Subgroups — C₁₃×#33468 #15719807

Order 3328.

652 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	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2943	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	C₁₃×#2155	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2148	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2145	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#347	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	C₂×C₁₃×#131	—	2	1	no	—
13	C₄×C₁₃×#41	—	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	—	2	2	no	—
22	C₁₃×#444	C₂²	1	4	yes	—
23	C₁₃×#442	C₂²	1	2	yes	complemented
24	C₁₃×#441	C₂²	1	2	yes	complemented
25	C₁₃×#440	—	2	2	no	—
26	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
27	C₁₃×#427	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#104	—	2	1	no	—
29	C₁₃×#416	—	2	1	no	—
30	C₂×C₁₃×#97	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	1	no	—
56	C₂²×C₈×C₁₃	—	4	1	no	—
57	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	4	2	no	—
62	C₁₃×#117	—	2	1	no	—
63	C₁₃×#117	—	4	1	no	—
64	C₂×C₄²×C₁₃	—	4	1	no	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₁₃×Q₃₂	C₂×C₄	1	4	yes	complemented
67	C₁₃×SD₃₂	C₂×C₄	1	4	yes	complemented
68	C₁₃×SD₃₂	C₂×C₄	1	4	yes	complemented
69	C₁₃×D₁₆	C₂×C₄	1	4	yes	complemented
70	C₁₃×M₃₂	—	2	1	no	—
71	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
72	C₁₃×M₃₂	C₂³	1	2	yes	—
73	C₁₃×M₃₂	C₂³	1	2	yes	—
74	C₂×C₁₃×C₁₆	—	2	1	no	—
75	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
76	C₁₃×#108	—	2	1	no	—
77	C₁₃×#108	C₂³	1	2	yes	—
78	C₁₃×#107	—	2	1	no	—
79	C₁₃×#106	C₂³	1	2	yes	—
80	C₁₃×#104	—	2	4	no	—
81	C₁₃×#103	—	2	2	no	—
82	C₁₃×#102	—	2	2	no	—
83	C₁₃×#97	D₄	1	2	yes	—
84	C₁₃×#97	C₂³	1	2	yes	—
85	#33468	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₁₃×#41	—	2	2	no	—
87	C₁₃×#41	—	2	2	no	—
88	C₁₃×#41	—	2	2	no	—
89	C₁₃×#41	—	2	2	no	—
90	C₁₃×#41	—	4	1	no	—
91	C₁₃×#41	—	4	1	no	—
92	C₁₃×#41	—	4	1	no	—
93	C₁₃×#41	—	4	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₁₃×Q₁₆	—	2	1	no	—
106	C₁₃×Q₁₆	—	2	1	no	—
107	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
108	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
109	C₁₃×SD₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	2	2	no	—
111	C₁₃×SD₁₆	—	2	2	no	—
112	C₁₃×SD₁₆	—	2	2	no	—
113	C₁₃×D₈	—	2	1	no	—
114	C₁₃×D₈	—	2	1	no	—
115	C₁₃×D₈	C₂²×C₄	1	2	yes	—
116	C₁₃×D₈	C₂²×C₄	1	2	yes	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₁₃×M₁₆	—	4	4	no	—
119	C₁₃×M₁₆	—	4	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	4	4	no	—
123	C₂×C₈×C₁₃	—	4	1	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
129	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	4	2	no	—
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×C₁₆	—	2	2	no	—
140	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
141	#3414	C₂×C₁₃	1	1	yes	characteristic
142	C₂×#444	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2943	C₂×C₁₃	1	1	yes	characteristic, complemented
144	AGL(1,ℤ/16)	C₂×C₁₃	1	4	yes	complemented
145	#2180	C₂×C₁₃	1	4	yes	complemented
146	#2155	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2148	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2145	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#347	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	2	2	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	1	no	—
157	D₄×C₁₃	—	2	2	no	—
158	D₄×C₁₃	—	2	2	no	—
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
173	C₂×C₄×C₁₃	—	8	1	no	—
174	C₂×C₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₄×D₄	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	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₁₃	—	2	2	no	—
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#131	—	2	1	no	—
190	C₄×#41	—	2	1	no	—
191	#510	C₄×C₁₃	1	2	yes	complemented
192	#510	C₂²×C₁₃	1	2	yes	—
193	#509	C₄×C₁₃	1	2	yes	complemented
194	#509	C₂²×C₁₃	1	2	yes	—
195	#508	C₄×C₁₃	1	4	yes	complemented
196	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
198	#444	—	2	2	no	—
199	#444	C₂²×C₁₃	1	4	yes	—
200	#442	C₂²×C₁₃	1	2	yes	complemented
201	#441	C₂²×C₁₃	1	2	yes	complemented
202	#440	—	2	2	no	—
203	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
204	#427	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#104	—	2	1	no	—
206	#416	—	2	1	no	—
207	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
208	#365	C₂²×C₁₃	1	4	yes	complemented
209	#362	C₂²×C₁₃	1	2	yes	complemented
210	#361	C₂²×C₁₃	1	2	yes	complemented
211	#360	C₂²×C₁₃	1	4	yes	—
212	#347	C₂²×C₁₃	1	4	yes	complemented
213	C₂²×C₁₃	—	4	1	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	2	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	1	no	—
249	C₂²×C₈	—	4	1	no	—
250	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₄×Q₈	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	4	2	no	—
255	#117	—	2	1	no	—
256	#117	—	4	1	no	—
257	C₂×C₄²	—	4	1	no	—
258	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
259	Q₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
260	SD₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
261	SD₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
262	D₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
263	M₃₂	—	2	1	no	—
264	M₃₂	C₂×C₄×C₁₃	1	2	yes	complemented
265	M₃₂	C₂³×C₁₃	1	2	yes	—
266	M₃₂	C₂³×C₁₃	1	2	yes	—
267	C₂×C₁₆	—	2	1	no	—
268	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	complemented
269	#108	—	2	1	no	—
270	#108	C₂³×C₁₃	1	2	yes	—
271	#107	—	2	1	no	—
272	#106	C₂³×C₁₃	1	2	yes	—
273	#104	—	2	4	no	—
274	#103	—	2	2	no	—
275	#102	—	2	2	no	—
276	#97	D₄×C₁₃	1	2	yes	—
277	#97	C₂³×C₁₃	1	2	yes	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	2	1	no	—
280	C₂×C₁₃	—	2	1	no	—
281	C₂×C₁₃	—	8	2	no	—
282	C₂×C₁₃	—	8	2	no	—
283	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	#41	—	2	2	no	—
288	#41	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	Q₁₆	—	2	1	no	—
304	Q₁₆	—	2	1	no	—
305	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
306	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	SD₁₆	—	2	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	2	1	no	—
313	D₈	C₂²×C₄×C₁₃	1	2	yes	—
314	D₈	C₂²×C₄×C₁₃	1	2	yes	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	4	4	no	—
317	M₁₆	—	4	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
323	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
327	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
328	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	4	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	C₂×D₄×C₁₃	1	2	yes	—
337	C₁₆	—	2	2	no	—
338	C₁₆	C₂²×C₄×C₁₃	1	4	yes	—
339	C₁₃	#33468	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	2	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	D₄	—	2	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	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	—	4	2	no	—
363	C₂×C₄	—	8	1	no	—
364	C₂×C₄	—	8	4	no	—
365	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄	C₄×D₄×C₁₃	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	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	—	4	2	no	—
373	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
374	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
375	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
376	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
377	C₂²	—	4	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	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	C₄×C₁₃	#442
commutator	C₈	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#442
prime radical	C₁₃×#3414	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#444	C₂	semidirect
3. C₁₃×#2943	C₂	semidirect
4. C₁₃×AGL(1,ℤ/16)	C₂	semidirect
5. C₁₃×#2180	C₂	semidirect
6. C₁₃×#2155	C₂	semidirect
7. C₁₃×#2148	C₂	semidirect
8. C₁₃×#2145	C₂	semidirect
9. C₂×C₁₃×#347	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
66. C₁₃×Q₃₂	C₂×C₄	semidirect
67. C₁₃×SD₃₂	C₂×C₄	semidirect
68. C₁₃×SD₃₂	C₂×C₄	semidirect
69. C₁₃×D₁₆	C₂×C₄	semidirect
71. C₁₃×M₃₂	C₂×C₄	semidirect
75. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
85. #33468	C₁₃	direct (N × H)
142. C₂×#444	C₂×C₁₃	semidirect
143. #2943	C₂×C₁₃	semidirect
144. AGL(1,ℤ/16)	C₂×C₁₃	semidirect
145. #2180	C₂×C₁₃	semidirect
146. #2155	C₂×C₁₃	semidirect
147. #2148	C₂×C₁₃	semidirect
148. #2145	C₂×C₁₃	semidirect
149. C₂×#347	C₂×C₁₃	semidirect
191. #510	C₄×C₁₃	semidirect
193. #509	C₄×C₁₃	semidirect
195. #508	C₄×C₁₃	semidirect
200. #442	C₂²×C₁₃	semidirect
201. #441	C₂²×C₁₃	semidirect
208. #365	C₂²×C₁₃	semidirect
209. #362	C₂²×C₁₃	semidirect
210. #361	C₂²×C₁₃	semidirect
212. #347	C₂²×C₁₃	semidirect
237. #135	C₂×C₄×C₁₃	semidirect
239. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
243. C₂×D₈	C₂×C₄×C₁₃	semidirect
259. Q₃₂	C₂×C₄×C₁₃	semidirect
260. SD₃₂	C₂×C₄×C₁₃	semidirect
261. SD₃₂	C₂×C₄×C₁₃	semidirect
262. D₁₆	C₂×C₄×C₁₃	semidirect
264. M₃₂	C₂×C₄×C₁₃	semidirect
268. C₂×C₁₆	C₂×C₄×C₁₃	semidirect
339. C₁₃	#33468	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
C₂×C₁₃×#444	2
C₁₃×#2943	2
C₁₃×AGL(1,ℤ/16)	2
C₁₃×#2180	2
C₁₃×#2155	2
C₁₃×#2148	2
C₁₃×#2145	2
C₂×C₁₃×#347	2
#33468	13

Subgroups — C13×#33468 #15719807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33468 #15719807