	semidirect
3. C₂×C₁₃×#424	C₂	semidirect
6. C₁₃×#1866	C₂	semidirect
7. C₁₃×#1733	C₂	semidirect
8. C₁₃×#1729	C₂	semidirect
23. C₂×C₁₃×#108	C₂²	semidirect
26. C₁₃×#424	C₂²	semidirect
30. C₁₃×#419	C₄	semidirect
31. C₁₃×#418	C₄	semidirect
32. C₁₃×#417	C₄	semidirect
34. C₁₃×#339	C₂²	semidirect
35. C₁₃×#336	C₂²	semidirect
95. #20884	C₁₃	direct (N × H)
172. C₂×#430	C₂×C₁₃	semidirect
173. C₂×#424	C₂×C₁₃	semidirect
176. #1866	C₂×C₁₃	semidirect
177. #1733	C₂×C₁₃	semidirect
178. #1729	C₂×C₁₃	semidirect
243. C₂×#108	C₂²×C₁₃	semidirect
246. #424	C₂²×C₁₃	semidirect
250. #419	C₄×C₁₃	semidirect
251. #418	C₄×C₁₃	semidirect
252. #417	C₄×C₁₃	semidirect
254. #339	C₂²×C₁₃	semidirect
255. #336	C₂²×C₁₃	semidirect
419. C₁₃	#20884	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#131	2
C₂×C₁₃×#430	2
C₂×C₁₃×#424	2
C₂×C₁₃×#421	2
C₁₃×#2896	2
C₁₃×#1866	2
C₁₃×#1733	2
C₁₃×#1729	2
#20884	13

Subgroups — C13×#20884 #15707223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20884 #15707223