Subgroups — C₁₃×#22687 #15709026

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2906	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1866	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1866	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1849	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1806	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	C₄×C₁₃×#41	C₂²	1	2	yes	—
16	C₁₃×#444	—	2	4	no	—
17	C₁₃×#443	—	2	4	no	—
18	C₁₃×#442	C₄	1	2	yes	complemented
19	C₁₃×#441	C₄	1	2	yes	complemented
20	C₁₃×#440	C₄	1	2	yes	complemented
21	C₁₃×#440	C₄	1	2	yes	complemented
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#108	C₂²	1	2	yes	—
25	C₁₃×#427	C₂²	1	1	yes	characteristic
26	C₁₃×#424	—	2	2	no	—
27	C₁₃×#424	—	2	2	no	—
28	C₁₃×#424	C₂²	1	2	yes	—
29	C₁₃×#424	C₂²	1	2	yes	—
30	C₁₃×#423	—	2	2	no	—
31	C₁₃×#423	C₂²	1	2	yes	—
32	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#104	C₂²	1	2	yes	—
35	C₂×C₁₃×#104	C₂²	1	2	yes	—
36	C₁₃×#416	C₂²	1	2	yes	—
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#339	C₂²	1	2	yes	—
42	C₁₃×#339	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	1	yes	characteristic
44	C₁₃×#336	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₁₃×#135	D₄	1	4	yes	—
47	C₁₃×#135	Q₈	1	4	yes	—
48	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
51	C₁₃×#131	—	2	4	no	—
52	C₁₃×#131	—	2	4	no	—
53	C₁₃×#131	—	4	2	no	—
54	C₁₃×#131	—	4	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
66	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
71	C₁₃×#117	—	2	2	no	—
72	C₁₃×#117	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#108	—	2	2	no	—
79	C₁₃×#108	—	2	2	no	—
80	C₁₃×#108	—	4	2	no	—
81	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#106	C₂×C₄	1	2	yes	—
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×C₄⋊C₈	—	2	2	no	—
89	C₁₃×C₄⋊C₈	—	2	2	no	—
90	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
91	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
92	C₁₃×#104	—	2	4	no	—
93	C₁₃×#104	—	2	4	no	—
94	C₁₃×#103	C₂×C₄	1	2	yes	—
95	C₁₃×#103	C₂×C₄	1	2	yes	—
96	C₁₃×#102	C₂×C₄	1	2	yes	—
97	C₁₃×#102	C₂×C₄	1	2	yes	—
98	C₁₃×#97	—	2	2	no	—
99	C₁₃×#97	C₂×C₄	1	2	yes	—
100	C₁₃×#97	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₁₃	—	2	2	no	—
102	C₁₃×#95	—	2	1	no	—
103	#22687	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₁₃×#41	—	2	2	no	—
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	C₂×D₄	1	4	yes	—
107	C₁₃×#41	C₂×Q₈	1	4	yes	—
108	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×Q₁₆	C₄⋊C₄	1	4	yes	complemented
120	C₁₃×SD₁₆	C₄⋊C₄	1	8	yes	complemented
121	C₁₃×D₈	C₄⋊C₄	1	4	yes	complemented
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	—	4	4	no	—
127	C₁₃×M₁₆	—	4	4	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	4	4	no	—
137	C₂×C₈×C₁₃	—	4	4	no	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
150	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
151	C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₁₃×C₂²⋊C₄	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×#444	C₂×C₁₃	1	1	yes	characteristic
164	C₂×#443	C₂×C₁₃	1	1	yes	characteristic
165	#2943	C₂×C₁₃	1	1	yes	characteristic
166	#2906	C₂×C₁₃	1	2	yes	complemented
167	#1946	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1945	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1866	C₂×C₁₃	1	2	yes	complemented
170	#1866	C₂×C₁₃	1	2	yes	complemented
171	#1849	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1806	C₂×C₁₃	1	2	yes	complemented
173	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	8	2	no	—
197	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	1	no	—
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
212	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
213	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#131	C₂²×C₁₃	1	2	yes	—
215	C₂×#131	C₂²×C₁₃	1	2	yes	—
216	C₄×#41	C₂²×C₁₃	1	2	yes	—
217	#444	—	2	4	no	—
218	#443	—	2	4	no	—
219	#442	C₄×C₁₃	1	2	yes	complemented
220	#441	C₄×C₁₃	1	2	yes	complemented
221	#440	C₄×C₁₃	1	2	yes	complemented
222	#440	C₄×C₁₃	1	2	yes	complemented
223	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#108	C₂²×C₁₃	1	2	yes	—
226	#427	C₂²×C₁₃	1	1	yes	characteristic
227	#424	—	2	2	no	—
228	#424	—	2	2	no	—
229	#424	C₂²×C₁₃	1	2	yes	—
230	#424	C₂²×C₁₃	1	2	yes	—
231	#423	—	2	2	no	—
232	#423	C₂²×C₁₃	1	2	yes	—
233	C₂×C₄⋊C₈	—	2	2	no	—
234	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#104	C₂²×C₁₃	1	2	yes	—
236	C₂×#104	C₂²×C₁₃	1	2	yes	—
237	#416	C₂²×C₁₃	1	2	yes	—
238	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	#339	C₂²×C₁₃	1	2	yes	—
243	#339	C₂²×C₁₃	1	2	yes	—
244	#336	C₂²×C₁₃	1	1	yes	characteristic
245	#336	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	4	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₁₃	#547	1	1	yes	characteristic
253	C₂²×C₁₃	#554	1	1	yes	characteristic
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	8	1	no	—
261	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
262	C₄×C₁₃	#520	1	1	yes	characteristic
263	C₄×C₁₃	D₄²	1	1	yes	characteristic
264	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
265	C₂×#41	C₂³×C₁₃	1	2	yes	—
266	#135	D₄×C₁₃	1	4	yes	—
267	#135	Q₈×C₁₃	1	4	yes	—
268	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
270	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
271	#131	—	2	4	no	—
272	#131	—	2	4	no	—
273	#131	—	4	2	no	—
274	#131	—	4	2	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
278	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
286	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
290	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
291	#117	—	2	2	no	—
292	#117	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	#108	—	2	2	no	—
299	#108	—	2	2	no	—
300	#108	—	4	2	no	—
301	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
302	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
303	#106	C₂×C₄×C₁₃	1	2	yes	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
311	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
312	#104	—	2	4	no	—
313	#104	—	2	4	no	—
314	#103	C₂×C₄×C₁₃	1	2	yes	—
315	#103	C₂×C₄×C₁₃	1	2	yes	—
316	#102	C₂×C₄×C₁₃	1	2	yes	—
317	#102	C₂×C₄×C₁₃	1	2	yes	—
318	#97	—	2	2	no	—
319	#97	C₂×C₄×C₁₃	1	2	yes	—
320	#97	C₂×C₄×C₁₃	1	2	yes	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	1	no	—
323	C₂×C₁₃	—	2	1	no	—
324	C₂×C₁₃	—	2	1	no	—
325	C₂×C₁₃	—	4	4	no	—
326	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₁₃	#2955	1	1	yes	characteristic
328	C₂×C₁₃	#2956	1	1	yes	characteristic
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	C₂×D₄×C₁₃	1	4	yes	—
332	#41	C₂×Q₈×C₁₃	1	4	yes	—
333	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
342	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
344	Q₁₆	C₁₃×C₄⋊C₄	1	4	yes	complemented
345	SD₁₆	C₁₃×C₄⋊C₄	1	8	yes	complemented
346	D₈	C₁₃×C₄⋊C₄	1	4	yes	complemented
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	4	no	—
352	M₁₆	—	4	4	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	—	4	4	no	—
363	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
364	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
370	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
375	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
387	C₄²	C₂×D₄×C₁₃	1	2	yes	—
388	C₁₃	#22687	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	2	no	—
390	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
413	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
414	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	2	no	—
423	C₈	—	2	1	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
427	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
434	C₂²	C₁₃×#547	1	1	yes	characteristic
435	C₂²	C₁₃×#554	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
444	C₄	C₁₃×#520	1	1	yes	characteristic
445	C₄	D₄²×C₁₃	1	1	yes	characteristic
446	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
451	C₂	C₁₃×#2955	1	1	yes	characteristic
452	C₂	C₁₃×#2956	1	1	yes	characteristic

	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	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#2906	C₂	semidirect
5. C₁₃×#1946	C₂	semidirect
6. C₁₃×#1945	C₂	semidirect
7. C₁₃×#1866	C₂	semidirect
8. C₁₃×#1866	C₂	semidirect
9. C₁₃×#1849	C₂	semidirect
10. C₁₃×#1806	C₂	semidirect
11. C₁₃×#1771	C₂	semidirect
18. C₁₃×#442	C₄	semidirect
19. C₁₃×#441	C₄	semidirect
20. C₁₃×#440	C₄	semidirect
21. C₁₃×#440	C₄	semidirect
103. #22687	C₁₃	direct (N × H)
119. C₁₃×Q₁₆	C₄⋊C₄	semidirect
120. C₁₃×SD₁₆	C₄⋊C₄	semidirect
121. C₁₃×D₈	C₄⋊C₄	semidirect
166. #2906	C₂×C₁₃	semidirect
167. #1946	C₂×C₁₃	semidirect
168. #1945	C₂×C₁₃	semidirect
169. #1866	C₂×C₁₃	semidirect
170. #1866	C₂×C₁₃	semidirect
171. #1849	C₂×C₁₃	semidirect
172. #1806	C₂×C₁₃	semidirect
173. #1771	C₂×C₁₃	semidirect
219. #442	C₄×C₁₃	semidirect
220. #441	C₄×C₁₃	semidirect
221. #440	C₄×C₁₃	semidirect
222. #440	C₄×C₁₃	semidirect
344. Q₁₆	C₁₃×C₄⋊C₄	semidirect
345. SD₁₆	C₁₃×C₄⋊C₄	semidirect
346. D₈	C₁₃×C₄⋊C₄	semidirect
388. C₁₃	#22687	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×#444	2
C₂×C₁₃×#443	2
C₁₃×#2943	2
C₁₃×#2906	2
C₁₃×#1946	2
C₁₃×#1945	2
C₁₃×#1866	2
C₁₃×#1849	2
C₁₃×#1806	2
C₁₃×#1771	2
#22687	13

Subgroups — C13×#22687 #15709026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22687 #15709026