Subgroups — C₁₃×#33469 #15719808

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 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	1	yes	maximal, characteristic
2	C₁₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×AGL(1,ℤ/16)	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2180	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2148	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#360	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2110	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
12	C₁₃×#568	—	2	1	no	—
13	C₁₃×#520	—	2	1	no	—
14	C₁₃×#510	C₄	1	2	yes	complemented
15	C₁₃×#510	C₂²	1	2	yes	—
16	C₁₃×#509	C₄	1	2	yes	complemented
17	C₁₃×#509	C₂²	1	2	yes	—
18	C₁₃×#508	C₄	1	4	yes	complemented
19	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
21	C₁₃×#444	C₂²	1	4	yes	—
22	C₁₃×#443	—	2	2	no	—
23	C₁₃×#442	C₂²	1	2	yes	complemented
24	C₁₃×#441	C₂²	1	2	yes	complemented
25	C₄×C₁₃×SD₁₆	—	2	2	no	—
26	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₁₃×#421	—	2	1	no	—
29	C₁₃×#417	—	2	1	no	—
30	C₁₃×#405	C₂²	1	1	yes	characteristic
31	C₁₃×#365	C₂²	1	4	yes	complemented
32	C₁₃×#362	C₂²	1	2	yes	complemented
33	C₁₃×#361	C₂²	1	2	yes	complemented
34	C₁₃×#360	C₂²	1	4	yes	—
35	C₁₃×#347	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₁₃×#135	—	2	1	no	—
39	C₁₃×#135	—	2	1	no	—
40	C₁₃×#135	—	2	1	no	—
41	C₁₃×#135	—	2	1	no	—
42	C₁₃×#135	C₂×C₄	1	2	yes	—
43	C₁₃×#135	C₂×C₄	1	2	yes	—
44	C₁₃×#135	C₂×C₄	1	2	yes	complemented
45	C₁₃×#135	C₂³	1	2	yes	—
46	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
52	C₁₃×#131	—	2	4	no	—
53	C₁₃×#131	—	4	2	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	4	2	no	—
56	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	4	2	no	—
61	C₁₃×#117	—	4	1	no	—
62	C₁₃×#117	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
65	C₁₃×Q₃₂	C₂×C₄	1	4	yes	complemented
66	C₁₃×SD₃₂	C₂×C₄	1	4	yes	complemented
67	C₁₃×SD₃₂	C₂×C₄	1	4	yes	complemented
68	C₁₃×D₁₆	C₂×C₄	1	4	yes	complemented
69	C₁₃×M₃₂	—	2	1	no	—
70	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
71	C₁₃×M₃₂	C₂³	1	2	yes	—
72	C₁₃×M₃₂	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	—	2	1	no	—
74	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
75	C₁₃×#108	—	2	1	no	—
76	C₁₃×#108	C₂³	1	2	yes	—
77	C₁₃×#106	—	2	1	no	—
78	C₁₃×#106	C₂³	1	2	yes	—
79	C₁₃×#104	—	2	4	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#97	C₂³	1	2	yes	—
83	C₄×C₈×C₁₃	D₄	1	2	yes	—
84	#33469	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₁₃×#41	—	2	2	no	—
86	C₁₃×#41	—	2	2	no	—
87	C₁₃×#41	—	2	2	no	—
88	C₁₃×#41	—	2	2	no	—
89	C₁₃×#41	—	4	1	no	—
90	C₁₃×#41	—	4	1	no	—
91	C₁₃×#41	—	4	1	no	—
92	C₁₃×#41	—	4	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₁₃×Q₁₆	—	2	1	no	—
105	C₁₃×Q₁₆	—	2	1	no	—
106	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
107	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
108	C₁₃×SD₁₆	—	2	2	no	—
109	C₁₃×SD₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	2	2	no	—
111	C₁₃×SD₁₆	—	2	2	no	—
112	C₁₃×D₈	—	2	1	no	—
113	C₁₃×D₈	—	2	1	no	—
114	C₁₃×D₈	C₂²×C₄	1	2	yes	—
115	C₁₃×D₈	C₂²×C₄	1	2	yes	—
116	C₁₃×M₁₆	—	2	1	no	—
117	C₁₃×M₁₆	—	2	1	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	4	4	no	—
120	C₁₃×M₁₆	—	4	1	no	—
121	C₂×C₈×C₁₃	—	4	4	no	—
122	C₂×C₈×C₁₃	—	4	1	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
128	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₄²×C₁₃	—	4	2	no	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
140	#3414	C₂×C₁₃	1	1	yes	characteristic
141	#2957	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
143	AGL(1,ℤ/16)	C₂×C₁₃	1	4	yes	complemented
144	#2180	C₂×C₁₃	1	4	yes	complemented
145	C₂×#365	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2148	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂×#360	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2110	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
152	Q₈×C₁₃	—	2	2	no	—
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	4	1	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	D₄×C₁₃	—	2	2	no	—
157	D₄×C₁₃	—	2	2	no	—
158	D₄×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	16	2	no	—
173	C₂×C₄×C₁₃	—	16	1	no	—
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₈×C₁₃	—	2	2	no	—
181	C₈×C₁₃	—	4	2	no	—
182	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
183	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
188	#568	—	2	1	no	—
189	#520	—	2	1	no	—
190	#510	C₄×C₁₃	1	2	yes	complemented
191	#510	C₂²×C₁₃	1	2	yes	—
192	#509	C₄×C₁₃	1	2	yes	complemented
193	#509	C₂²×C₁₃	1	2	yes	—
194	#508	C₄×C₁₃	1	4	yes	complemented
195	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
197	#444	C₂²×C₁₃	1	4	yes	—
198	#443	—	2	2	no	—
199	#442	C₂²×C₁₃	1	2	yes	complemented
200	#441	C₂²×C₁₃	1	2	yes	complemented
201	C₄×SD₁₆	—	2	2	no	—
202	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
204	#421	—	2	1	no	—
205	#417	—	2	1	no	—
206	#405	C₂²×C₁₃	1	1	yes	characteristic
207	#365	C₂²×C₁₃	1	4	yes	complemented
208	#362	C₂²×C₁₃	1	2	yes	complemented
209	#361	C₂²×C₁₃	1	2	yes	complemented
210	#360	C₂²×C₁₃	1	4	yes	—
211	#347	C₂²×C₁₃	1	4	yes	complemented
212	C₂²×C₁₃	—	4	1	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	8	1	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	16	1	no	—
218	C₂²×C₁₃	#442	1	1	yes	characteristic
219	C₂²×C₁₃	#442	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	#442	1	1	yes	characteristic
226	C₄×C₁₃	#442	1	1	yes	characteristic
227	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×#41	—	2	1	no	—
231	#135	—	2	1	no	—
232	#135	—	2	1	no	—
233	#135	—	2	1	no	—
234	#135	—	2	1	no	—
235	#135	C₂×C₄×C₁₃	1	2	yes	—
236	#135	C₂×C₄×C₁₃	1	2	yes	—
237	#135	C₂×C₄×C₁₃	1	2	yes	complemented
238	#135	C₂³×C₁₃	1	2	yes	—
239	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
240	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
244	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
245	#131	—	2	4	no	—
246	#131	—	4	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	4	2	no	—
249	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
251	C₄×Q₈	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	4	2	no	—
254	#117	—	4	1	no	—
255	#117	D₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	4	1	no	—
258	Q₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
259	SD₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
260	SD₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
261	D₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
262	M₃₂	—	2	1	no	—
263	M₃₂	C₂×C₄×C₁₃	1	2	yes	complemented
264	M₃₂	C₂³×C₁₃	1	2	yes	—
265	M₃₂	C₂³×C₁₃	1	2	yes	—
266	C₂×C₁₆	—	2	1	no	—
267	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	complemented
268	#108	—	2	1	no	—
269	#108	C₂³×C₁₃	1	2	yes	—
270	#106	—	2	1	no	—
271	#106	C₂³×C₁₃	1	2	yes	—
272	#104	—	2	4	no	—
273	#103	—	2	2	no	—
274	#102	—	2	2	no	—
275	#97	C₂³×C₁₃	1	2	yes	—
276	C₄×C₈	D₄×C₁₃	1	2	yes	—
277	C₂×C₁₃	—	2	1	no	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	2	1	no	—
280	C₂×C₁₃	—	8	2	no	—
281	C₂×C₁₃	—	8	2	no	—
282	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	#41	—	4	1	no	—
288	#41	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	1	no	—
304	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
305	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
306	SD₁₆	—	2	2	no	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	D₈	—	2	1	no	—
311	D₈	—	2	1	no	—
312	D₈	C₂²×C₄×C₁₃	1	2	yes	—
313	D₈	C₂²×C₄×C₁₃	1	2	yes	—
314	M₁₆	—	2	1	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	4	4	no	—
318	M₁₆	—	4	1	no	—
319	C₂×C₈	—	4	4	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
322	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
324	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
326	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
327	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₄²	—	4	2	no	—
335	C₄²	C₂×D₄×C₁₃	1	2	yes	—
336	C₁₆	—	2	2	no	—
337	C₁₆	C₂²×C₄×C₁₃	1	4	yes	—
338	C₁₃	#33469	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
342	Q₈	—	2	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	4	1	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	16	2	no	—
363	C₂×C₄	—	16	1	no	—
364	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
367	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
368	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	4	2	no	—
372	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
373	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
374	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
375	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	16	1	no	—
382	C₂²	C₁₃×#442	1	1	yes	characteristic
383	C₂²	C₁₃×#442	1	1	yes	characteristic
384	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₁₃×#442	1	1	yes	characteristic
390	C₄	C₁₃×#442	1	1	yes	characteristic
391	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
392	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	8	2	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×C₁₃×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#442
commutator	C₈	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3414	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2957	C₂	semidirect
3. C₁₃×#2952	C₂	semidirect
4. C₁₃×AGL(1,ℤ/16)	C₂	semidirect
5. C₁₃×#2180	C₂	semidirect
6. C₂×C₁₃×#365	C₂	semidirect
7. C₁₃×#2148	C₂	semidirect
8. C₂×C₁₃×#360	C₂	semidirect
9. C₁₃×#2110	C₂	semidirect
14. C₁₃×#510	C₄	semidirect
16. C₁₃×#509	C₄	semidirect
18. C₁₃×#508	C₄	semidirect
23. C₁₃×#442	C₂²	semidirect
24. C₁₃×#441	C₂²	semidirect
31. C₁₃×#365	C₂²	semidirect
32. C₁₃×#362	C₂²	semidirect
33. C₁₃×#361	C₂²	semidirect
35. C₁₃×#347	C₂²	semidirect
44. C₁₃×#135	C₂×C₄	semidirect
46. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
50. C₂×C₁₃×D₈	C₂×C₄	semidirect
65. C₁₃×Q₃₂	C₂×C₄	semidirect
66. C₁₃×SD₃₂	C₂×C₄	semidirect
67. C₁₃×SD₃₂	C₂×C₄	semidirect
68. C₁₃×D₁₆	C₂×C₄	semidirect
70. C₁₃×M₃₂	C₂×C₄	semidirect
74. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
84. #33469	C₁₃	direct (N × H)
141. #2957	C₂×C₁₃	semidirect
142. #2952	C₂×C₁₃	semidirect
143. AGL(1,ℤ/16)	C₂×C₁₃	semidirect
144. #2180	C₂×C₁₃	semidirect
145. C₂×#365	C₂×C₁₃	semidirect
146. #2148	C₂×C₁₃	semidirect
147. C₂×#360	C₂×C₁₃	semidirect
148. #2110	C₂×C₁₃	semidirect
190. #510	C₄×C₁₃	semidirect
192. #509	C₄×C₁₃	semidirect
194. #508	C₄×C₁₃	semidirect
199. #442	C₂²×C₁₃	semidirect
200. #441	C₂²×C₁₃	semidirect
207. #365	C₂²×C₁₃	semidirect
208. #362	C₂²×C₁₃	semidirect
209. #361	C₂²×C₁₃	semidirect
211. #347	C₂²×C₁₃	semidirect
237. #135	C₂×C₄×C₁₃	semidirect
239. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
243. C₂×D₈	C₂×C₄×C₁₃	semidirect
258. Q₃₂	C₂×C₄×C₁₃	semidirect
259. SD₃₂	C₂×C₄×C₁₃	semidirect
260. SD₃₂	C₂×C₄×C₁₃	semidirect
261. D₁₆	C₂×C₄×C₁₃	semidirect
263. M₃₂	C₂×C₄×C₁₃	semidirect
267. C₂×C₁₆	C₂×C₄×C₁₃	semidirect
338. C₁₃	#33469	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×#2957	2
C₁₃×#2952	2
C₁₃×AGL(1,ℤ/16)	2
C₁₃×#2180	2
C₂×C₁₃×#365	2
C₁₃×#2148	2
C₂×C₁₃×#360	2
C₁₃×#2110	2
#33469	13

Subgroups — C13×#33469 #15719808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33469 #15719808