Subgroups — C₁₃×#61111 #15747450

Order 3328.

2600 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3586	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3293	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3291	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3289	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3069	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3018	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#456	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2956	C₂	1	2	yes	maximal, complemented
10	C₁₃×#585	C₂²	1	2	yes	complemented
11	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
12	C₁₃×#578	—	2	8	no	—
13	C₁₃×#578	C₂²	1	16	yes	complemented
14	C₁₃×#577	—	2	8	no	—
15	C₁₃×#577	C₂²	1	16	yes	complemented
16	C₁₃×#575	—	2	8	no	—
17	C₁₃×#575	C₂²	1	4	yes	—
18	C₁₃×#575	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	—	2	8	no	—
20	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
22	C₁₃×#568	C₂²	1	4	yes	complemented
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#497	C₂²	1	4	yes	complemented
26	C₁₃×#494	C₂²	1	2	yes	complemented
27	C₁₃×#492	C₂²	1	2	yes	complemented
28	C₁₃×#473	C₂²	1	16	yes	complemented
29	C₁₃×#471	C₂²	1	16	yes	complemented
30	C₁₃×#456	C₂²	1	8	yes	complemented
31	C₁₃×#456	C₂²	1	8	yes	complemented
32	C₁₃×#456	C₂²	1	4	yes	complemented
33	C₁₃×#455	C₂²	1	4	yes	complemented
34	C₁₃×#454	C₂²	1	4	yes	complemented
35	C₁₃×#453	C₂²	1	4	yes	complemented
36	C₁₃×#444	C₂²	1	8	yes	complemented
37	C₁₃×#443	C₂²	1	8	yes	complemented
38	C₁₃×#430	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
40	C₁₃×#413	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
42	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×2₋¹⁺⁴	—	2	8	no	—
44	C₁₃×2₋¹⁺⁴	—	2	4	no	—
45	C₁₃×2₋¹⁺⁴	—	4	2	no	—
46	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	—
47	C₁₃×2₋¹⁺⁴	C₂³	1	8	yes	—
48	C₁₃×H(5,𝔽₂)	—	2	4	no	—
49	C₁₃×H(5,𝔽₂)	—	4	2	no	—
50	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
51	C₂×C₁₃×#41	—	2	8	no	—
52	C₂×C₁₃×#41	—	2	4	no	—
53	C₂×C₁₃×#41	—	4	2	no	—
54	C₂×C₁₃×#41	—	4	2	no	—
55	C₂×C₁₃×#41	C₂³	1	4	yes	—
56	C₂×C₁₃×#41	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	—	2	4	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#137	—	2	8	no	—
60	C₁₃×#137	—	2	4	no	—
61	C₁₃×#137	—	2	16	no	—
62	C₁₃×#137	—	2	16	no	—
63	C₁₃×#137	—	2	16	no	—
64	C₁₃×#137	—	2	8	no	—
65	C₁₃×#137	—	2	8	no	—
66	C₁₃×#137	D₄	1	8	yes	complemented
67	C₁₃×#137	C₂³	1	8	yes	—
68	C₁₃×#137	C₂³	1	16	yes	—
69	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
70	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
71	C₁₃×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
72	C₁₃×AGL(1,ℤ/8)	C₂³	1	8	yes	—
73	C₁₃×#135	—	2	8	no	—
74	C₁₃×#135	—	2	16	no	—
75	C₁₃×#135	—	2	16	no	—
76	C₁₃×#135	C₂³	1	8	yes	—
77	C₂×C₁₃×Q₁₆	—	2	4	no	—
78	C₂×C₁₃×Q₁₆	—	2	16	no	—
79	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
80	C₂×C₁₃×SD₁₆	—	2	4	no	—
81	C₂×C₁₃×SD₁₆	—	2	16	no	—
82	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
83	C₁₃×#131	—	2	8	no	—
84	C₁₃×#131	C₂³	1	16	yes	—
85	C₂×C₁₃×M₁₆	—	2	8	no	—
86	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
88	C₁₃×C₄⋊Q₈	—	4	1	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×#127	C₂³	1	1	yes	characteristic
93	C₁₃×#124	C₂³	1	2	yes	—
94	C₁₃×#121	—	4	1	no	—
95	C₄×D₄×C₁₃	—	4	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#108	C₂³	1	8	yes	—
99	C₁₃×#104	C₂³	1	8	yes	—
100	C₁₃×#104	C₂³	1	8	yes	—
101	C₁₃×#101	C₂³	1	8	yes	—
102	C₁₃×#101	C₂³	1	4	yes	—
103	C₁₃×#100	C₂³	1	4	yes	—
104	C₁₃×#97	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃	C₂³	1	2	yes	—
106	#61111	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₁₃×#41	—	2	4	no	—
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	—	2	8	no	—
110	C₁₃×#41	—	2	16	no	—
111	C₁₃×#41	—	2	8	no	—
112	C₁₃×#41	—	2	4	no	—
113	C₁₃×#41	—	2	4	no	—
114	C₁₃×#41	—	4	4	no	—
115	C₁₃×#41	—	4	4	no	—
116	C₁₃×#41	—	4	8	no	—
117	C₁₃×#41	—	4	8	no	—
118	C₁₃×#41	—	4	8	no	—
119	C₁₃×#41	—	4	8	no	—
120	C₁₃×#41	—	4	4	no	—
121	C₁₃×#41	C₂×D₄	1	8	yes	—
122	C₁₃×#41	C₂⁴	1	8	yes	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	16	no	—
125	C₂×Q₈×C₁₃	—	2	8	no	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	—	4	8	no	—
130	C₂×Q₈×C₁₃	—	4	2	no	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
132	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
133	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	4	1	no	—
138	C₂×D₄×C₁₃	—	4	4	no	—
139	C₂×D₄×C₁₃	—	4	2	no	—
140	C₂×D₄×C₁₃	—	4	8	no	—
141	C₂×D₄×C₁₃	—	4	2	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×Q₁₆	—	2	16	no	—
152	C₁₃×Q₁₆	—	2	8	no	—
153	C₁₃×Q₁₆	—	2	16	no	—
154	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
155	C₁₃×SD₁₆	—	2	8	no	—
156	C₁₃×SD₁₆	—	2	16	no	—
157	C₁₃×SD₁₆	—	2	8	no	—
158	C₁₃×SD₁₆	—	2	16	no	—
159	C₁₃×SD₁₆	C₂×D₄	1	16	yes	—
160	C₁₃×D₈	—	2	8	no	—
161	C₁₃×D₈	C₂×D₄	1	8	yes	—
162	C₁₃×M₁₆	—	2	4	no	—
163	C₁₃×M₁₆	—	2	16	no	—
164	C₁₃×M₁₆	C₂×D₄	1	8	yes	—
165	C₁₃×M₁₆	C₂⁴	1	8	yes	—
166	C₂×C₈×C₁₃	—	2	4	no	—
167	C₂×C₈×C₁₃	—	2	16	no	—
168	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₄⋊C₄	—	4	2	no	—
171	C₁₃×C₄⋊C₄	—	4	1	no	—
172	C₁₃×C₂²⋊C₄	—	4	2	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
176	#3586	C₂×C₁₃	1	4	yes	complemented
177	#3293	C₂×C₁₃	1	4	yes	complemented
178	#3291	C₂×C₁₃	1	4	yes	complemented
179	#3289	C₂×C₁₃	1	8	yes	complemented
180	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#3069	C₂×C₁₃	1	4	yes	complemented
182	#3018	C₂×C₁₃	1	2	yes	complemented
183	C₂×#456	C₂×C₁₃	1	2	yes	complemented
184	#2956	C₂×C₁₃	1	2	yes	complemented
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	4	4	no	—
188	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
189	Q₈×C₁₃	—	2	4	no	—
190	Q₈×C₁₃	—	2	8	no	—
191	Q₈×C₁₃	—	2	4	no	—
192	Q₈×C₁₃	—	4	8	no	—
193	Q₈×C₁₃	—	4	4	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
196	D₄×C₁₃	—	2	8	no	—
197	D₄×C₁₃	—	2	8	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	—	2	4	no	—
200	D₄×C₁₃	—	4	8	no	—
201	D₄×C₁₃	—	4	4	no	—
202	D₄×C₁₃	—	4	8	no	—
203	D₄×C₁₃	—	4	4	no	—
204	D₄×C₁₃	—	8	2	no	—
205	D₄×C₁₃	C₂²×D₄	1	8	yes	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	8	no	—
215	C₂×C₄×C₁₃	—	4	16	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
224	C₈×C₁₃	—	2	8	no	—
225	C₈×C₁₃	C₂²×D₄	1	8	yes	—
226	#585	C₂²×C₁₃	1	2	yes	complemented
227	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
228	#578	—	2	8	no	—
229	#578	C₂²×C₁₃	1	16	yes	complemented
230	#577	—	2	8	no	—
231	#577	C₂²×C₁₃	1	16	yes	complemented
232	#575	—	2	8	no	—
233	#575	C₂²×C₁₃	1	4	yes	—
234	#575	C₂²×C₁₃	1	2	yes	—
235	C₂×#137	—	2	8	no	—
236	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
237	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
238	#568	C₂²×C₁₃	1	4	yes	complemented
239	#532	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	#497	C₂²×C₁₃	1	4	yes	complemented
242	#494	C₂²×C₁₃	1	2	yes	complemented
243	#492	C₂²×C₁₃	1	2	yes	complemented
244	#473	C₂²×C₁₃	1	16	yes	complemented
245	#471	C₂²×C₁₃	1	16	yes	complemented
246	#456	C₂²×C₁₃	1	8	yes	complemented
247	#456	C₂²×C₁₃	1	8	yes	complemented
248	#456	C₂²×C₁₃	1	4	yes	complemented
249	#455	C₂²×C₁₃	1	4	yes	complemented
250	#454	C₂²×C₁₃	1	4	yes	complemented
251	#453	C₂²×C₁₃	1	4	yes	complemented
252	#444	C₂²×C₁₃	1	8	yes	complemented
253	#443	C₂²×C₁₃	1	8	yes	complemented
254	#430	C₂²×C₁₃	1	2	yes	complemented
255	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
256	#413	C₂²×C₁₃	1	2	yes	complemented
257	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
258	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
259	C₂²×C₁₃	—	2	8	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	8	4	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	16	4	no	—
265	C₂²×C₁₃	D₄²	1	2	yes	—
266	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	8	no	—
269	C₄×C₁₃	—	4	1	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	4	no	—
272	C₄×C₁₃	D₄²	1	2	yes	—
273	C₄×C₁₃	C₂³×D₄	1	2	yes	—
274	2₋¹⁺⁴	—	2	8	no	—
275	2₋¹⁺⁴	—	2	4	no	—
276	2₋¹⁺⁴	—	4	2	no	—
277	2₋¹⁺⁴	C₂³×C₁₃	1	8	yes	—
278	2₋¹⁺⁴	C₂³×C₁₃	1	4	yes	—
279	H(5,𝔽₂)	—	2	4	no	—
280	H(5,𝔽₂)	—	4	2	no	—
281	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	—
282	C₂×#41	—	2	8	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	—	4	2	no	—
285	C₂×#41	—	4	2	no	—
286	C₂×#41	C₂³×C₁₃	1	4	yes	—
287	C₂×#41	C₂³×C₁₃	1	2	yes	—
288	C₂²×Q₈	—	2	4	no	—
289	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
290	#137	—	2	8	no	—
291	#137	—	2	4	no	—
292	#137	—	2	16	no	—
293	#137	—	2	16	no	—
294	#137	—	2	16	no	—
295	#137	—	2	8	no	—
296	#137	—	2	8	no	—
297	#137	D₄×C₁₃	1	8	yes	complemented
298	#137	C₂³×C₁₃	1	16	yes	—
299	#137	C₂³×C₁₃	1	8	yes	—
300	AGL(1,ℤ/8)	—	2	4	no	—
301	AGL(1,ℤ/8)	—	2	16	no	—
302	AGL(1,ℤ/8)	D₄×C₁₃	1	8	yes	complemented
303	AGL(1,ℤ/8)	C₂³×C₁₃	1	8	yes	—
304	#135	—	2	8	no	—
305	#135	—	2	16	no	—
306	#135	—	2	16	no	—
307	#135	C₂³×C₁₃	1	8	yes	—
308	C₂×Q₁₆	—	2	4	no	—
309	C₂×Q₁₆	—	2	16	no	—
310	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
311	C₂×SD₁₆	—	2	4	no	—
312	C₂×SD₁₆	—	2	16	no	—
313	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
314	#131	—	2	8	no	—
315	#131	C₂³×C₁₃	1	16	yes	—
316	C₂×M₁₆	—	2	8	no	—
317	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
318	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
319	C₄⋊Q₈	—	4	1	no	—
320	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
321	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
323	#127	C₂³×C₁₃	1	1	yes	characteristic
324	#124	C₂³×C₁₃	1	2	yes	—
325	#121	—	4	1	no	—
326	C₄×D₄	—	4	1	no	—
327	C₂×C₄⋊C₄	—	4	1	no	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	#108	C₂³×C₁₃	1	8	yes	—
330	#104	C₂³×C₁₃	1	8	yes	—
331	#104	C₂³×C₁₃	1	8	yes	—
332	#101	C₂³×C₁₃	1	8	yes	—
333	#101	C₂³×C₁₃	1	4	yes	—
334	#100	C₂³×C₁₃	1	4	yes	—
335	#97	C₂³×C₁₃	1	2	yes	—
336	C₄×C₈	C₂³×C₁₃	1	2	yes	—
337	C₂×C₁₃	—	2	1	no	—
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	4	8	no	—
340	C₂×C₁₃	—	8	2	no	—
341	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	8	no	—
345	#41	—	2	16	no	—
346	#41	—	2	8	no	—
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	4	4	no	—
350	#41	—	4	4	no	—
351	#41	—	4	8	no	—
352	#41	—	4	8	no	—
353	#41	—	4	8	no	—
354	#41	—	4	8	no	—
355	#41	—	4	4	no	—
356	#41	C₂×D₄×C₁₃	1	8	yes	—
357	#41	C₂⁴×C₁₃	1	8	yes	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	16	no	—
360	C₂×Q₈	—	2	8	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	8	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
367	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
368	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	8	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
378	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	Q₁₆	—	2	16	no	—
387	Q₁₆	—	2	8	no	—
388	Q₁₆	—	2	16	no	—
389	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
390	SD₁₆	—	2	8	no	—
391	SD₁₆	—	2	16	no	—
392	SD₁₆	—	2	8	no	—
393	SD₁₆	—	2	16	no	—
394	SD₁₆	C₂×D₄×C₁₃	1	16	yes	—
395	D₈	—	2	8	no	—
396	D₈	C₂×D₄×C₁₃	1	8	yes	—
397	M₁₆	—	2	4	no	—
398	M₁₆	—	2	16	no	—
399	M₁₆	C₂×D₄×C₁₃	1	8	yes	—
400	M₁₆	C₂⁴×C₁₃	1	8	yes	—
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	2	16	no	—
403	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₄²	—	2	1	no	—
409	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
410	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
411	C₁₃	#61111	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	4	no	—
415	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	8	no	—
418	Q₈	—	2	4	no	—
419	Q₈	—	4	8	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	4	no	—
422	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
423	D₄	—	2	8	no	—
424	D₄	—	2	8	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	8	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	4	no	—
431	D₄	—	8	2	no	—
432	D₄	C₂²×D₄×C₁₃	1	8	yes	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	16	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
449	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
451	C₈	—	2	8	no	—
452	C₈	C₂²×D₄×C₁₃	1	8	yes	—
453	C₂²	—	2	8	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	16	4	no	—
459	C₂²	D₄²×C₁₃	1	2	yes	—
460	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	8	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	4	no	—
466	C₄	D₄²×C₁₃	1	2	yes	—
467	C₄	C₂³×D₄×C₁₃	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	4	8	no	—
471	C₂	—	8	2	no	—
472	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3586	C₂	semidirect
2. C₁₃×#3293	C₂	semidirect
3. C₁₃×#3291	C₂	semidirect
4. C₁₃×#3289	C₂	semidirect
5. C₁₃×#3152	C₂	semidirect
6. C₁₃×#3069	C₂	semidirect
7. C₁₃×#3018	C₂	semidirect
8. C₂×C₁₃×#456	C₂	semidirect
9. C₁₃×#2956	C₂	semidirect
10. C₁₃×#585	C₂²	semidirect
13. C₁₃×#578	C₂²	semidirect
15. C₁₃×#577	C₂²	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₁₃×#568	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₁₃×#497	C₂²	semidirect
26. C₁₃×#494	C₂²	semidirect
27. C₁₃×#492	C₂²	semidirect
28. C₁₃×#473	C₂²	semidirect
29. C₁₃×#471	C₂²	semidirect
30. C₁₃×#456	C₂²	semidirect
31. C₁₃×#456	C₂²	semidirect
32. C₁₃×#456	C₂²	semidirect
33. C₁₃×#455	C₂²	semidirect
34. C₁₃×#454	C₂²	semidirect
35. C₁₃×#453	C₂²	semidirect
36. C₁₃×#444	C₂²	semidirect
37. C₁₃×#443	C₂²	semidirect
38. C₁₃×#430	C₂²	semidirect
39. C₂×C₁₃×#104	C₂²	semidirect
40. C₁₃×#413	C₂²	semidirect
41. C₂×C₁₃×#101	C₂²	semidirect
42. C₄×C₁₃×M₁₆	C₂²	semidirect
66. C₁₃×#137	D₄	semidirect
71. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
106. #61111	C₁₃	direct (N × H)
176. #3586	C₂×C₁₃	semidirect
177. #3293	C₂×C₁₃	semidirect
178. #3291	C₂×C₁₃	semidirect
179. #3289	C₂×C₁₃	semidirect
180. #3152	C₂×C₁₃	semidirect
181. #3069	C₂×C₁₃	semidirect
182. #3018	C₂×C₁₃	semidirect
183. C₂×#456	C₂×C₁₃	semidirect
184. #2956	C₂×C₁₃	semidirect
226. #585	C₂²×C₁₃	semidirect
229. #578	C₂²×C₁₃	semidirect
231. #577	C₂²×C₁₃	semidirect
236. C₂×#137	C₂²×C₁₃	semidirect
237. C₂×#137	C₂²×C₁₃	semidirect
238. #568	C₂²×C₁₃	semidirect
240. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
241. #497	C₂²×C₁₃	semidirect
242. #494	C₂²×C₁₃	semidirect
243. #492	C₂²×C₁₃	semidirect
244. #473	C₂²×C₁₃	semidirect
245. #471	C₂²×C₁₃	semidirect
246. #456	C₂²×C₁₃	semidirect
247. #456	C₂²×C₁₃	semidirect
248. #456	C₂²×C₁₃	semidirect
249. #455	C₂²×C₁₃	semidirect
250. #454	C₂²×C₁₃	semidirect
251. #453	C₂²×C₁₃	semidirect
252. #444	C₂²×C₁₃	semidirect
253. #443	C₂²×C₁₃	semidirect
254. #430	C₂²×C₁₃	semidirect
255. C₂×#104	C₂²×C₁₃	semidirect
256. #413	C₂²×C₁₃	semidirect
257. C₂×#101	C₂²×C₁₃	semidirect
258. C₄×M₁₆	C₂²×C₁₃	semidirect
297. #137	D₄×C₁₃	semidirect
302. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
411. C₁₃	#61111	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×#3586	2
C₁₃×#3293	2
C₁₃×#3291	2
C₁₃×#3289	2
C₁₃×#3152	2
C₁₃×#3069	2
C₁₃×#3018	2
C₂×C₁₃×#456	2
C₁₃×#2956	2
#61111	13

Subgroups — C13×#61111 #15747450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61111 #15747450