Subgroups — C₁₃×#32628 #15718967

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2041	C₂	1	2	yes	maximal
5	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1918	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#398	—	2	1	no	—
23	C₁₃×#398	—	2	1	no	—
24	C₁₃×#394	—	2	1	no	—
25	C₁₃×#394	—	2	1	no	—
26	C₁₃×#391	—	2	1	no	—
27	C₁₃×#390	—	2	1	no	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#390	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	4	1	no	—
47	C₁₃×C₄⋊Q₈	—	4	1	no	—
48	C₁₃×C₄⋊Q₈	—	4	4	no	—
49	C₁₃×#127	—	4	1	no	—
50	C₁₃×#127	—	4	1	no	—
51	C₁₃×#124	—	4	4	no	—
52	C₄×Q₈×C₁₃	—	4	1	no	—
53	C₄×Q₈×C₁₃	—	4	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#107	—	2	4	no	—
73	C₁₃×C₄⋊C₈	—	4	1	no	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×#102	—	2	4	no	—
76	C₁₃×#102	—	4	2	no	—
77	C₁₃×#102	—	4	2	no	—
78	C₄×C₈×C₁₃	—	4	1	no	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	#32628	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	4	1	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×Q₈×C₁₃	—	4	2	no	—
90	C₂×Q₈×C₁₃	D₈	1	4	yes	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	8	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	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	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	4	no	—
129	C₁₃×C₄⋊C₄	#41	1	4	yes	—
130	C₁₃×C₂²⋊C₄	—	4	4	no	—
131	C₁₃×C₂²⋊C₄	—	4	4	no	—
132	C₁₃×C₂²⋊C₄	—	8	2	no	—
133	C₁₃×C₂²⋊C₄	—	8	2	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	4	2	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	#2548	C₂×C₁₃	1	1	yes	characteristic
143	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2067	C₂×C₁₃	1	2	yes	complemented
145	#2041	C₂×C₁₃	1	2	yes	—
146	#2023	C₂×C₁₃	1	2	yes	complemented
147	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1934	C₂×C₁₃	1	2	yes	complemented
149	#1925	C₂×C₁₃	1	2	yes	complemented
150	#1918	C₂×C₁₃	1	2	yes	complemented
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₃	—	4	4	no	—
160	Q₈×C₁₃	—	8	4	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	8	4	no	—
166	D₄×C₁₃	—	8	4	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	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	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	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	—	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	C₂×D₈	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
195	C₈×C₁₃	—	4	2	no	—
196	C₈×C₁₃	—	4	2	no	—
197	C₂×C₄⋊Q₈	—	2	1	no	—
198	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#124	—	2	1	no	—
201	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#107	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#102	C₂²×C₁₃	1	2	yes	—
205	C₂×#102	C₂²×C₁₃	1	2	yes	—
206	C₂×#102	C₂²×C₁₃	1	2	yes	—
207	C₂×#102	C₂²×C₁₃	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
209	#398	—	2	1	no	—
210	#398	—	2	1	no	—
211	#394	—	2	1	no	—
212	#394	—	2	1	no	—
213	#391	—	2	1	no	—
214	#390	—	2	1	no	—
215	#390	C₂²×C₁₃	1	2	yes	—
216	#390	C₂²×C₁₃	1	2	yes	—
217	#389	C₂²×C₁₃	1	2	yes	—
218	#389	C₂²×C₁₃	1	2	yes	—
219	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	#340	C₂²×C₁₃	1	2	yes	—
222	#340	C₂²×C₁₃	1	2	yes	—
223	#340	C₂²×C₁₃	1	2	yes	—
224	#336	C₂²×C₁₃	1	2	yes	—
225	#336	C₂²×C₁₃	1	2	yes	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	#534	1	1	yes	characteristic
234	C₂²×C₁₃	#548	1	2	yes	—
235	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
236	C₂²×C₁₃	#575	1	1	yes	characteristic
237	C₂²×C₁₃	#577	1	2	yes	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	—	4	4	no	—
242	C₄×C₁₃	—	4	1	no	—
243	C₄×C₁₃	—	4	1	no	—
244	C₄×C₁₃	—	4	1	no	—
245	C₄×C₁₃	—	8	2	no	—
246	C₄×C₁₃	—	8	2	no	—
247	C₄×C₁₃	#542	1	2	yes	—
248	C₄×C₁₃	#555	1	1	yes	characteristic
249	C₄×C₁₃	#563	1	1	yes	characteristic
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
257	C₄⋊Q₈	—	4	1	no	—
258	C₄⋊Q₈	—	4	1	no	—
259	C₄⋊Q₈	—	4	4	no	—
260	#127	—	4	1	no	—
261	#127	—	4	1	no	—
262	#124	—	4	4	no	—
263	C₄×Q₈	—	4	1	no	—
264	C₄×Q₈	—	4	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	#107	—	2	4	no	—
284	C₄⋊C₈	—	4	1	no	—
285	#102	—	2	4	no	—
286	#102	—	2	4	no	—
287	#102	—	4	2	no	—
288	#102	—	4	2	no	—
289	C₄×C₈	—	4	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	C₂×C₁₃	—	16	2	no	—
295	C₂×C₁₃	#2731	1	1	yes	characteristic
296	C₂×C₁₃	#3186	1	1	yes	characteristic
297	C₂×C₁₃	#3200	1	1	yes	characteristic
298	C₂×C₁₃	#3358	1	2	yes	—
299	C₂×C₁₃	#3371	1	2	yes	—
300	C₂⁴	—	2	2	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₁₃×D₈	1	4	yes	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	8	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	C₂×C₈	—	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	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	C₁₃×#41	1	4	yes	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₂²⋊C₄	—	8	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	4	2	no	—
357	C₄²	—	4	2	no	—
358	C₁₃	#32628	1	1	yes	characteristic, direct product factor, Sylow
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
367	Q₈	—	4	4	no	—
368	Q₈	—	8	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	4	no	—
374	D₄	—	8	4	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	2	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	C₂×C₁₃×D₈	1	2	yes	—
397	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
398	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
399	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
400	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	C₁₃×#534	1	1	yes	characteristic
413	C₂²	C₁₃×#548	1	2	yes	—
414	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
415	C₂²	C₁₃×#575	1	1	yes	characteristic
416	C₂²	C₁₃×#577	1	2	yes	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	2	no	—
426	C₄	C₁₃×#542	1	2	yes	—
427	C₄	C₁₃×#555	1	1	yes	characteristic
428	C₄	C₁₃×#563	1	1	yes	characteristic
429	C₂	—	16	2	no	—
430	C₂	C₁₃×#2731	1	1	yes	characteristic
431	C₂	C₁₃×#3186	1	1	yes	characteristic
432	C₂	C₁₃×#3200	1	1	yes	characteristic
433	C₂	C₁₃×#3358	1	2	yes	—
434	C₂	C₁₃×#3371	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2546	C₂	semidirect
3. C₁₃×#2067	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
6. C₁₃×#1984	C₂	semidirect
7. C₁₃×#1934	C₂	semidirect
8. C₁₃×#1925	C₂	semidirect
9. C₁₃×#1918	C₂	semidirect
83. #32628	C₁₃	direct (N × H)
143. #2546	C₂×C₁₃	semidirect
144. #2067	C₂×C₁₃	semidirect
146. #2023	C₂×C₁₃	semidirect
147. #1984	C₂×C₁₃	semidirect
148. #1934	C₂×C₁₃	semidirect
149. #1925	C₂×C₁₃	semidirect
150. #1918	C₂×C₁₃	semidirect
358. C₁₃	#32628	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×#2548	2
C₁₃×#2546	2
C₁₃×#2067	2
C₁₃×#2041	2
C₁₃×#2023	2
C₁₃×#1984	2
C₁₃×#1934	2
C₁₃×#1925	2
C₁₃×#1918	2
#32628	13

Subgroups — C13×#32628 #15718967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32628 #15718967