Subgroups — C₁₃×#29204 #15715543

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	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×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#400	—	2	2	no	—
25	C₁₃×#398	—	2	2	no	—
26	C₁₃×#390	C₂²	1	1	yes	characteristic
27	C₁₃×#390	C₂²	1	1	yes	characteristic
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#386	—	2	2	no	—
31	C₁₃×#386	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#382	C₂²	1	1	yes	characteristic
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₁₃×#376	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×#127	—	2	2	no	—
47	C₁₃×#127	Q₈	1	4	yes	—
48	C₄×D₄×C₁₃	—	4	2	no	—
49	C₄×D₄×C₁₃	—	4	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#107	—	4	2	no	—
65	C₁₃×#106	—	4	2	no	—
66	C₁₃×C₄⋊C₈	—	2	4	no	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×#102	—	2	4	no	—
69	C₁₃×#102	—	4	2	no	—
70	C₁₃×#102	—	4	2	no	—
71	C₁₃×#97	—	2	2	no	—
72	C₄×C₈×C₁₃	—	2	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	D₄	1	2	yes	—
78	C₁₃×#95	D₄	1	2	yes	—
79	#29204	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	—	2	1	no	—
81	C₂⁴×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	—	2	8	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	8	2	no	—
90	C₂×D₄×C₁₃	—	8	2	no	—
91	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
92	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	8	2	no	—
100	C₂²×C₄×C₁₃	—	8	2	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	#41	1	4	yes	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	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	—	8	2	no	—
119	C₁₃×C₄⋊C₄	—	8	2	no	—
120	C₁₃×C₄⋊C₄	—	8	2	no	—
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	—	8	2	no	—
124	C₁₃×C₂²⋊C₄	—	8	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
128	C₄²×C₁₃	#41	1	2	yes	—
129	#2647	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2328	C₂×C₁₃	1	1	yes	characteristic
131	#2067	C₂×C₁₃	1	2	yes	complemented
132	#2065	C₂×C₁₃	1	2	yes	complemented
133	#1961	C₂×C₁₃	1	1	yes	characteristic
134	#1957	C₂×C₁₃	1	1	yes	characteristic
135	#1864	C₂×C₁₃	1	2	yes	complemented
136	#1862	C₂×C₁₃	1	2	yes	complemented
137	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1835	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	1	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	—	4	1	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	D₄×C₁₃	—	2	4	no	—
152	D₄×C₁₃	—	2	4	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	8	8	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	4	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	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	—	8	4	no	—
177	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
178	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
182	C₈×C₁₃	—	2	4	no	—
183	C₈×C₁₃	—	4	2	no	—
184	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#107	C₂²×C₁₃	1	2	yes	—
188	C₂×#106	C₂²×C₁₃	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
190	C₂×#102	C₂²×C₁₃	1	2	yes	—
191	C₂×#102	C₂²×C₁₃	1	2	yes	—
192	C₂×#102	C₂²×C₁₃	1	2	yes	—
193	C₂×#102	C₂²×C₁₃	1	2	yes	—
194	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
196	#400	—	2	2	no	—
197	#398	—	2	2	no	—
198	#390	C₂²×C₁₃	1	1	yes	characteristic
199	#390	C₂²×C₁₃	1	1	yes	characteristic
200	#389	C₂²×C₁₃	1	2	yes	—
201	#389	C₂²×C₁₃	1	2	yes	—
202	#386	—	2	2	no	—
203	#386	—	2	2	no	—
204	#384	C₂²×C₁₃	1	1	yes	characteristic
205	#382	C₂²×C₁₃	1	1	yes	characteristic
206	#382	C₂²×C₁₃	1	1	yes	characteristic
207	#376	C₂²×C₁₃	1	1	yes	characteristic
208	#340	C₂²×C₁₃	1	2	yes	—
209	#340	C₂²×C₁₃	1	2	yes	—
210	#336	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	4	no	—
214	C₂²×C₁₃	—	4	4	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	—	8	1	no	—
219	C₂²×C₁₃	—	8	1	no	—
220	C₂²×C₁₃	—	8	1	no	—
221	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
222	C₂²×C₁₃	#532	1	1	yes	characteristic
223	C₂²×C₁₃	#535	1	1	yes	characteristic
224	C₂²×C₁₃	#576	1	2	yes	—
225	C₂²×C₁₃	#577	1	2	yes	—
226	C₄×C₁₃	—	2	4	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	#553	1	2	yes	—
235	C₄×C₁₃	#554	1	2	yes	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	2	1	no	—
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	#127	—	2	2	no	—
244	#127	Q₈×C₁₃	1	4	yes	—
245	C₄×D₄	—	4	2	no	—
246	C₄×D₄	—	4	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	#107	—	4	2	no	—
262	#106	—	4	2	no	—
263	C₄⋊C₈	—	2	4	no	—
264	#102	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	4	2	no	—
267	#102	—	4	2	no	—
268	#97	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	D₄×C₁₃	1	2	yes	—
275	#95	D₄×C₁₃	1	2	yes	—
276	C₂×C₁₃	—	8	2	no	—
277	C₂×C₁₃	—	8	2	no	—
278	C₂×C₁₃	#2566	1	1	yes	characteristic
279	C₂×C₁₃	#3081	1	2	yes	—
280	C₂×C₁₃	#3179	1	2	yes	—
281	C₂×C₁₃	#3220	1	1	yes	characteristic
282	C₂×C₁₃	#3222	1	1	yes	characteristic
283	C₂⁴	—	2	1	no	—
284	C₂⁴	—	2	1	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	8	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
295	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	C₁₃×#41	1	4	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	8	2	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	—	8	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
331	C₄²	C₁₃×#41	1	2	yes	—
332	C₁₃	#29204	1	1	yes	characteristic, direct product factor, Sylow
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	D₄	—	2	4	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	8	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
371	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
374	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
375	C₈	—	2	4	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
388	C₂²	C₁₃×#532	1	1	yes	characteristic
389	C₂²	C₁₃×#535	1	1	yes	characteristic
390	C₂²	C₁₃×#576	1	2	yes	—
391	C₂²	C₁₃×#577	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	C₁₃×#553	1	2	yes	—
401	C₄	C₁₃×#554	1	2	yes	—
402	C₂	—	8	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₁₃×#2566	1	1	yes	characteristic
405	C₂	C₁₃×#3081	1	2	yes	—
406	C₂	C₁₃×#3179	1	2	yes	—
407	C₂	C₁₃×#3220	1	1	yes	characteristic
408	C₂	C₁₃×#3222	1	1	yes	characteristic

	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 ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2647	C₂	semidirect
3. C₁₃×#2067	C₂	semidirect
4. C₁₃×#2065	C₂	semidirect
7. C₁₃×#1864	C₂	semidirect
8. C₁₃×#1862	C₂	semidirect
9. C₁₃×#1847	C₂	semidirect
10. C₁₃×#1835	C₂	semidirect
11. C₁₃×#1768	C₂	semidirect
79. #29204	C₁₃	direct (N × H)
129. #2647	C₂×C₁₃	semidirect
131. #2067	C₂×C₁₃	semidirect
132. #2065	C₂×C₁₃	semidirect
135. #1864	C₂×C₁₃	semidirect
136. #1862	C₂×C₁₃	semidirect
137. #1847	C₂×C₁₃	semidirect
138. #1835	C₂×C₁₃	semidirect
139. #1768	C₂×C₁₃	semidirect
332. C₁₃	#29204	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×#2647	2
C₁₃×#2328	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1961	2
C₁₃×#1957	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1847	2
C₁₃×#1835	2
C₁₃×#1768	2
#29204	13

Subgroups — C13×#29204 #15715543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29204 #15715543