Subgroups — C₁₃×#32782 #15719121

Order 3328.

744 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	C₁₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2619	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₃×#398	—	2	2	no	—
25	C₁₃×#396	—	2	2	no	—
26	C₁₃×#394	—	2	2	no	—
27	C₁₃×#392	—	2	2	no	—
28	C₁₃×#390	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#380	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₁₃×#127	—	4	2	no	—
48	C₁₃×#125	—	4	2	no	—
49	C₁₃×#121	—	4	2	no	—
50	C₁₃×#121	—	4	2	no	—
51	C₁₃×#117	—	4	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#107	—	4	2	no	—
69	C₁₃×#106	—	4	2	no	—
70	C₁₃×#102	—	4	2	no	—
71	C₁₃×#102	—	4	2	no	—
72	C₁₃×#102	—	4	2	no	—
73	C₁₃×#102	—	4	2	no	—
74	C₁₃×C₂²⋊C₈	—	4	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	#32782	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	2	1	no	—
80	C₂⁴×C₁₃	—	2	1	no	—
81	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	4	4	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	8	2	no	—
94	C₂×D₄×C₁₃	—	8	2	no	—
95	C₂×D₄×C₁₃	—	8	2	no	—
96	C₂×D₄×C₁₃	—	8	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	4	2	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	8	2	no	—
124	C₁₃×C₄⋊C₄	—	8	2	no	—
125	C₁₃×C₂²⋊C₄	—	4	2	no	—
126	C₁₃×C₂²⋊C₄	—	4	2	no	—
127	C₁₃×C₂²⋊C₄	—	4	2	no	—
128	C₁₃×C₂²⋊C₄	—	8	2	no	—
129	C₁₃×C₂²⋊C₄	—	8	2	no	—
130	C₁₃×C₂²⋊C₄	—	8	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	#2629	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#2619	C₂×C₁₃	1	1	yes	characteristic
135	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2085	C₂×C₁₃	1	2	yes	complemented
138	#2041	C₂×C₁₃	1	2	yes	complemented
139	#2034	C₂×C₁₃	1	2	yes	complemented
140	#2033	C₂×C₁₃	1	2	yes	complemented
141	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1818	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	2	1	no	—
145	C₂³×C₁₃	—	2	1	no	—
146	C₂³×C₁₃	—	2	1	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	8	8	no	—
165	D₄×C₁₃	—	8	4	no	—
166	D₄×C₁₃	—	8	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	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	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
189	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
190	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
192	C₈×C₁₃	—	4	2	no	—
193	C₈×C₁₃	—	4	2	no	—
194	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#107	C₂²×C₁₃	1	2	yes	—
200	C₂×#106	C₂²×C₁₃	1	2	yes	—
201	C₂×#102	C₂²×C₁₃	1	2	yes	—
202	C₂×#102	C₂²×C₁₃	1	2	yes	—
203	C₂×#102	C₂²×C₁₃	1	2	yes	—
204	C₂×#102	C₂²×C₁₃	1	2	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
206	#398	—	2	2	no	—
207	#396	—	2	2	no	—
208	#394	—	2	2	no	—
209	#392	—	2	2	no	—
210	#390	C₂²×C₁₃	1	1	yes	characteristic
211	#390	C₂²×C₁₃	1	1	yes	characteristic
212	#389	C₂²×C₁₃	1	2	yes	—
213	#384	C₂²×C₁₃	1	1	yes	characteristic
214	#382	C₂²×C₁₃	1	1	yes	characteristic
215	#380	C₂²×C₁₃	1	2	yes	—
216	#340	C₂²×C₁₃	1	2	yes	—
217	#340	C₂²×C₁₃	1	2	yes	—
218	#336	C₂²×C₁₃	1	2	yes	—
219	#336	C₂²×C₁₃	1	1	yes	characteristic
220	#336	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₁₃	—	4	1	no	—
222	C₂²×C₁₃	—	4	2	no	—
223	C₂²×C₁₃	—	4	1	no	—
224	C₂²×C₁₃	—	4	1	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	1	no	—
231	C₂²×C₁₃	—	8	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	8	2	no	—
235	C₂²×C₁₃	—	8	2	no	—
236	C₂²×C₁₃	#534	1	1	yes	characteristic
237	C₂²×C₁₃	#535	1	1	yes	characteristic
238	C₂²×C₁₃	#536	1	1	yes	characteristic
239	C₂²×C₁₃	#576	1	2	yes	—
240	C₂²×C₁₃	#577	1	2	yes	—
241	C₄×C₁₃	—	4	1	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	—	8	2	no	—
246	C₄×C₁₃	—	8	1	no	—
247	C₄×C₁₃	—	8	1	no	—
248	C₄×C₁₃	#562	1	2	yes	—
249	C₄×C₁₃	#562	1	2	yes	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
258	#127	—	4	2	no	—
259	#125	—	4	2	no	—
260	#121	—	4	2	no	—
261	#121	—	4	2	no	—
262	#117	—	4	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
277	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	#107	—	4	2	no	—
280	#106	—	4	2	no	—
281	#102	—	4	2	no	—
282	#102	—	4	2	no	—
283	#102	—	4	2	no	—
284	#102	—	4	2	no	—
285	C₂²⋊C₈	—	4	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	C₂×C₁₃	—	8	1	no	—
290	C₂×C₁₃	—	16	1	no	—
291	C₂×C₁₃	—	16	1	no	—
292	C₂×C₁₃	#2816	1	1	yes	characteristic
293	C₂×C₁₃	#3198	1	2	yes	—
294	C₂×C₁₃	#3220	1	1	yes	characteristic
295	C₂×C₁₃	#3222	1	1	yes	characteristic
296	C₂×C₁₃	#3241	1	2	yes	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	8	2	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₄⋊C₄	—	8	2	no	—
342	C₄⋊C₄	—	8	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	8	2	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₁₃	#32782	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	8	no	—
373	D₄	—	8	4	no	—
374	D₄	—	8	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
398	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
399	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₁₃×#534	1	1	yes	characteristic
418	C₂²	C₁₃×#535	1	1	yes	characteristic
419	C₂²	C₁₃×#536	1	1	yes	characteristic
420	C₂²	C₁₃×#576	1	2	yes	—
421	C₂²	C₁₃×#577	1	2	yes	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	C₁₃×#562	1	2	yes	—
430	C₄	C₁₃×#562	1	2	yes	—
431	C₂	—	8	1	no	—
432	C₂	—	16	1	no	—
433	C₂	—	16	1	no	—
434	C₂	C₁₃×#2816	1	1	yes	characteristic
435	C₂	C₁₃×#3198	1	2	yes	—
436	C₂	C₁₃×#3220	1	1	yes	characteristic
437	C₂	C₁₃×#3222	1	1	yes	characteristic
438	C₂	C₁₃×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2629	C₂	semidirect
3. C₁₃×#2094	C₂	semidirect
4. C₁₃×#2093	C₂	semidirect
5. C₁₃×#2085	C₂	semidirect
6. C₁₃×#2041	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#2025	C₂	semidirect
10. C₁₃×#2025	C₂	semidirect
11. C₁₃×#1818	C₂	semidirect
78. #32782	C₁₃	direct (N × H)
133. #2629	C₂×C₁₃	semidirect
135. #2094	C₂×C₁₃	semidirect
136. #2093	C₂×C₁₃	semidirect
137. #2085	C₂×C₁₃	semidirect
138. #2041	C₂×C₁₃	semidirect
139. #2034	C₂×C₁₃	semidirect
140. #2033	C₂×C₁₃	semidirect
141. #2025	C₂×C₁₃	semidirect
142. #2025	C₂×C₁₃	semidirect
143. #1818	C₂×C₁₃	semidirect
351. C₁₃	#32782	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×#2629	2
C₁₃×#2619	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2085	2
C₁₃×#2041	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#2025	2
C₁₃×#1818	2
#32782	13

Subgroups — C13×#32782 #15719121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32782 #15719121