Subgroups — C₁₃×#26444 #15712783

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2088	C₂	1	2	yes	maximal
4	C₁₃×#2058	C₂	1	2	yes	maximal
5	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1987	C₂	1	2	yes	maximal
8	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1920	C₂	1	2	yes	maximal
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#395	—	2	2	no	—
23	C₁₃×#391	—	2	1	no	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₁₃×#340	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×C₄⋊Q₈	—	2	4	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	4	2	no	—
49	C₁₃×C₄⋊Q₈	—	4	4	no	—
50	C₁₃×C₄⋊Q₈	Q₈	1	4	yes	complemented
51	C₄×Q₈×C₁₃	—	4	4	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×#106	—	4	2	no	—
73	C₁₃×#106	Q₈	1	4	yes	complemented
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×C₄⋊C₈	—	4	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₁₃×#95	—	2	1	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	D₄	1	2	yes	—
83	#26444	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×Q₈×C₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₃	—	4	4	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×Q₈×C₁₃	—	8	2	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	4	4	no	—
121	C₁₃×C₄⋊C₄	—	4	4	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	4	2	no	—
124	C₁₃×C₄⋊C₄	—	8	1	no	—
125	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
126	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
127	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
129	C₁₃×C₄⋊C₄	#41	1	2	yes	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	4	4	no	—
133	C₄²×C₁₃	—	4	2	no	—
134	C₄²×C₁₃	—	4	2	no	—
135	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
136	C₄²×C₁₃	#41	1	2	yes	—
137	#2551	C₂×C₁₃	1	1	yes	characteristic
138	#2365	C₂×C₁₃	1	1	yes	characteristic
139	#2088	C₂×C₁₃	1	2	yes	—
140	#2058	C₂×C₁₃	1	2	yes	—
141	#1990	C₂×C₁₃	1	1	yes	characteristic
142	#1988	C₂×C₁₃	1	1	yes	characteristic
143	#1987	C₂×C₁₃	1	2	yes	—
144	#1948	C₂×C₁₃	1	1	yes	characteristic
145	#1939	C₂×C₁₃	1	1	yes	characteristic
146	#1920	C₂×C₁₃	1	2	yes	—
147	C₄×#106	C₂×C₁₃	1	1	yes	characteristic
148	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₃	—	4	8	no	—
150	Q₈×C₁₃	—	8	8	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	—	4	1	no	—
189	C₈×C₁₃	—	4	2	no	—
190	C₂×C₄⋊Q₈	—	2	1	no	—
191	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
192	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#106	C₂²×C₁₃	1	2	yes	—
196	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	#395	—	2	2	no	—
201	#391	—	2	1	no	—
202	#389	—	2	1	no	—
203	#389	C₂²×C₁₃	1	2	yes	—
204	#389	C₂²×C₁₃	1	2	yes	—
205	#387	—	2	2	no	—
206	#384	C₂²×C₁₃	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
209	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	#340	C₂²×C₁₃	1	2	yes	—
212	#340	C₂²×C₁₃	1	2	yes	—
213	#340	C₂²×C₁₃	1	1	yes	characteristic
214	#340	C₂²×C₁₃	1	2	yes	—
215	#340	C₂²×C₁₃	1	2	yes	—
216	#340	C₂²×C₁₃	1	2	yes	—
217	#340	C₂²×C₁₃	1	1	yes	characteristic
218	#336	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₂²×C₁₃	#546	1	1	yes	characteristic
221	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
222	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
223	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂²×C₁₃	#577	1	1	yes	characteristic
225	C₂²×C₁₃	#578	1	1	yes	characteristic
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	4	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	#476	1	4	yes	—
236	C₄×C₁₃	#533	1	1	yes	characteristic
237	C₄×C₁₃	#542	1	1	yes	characteristic
238	C₄×C₁₃	#557	1	1	yes	characteristic
239	C₄×C₁₃	Q₈²	1	1	yes	characteristic
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₄⋊Q₈	—	2	4	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	4	2	no	—
248	C₄⋊Q₈	—	4	4	no	—
249	C₄⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
250	C₄×Q₈	—	4	4	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	#106	—	2	2	no	—
271	#106	—	4	2	no	—
272	#106	Q₈×C₁₃	1	4	yes	complemented
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	4	2	no	—
275	C₄×C₈	—	2	2	no	—
276	#95	—	2	1	no	—
277	#95	—	2	2	no	—
278	#95	—	2	1	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	D₄×C₁₃	1	2	yes	—
282	C₂×C₁₃	#2451	1	1	yes	characteristic
283	C₂×C₁₃	C₂×#476	1	1	yes	characteristic
284	C₂×C₁₃	#3082	1	1	yes	characteristic
285	C₂×C₁₃	#3298	1	1	yes	characteristic
286	C₂×C₁₃	#3324	1	1	yes	characteristic
287	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
288	C₂×C₁₃	#3386	1	1	yes	characteristic
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	8	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	8	1	no	—
330	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
331	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
332	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
333	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
334	C₄⋊C₄	C₁₃×#41	1	2	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	4	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
341	C₄²	C₁₃×#41	1	2	yes	—
342	C₁₃	#26444	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	Q₈	—	4	8	no	—
345	Q₈	—	8	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
372	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
374	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
375	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
380	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
386	C₂²	C₁₃×#546	1	1	yes	characteristic
387	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
388	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
389	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₂²	C₁₃×#577	1	1	yes	characteristic
391	C₂²	C₁₃×#578	1	1	yes	characteristic
392	C₄	—	2	4	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	2	no	—
401	C₄	C₁₃×#476	1	4	yes	—
402	C₄	C₁₃×#533	1	1	yes	characteristic
403	C₄	C₁₃×#542	1	1	yes	characteristic
404	C₄	C₁₃×#557	1	1	yes	characteristic
405	C₄	Q₈²×C₁₃	1	1	yes	characteristic
406	C₂	C₁₃×#2451	1	1	yes	characteristic
407	C₂	C₂×C₁₃×#476	1	1	yes	characteristic
408	C₂	C₁₃×#3082	1	1	yes	characteristic
409	C₂	C₁₃×#3298	1	1	yes	characteristic
410	C₂	C₁₃×#3324	1	1	yes	characteristic
411	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
412	C₂	C₁₃×#3386	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
50. C₁₃×C₄⋊Q₈	Q₈	semidirect
73. C₁₃×#106	Q₈	semidirect
83. #26444	C₁₃	direct (N × H)
249. C₄⋊Q₈	Q₈×C₁₃	semidirect
272. #106	Q₈×C₁₃	semidirect
342. C₁₃	#26444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2551	2
C₁₃×#2365	2
C₁₃×#2088	2
C₁₃×#2058	2
C₁₃×#1990	2
C₁₃×#1988	2
C₁₃×#1987	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1920	2
C₄×C₁₃×#106	2
#26444	13

Subgroups — C13×#26444 #15712783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26444 #15712783