Subgroups — C₁₃×#33785 #15720124

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₁₃×#532	—	2	1	no	—
15	C₁₃×#529	—	2	1	no	—
16	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
20	C₁₃×#499	C₂²	1	1	yes	characteristic
21	C₁₃×#495	—	2	1	no	—
22	C₁₃×#495	C₂²	1	1	yes	characteristic
23	C₁₃×#495	C₂²	1	2	yes	—
24	C₁₃×#494	C₂²	1	1	yes	characteristic
25	C₁₃×#493	C₂²	1	1	yes	characteristic
26	C₁₃×#492	—	2	1	no	—
27	C₁₃×#488	—	2	1	no	—
28	C₁₃×#467	C₂²	1	1	yes	characteristic
29	C₁₃×#466	C₂²	1	1	yes	characteristic
30	C₁₃×#465	—	2	1	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×SD₁₆	—	2	1	no	—
33	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₁₃×#358	C₂²	1	2	yes	—
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#357	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₁₃×#346	C₂²	1	1	yes	characteristic
42	C₁₃×#346	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₁₃×#135	—	4	2	no	—
45	C₁₃×#135	—	4	2	no	—
46	C₁₃×#135	—	4	4	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	C₂³	1	2	yes	—
55	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#126	—	4	1	no	—
61	C₁₃×#125	—	2	1	no	—
62	C₁₃×#124	—	2	1	no	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#123	—	4	1	no	—
65	C₁₃×C₂²⋊Q₈	—	2	1	no	—
66	C₁₃×#121	—	2	1	no	—
67	C₁₃×#121	—	4	1	no	—
68	C₁₃×#121	—	4	1	no	—
69	C₄×Q₈×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	4	1	no	—
72	C₄×D₄×C₁₃	—	4	1	no	—
73	C₄×D₄×C₁₃	—	4	1	no	—
74	C₁₃×#117	—	4	1	no	—
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₁₃×Q₃₂	—	4	2	no	—
77	C₁₃×SD₃₂	—	4	2	no	—
78	C₁₃×SD₃₂	—	4	2	no	—
79	C₁₃×D₁₆	—	4	2	no	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
82	C₁₃×#107	C₂³	1	1	yes	characteristic
83	C₁₃×#107	C₂³	1	1	yes	characteristic
84	C₁₃×#106	—	2	1	no	—
85	C₁₃×#103	—	2	1	no	—
86	C₁₃×#103	—	2	1	no	—
87	C₁₃×#102	—	2	1	no	—
88	C₁₃×#102	—	2	1	no	—
89	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	#33785	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₁₃×#41	—	4	4	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×Q₁₆	—	2	2	no	—
111	C₁₃×Q₁₆	—	2	2	no	—
112	C₁₃×Q₁₆	—	4	2	no	—
113	C₁₃×SD₁₆	—	4	4	no	—
114	C₁₃×SD₁₆	—	4	4	no	—
115	C₁₃×SD₁₆	—	4	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	—	4	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	1	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	1	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	C₄²×C₁₃	D₈	1	1	yes	characteristic
143	C₄²×C₁₃	D₈	1	1	yes	characteristic
144	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×C₁₆	—	2	2	no	—
147	C₁₃×C₁₆	—	2	2	no	—
148	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2250	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2245	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2244	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2211	C₂×C₁₃	1	2	yes	complemented
155	#2210	C₂×C₁₃	1	2	yes	complemented
156	#2189	C₂×C₁₃	1	2	yes	complemented
157	#2186	C₂×C₁₃	1	2	yes	complemented
158	#2163	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	1	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	1	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	1	no	—
170	D₄×C₁₃	—	8	2	no	—
171	D₄×C₁₃	—	8	2	no	—
172	D₄×C₁₃	—	8	2	no	—
173	D₄×C₁₃	—	8	4	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	8	2	no	—
183	C₂×C₄×C₁₃	—	8	4	no	—
184	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×D₈	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	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	—	2	1	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
193	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
194	C₂×#135	—	2	1	no	—
195	C₂×#135	C₂²×C₁₃	1	2	yes	—
196	#532	—	2	1	no	—
197	#529	—	2	1	no	—
198	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
199	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
200	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
201	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
202	#499	C₂²×C₁₃	1	1	yes	characteristic
203	#495	—	2	1	no	—
204	#495	C₂²×C₁₃	1	2	yes	—
205	#495	C₂²×C₁₃	1	1	yes	characteristic
206	#494	C₂²×C₁₃	1	1	yes	characteristic
207	#493	C₂²×C₁₃	1	1	yes	characteristic
208	#492	—	2	1	no	—
209	#488	—	2	1	no	—
210	#467	C₂²×C₁₃	1	1	yes	characteristic
211	#466	C₂²×C₁₃	1	1	yes	characteristic
212	#465	—	2	1	no	—
213	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×SD₁₆	—	2	1	no	—
215	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
218	#358	C₂²×C₁₃	1	2	yes	—
219	#358	C₂²×C₁₃	1	2	yes	—
220	#357	C₂²×C₁₃	1	2	yes	—
221	#357	C₂²×C₁₃	1	2	yes	—
222	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
223	#346	C₂²×C₁₃	1	1	yes	characteristic
224	#346	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	—	8	1	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	8	1	no	—
241	C₄×C₁₃	—	8	1	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	#535	1	1	yes	characteristic
245	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂×#41	—	2	2	no	—
247	#135	—	4	2	no	—
248	#135	—	4	2	no	—
249	#135	—	4	4	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
252	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	C₂³×C₁₃	1	2	yes	—
258	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	1	no	—
262	#127	—	2	1	no	—
263	#126	—	4	1	no	—
264	#125	—	2	1	no	—
265	#124	—	2	1	no	—
266	#124	—	2	2	no	—
267	#123	—	4	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	#121	—	2	1	no	—
270	#121	—	4	1	no	—
271	#121	—	4	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	4	1	no	—
276	C₄×D₄	—	4	1	no	—
277	#117	—	4	1	no	—
278	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
279	Q₃₂	—	4	2	no	—
280	SD₃₂	—	4	2	no	—
281	SD₃₂	—	4	2	no	—
282	D₁₆	—	4	2	no	—
283	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
284	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
285	#107	C₂³×C₁₃	1	1	yes	characteristic
286	#107	C₂³×C₁₃	1	1	yes	characteristic
287	#106	—	2	1	no	—
288	#103	—	2	1	no	—
289	#103	—	2	1	no	—
290	#102	—	2	1	no	—
291	#102	—	2	1	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	—	4	1	no	—
297	C₂×C₁₃	—	16	1	no	—
298	C₂×C₁₃	—	16	2	no	—
299	C₂×C₁₃	#3205	1	1	yes	characteristic
300	C₂×C₁₃	#3414	1	1	yes	characteristic
301	C₂×C₁₃	#3414	1	1	yes	characteristic
302	#41	—	4	4	no	—
303	#41	—	4	4	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
315	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	Q₁₆	—	2	2	no	—
318	Q₁₆	—	2	2	no	—
319	Q₁₆	—	2	2	no	—
320	Q₁₆	—	4	2	no	—
321	SD₁₆	—	4	4	no	—
322	SD₁₆	—	4	4	no	—
323	SD₁₆	—	4	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	C₁₃×D₈	1	1	yes	characteristic
351	C₄²	C₁₃×D₈	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₁₆	—	2	2	no	—
355	C₁₆	—	2	2	no	—
356	C₁₃	#33785	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
360	Q₈	—	4	2	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	1	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	1	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	4	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	8	4	no	—
382	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
391	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	C₁₃×#535	1	1	yes	characteristic
412	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₂	—	4	1	no	—
414	C₂	—	16	1	no	—
415	C₂	—	16	2	no	—
416	C₂	C₁₃×#3205	1	1	yes	characteristic
417	C₂	C₁₃×#3414	1	1	yes	characteristic
418	C₂	C₁₃×#3414	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 ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3168	C₂	semidirect
2. C₁₃×#3147	C₂	semidirect
3. C₁₃×#2251	C₂	semidirect
4. C₁₃×#2250	C₂	semidirect
5. C₁₃×#2245	C₂	semidirect
6. C₁₃×#2244	C₂	semidirect
7. C₁₃×#2211	C₂	semidirect
8. C₁₃×#2210	C₂	semidirect
9. C₁₃×#2189	C₂	semidirect
10. C₁₃×#2186	C₂	semidirect
11. C₁₃×#2163	C₂	semidirect
93. #33785	C₁₃	direct (N × H)
148. #3168	C₂×C₁₃	semidirect
149. #3147	C₂×C₁₃	semidirect
150. #2251	C₂×C₁₃	semidirect
151. #2250	C₂×C₁₃	semidirect
152. #2245	C₂×C₁₃	semidirect
153. #2244	C₂×C₁₃	semidirect
154. #2211	C₂×C₁₃	semidirect
155. #2210	C₂×C₁₃	semidirect
156. #2189	C₂×C₁₃	semidirect
157. #2186	C₂×C₁₃	semidirect
158. #2163	C₂×C₁₃	semidirect
356. C₁₃	#33785	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×#3168	2
C₁₃×#3147	2
C₁₃×#2251	2
C₁₃×#2250	2
C₁₃×#2245	2
C₁₃×#2244	2
C₁₃×#2211	2
C₁₃×#2210	2
C₁₃×#2189	2
C₁₃×#2186	2
C₁₃×#2163	2
#33785	13

Subgroups — C13×#33785 #15720124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33785 #15720124