Subgroups — C₁₃×#61414 #15747753

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3401	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3399	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3155	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3045	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2952	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
12	C₂×C₁₃×#135	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#559	C₂²	1	8	yes	complemented
16	C₁₃×#556	C₂²	1	4	yes	complemented
17	C₁₃×#555	—	2	2	no	—
18	C₁₃×#553	—	2	4	no	—
19	C₁₃×#550	C₂²	1	4	yes	complemented
20	C₁₃×#547	—	2	2	no	—
21	C₁₃×#538	—	2	4	no	—
22	C₁₃×#535	C₂²	1	4	yes	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#525	—	2	4	no	—
26	C₁₃×#520	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#497	C₂²	1	4	yes	complemented
29	C₁₃×#496	C₂²	1	8	yes	—
30	C₁₃×#496	C₂²	1	4	yes	complemented
31	C₁₃×#495	C₂²	1	4	yes	—
32	C₁₃×#493	C₂²	1	4	yes	—
33	C₁₃×#464	C₂²	1	8	yes	complemented
34	C₁₃×#463	C₂²	1	8	yes	complemented
35	C₁₃×#463	C₂²	1	8	yes	complemented
36	C₁₃×#461	C₂²	1	4	yes	complemented
37	C₁₃×#460	C₂²	1	8	yes	complemented
38	C₁₃×#459	C₂²	1	4	yes	complemented
39	C₁₃×#459	C₂²	1	8	yes	complemented
40	C₁₃×#446	C₂²	1	8	yes	complemented
41	C₁₃×#442	C₂²	1	8	yes	—
42	C₁₃×#442	C₂²	1	4	yes	complemented
43	C₁₃×#441	C₂²	1	4	yes	complemented
44	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
45	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	2	yes	—
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	4	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₁₃×#405	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#41	—	2	4	no	—
53	C₂×C₁₃×#41	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
57	C₁₃×#135	—	2	8	no	—
58	C₁₃×#135	—	4	4	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
63	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
64	C₂×C₁₃×D₈	—	2	4	no	—
65	C₂×C₁₃×D₈	C₂³	1	4	yes	—
66	C₂×C₁₃×D₈	C₂³	1	2	yes	—
67	C₂×C₁₃×D₈	C₂³	1	2	yes	—
68	C₂×C₁₃×D₈	C₂³	1	8	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×#127	C₂³	1	2	yes	—
75	C₁₃×#127	C₂³	1	8	yes	—
76	C₁₃×#126	—	2	8	no	—
77	C₁₃×#125	D₄	1	2	yes	—
78	C₁₃×#124	—	2	8	no	—
79	C₁₃×#124	C₂³	1	4	yes	—
80	C₁₃×#124	C₂³	1	8	yes	—
81	C₁₃×#123	—	2	8	no	—
82	C₁₃×#123	—	2	8	no	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	4	no	—
88	C₁₃×#121	—	2	4	no	—
89	C₁₃×#121	—	2	4	no	—
90	C₁₃×#121	—	2	8	no	—
91	C₁₃×#120	—	2	8	no	—
92	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
94	C₄×D₄×C₁₃	—	2	8	no	—
95	C₄×D₄×C₁₃	—	2	8	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	C₂³	1	8	yes	—
101	C₄×D₄×C₁₃	C₂³	1	4	yes	—
102	C₄×D₄×C₁₃	C₂³	1	4	yes	—
103	C₁₃×#117	—	2	4	no	—
104	C₁₃×#117	—	2	4	no	—
105	C₁₃×#117	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#106	C₂³	1	4	yes	—
111	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
113	C₁₃×#103	C₂³	1	8	yes	—
114	C₁₃×#102	C₂³	1	8	yes	—
115	C₁₃×#102	C₂³	1	8	yes	—
116	C₁₃×#97	C₂³	1	4	yes	—
117	C₁₃×#97	C₂³	1	4	yes	—
118	C₄×C₈×C₁₃	C₂³	1	4	yes	—
119	#61414	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₁₃×#41	—	2	8	no	—
123	C₁₃×#41	—	8	8	no	—
124	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	8	4	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₁₃×Q₁₆	—	2	4	no	—
145	C₁₃×Q₁₆	—	4	2	no	—
146	C₁₃×SD₁₆	—	2	8	no	—
147	C₁₃×SD₁₆	—	4	4	no	—
148	C₁₃×SD₁₆	—	4	8	no	—
149	C₁₃×D₈	—	2	8	no	—
150	C₁₃×D₈	—	2	4	no	—
151	C₁₃×D₈	—	4	2	no	—
152	C₁₃×D₈	—	4	8	no	—
153	C₁₃×M₁₆	—	2	4	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	#41	1	4	yes	complemented
156	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
175	C₄²×C₁₃	—	2	8	no	—
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂⁴	1	4	yes	—
179	C₄²×C₁₃	C₂⁴	1	2	yes	—
180	#3506	C₂×C₁₃	1	2	yes	complemented
181	#3401	C₂×C₁₃	1	8	yes	complemented
182	#3399	C₂×C₁₃	1	8	yes	complemented
183	#3155	C₂×C₁₃	1	2	yes	complemented
184	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#3045	C₂×C₁₃	1	4	yes	complemented
186	#3036	C₂×C₁₃	1	2	yes	complemented
187	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2952	C₂×C₁₃	1	2	yes	complemented
189	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	8	2	no	—
194	C₂³×C₁₃	—	8	2	no	—
195	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₃	—	2	4	no	—
197	Q₈×C₁₃	—	2	4	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	D₄×C₁₃	—	2	4	no	—
200	D₄×C₁₃	—	2	4	no	—
201	D₄×C₁₃	—	2	4	no	—
202	D₄×C₁₃	—	2	4	no	—
203	D₄×C₁₃	—	4	4	no	—
204	D₄×C₁₃	—	4	8	no	—
205	D₄×C₁₃	—	4	4	no	—
206	D₄×C₁₃	—	8	2	no	—
207	D₄×C₁₃	—	8	8	no	—
208	D₄×C₁₃	—	8	8	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	4	8	no	—
214	C₂×C₄×C₁₃	—	8	4	no	—
215	C₂×C₄×C₁₃	—	8	8	no	—
216	C₂×C₄×C₁₃	—	8	2	no	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
222	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
224	C₈×C₁₃	—	2	2	no	—
225	C₈×C₁₃	—	2	4	no	—
226	C₈×C₁₃	C₂×#41	1	4	yes	—
227	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
228	C₂×#135	C₂²×C₁₃	1	2	yes	—
229	C₂×#135	C₂²×C₁₃	1	2	yes	—
230	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
231	#559	C₂²×C₁₃	1	8	yes	complemented
232	#556	C₂²×C₁₃	1	4	yes	complemented
233	#555	—	2	2	no	—
234	#553	—	2	4	no	—
235	#550	C₂²×C₁₃	1	4	yes	complemented
236	#547	—	2	2	no	—
237	#538	—	2	4	no	—
238	#535	C₂²×C₁₃	1	4	yes	—
239	#533	C₂²×C₁₃	1	1	yes	characteristic
240	#532	C₂²×C₁₃	1	2	yes	—
241	#525	—	2	4	no	—
242	#520	C₂²×C₁₃	1	4	yes	—
243	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
244	#497	C₂²×C₁₃	1	4	yes	complemented
245	#496	C₂²×C₁₃	1	8	yes	—
246	#496	C₂²×C₁₃	1	4	yes	complemented
247	#495	C₂²×C₁₃	1	4	yes	—
248	#493	C₂²×C₁₃	1	4	yes	—
249	#464	C₂²×C₁₃	1	8	yes	complemented
250	#463	C₂²×C₁₃	1	8	yes	complemented
251	#463	C₂²×C₁₃	1	8	yes	complemented
252	#461	C₂²×C₁₃	1	4	yes	complemented
253	#460	C₂²×C₁₃	1	8	yes	complemented
254	#459	C₂²×C₁₃	1	4	yes	complemented
255	#459	C₂²×C₁₃	1	8	yes	complemented
256	#446	C₂²×C₁₃	1	8	yes	complemented
257	#442	C₂²×C₁₃	1	8	yes	—
258	#442	C₂²×C₁₃	1	4	yes	complemented
259	#441	C₂²×C₁₃	1	4	yes	complemented
260	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
261	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
262	#424	C₂²×C₁₃	1	2	yes	—
263	#423	C₂²×C₁₃	1	1	yes	characteristic
264	#417	C₂²×C₁₃	1	4	yes	—
265	C₂×#102	C₂²×C₁₃	1	2	yes	—
266	#405	C₂²×C₁₃	1	2	yes	—
267	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	8	8	no	—
276	C₂²×C₁₃	#550	1	2	yes	—
277	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	8	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	#550	1	2	yes	—
284	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
285	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
286	C₂×#41	—	2	4	no	—
287	C₂×#41	C₂³×C₁₃	1	4	yes	—
288	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
289	C₂³×C₄	—	2	2	no	—
290	AGL(1,ℤ/8)	—	4	8	no	—
291	#135	—	2	8	no	—
292	#135	—	4	4	no	—
293	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
294	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
295	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
296	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
297	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
298	C₂×D₈	—	2	4	no	—
299	C₂×D₈	C₂³×C₁₃	1	4	yes	—
300	C₂×D₈	C₂³×C₁₃	1	2	yes	—
301	C₂×D₈	C₂³×C₁₃	1	2	yes	—
302	C₂×D₈	C₂³×C₁₃	1	8	yes	—
303	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
308	#127	C₂³×C₁₃	1	2	yes	—
309	#127	C₂³×C₁₃	1	8	yes	—
310	#126	—	2	8	no	—
311	#125	D₄×C₁₃	1	2	yes	—
312	#124	—	2	8	no	—
313	#124	C₂³×C₁₃	1	4	yes	—
314	#124	C₂³×C₁₃	1	8	yes	—
315	#123	—	2	8	no	—
316	#123	—	2	8	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
319	#121	—	2	2	no	—
320	#121	—	2	2	no	—
321	#121	—	2	4	no	—
322	#121	—	2	4	no	—
323	#121	—	2	4	no	—
324	#121	—	2	8	no	—
325	#120	—	2	8	no	—
326	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
327	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
328	C₄×D₄	—	2	8	no	—
329	C₄×D₄	—	2	8	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	C₂³×C₁₃	1	4	yes	—
335	C₄×D₄	C₂³×C₁₃	1	4	yes	—
336	C₄×D₄	C₂³×C₁₃	1	8	yes	—
337	#117	—	2	4	no	—
338	#117	—	2	4	no	—
339	#117	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄⋊C₄	—	2	4	no	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	#106	C₂³×C₁₃	1	4	yes	—
345	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
346	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
347	#103	C₂³×C₁₃	1	8	yes	—
348	#102	C₂³×C₁₃	1	8	yes	—
349	#102	C₂³×C₁₃	1	8	yes	—
350	#97	C₂³×C₁₃	1	4	yes	—
351	#97	C₂³×C₁₃	1	4	yes	—
352	C₄×C₈	C₂³×C₁₃	1	4	yes	—
353	C₂×C₁₃	—	2	2	no	—
354	C₂×C₁₃	—	8	4	no	—
355	C₂×C₁₃	—	8	4	no	—
356	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
357	C₂×C₁₃	#3585	1	2	yes	—
358	C₂⁴	—	2	2	no	—
359	#41	—	2	8	no	—
360	#41	—	2	8	no	—
361	#41	—	8	8	no	—
362	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
363	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
373	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	8	4	no	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
382	Q₁₆	—	2	4	no	—
383	Q₁₆	—	4	2	no	—
384	SD₁₆	—	2	8	no	—
385	SD₁₆	—	4	4	no	—
386	SD₁₆	—	4	8	no	—
387	D₈	—	2	8	no	—
388	D₈	—	2	4	no	—
389	D₈	—	4	2	no	—
390	D₈	—	4	8	no	—
391	M₁₆	—	2	4	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	C₁₃×#41	1	4	yes	complemented
394	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
395	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
396	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
404	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₄²	—	2	8	no	—
414	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₄²	C₂⁴×C₁₃	1	4	yes	—
417	C₄²	C₂⁴×C₁₃	1	2	yes	—
418	C₁₃	#61414	1	1	yes	characteristic, direct product factor, Sylow
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	8	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	2	4	no	—
432	D₄	—	4	4	no	—
433	D₄	—	4	8	no	—
434	D₄	—	4	4	no	—
435	D₄	—	8	2	no	—
436	D₄	—	8	8	no	—
437	D₄	—	8	8	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	—	8	8	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
451	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
452	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	4	no	—
455	C₈	C₂×C₁₃×#41	1	4	yes	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	8	no	—
464	C₂²	C₁₃×#550	1	2	yes	—
465	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	8	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	C₁₃×#550	1	2	yes	—
472	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
473	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂	—	2	2	no	—
475	C₂	—	8	4	no	—
476	C₂	—	8	4	no	—
477	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
478	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₁₃×#3401	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3155	C₂	semidirect
5. C₁₃×#3150	C₂	semidirect
6. C₁₃×#3045	C₂	semidirect
7. C₁₃×#3036	C₂	semidirect
8. C₁₃×#2961	C₂	semidirect
9. C₁₃×#2952	C₂	semidirect
10. C₂×C₁₃×#442	C₂	semidirect
15. C₁₃×#559	C₂²	semidirect
16. C₁₃×#556	C₂²	semidirect
19. C₁₃×#550	C₂²	semidirect
28. C₁₃×#497	C₂²	semidirect
30. C₁₃×#496	C₂²	semidirect
33. C₁₃×#464	C₂²	semidirect
34. C₁₃×#463	C₂²	semidirect
35. C₁₃×#463	C₂²	semidirect
36. C₁₃×#461	C₂²	semidirect
37. C₁₃×#460	C₂²	semidirect
38. C₁₃×#459	C₂²	semidirect
39. C₁₃×#459	C₂²	semidirect
40. C₁₃×#446	C₂²	semidirect
42. C₁₃×#442	C₂²	semidirect
43. C₁₃×#441	C₂²	semidirect
44. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. #61414	C₁₃	direct (N × H)
155. C₂×C₈×C₁₃	#41	semidirect
180. #3506	C₂×C₁₃	semidirect
181. #3401	C₂×C₁₃	semidirect
182. #3399	C₂×C₁₃	semidirect
183. #3155	C₂×C₁₃	semidirect
184. #3150	C₂×C₁₃	semidirect
185. #3045	C₂×C₁₃	semidirect
186. #3036	C₂×C₁₃	semidirect
187. #2961	C₂×C₁₃	semidirect
188. #2952	C₂×C₁₃	semidirect
189. C₂×#442	C₂×C₁₃	semidirect
231. #559	C₂²×C₁₃	semidirect
232. #556	C₂²×C₁₃	semidirect
235. #550	C₂²×C₁₃	semidirect
244. #497	C₂²×C₁₃	semidirect
246. #496	C₂²×C₁₃	semidirect
249. #464	C₂²×C₁₃	semidirect
250. #463	C₂²×C₁₃	semidirect
251. #463	C₂²×C₁₃	semidirect
252. #461	C₂²×C₁₃	semidirect
253. #460	C₂²×C₁₃	semidirect
254. #459	C₂²×C₁₃	semidirect
255. #459	C₂²×C₁₃	semidirect
256. #446	C₂²×C₁₃	semidirect
258. #442	C₂²×C₁₃	semidirect
259. #441	C₂²×C₁₃	semidirect
260. C₄×SD₁₆	C₂²×C₁₃	semidirect
393. C₂×C₈	C₁₃×#41	semidirect
418. C₁₃	#61414	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×#3506	2
C₁₃×#3401	2
C₁₃×#3399	2
C₁₃×#3155	2
C₁₃×#3150	2
C₁₃×#3045	2
C₁₃×#3036	2
C₁₃×#2961	2
C₁₃×#2952	2
C₂×C₁₃×#442	2
#61414	13

Subgroups — C13×#61414 #15747753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61414 #15747753