Subgroups — C₁₃×#33589 #15719928

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2207	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2206	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₁₃×#535	—	2	1	no	—
17	C₁₃×#520	—	2	1	no	—
18	C₁₃×#509	—	2	4	no	—
19	C₁₃×#508	—	2	4	no	—
20	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
25	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
28	C₁₃×#496	—	2	2	no	—
29	C₁₃×#495	C₂²	1	2	yes	—
30	C₁₃×#493	C₂²	1	2	yes	—
31	C₁₃×#440	—	2	2	no	—
32	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
33	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₁₃×#417	—	2	1	no	—
36	C₁₃×#405	C₂²	1	1	yes	characteristic
37	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
38	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
39	C₁₃×#358	C₂²	1	2	yes	complemented
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×#357	C₂²	1	2	yes	—
42	C₁₃×#357	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	—	2	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	D₄	1	4	yes	complemented
51	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	—	2	1	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	—	2	1	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×D₈	C₂³	1	2	yes	—
61	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#121	—	4	1	no	—
68	C₁₃×#121	—	4	1	no	—
69	C₁₃×#120	—	4	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₁₃×#117	—	4	1	no	—
74	C₁₃×#117	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
77	C₁₃×Q₃₂	—	2	2	no	—
78	C₁₃×SD₃₂	—	2	4	no	—
79	C₁₃×SD₃₂	—	2	2	no	—
80	C₁₃×SD₃₂	—	2	2	no	—
81	C₁₃×D₁₆	—	2	4	no	—
82	C₁₃×D₁₆	—	2	2	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₂×C₁₃×C₁₆	—	2	2	no	—
85	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
88	C₁₃×#107	—	2	1	no	—
89	C₁₃×#107	C₂³	1	2	yes	—
90	C₁₃×#103	—	2	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#97	D₄	1	2	yes	—
93	C₄×C₈×C₁₃	C₂³	1	2	yes	—
94	#33589	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	4	1	no	—
96	C₁₃×#41	—	2	4	no	—
97	C₁₃×#41	—	4	2	no	—
98	C₁₃×#41	—	4	2	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	4	1	no	—
106	C₂×D₄×C₁₃	—	4	1	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	1	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₁₃×Q₁₆	—	2	1	no	—
118	C₁₃×Q₁₆	—	2	1	no	—
119	C₁₃×Q₁₆	—	2	1	no	—
120	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
121	C₁₃×SD₁₆	—	2	4	no	—
122	C₁₃×SD₁₆	—	4	4	no	—
123	C₁₃×SD₁₆	—	4	2	no	—
124	C₁₃×D₈	—	2	2	no	—
125	C₁₃×D₈	—	2	1	no	—
126	C₁₃×D₈	—	2	1	no	—
127	C₁₃×D₈	—	2	2	no	—
128	C₁₃×D₈	—	2	1	no	—
129	C₁₃×D₈	—	4	4	no	—
130	C₁₃×D₈	—	4	2	no	—
131	C₁₃×D₈	C₂×D₄	1	2	yes	—
132	C₁₃×M₁₆	—	2	2	no	—
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃	#41	1	2	yes	—
137	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	4	1	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	4	2	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₁₃×C₁₆	—	2	1	no	—
150	C₁₃×C₁₆	—	2	1	no	—
151	C₁₃×C₁₆	—	2	2	no	—
152	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2211	C₂×C₁₃	1	2	yes	complemented
157	#2210	C₂×C₁₃	1	2	yes	complemented
158	#2207	C₂×C₁₃	1	2	yes	complemented
159	#2206	C₂×C₁₃	1	2	yes	complemented
160	#2151	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	8	2	no	—
167	C₂³×C₁₃	—	16	1	no	—
168	C₂³×C₁₃	—	16	1	no	—
169	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	Q₈×C₁₃	—	4	1	no	—
173	Q₈×C₁₃	—	4	1	no	—
174	D₄×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	4	4	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	1	no	—
178	D₄×C₁₃	—	4	1	no	—
179	D₄×C₁₃	—	4	1	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	8	2	no	—
182	D₄×C₁₃	—	8	2	no	—
183	D₄×C₁₃	—	16	2	no	—
184	D₄×C₁₃	—	16	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	8	2	no	—
190	C₂×C₄×C₁₃	—	16	2	no	—
191	C₂×C₄×C₁₃	—	16	1	no	—
192	C₂×C₄×C₁₃	#121	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	#121	1	2	yes	—
200	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×AGL(1,ℤ/8)	—	2	1	no	—
203	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
205	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
206	#535	—	2	1	no	—
207	#520	—	2	1	no	—
208	#509	—	2	4	no	—
209	#508	—	2	4	no	—
210	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
212	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
213	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
214	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
215	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
218	#496	—	2	2	no	—
219	#495	C₂²×C₁₃	1	2	yes	—
220	#493	C₂²×C₁₃	1	2	yes	—
221	#440	—	2	2	no	—
222	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
223	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
224	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
225	#417	—	2	1	no	—
226	#405	C₂²×C₁₃	1	1	yes	characteristic
227	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
228	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
229	#358	C₂²×C₁₃	1	2	yes	complemented
230	#357	C₂²×C₁₃	1	2	yes	—
231	#357	C₂²×C₁₃	1	2	yes	—
232	#357	C₂²×C₁₃	1	2	yes	complemented
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	8	1	no	—
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	—	8	1	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	1	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	—	16	4	no	—
245	C₂²×C₁₃	#459	1	2	yes	—
246	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	#459	1	2	yes	—
253	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
254	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂×#41	—	2	1	no	—
256	C₂×#41	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	AGL(1,ℤ/8)	—	4	4	no	—
259	#135	—	2	2	no	—
260	#135	—	2	2	no	—
261	#135	—	2	2	no	—
262	#135	D₄×C₁₃	1	4	yes	complemented
263	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×SD₁₆	—	2	1	no	—
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	C₂³×C₁₃	1	2	yes	—
273	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	#127	—	2	2	no	—
278	#124	—	2	2	no	—
279	#121	—	4	1	no	—
280	#121	—	4	1	no	—
281	#120	—	4	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×D₄	—	2	2	no	—
284	C₄×D₄	—	4	2	no	—
285	#117	—	4	1	no	—
286	#117	D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	4	1	no	—
289	Q₃₂	—	2	2	no	—
290	SD₃₂	—	2	4	no	—
291	SD₃₂	—	2	2	no	—
292	SD₃₂	—	2	2	no	—
293	D₁₆	—	2	4	no	—
294	D₁₆	—	2	2	no	—
295	M₃₂	—	2	2	no	—
296	C₂×C₁₆	—	2	2	no	—
297	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
300	#107	—	2	1	no	—
301	#107	C₂³×C₁₃	1	2	yes	—
302	#103	—	2	2	no	—
303	#102	—	2	2	no	—
304	#97	D₄×C₁₃	1	2	yes	—
305	C₄×C₈	C₂³×C₁₃	1	2	yes	—
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	—	8	2	no	—
308	C₂×C₁₃	—	16	1	no	—
309	C₂×C₁₃	—	16	2	no	—
310	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
311	C₂×C₁₃	#3415	1	1	yes	characteristic
312	C₂×C₁₃	#3416	1	1	yes	characteristic
313	C₂⁴	—	4	1	no	—
314	#41	—	2	4	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	Q₁₆	—	2	1	no	—
336	Q₁₆	—	2	1	no	—
337	Q₁₆	—	2	1	no	—
338	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
339	SD₁₆	—	2	4	no	—
340	SD₁₆	—	4	4	no	—
341	SD₁₆	—	4	2	no	—
342	D₈	—	2	2	no	—
343	D₈	—	2	1	no	—
344	D₈	—	2	1	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	1	no	—
347	D₈	—	4	4	no	—
348	D₈	—	4	2	no	—
349	D₈	C₂×D₄×C₁₃	1	2	yes	—
350	M₁₆	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
352	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
354	C₂×C₈	C₁₃×#41	1	2	yes	—
355	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
360	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
365	C₄²	—	4	2	no	—
366	C₄²	C₂×D₄×C₁₃	1	2	yes	—
367	C₁₆	—	2	1	no	—
368	C₁₆	—	2	1	no	—
369	C₁₆	—	2	2	no	—
370	C₁₃	#33589	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	8	2	no	—
375	C₂³	—	16	1	no	—
376	C₂³	—	16	1	no	—
377	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	16	2	no	—
392	D₄	—	16	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	16	2	no	—
399	C₂×C₄	—	16	1	no	—
400	C₂×C₄	C₁₃×#121	1	2	yes	—
401	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
402	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
403	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
404	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	C₁₃×#121	1	2	yes	—
408	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₁₃×#459	1	2	yes	—
423	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	C₁₃×#459	1	2	yes	—
430	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
431	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	8	2	no	—
434	C₂	—	16	2	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
437	C₂	C₁₃×#3415	1	1	yes	characteristic
438	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#509	C₂	semidirect
2. C₂×C₁₃×#508	C₂	semidirect
3. C₁₃×#3155	C₂	semidirect
4. C₁₃×#2951	C₂	semidirect
5. C₁₃×#2211	C₂	semidirect
6. C₁₃×#2210	C₂	semidirect
7. C₁₃×#2207	C₂	semidirect
8. C₁₃×#2206	C₂	semidirect
9. C₁₃×#2151	C₂	semidirect
10. C₁₃×#2139	C₂	semidirect
11. C₂×C₁₃×#357	C₂	semidirect
20. C₂×C₁₃×Q₃₂	C₂²	semidirect
22. C₂×C₁₃×SD₃₂	C₂²	semidirect
23. C₂×C₁₃×SD₃₂	C₂²	semidirect
25. C₂×C₁₃×D₁₆	C₂²	semidirect
32. C₄×C₁₃×Q₁₆	C₂²	semidirect
33. C₄×C₁₃×D₈	C₂²	semidirect
37. C₁₃×C₄⋊C₁₆	C₂²	semidirect
38. C₁₃×C₄⋊C₁₆	C₂²	semidirect
39. C₁₃×#358	C₂²	semidirect
42. C₁₃×#357	C₂²	semidirect
50. C₁₃×#135	D₄	semidirect
94. #33589	C₁₃	direct (N × H)
152. C₂×#509	C₂×C₁₃	semidirect
153. C₂×#508	C₂×C₁₃	semidirect
154. #3155	C₂×C₁₃	semidirect
155. #2951	C₂×C₁₃	semidirect
156. #2211	C₂×C₁₃	semidirect
157. #2210	C₂×C₁₃	semidirect
158. #2207	C₂×C₁₃	semidirect
159. #2206	C₂×C₁₃	semidirect
160. #2151	C₂×C₁₃	semidirect
161. #2139	C₂×C₁₃	semidirect
162. C₂×#357	C₂×C₁₃	semidirect
210. C₂×Q₃₂	C₂²×C₁₃	semidirect
212. C₂×SD₃₂	C₂²×C₁₃	semidirect
213. C₂×SD₃₂	C₂²×C₁₃	semidirect
215. C₂×D₁₆	C₂²×C₁₃	semidirect
222. C₄×Q₁₆	C₂²×C₁₃	semidirect
223. C₄×D₈	C₂²×C₁₃	semidirect
227. C₄⋊C₁₆	C₂²×C₁₃	semidirect
228. C₄⋊C₁₆	C₂²×C₁₃	semidirect
229. #358	C₂²×C₁₃	semidirect
232. #357	C₂²×C₁₃	semidirect
262. #135	D₄×C₁₃	semidirect
370. C₁₃	#33589	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×#509	2
C₂×C₁₃×#508	2
C₁₃×#3155	2
C₁₃×#2951	2
C₁₃×#2211	2
C₁₃×#2210	2
C₁₃×#2207	2
C₁₃×#2206	2
C₁₃×#2151	2
C₁₃×#2139	2
C₂×C₁₃×#357	2
#33589	13

Subgroups — C13×#33589 #15719928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33589 #15719928