Subgroups — C₁₃×#33594 #15719933

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3414	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2214	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2213	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2212	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2148	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#135	—	2	1	no	—
10	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#135	C₂²	1	2	yes	—
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#532	—	2	1	no	—
14	C₁₃×#510	—	2	2	no	—
15	C₁₃×#510	C₂²	1	4	yes	—
16	C₁₃×#509	—	2	2	no	—
17	C₁₃×#509	C₂²	1	4	yes	—
18	C₁₃×#508	—	2	4	no	—
19	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
20	C₁₃×#495	—	2	1	no	—
21	C₁₃×#495	C₂²	1	2	yes	complemented
22	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#492	—	2	1	no	—
25	C₁₃×#443	—	2	1	no	—
26	C₁₃×#443	—	2	1	no	—
27	C₁₃×#443	C₂²	1	2	yes	—
28	C₁₃×#443	C₂²	1	2	yes	—
29	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#104	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#364	C₂²	1	2	yes	complemented
33	C₁₃×#364	C₂²	1	2	yes	complemented
34	C₁₃×#362	C₂²	1	4	yes	complemented
35	C₁₃×#361	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₁₃×#135	—	2	1	no	—
39	C₁₃×#135	—	2	2	no	—
40	C₁₃×#135	—	2	2	no	—
41	C₁₃×#135	—	2	1	no	—
42	C₁₃×#135	—	2	2	no	—
43	C₁₃×#135	—	2	2	no	—
44	C₁₃×#135	—	4	1	no	—
45	C₁₃×#135	—	4	1	no	—
46	C₁₃×#135	—	4	1	no	—
47	C₁₃×#135	—	4	1	no	—
48	C₁₃×#135	D₄	1	2	yes	complemented
49	C₁₃×#135	C₂³	1	2	yes	—
50	C₂×C₁₃×Q₁₆	—	2	1	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic, complemented
52	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic, complemented
58	C₂×C₁₃×D₈	C₂³	1	2	yes	—
59	C₁₃×#131	—	2	2	no	—
60	C₁₃×#131	—	2	2	no	—
61	C₁₃×#131	—	4	1	no	—
62	C₁₃×#131	—	4	1	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	4	1	no	—
65	C₂²×C₈×C₁₃	—	4	1	no	—
66	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×#127	—	2	1	no	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#121	—	4	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₁₃×Q₃₂	—	2	4	no	—
75	C₁₃×SD₃₂	—	2	4	no	—
76	C₁₃×SD₃₂	—	2	4	no	—
77	C₁₃×D₁₆	—	2	4	no	—
78	C₁₃×M₃₂	—	2	2	no	—
79	C₁₃×M₃₂	C₂³	1	4	yes	—
80	C₂×C₁₃×C₁₆	—	2	2	no	—
81	C₁₃×#108	—	2	1	no	—
82	C₁₃×#108	C₂³	1	2	yes	—
83	C₁₃×#104	—	2	2	no	—
84	C₁₃×#104	—	2	2	no	—
85	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33594	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	2	2	no	—
91	C₁₃×#41	—	2	2	no	—
92	C₁₃×#41	—	4	1	no	—
93	C₁₃×#41	—	4	1	no	—
94	C₁₃×#41	—	4	2	no	—
95	C₁₃×#41	—	4	2	no	—
96	C₁₃×#41	—	4	2	no	—
97	C₁₃×#41	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	1	no	—
110	C₁₃×Q₁₆	—	2	2	no	—
111	C₁₃×Q₁₆	—	2	2	no	—
112	C₁₃×Q₁₆	—	4	1	no	—
113	C₁₃×Q₁₆	—	4	1	no	—
114	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
115	C₁₃×SD₁₆	—	2	2	no	—
116	C₁₃×SD₁₆	—	2	2	no	—
117	C₁₃×SD₁₆	—	4	2	no	—
118	C₁₃×SD₁₆	—	4	2	no	—
119	C₁₃×SD₁₆	—	4	2	no	—
120	C₁₃×SD₁₆	—	4	2	no	—
121	C₁₃×D₈	—	2	1	no	—
122	C₁₃×D₈	—	2	2	no	—
123	C₁₃×D₈	—	2	2	no	—
124	C₁₃×D₈	—	4	1	no	—
125	C₁₃×D₈	—	4	1	no	—
126	C₁₃×D₈	C₂×D₄	1	2	yes	—
127	C₁₃×M₁₆	—	2	2	no	—
128	C₁₃×M₁₆	—	4	1	no	—
129	C₁₃×M₁₆	—	4	2	no	—
130	C₁₃×M₁₆	—	4	2	no	—
131	C₂×C₈×C₁₃	—	4	1	no	—
132	C₂×C₈×C₁₃	—	4	2	no	—
133	C₂×C₈×C₁₃	—	4	2	no	—
134	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
135	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
136	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
137	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
144	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₁₃×C₁₆	—	2	4	no	—
152	#3414	C₂×C₁₃	1	2	yes	complemented
153	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂×#443	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2214	C₂×C₁₃	1	2	yes	complemented
156	#2213	C₂×C₁₃	1	2	yes	complemented
157	#2212	C₂×C₁₃	1	4	yes	complemented
158	C₂×#364	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2148	C₂×C₁₃	1	2	yes	complemented
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	—	4	1	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	1	no	—
173	D₄×C₁₃	—	8	4	no	—
174	D₄×C₁₃	—	8	2	no	—
175	D₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	8	2	no	—
184	C₂×C₄×C₁₃	—	8	2	no	—
185	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₃	—	4	2	no	—
192	C₈×C₁₃	#121	1	1	yes	characteristic
193	C₈×C₁₃	#121	1	1	yes	characteristic
194	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
195	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
197	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
198	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×#135	—	2	1	no	—
201	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#135	C₂²×C₁₃	1	2	yes	—
203	C₂×#131	—	2	1	no	—
204	#532	—	2	1	no	—
205	#510	—	2	2	no	—
206	#510	C₂²×C₁₃	1	4	yes	—
207	#509	—	2	2	no	—
208	#509	C₂²×C₁₃	1	4	yes	—
209	#508	—	2	4	no	—
210	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
211	#495	—	2	1	no	—
212	#495	C₂²×C₁₃	1	2	yes	complemented
213	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
214	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
215	#492	—	2	1	no	—
216	#443	—	2	1	no	—
217	#443	—	2	1	no	—
218	#443	C₂²×C₁₃	1	2	yes	—
219	#443	C₂²×C₁₃	1	2	yes	—
220	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#104	—	2	1	no	—
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	#364	C₂²×C₁₃	1	2	yes	complemented
224	#364	C₂²×C₁₃	1	2	yes	complemented
225	#362	C₂²×C₁₃	1	4	yes	complemented
226	#361	C₂²×C₁₃	1	4	yes	complemented
227	C₂²×C₁₃	—	4	1	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	4	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	#459	1	1	yes	characteristic
233	C₂²×C₁₃	#459	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	1	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	#459	1	1	yes	characteristic
240	C₄×C₁₃	#459	1	1	yes	characteristic
241	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
242	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	2	2	no	—
245	#135	—	2	1	no	—
246	#135	—	2	2	no	—
247	#135	—	2	2	no	—
248	#135	—	2	1	no	—
249	#135	—	2	2	no	—
250	#135	—	2	2	no	—
251	#135	—	4	1	no	—
252	#135	—	4	1	no	—
253	#135	—	4	1	no	—
254	#135	—	4	1	no	—
255	#135	D₄×C₁₃	1	2	yes	complemented
256	#135	C₂³×C₁₃	1	2	yes	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic, complemented
259	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	1	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic, complemented
265	C₂×D₈	C₂³×C₁₃	1	2	yes	—
266	#131	—	2	2	no	—
267	#131	—	2	2	no	—
268	#131	—	4	1	no	—
269	#131	—	4	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	4	1	no	—
272	C₂²×C₈	—	4	1	no	—
273	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	1	no	—
276	#127	—	2	1	no	—
277	#124	—	2	2	no	—
278	#121	—	4	2	no	—
279	C₄×D₄	—	4	2	no	—
280	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
281	Q₃₂	—	2	4	no	—
282	SD₃₂	—	2	4	no	—
283	SD₃₂	—	2	4	no	—
284	D₁₆	—	2	4	no	—
285	M₃₂	—	2	2	no	—
286	M₃₂	C₂³×C₁₃	1	4	yes	—
287	C₂×C₁₆	—	2	2	no	—
288	#108	—	2	1	no	—
289	#108	C₂³×C₁₃	1	2	yes	—
290	#104	—	2	2	no	—
291	#104	—	2	2	no	—
292	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
293	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₁₃	—	2	1	no	—
297	C₂×C₁₃	—	2	1	no	—
298	C₂×C₁₃	—	2	1	no	—
299	C₂×C₁₃	—	8	2	no	—
300	C₂×C₁₃	—	16	2	no	—
301	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
302	#41	—	2	2	no	—
303	#41	—	2	2	no	—
304	#41	—	4	1	no	—
305	#41	—	4	1	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	Q₁₆	—	2	1	no	—
322	Q₁₆	—	2	2	no	—
323	Q₁₆	—	2	2	no	—
324	Q₁₆	—	4	1	no	—
325	Q₁₆	—	4	1	no	—
326	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
327	SD₁₆	—	2	2	no	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	4	2	no	—
330	SD₁₆	—	4	2	no	—
331	SD₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	D₈	—	2	1	no	—
334	D₈	—	2	2	no	—
335	D₈	—	2	2	no	—
336	D₈	—	4	1	no	—
337	D₈	—	4	1	no	—
338	D₈	C₂×D₄×C₁₃	1	2	yes	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	4	1	no	—
341	M₁₆	—	4	2	no	—
342	M₁₆	—	4	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
347	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
348	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
349	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
356	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
357	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
358	C₄⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₄²	—	2	1	no	—
361	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₁₆	—	2	4	no	—
364	C₁₃	#33594	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	4	1	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	4	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
391	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
392	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
393	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
394	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	C₁₃×#121	1	1	yes	characteristic
398	C₈	C₁₃×#121	1	1	yes	characteristic
399	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
400	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
401	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
402	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
403	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
404	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	C₁₃×#459	1	1	yes	characteristic
411	C₂²	C₁₃×#459	1	1	yes	characteristic
412	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₁₃×#459	1	1	yes	characteristic
418	C₄	C₁₃×#459	1	1	yes	characteristic
419	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
420	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	16	2	no	—
426	C₂	C₂×C₁₃×#459	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#459
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3414	C₂	semidirect
2. C₁₃×#3147	C₂	semidirect
3. C₂×C₁₃×#443	C₂	semidirect
4. C₁₃×#2214	C₂	semidirect
5. C₁₃×#2213	C₂	semidirect
6. C₁₃×#2212	C₂	semidirect
7. C₂×C₁₃×#364	C₂	semidirect
8. C₁₃×#2148	C₂	semidirect
21. C₁₃×#495	C₂²	semidirect
22. C₁₃×#494	C₂²	semidirect
23. C₁₃×#493	C₂²	semidirect
32. C₁₃×#364	C₂²	semidirect
33. C₁₃×#364	C₂²	semidirect
34. C₁₃×#362	C₂²	semidirect
35. C₁₃×#361	C₂²	semidirect
48. C₁₃×#135	D₄	semidirect
51. C₂×C₁₃×Q₁₆	D₄	semidirect
57. C₂×C₁₃×D₈	D₄	semidirect
89. #33594	C₁₃	direct (N × H)
152. #3414	C₂×C₁₃	semidirect
153. #3147	C₂×C₁₃	semidirect
154. C₂×#443	C₂×C₁₃	semidirect
155. #2214	C₂×C₁₃	semidirect
156. #2213	C₂×C₁₃	semidirect
157. #2212	C₂×C₁₃	semidirect
158. C₂×#364	C₂×C₁₃	semidirect
159. #2148	C₂×C₁₃	semidirect
212. #495	C₂²×C₁₃	semidirect
213. #494	C₂²×C₁₃	semidirect
214. #493	C₂²×C₁₃	semidirect
223. #364	C₂²×C₁₃	semidirect
224. #364	C₂²×C₁₃	semidirect
225. #362	C₂²×C₁₃	semidirect
226. #361	C₂²×C₁₃	semidirect
255. #135	D₄×C₁₃	semidirect
258. C₂×Q₁₆	D₄×C₁₃	semidirect
264. C₂×D₈	D₄×C₁₃	semidirect
364. C₁₃	#33594	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×#3414	2
C₁₃×#3147	2
C₂×C₁₃×#443	2
C₁₃×#2214	2
C₁₃×#2213	2
C₁₃×#2212	2
C₂×C₁₃×#364	2
C₁₃×#2148	2
#33594	13

Subgroups — C13×#33594 #15719933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33594 #15719933