Subgroups — C₁₃×#24797 #15711136

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2037	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1883	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
17	C₁₃×#535	C₂²	1	2	yes	—
18	C₁₃×#520	C₂²	1	2	yes	—
19	C₁₃×#472	—	2	4	no	—
20	C₁₃×#469	—	2	2	no	—
21	C₁₃×#466	—	2	1	no	—
22	C₁₃×#466	—	2	1	no	—
23	C₁₃×#464	—	2	2	no	—
24	C₁₃×#463	—	2	2	no	—
25	C₁₃×#460	—	2	2	no	—
26	C₁₃×#459	—	2	2	no	—
27	C₁₃×#443	—	2	4	no	—
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
30	C₁₃×#428	—	2	2	no	—
31	C₁₃×#428	C₂²	1	2	yes	—
32	C₁₃×#427	—	2	1	no	—
33	C₁₃×#427	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	—	2	1	no	—
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₁₃×#424	C₂²	1	2	yes	—
37	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
39	C₁₃×#418	C₂²	1	2	yes	—
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₂×C₁₃×#102	C₂²	1	2	yes	—
42	C₂×C₁₃×#100	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	2	yes	—
45	C₁₃×#343	C₂²	1	2	yes	—
46	C₁₃×#339	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
51	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
57	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×D₈	—	2	1	no	—
60	C₂×C₁₃×D₈	—	2	1	no	—
61	C₂×C₁₃×D₈	—	2	2	no	—
62	C₂×C₁₃×D₈	—	2	2	no	—
63	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
64	C₁₃×#131	—	2	2	no	—
65	C₁₃×#131	—	2	2	no	—
66	C₁₃×#131	—	2	2	no	—
67	C₁₃×#131	D₄	1	4	yes	complemented
68	C₂×C₁₃×M₁₆	—	2	1	no	—
69	C₂×C₁₃×M₁₆	—	2	1	no	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#127	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	2	no	—
81	C₁₃×#120	—	4	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	4	2	no	—
85	C₁₃×#117	—	2	2	no	—
86	C₁₃×#117	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#108	—	2	2	no	—
92	C₁₃×#108	—	2	2	no	—
93	C₁₃×#107	—	2	1	no	—
94	C₁₃×#107	—	2	1	no	—
95	C₁₃×#107	—	2	2	no	—
96	C₁₃×#107	D₄	1	1	yes	characteristic
97	C₁₃×#107	D₄	1	1	yes	characteristic
98	C₁₃×#106	—	2	2	no	—
99	C₁₃×#106	D₄	1	2	yes	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×#104	—	2	2	no	—
103	C₁₃×#104	—	2	2	no	—
104	C₁₃×#103	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#100	—	2	4	no	—
111	C₄×C₈×C₁₃	—	2	2	no	—
112	#24797	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	—	2	1	no	—
119	C₁₃×#41	—	2	1	no	—
120	C₁₃×#41	C₂×D₄	1	2	yes	—
121	C₁₃×#41	#41	1	2	yes	—
122	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	4	2	no	—
133	C₂×D₄×C₁₃	—	4	2	no	—
134	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×Q₁₆	—	2	2	no	—
143	C₁₃×SD₁₆	—	2	2	no	—
144	C₁₃×SD₁₆	—	2	2	no	—
145	C₁₃×SD₁₆	—	4	4	no	—
146	C₁₃×D₈	—	2	2	no	—
147	C₁₃×D₈	—	4	4	no	—
148	C₁₃×D₈	—	4	2	no	—
149	C₁₃×D₈	—	4	2	no	—
150	C₁₃×M₁₆	—	2	1	no	—
151	C₁₃×M₁₆	—	2	4	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	2	1	no	—
154	C₁₃×M₁₆	—	2	1	no	—
155	C₁₃×M₁₆	—	2	2	no	—
156	C₁₃×M₁₆	—	4	2	no	—
157	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	4	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	4	2	no	—
165	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₃	#41	1	2	yes	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	4	2	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	4	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	2	no	—
179	C₁₃×C₂²⋊C₄	—	4	2	no	—
180	C₁₃×C₂²⋊C₄	—	8	4	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	4	2	no	—
185	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#3045	C₂×C₁₃	1	2	yes	complemented
188	C₂×#443	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#2063	C₂×C₁₃	1	2	yes	complemented
191	#2037	C₂×C₁₃	1	2	yes	complemented
192	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1945	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1883	C₂×C₁₃	1	2	yes	complemented
195	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	8	2	no	—
202	C₂³×C₁₃	—	8	2	no	—
203	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	1	no	—
205	Q₈×C₁₃	—	2	1	no	—
206	Q₈×C₁₃	—	2	1	no	—
207	Q₈×C₁₃	#121	1	2	yes	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	1	no	—
211	D₄×C₁₃	—	2	1	no	—
212	D₄×C₁₃	—	2	1	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	2	no	—
216	D₄×C₁₃	—	4	2	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	4	2	no	—
219	D₄×C₁₃	—	16	2	no	—
220	D₄×C₁₃	—	16	2	no	—
221	D₄×C₁₃	#121	1	2	yes	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	8	2	no	—
235	C₂×C₄×C₁₃	—	16	2	no	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	2	1	no	—
244	C₈×C₁₃	—	2	1	no	—
245	C₈×C₁₃	—	4	1	no	—
246	C₈×C₁₃	—	4	2	no	—
247	C₈×C₁₃	#121	1	2	yes	—
248	C₈×C₁₃	#121	1	2	yes	—
249	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
250	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
254	#535	C₂²×C₁₃	1	2	yes	—
255	#520	C₂²×C₁₃	1	2	yes	—
256	#472	—	2	4	no	—
257	#469	—	2	2	no	—
258	#466	—	2	1	no	—
259	#466	—	2	1	no	—
260	#464	—	2	2	no	—
261	#463	—	2	2	no	—
262	#460	—	2	2	no	—
263	#459	—	2	2	no	—
264	#443	—	2	4	no	—
265	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
267	#428	—	2	2	no	—
268	#428	C₂²×C₁₃	1	2	yes	—
269	#427	—	2	1	no	—
270	#427	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#107	—	2	1	no	—
272	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
273	#424	C₂²×C₁₃	1	2	yes	—
274	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
276	#418	C₂²×C₁₃	1	2	yes	—
277	#417	C₂²×C₁₃	1	2	yes	—
278	C₂×#102	C₂²×C₁₃	1	2	yes	—
279	C₂×#100	C₂²×C₁₃	1	2	yes	—
280	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
281	#390	C₂²×C₁₃	1	2	yes	—
282	#343	C₂²×C₁₃	1	2	yes	—
283	#339	C₂²×C₁₃	1	2	yes	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	8	4	no	—
293	C₂²×C₁₃	—	8	2	no	—
294	C₂²×C₁₃	—	8	2	no	—
295	C₂²×C₁₃	—	8	2	no	—
296	C₂²×C₁₃	—	16	2	no	—
297	C₂²×C₁₃	#537	1	1	yes	characteristic
298	C₂²×C₁₃	D₄²	1	1	yes	characteristic
299	C₂²×C₁₃	#553	1	1	yes	characteristic
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	1	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	8	2	no	—
306	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
307	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
308	C₄×C₁₃	#547	1	1	yes	characteristic
309	C₄×C₁₃	#548	1	1	yes	characteristic
310	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
313	AGL(1,ℤ/8)	—	2	4	no	—
314	AGL(1,ℤ/8)	—	2	4	no	—
315	#135	—	2	2	no	—
316	#135	—	2	2	no	—
317	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
320	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
321	C₂×D₈	—	2	2	no	—
322	C₂×D₈	—	2	1	no	—
323	C₂×D₈	—	2	1	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
327	#131	—	2	2	no	—
328	#131	—	2	2	no	—
329	#131	—	2	2	no	—
330	#131	D₄×C₁₃	1	4	yes	complemented
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
335	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
340	#127	—	2	2	no	—
341	#124	—	2	2	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#120	—	4	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	4	2	no	—
348	#117	—	2	2	no	—
349	#117	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂×C₂²⋊C₄	—	4	2	no	—
353	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
354	#108	—	2	2	no	—
355	#108	—	2	2	no	—
356	#107	—	2	1	no	—
357	#107	—	2	1	no	—
358	#107	—	2	2	no	—
359	#107	D₄×C₁₃	1	1	yes	characteristic
360	#107	D₄×C₁₃	1	1	yes	characteristic
361	#106	—	2	2	no	—
362	#106	D₄×C₁₃	1	2	yes	—
363	C₄⋊C₈	—	2	2	no	—
364	C₄⋊C₈	—	2	2	no	—
365	#104	—	2	2	no	—
366	#104	—	2	2	no	—
367	#103	—	2	2	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	2	2	no	—
373	#100	—	2	4	no	—
374	C₄×C₈	—	2	2	no	—
375	C₂×C₁₃	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	—	4	2	no	—
378	C₂×C₁₃	—	8	1	no	—
379	C₂×C₁₃	—	16	2	no	—
380	C₂×C₁₃	#2416	1	1	yes	characteristic
381	C₂×C₁₃	#3290	1	1	yes	characteristic
382	C₂×C₁₃	#3292	1	1	yes	characteristic
383	C₂⁴	—	2	2	no	—
384	#41	—	2	1	no	—
385	#41	—	2	1	no	—
386	#41	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	2	1	no	—
390	#41	C₂×D₄×C₁₃	1	2	yes	—
391	#41	C₁₃×#41	1	2	yes	—
392	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
412	Q₁₆	—	2	2	no	—
413	SD₁₆	—	2	2	no	—
414	SD₁₆	—	2	2	no	—
415	SD₁₆	—	4	4	no	—
416	D₈	—	2	2	no	—
417	D₈	—	4	4	no	—
418	D₈	—	4	2	no	—
419	D₈	—	4	2	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	2	4	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	4	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	4	2	no	—
435	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
438	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₈	C₁₃×#41	1	2	yes	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	8	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	4	2	no	—
455	C₁₃	#24797	1	1	yes	characteristic, direct product factor, Sylow
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	C₁₃×#121	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	16	2	no	—
480	D₄	—	16	2	no	—
481	D₄	C₁₃×#121	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	16	2	no	—
496	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
500	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
501	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	4	1	no	—
506	C₈	—	4	2	no	—
507	C₈	C₁₃×#121	1	2	yes	—
508	C₈	C₁₃×#121	1	2	yes	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	8	4	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	16	2	no	—
522	C₂²	C₁₃×#537	1	1	yes	characteristic
523	C₂²	D₄²×C₁₃	1	1	yes	characteristic
524	C₂²	C₁₃×#553	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	1	no	—
530	C₄	—	8	2	no	—
531	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
532	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
533	C₄	C₁₃×#547	1	1	yes	characteristic
534	C₄	C₁₃×#548	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	1	no	—
537	C₂	—	4	2	no	—
538	C₂	—	8	1	no	—
539	C₂	—	16	2	no	—
540	C₂	C₁₃×#2416	1	1	yes	characteristic
541	C₂	C₁₃×#3290	1	1	yes	characteristic
542	C₂	C₁₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#472	C₂	semidirect
2. C₁₃×#3058	C₂	semidirect
3. C₁₃×#3045	C₂	semidirect
4. C₂×C₁₃×#443	C₂	semidirect
5. C₁₃×#2913	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2037	C₂	semidirect
8. C₁₃×#1970	C₂	semidirect
9. C₁₃×#1945	C₂	semidirect
10. C₁₃×#1883	C₂	semidirect
11. C₁₃×#1816	C₂	semidirect
67. C₁₃×#131	D₄	semidirect
112. #24797	C₁₃	direct (N × H)
185. C₂×#472	C₂×C₁₃	semidirect
186. #3058	C₂×C₁₃	semidirect
187. #3045	C₂×C₁₃	semidirect
188. C₂×#443	C₂×C₁₃	semidirect
189. #2913	C₂×C₁₃	semidirect
190. #2063	C₂×C₁₃	semidirect
191. #2037	C₂×C₁₃	semidirect
192. #1970	C₂×C₁₃	semidirect
193. #1945	C₂×C₁₃	semidirect
194. #1883	C₂×C₁₃	semidirect
195. #1816	C₂×C₁₃	semidirect
330. #131	D₄×C₁₃	semidirect
455. C₁₃	#24797	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#472	2
C₁₃×#3058	2
C₁₃×#3045	2
C₂×C₁₃×#443	2
C₁₃×#2913	2
C₁₃×#2063	2
C₁₃×#2037	2
C₁₃×#1970	2
C₁₃×#1945	2
C₁₃×#1883	2
C₁₃×#1816	2
#24797	13

Subgroups — C13×#24797 #15711136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24797 #15711136