Subgroups — C₁₃×#61105 #15747444

Order 3328.

2620 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3584	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3293	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3292	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3291	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3290	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3067	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3018	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#443	C₂	1	2	yes	maximal, complemented
10	C₁₃×#585	C₂²	1	4	yes	complemented
11	C₁₃×#578	—	2	4	no	—
12	C₁₃×#578	C₂²	1	8	yes	complemented
13	C₁₃×#577	—	2	8	no	—
14	C₁₃×#577	C₂²	1	16	yes	complemented
15	C₁₃×#576	—	2	4	no	—
16	C₁₃×#576	C₂²	1	8	yes	complemented
17	C₁₃×#575	—	2	8	no	—
18	C₁₃×#575	C₂²	1	8	yes	complemented
19	C₂×C₁₃×#135	—	2	8	no	—
20	C₂×C₁₃×#135	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#131	C₂²	1	4	yes	complemented
23	C₁₃×#532	C₂²	1	2	yes	complemented
24	C₁₃×#495	C₂²	1	4	yes	complemented
25	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#492	C₂²	1	2	yes	complemented
28	C₁₃×#473	C₂²	1	8	yes	complemented
29	C₁₃×#472	C₂²	1	8	yes	complemented
30	C₁₃×#471	C₂²	1	16	yes	complemented
31	C₁₃×#456	C₂²	1	8	yes	complemented
32	C₁₃×#455	C₂²	1	8	yes	complemented
33	C₁₃×#454	C₂²	1	8	yes	complemented
34	C₁₃×#453	C₂²	1	8	yes	complemented
35	C₁₃×#443	C₂²	1	4	yes	complemented
36	C₁₃×#443	C₂²	1	4	yes	complemented
37	C₁₃×#443	C₂²	1	4	yes	complemented
38	C₁₃×#443	C₂²	1	4	yes	complemented
39	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
41	C₁₃×#413	C₂²	1	4	yes	complemented
42	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×2₋¹⁺⁴	—	2	8	no	—
44	C₁₃×2₋¹⁺⁴	C₂³	1	8	yes	—
45	C₁₃×H(5,𝔽₂)	—	2	8	no	—
46	C₁₃×H(5,𝔽₂)	—	4	4	no	—
47	C₁₃×H(5,𝔽₂)	C₂³	1	8	yes	—
48	C₂×C₁₃×#41	—	2	16	no	—
49	C₂×C₁₃×#41	—	4	4	no	—
50	C₂×C₁₃×#41	C₂³	1	4	yes	—
51	C₂×C₁₃×#41	C₂³	1	4	yes	—
52	C₁₃×#137	—	2	8	no	—
53	C₁₃×#137	—	2	16	no	—
54	C₁₃×#137	—	2	16	no	—
55	C₁₃×#137	C₂³	1	16	yes	—
56	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
57	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
58	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
59	C₁₃×AGL(1,ℤ/8)	C₂³	1	16	yes	—
60	C₁₃×#135	—	2	16	no	—
61	C₁₃×#135	—	2	8	no	—
62	C₁₃×#135	—	2	16	no	—
63	C₁₃×#135	—	2	8	no	—
64	C₁₃×#135	—	2	4	no	—
65	C₁₃×#135	—	2	4	no	—
66	C₁₃×#135	—	2	4	no	—
67	C₁₃×#135	—	2	4	no	—
68	C₁₃×#135	D₄	1	4	yes	complemented
69	C₁₃×#135	D₄	1	4	yes	complemented
70	C₁₃×#135	C₂³	1	4	yes	—
71	C₁₃×#135	C₂³	1	4	yes	—
72	C₂×C₁₃×Q₁₆	—	2	8	no	—
73	C₂×C₁₃×Q₁₆	D₄	1	2	yes	complemented
74	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
75	C₂×C₁₃×SD₁₆	—	2	16	no	—
76	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
77	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
78	C₂×C₁₃×D₈	—	2	8	no	—
79	C₂×C₁₃×D₈	D₄	1	2	yes	complemented
80	C₂×C₁₃×D₈	C₂³	1	4	yes	—
81	C₁₃×#131	—	2	4	no	—
82	C₁₃×#131	—	2	4	no	—
83	C₁₃×#131	C₂³	1	8	yes	—
84	C₁₃×#131	C₂³	1	8	yes	—
85	C₂×C₁₃×M₁₆	—	2	4	no	—
86	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
87	C₂²×C₈×C₁₃	—	2	4	no	—
88	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₃×#127	C₂³	1	2	yes	—
91	C₁₃×#124	C₂³	1	4	yes	—
92	C₁₃×#121	—	4	2	no	—
93	C₄×D₄×C₁₃	—	4	2	no	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#108	C₂³	1	4	yes	—
96	C₁₃×#108	C₂³	1	4	yes	—
97	C₁₃×#104	C₂³	1	8	yes	—
98	C₁₃×#104	C₂³	1	8	yes	—
99	C₁₃×#101	C₂³	1	8	yes	—
100	C₁₃×#100	C₂³	1	8	yes	—
101	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₁₃	C₂³	1	2	yes	—
104	#61105	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₁₃×#41	—	2	4	no	—
106	C₁₃×#41	—	2	4	no	—
107	C₁₃×#41	—	2	16	no	—
108	C₁₃×#41	—	2	16	no	—
109	C₁₃×#41	—	2	8	no	—
110	C₁₃×#41	—	2	8	no	—
111	C₁₃×#41	—	4	8	no	—
112	C₁₃×#41	—	4	8	no	—
113	C₁₃×#41	—	4	16	no	—
114	C₁₃×#41	—	4	8	no	—
115	C₁₃×#41	C₂×D₄	1	8	yes	—
116	C₁₃×#41	C₂⁴	1	8	yes	—
117	C₂×Q₈×C₁₃	—	2	16	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	16	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	4	8	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	16	no	—
128	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	4	8	no	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×Q₁₆	—	2	16	no	—
136	C₁₃×Q₁₆	—	2	4	no	—
137	C₁₃×Q₁₆	—	2	4	no	—
138	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
139	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
140	C₁₃×SD₁₆	—	2	16	no	—
141	C₁₃×SD₁₆	—	2	16	no	—
142	C₁₃×SD₁₆	—	2	8	no	—
143	C₁₃×SD₁₆	—	2	8	no	—
144	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
145	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
146	C₁₃×D₈	—	2	16	no	—
147	C₁₃×D₈	—	2	4	no	—
148	C₁₃×D₈	—	2	4	no	—
149	C₁₃×D₈	C₂×D₄	1	4	yes	—
150	C₁₃×D₈	C₂×D₄	1	4	yes	—
151	C₁₃×M₁₆	—	2	4	no	—
152	C₁₃×M₁₆	—	2	8	no	—
153	C₁₃×M₁₆	—	2	8	no	—
154	C₁₃×M₁₆	C₂⁴	1	8	yes	—
155	C₂×C₈×C₁₃	—	2	4	no	—
156	C₂×C₈×C₁₃	—	2	8	no	—
157	C₂×C₈×C₁₃	—	2	8	no	—
158	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
163	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₂²⋊C₄	—	4	4	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
169	#3584	C₂×C₁₃	1	4	yes	complemented
170	#3293	C₂×C₁₃	1	2	yes	complemented
171	#3292	C₂×C₁₃	1	2	yes	complemented
172	#3291	C₂×C₁₃	1	4	yes	complemented
173	#3290	C₂×C₁₃	1	8	yes	complemented
174	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#3067	C₂×C₁₃	1	4	yes	complemented
176	#3018	C₂×C₁₃	1	4	yes	complemented
177	C₂×#443	C₂×C₁₃	1	2	yes	complemented
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	4	8	no	—
181	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	4	no	—
183	Q₈×C₁₃	—	2	8	no	—
184	Q₈×C₁₃	—	4	8	no	—
185	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
186	D₄×C₁₃	—	2	8	no	—
187	D₄×C₁₃	—	2	8	no	—
188	D₄×C₁₃	—	2	4	no	—
189	D₄×C₁₃	—	2	8	no	—
190	D₄×C₁₃	—	4	16	no	—
191	D₄×C₁₃	—	4	8	no	—
192	D₄×C₁₃	—	4	8	no	—
193	D₄×C₁₃	—	8	4	no	—
194	D₄×C₁₃	C₂²×D₄	1	8	yes	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	8	no	—
198	C₂×C₄×C₁₃	—	2	8	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
210	C₈×C₁₃	—	2	8	no	—
211	C₈×C₁₃	C₂²×D₄	1	2	yes	—
212	C₈×C₁₃	C₂²×D₄	1	2	yes	—
213	C₈×C₁₃	C₂²×D₄	1	2	yes	—
214	C₈×C₁₃	C₂²×D₄	1	2	yes	—
215	#585	C₂²×C₁₃	1	4	yes	complemented
216	#578	—	2	4	no	—
217	#578	C₂²×C₁₃	1	8	yes	complemented
218	#577	—	2	8	no	—
219	#577	C₂²×C₁₃	1	16	yes	complemented
220	#576	—	2	4	no	—
221	#576	C₂²×C₁₃	1	8	yes	complemented
222	#575	—	2	8	no	—
223	#575	C₂²×C₁₃	1	8	yes	complemented
224	C₂×#135	—	2	8	no	—
225	C₂×#135	C₂²×C₁₃	1	2	yes	—
226	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
227	C₂×#131	C₂²×C₁₃	1	4	yes	complemented
228	#532	C₂²×C₁₃	1	2	yes	complemented
229	#495	C₂²×C₁₃	1	4	yes	complemented
230	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
231	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	#492	C₂²×C₁₃	1	2	yes	complemented
233	#473	C₂²×C₁₃	1	8	yes	complemented
234	#472	C₂²×C₁₃	1	8	yes	complemented
235	#471	C₂²×C₁₃	1	16	yes	complemented
236	#456	C₂²×C₁₃	1	8	yes	complemented
237	#455	C₂²×C₁₃	1	8	yes	complemented
238	#454	C₂²×C₁₃	1	8	yes	complemented
239	#453	C₂²×C₁₃	1	8	yes	complemented
240	#443	C₂²×C₁₃	1	4	yes	complemented
241	#443	C₂²×C₁₃	1	4	yes	complemented
242	#443	C₂²×C₁₃	1	4	yes	complemented
243	#443	C₂²×C₁₃	1	4	yes	complemented
244	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
245	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
246	#413	C₂²×C₁₃	1	4	yes	complemented
247	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
248	C₂²×C₁₃	—	2	8	no	—
249	C₂²×C₁₃	—	4	1	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	8	4	no	—
252	C₂²×C₁₃	—	8	4	no	—
253	C₂²×C₁₃	—	16	8	no	—
254	C₂²×C₁₃	D₄²	1	2	yes	—
255	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	8	no	—
258	C₄×C₁₃	—	4	1	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	D₄²	1	1	yes	characteristic
261	C₄×C₁₃	D₄²	1	1	yes	characteristic
262	C₄×C₁₃	C₂³×D₄	1	2	yes	—
263	2₋¹⁺⁴	—	2	8	no	—
264	2₋¹⁺⁴	C₂³×C₁₃	1	8	yes	—
265	H(5,𝔽₂)	—	2	8	no	—
266	H(5,𝔽₂)	—	4	4	no	—
267	H(5,𝔽₂)	C₂³×C₁₃	1	8	yes	—
268	C₂×#41	—	2	16	no	—
269	C₂×#41	—	4	4	no	—
270	C₂×#41	C₂³×C₁₃	1	4	yes	—
271	C₂×#41	C₂³×C₁₃	1	4	yes	—
272	#137	—	2	8	no	—
273	#137	—	2	16	no	—
274	#137	—	2	16	no	—
275	#137	C₂³×C₁₃	1	16	yes	—
276	AGL(1,ℤ/8)	—	2	8	no	—
277	AGL(1,ℤ/8)	—	2	16	no	—
278	AGL(1,ℤ/8)	—	2	16	no	—
279	AGL(1,ℤ/8)	C₂³×C₁₃	1	16	yes	—
280	#135	—	2	16	no	—
281	#135	—	2	8	no	—
282	#135	—	2	16	no	—
283	#135	—	2	8	no	—
284	#135	—	2	4	no	—
285	#135	—	2	4	no	—
286	#135	—	2	4	no	—
287	#135	—	2	4	no	—
288	#135	D₄×C₁₃	1	4	yes	complemented
289	#135	D₄×C₁₃	1	4	yes	complemented
290	#135	C₂³×C₁₃	1	4	yes	—
291	#135	C₂³×C₁₃	1	4	yes	—
292	C₂×Q₁₆	—	2	8	no	—
293	C₂×Q₁₆	D₄×C₁₃	1	2	yes	complemented
294	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
295	C₂×SD₁₆	—	2	16	no	—
296	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
297	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
298	C₂×D₈	—	2	8	no	—
299	C₂×D₈	D₄×C₁₃	1	2	yes	complemented
300	C₂×D₈	C₂³×C₁₃	1	4	yes	—
301	#131	—	2	4	no	—
302	#131	—	2	4	no	—
303	#131	C₂³×C₁₃	1	8	yes	—
304	#131	C₂³×C₁₃	1	8	yes	—
305	C₂×M₁₆	—	2	4	no	—
306	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
307	C₂²×C₈	—	2	4	no	—
308	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
309	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
310	#127	C₂³×C₁₃	1	2	yes	—
311	#124	C₂³×C₁₃	1	4	yes	—
312	#121	—	4	2	no	—
313	C₄×D₄	—	4	2	no	—
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	#108	C₂³×C₁₃	1	4	yes	—
316	#108	C₂³×C₁₃	1	4	yes	—
317	#104	C₂³×C₁₃	1	8	yes	—
318	#104	C₂³×C₁₃	1	8	yes	—
319	#101	C₂³×C₁₃	1	8	yes	—
320	#100	C₂³×C₁₃	1	8	yes	—
321	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₁₃	1	2	yes	—
324	C₂×C₁₃	—	2	1	no	—
325	C₂×C₁₃	—	2	2	no	—
326	C₂×C₁₃	—	4	8	no	—
327	C₂×C₁₃	—	8	4	no	—
328	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	2	16	no	—
332	#41	—	2	16	no	—
333	#41	—	2	8	no	—
334	#41	—	2	8	no	—
335	#41	—	4	8	no	—
336	#41	—	4	8	no	—
337	#41	—	4	16	no	—
338	#41	—	4	8	no	—
339	#41	C₂×D₄×C₁₃	1	8	yes	—
340	#41	C₂⁴×C₁₃	1	8	yes	—
341	C₂×Q₈	—	2	16	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
344	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	16	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	16	no	—
352	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
353	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	8	no	—
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	Q₁₆	—	2	16	no	—
360	Q₁₆	—	2	4	no	—
361	Q₁₆	—	2	4	no	—
362	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
363	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
364	SD₁₆	—	2	16	no	—
365	SD₁₆	—	2	16	no	—
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	2	8	no	—
368	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
369	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
370	D₈	—	2	16	no	—
371	D₈	—	2	4	no	—
372	D₈	—	2	4	no	—
373	D₈	C₂×D₄×C₁₃	1	4	yes	—
374	D₈	C₂×D₄×C₁₃	1	4	yes	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	2	8	no	—
377	M₁₆	—	2	8	no	—
378	M₁₆	C₂⁴×C₁₃	1	8	yes	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	8	no	—
381	C₂×C₈	—	2	8	no	—
382	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
384	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
385	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
386	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
387	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
388	C₄⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₁₃	#61105	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	8	no	—
397	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	8	no	—
400	Q₈	—	4	8	no	—
401	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
402	D₄	—	2	8	no	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	8	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	8	no	—
408	D₄	—	4	8	no	—
409	D₄	—	8	4	no	—
410	D₄	C₂²×D₄×C₁₃	1	8	yes	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	16	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
424	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
426	C₈	—	2	8	no	—
427	C₈	C₂²×D₄×C₁₃	1	2	yes	—
428	C₈	C₂²×D₄×C₁₃	1	2	yes	—
429	C₈	C₂²×D₄×C₁₃	1	2	yes	—
430	C₈	C₂²×D₄×C₁₃	1	2	yes	—
431	C₂²	—	2	8	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	4	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	16	8	no	—
437	C₂²	D₄²×C₁₃	1	2	yes	—
438	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	8	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	4	no	—
443	C₄	D₄²×C₁₃	1	1	yes	characteristic
444	C₄	D₄²×C₁₃	1	1	yes	characteristic
445	C₄	C₂³×D₄×C₁₃	1	2	yes	—
446	C₂	—	2	1	no	—
447	C₂	—	2	2	no	—
448	C₂	—	4	8	no	—
449	C₂	—	8	4	no	—
450	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3584	C₂	semidirect
2. C₁₃×#3293	C₂	semidirect
3. C₁₃×#3292	C₂	semidirect
4. C₁₃×#3291	C₂	semidirect
5. C₁₃×#3290	C₂	semidirect
6. C₁₃×#3147	C₂	semidirect
7. C₁₃×#3067	C₂	semidirect
8. C₁₃×#3018	C₂	semidirect
9. C₂×C₁₃×#443	C₂	semidirect
10. C₁₃×#585	C₂²	semidirect
12. C₁₃×#578	C₂²	semidirect
14. C₁₃×#577	C₂²	semidirect
16. C₁₃×#576	C₂²	semidirect
18. C₁₃×#575	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂×C₁₃×#131	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
24. C₁₃×#495	C₂²	semidirect
25. C₁₃×#494	C₂²	semidirect
26. C₁₃×#493	C₂²	semidirect
27. C₁₃×#492	C₂²	semidirect
28. C₁₃×#473	C₂²	semidirect
29. C₁₃×#472	C₂²	semidirect
30. C₁₃×#471	C₂²	semidirect
31. C₁₃×#456	C₂²	semidirect
32. C₁₃×#455	C₂²	semidirect
33. C₁₃×#454	C₂²	semidirect
34. C₁₃×#453	C₂²	semidirect
35. C₁₃×#443	C₂²	semidirect
36. C₁₃×#443	C₂²	semidirect
37. C₁₃×#443	C₂²	semidirect
38. C₁₃×#443	C₂²	semidirect
39. C₂×C₁₃×#108	C₂²	semidirect
40. C₂×C₁₃×#104	C₂²	semidirect
41. C₁₃×#413	C₂²	semidirect
42. C₂×C₄×C₈×C₁₃	C₂²	semidirect
68. C₁₃×#135	D₄	semidirect
69. C₁₃×#135	D₄	semidirect
73. C₂×C₁₃×Q₁₆	D₄	semidirect
76. C₂×C₁₃×SD₁₆	D₄	semidirect
79. C₂×C₁₃×D₈	D₄	semidirect
104. #61105	C₁₃	direct (N × H)
169. #3584	C₂×C₁₃	semidirect
170. #3293	C₂×C₁₃	semidirect
171. #3292	C₂×C₁₃	semidirect
172. #3291	C₂×C₁₃	semidirect
173. #3290	C₂×C₁₃	semidirect
174. #3147	C₂×C₁₃	semidirect
175. #3067	C₂×C₁₃	semidirect
176. #3018	C₂×C₁₃	semidirect
177. C₂×#443	C₂×C₁₃	semidirect
215. #585	C₂²×C₁₃	semidirect
217. #578	C₂²×C₁₃	semidirect
219. #577	C₂²×C₁₃	semidirect
221. #576	C₂²×C₁₃	semidirect
223. #575	C₂²×C₁₃	semidirect
226. C₂×#135	C₂²×C₁₃	semidirect
227. C₂×#131	C₂²×C₁₃	semidirect
228. #532	C₂²×C₁₃	semidirect
229. #495	C₂²×C₁₃	semidirect
230. #494	C₂²×C₁₃	semidirect
231. #493	C₂²×C₁₃	semidirect
232. #492	C₂²×C₁₃	semidirect
233. #473	C₂²×C₁₃	semidirect
234. #472	C₂²×C₁₃	semidirect
235. #471	C₂²×C₁₃	semidirect
236. #456	C₂²×C₁₃	semidirect
237. #455	C₂²×C₁₃	semidirect
238. #454	C₂²×C₁₃	semidirect
239. #453	C₂²×C₁₃	semidirect
240. #443	C₂²×C₁₃	semidirect
241. #443	C₂²×C₁₃	semidirect
242. #443	C₂²×C₁₃	semidirect
243. #443	C₂²×C₁₃	semidirect
244. C₂×#108	C₂²×C₁₃	semidirect
245. C₂×#104	C₂²×C₁₃	semidirect
246. #413	C₂²×C₁₃	semidirect
247. C₂×C₄×C₈	C₂²×C₁₃	semidirect
288. #135	D₄×C₁₃	semidirect
289. #135	D₄×C₁₃	semidirect
293. C₂×Q₁₆	D₄×C₁₃	semidirect
296. C₂×SD₁₆	D₄×C₁₃	semidirect
299. C₂×D₈	D₄×C₁₃	semidirect
393. C₁₃	#61105	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×#3584	2
C₁₃×#3293	2
C₁₃×#3292	2
C₁₃×#3291	2
C₁₃×#3290	2
C₁₃×#3147	2
C₁₃×#3067	2
C₁₃×#3018	2
C₂×C₁₃×#443	2
#61105	13

Subgroups — C13×#61105 #15747444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61105 #15747444