Subgroups — C₁₃×#22688 #15709027

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#443	C₂	1	2	yes	maximal
2	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2906	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1945	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1866	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1806	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#131	C₂²	1	4	yes	—
11	C₄×C₁₃×#41	C₂²	1	2	yes	—
12	C₁₃×#443	—	2	8	no	—
13	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
15	C₄×C₁₃×SD₁₆	C₄	1	2	yes	complemented
16	C₄×C₁₃×SD₁₆	C₄	1	2	yes	complemented
17	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
18	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₃×#108	C₂²	1	2	yes	—
20	C₂×C₁₃×#108	C₂²	1	2	yes	—
21	C₁₃×#427	C₂²	1	1	yes	characteristic
22	C₁₃×#424	—	2	4	no	—
23	C₁₃×#424	C₂²	1	4	yes	—
24	C₁₃×#423	—	2	2	no	—
25	C₁₃×#423	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#104	C₂²	1	4	yes	—
29	C₁₃×#416	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₁₃×#339	C₂²	1	4	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂×C₁₃×#41	C₂³	1	2	yes	—
36	C₁₃×#135	D₄	1	4	yes	—
37	C₁₃×#135	Q₈	1	4	yes	—
38	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
40	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
41	C₁₃×#131	—	2	8	no	—
42	C₁₃×#131	—	4	4	no	—
43	C₂×C₁₃×M₁₆	—	2	4	no	—
44	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₃	—	2	4	no	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#108	—	2	4	no	—
62	C₁₃×#108	—	4	2	no	—
63	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#106	C₂×C₄	1	2	yes	—
66	C₁₃×C₄⋊C₈	—	2	4	no	—
67	C₁₃×C₄⋊C₈	—	2	4	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	—	2	2	no	—
70	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
73	C₁₃×#104	—	2	8	no	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#103	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₁₃×#102	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃	—	2	4	no	—
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#95	—	2	1	no	—
84	#22688	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₁₃×#41	—	2	2	no	—
86	C₁₃×#41	—	2	2	no	—
87	C₁₃×#41	C₂×D₄	1	4	yes	—
88	C₁₃×#41	C₂×Q₈	1	4	yes	—
89	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₁₃×Q₁₆	C₄⋊C₄	1	4	yes	complemented
100	C₁₃×SD₁₆	C₄⋊C₄	1	8	yes	complemented
101	C₁₃×D₈	C₄⋊C₄	1	4	yes	complemented
102	C₁₃×M₁₆	—	2	4	no	—
103	C₁₃×M₁₆	—	2	4	no	—
104	C₁₃×M₁₆	—	4	8	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	4	no	—
110	C₂×C₈×C₁₃	—	4	8	no	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₁₃×C₂²⋊C₄	—	2	2	no	—
126	C₁₃×C₂²⋊C₄	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×#443	C₂×C₁₃	1	2	yes	—
137	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
138	#2906	C₂×C₁₃	1	2	yes	complemented
139	#1945	C₂×C₁₃	1	2	yes	complemented
140	#1866	C₂×C₁₃	1	4	yes	complemented
141	#1848	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#1806	C₂×C₁₃	1	2	yes	complemented
143	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	2	no	—
147	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
148	D₄×C₁₃	—	2	4	no	—
149	D₄×C₁₃	—	2	4	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	8	2	no	—
164	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₈×C₁₃	—	2	1	no	—
175	C₈×C₁₃	—	2	1	no	—
176	C₈×C₁₃	—	2	2	no	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	—	4	4	no	—
179	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
180	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
181	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×#131	C₂²×C₁₃	1	4	yes	—
183	C₄×#41	C₂²×C₁₃	1	2	yes	—
184	#443	—	2	8	no	—
185	C₄×Q₁₆	C₄×C₁₃	1	1	yes	characteristic, complemented
186	C₄×Q₁₆	C₄×C₁₃	1	1	yes	characteristic, complemented
187	C₄×SD₁₆	C₄×C₁₃	1	2	yes	complemented
188	C₄×SD₁₆	C₄×C₁₃	1	2	yes	complemented
189	C₄×D₈	C₄×C₁₃	1	1	yes	characteristic, complemented
190	C₄×D₈	C₄×C₁₃	1	1	yes	characteristic, complemented
191	C₂×#108	C₂²×C₁₃	1	2	yes	—
192	C₂×#108	C₂²×C₁₃	1	2	yes	—
193	#427	C₂²×C₁₃	1	1	yes	characteristic
194	#424	—	2	4	no	—
195	#424	C₂²×C₁₃	1	4	yes	—
196	#423	—	2	2	no	—
197	#423	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄⋊C₈	—	2	2	no	—
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#104	C₂²×C₁₃	1	4	yes	—
201	#416	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
205	#339	C₂²×C₁₃	1	4	yes	—
206	#336	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	4	no	—
210	C₂²×C₁₃	—	4	2	no	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₁₃	#547	1	1	yes	characteristic
214	C₂²×C₁₃	#554	1	1	yes	characteristic
215	C₄×C₁₃	—	2	4	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	#443	1	2	yes	complemented
223	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₄×C₁₃	#520	1	1	yes	characteristic
225	C₄×C₁₃	D₄²	1	1	yes	characteristic
226	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
227	C₂×#41	C₂³×C₁₃	1	2	yes	—
228	#135	D₄×C₁₃	1	4	yes	—
229	#135	Q₈×C₁₃	1	4	yes	—
230	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
231	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
232	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
233	#131	—	2	8	no	—
234	#131	—	4	4	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
237	C₂²×C₈	—	2	4	no	—
238	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
240	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
242	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
246	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
247	#117	—	2	2	no	—
248	#117	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	#108	—	2	4	no	—
254	#108	—	4	2	no	—
255	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
256	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
257	#106	C₂×C₄×C₁₃	1	2	yes	—
258	C₄⋊C₈	—	2	4	no	—
259	C₄⋊C₈	—	2	4	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
263	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
264	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
265	#104	—	2	8	no	—
266	#103	C₂×C₄×C₁₃	1	2	yes	—
267	#103	C₂×C₄×C₁₃	1	2	yes	—
268	#102	C₂×C₄×C₁₃	1	2	yes	—
269	#102	C₂×C₄×C₁₃	1	2	yes	—
270	C₄×C₈	—	2	4	no	—
271	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
273	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
274	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
275	#95	—	2	1	no	—
276	C₂×C₁₃	—	2	1	no	—
277	C₂×C₁₃	—	2	1	no	—
278	C₂×C₁₃	—	4	4	no	—
279	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
281	C₂×C₁₃	#2957	1	1	yes	characteristic
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	C₂×D₄×C₁₃	1	4	yes	—
285	#41	C₂×Q₈×C₁₃	1	4	yes	—
286	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
294	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
296	Q₁₆	C₁₃×C₄⋊C₄	1	4	yes	complemented
297	SD₁₆	C₁₃×C₄⋊C₄	1	8	yes	complemented
298	D₈	C₁₃×C₄⋊C₄	1	4	yes	complemented
299	M₁₆	—	2	4	no	—
300	M₁₆	—	2	4	no	—
301	M₁₆	—	4	8	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	4	8	no	—
308	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
309	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
314	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
315	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
320	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
330	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₁₃	#22688	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	—	2	2	no	—
335	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
338	D₄	—	2	4	no	—
339	D₄	—	2	4	no	—
340	D₄	—	2	2	no	—
341	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
362	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	4	4	no	—
369	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
370	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
377	C₂²	C₁₃×#547	1	1	yes	characteristic
378	C₂²	C₁₃×#554	1	1	yes	characteristic
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	C₁₃×#443	1	2	yes	complemented
387	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
388	C₄	C₁₃×#520	1	1	yes	characteristic
389	C₄	D₄²×C₁₃	1	1	yes	characteristic
390	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	4	no	—
394	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
395	C₂	C₂×C₁₃×#443	1	1	yes	characteristic
396	C₂	C₁₃×#2957	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
3. C₁₃×#2906	C₂	semidirect
4. C₁₃×#1945	C₂	semidirect
5. C₁₃×#1866	C₂	semidirect
6. C₁₃×#1848	C₂	semidirect
7. C₁₃×#1806	C₂	semidirect
8. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₄×C₁₃×Q₁₆	C₄	semidirect
14. C₄×C₁₃×Q₁₆	C₄	semidirect
15. C₄×C₁₃×SD₁₆	C₄	semidirect
16. C₄×C₁₃×SD₁₆	C₄	semidirect
17. C₄×C₁₃×D₈	C₄	semidirect
18. C₄×C₁₃×D₈	C₄	semidirect
84. #22688	C₁₃	direct (N × H)
99. C₁₃×Q₁₆	C₄⋊C₄	semidirect
100. C₁₃×SD₁₆	C₄⋊C₄	semidirect
101. C₁₃×D₈	C₄⋊C₄	semidirect
138. #2906	C₂×C₁₃	semidirect
139. #1945	C₂×C₁₃	semidirect
140. #1866	C₂×C₁₃	semidirect
141. #1848	C₂×C₁₃	semidirect
142. #1806	C₂×C₁₃	semidirect
143. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
185. C₄×Q₁₆	C₄×C₁₃	semidirect
186. C₄×Q₁₆	C₄×C₁₃	semidirect
187. C₄×SD₁₆	C₄×C₁₃	semidirect
188. C₄×SD₁₆	C₄×C₁₃	semidirect
189. C₄×D₈	C₄×C₁₃	semidirect
190. C₄×D₈	C₄×C₁₃	semidirect
222. C₄×C₁₃	#443	semidirect
296. Q₁₆	C₁₃×C₄⋊C₄	semidirect
297. SD₁₆	C₁₃×C₄⋊C₄	semidirect
298. D₈	C₁₃×C₄⋊C₄	semidirect
333. C₁₃	#22688	direct (N × H)
386. C₄	C₁₃×#443	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#443	2
C₄×C₁₃×#135	2
C₁₃×#2906	2
C₁₃×#1945	2
C₁₃×#1866	2
C₁₃×#1848	2
C₁₃×#1806	2
C₈×C₁₃×C₄⋊C₄	2
#22688	13

Subgroups — C13×#22688 #15709027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22688 #15709027