Subgroups — C₁₃×#32812 #15719151

Order 3328.

788 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2641	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2054	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2011	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	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	C₁₃×#397	—	2	2	no	—
24	C₁₃×#394	—	2	2	no	—
25	C₁₃×#394	—	2	2	no	—
26	C₁₃×#393	—	2	2	no	—
27	C₁₃×#391	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#376	C₂²	1	1	yes	characteristic
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	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂×C₁₃×SD₁₆	—	4	2	no	—
45	C₂×C₁₃×SD₁₆	—	4	2	no	—
46	C₂×C₁₃×SD₁₆	—	4	2	no	—
47	C₂×C₁₃×D₈	—	4	2	no	—
48	C₂×C₁₃×D₈	—	4	2	no	—
49	C₂×C₁₃×D₈	—	4	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	4	2	no	—
53	C₁₃×#127	—	4	2	no	—
54	C₁₃×#125	—	4	2	no	—
55	C₁₃×#124	—	4	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	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×C₄⋊C₈	—	4	2	no	—
73	C₁₃×#103	—	4	2	no	—
74	C₁₃×#102	—	4	2	no	—
75	C₁₃×#102	—	4	2	no	—
76	C₁₃×#102	—	4	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	D₄	1	2	yes	—
80	C₁₃×#95	D₄	1	2	yes	—
81	#32812	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	—	2	1	no	—
83	C₂⁴×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×Q₈×C₁₃	—	8	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
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	1	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	4	4	no	—
101	C₂×D₄×C₁₃	—	8	2	no	—
102	C₂×D₄×C₁₃	—	8	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	C₁₃×SD₁₆	—	4	8	no	—
113	C₁₃×D₈	—	4	8	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	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	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	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	4	4	no	—
125	C₁₃×C₄⋊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	C₁₃×C₂²⋊C₄	—	8	2	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	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	#2641	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2640	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#2055	C₂×C₁₃	1	2	yes	complemented
141	#2054	C₂×C₁₃	1	2	yes	complemented
142	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2023	C₂×C₁₃	1	2	yes	complemented
145	#2014	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2012	C₂×C₁₃	1	2	yes	complemented
147	#2011	C₂×C₁₃	1	1	yes	characteristic
148	#1832	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	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	—	4	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	2	no	—
164	Q₈×C₁₃	—	8	4	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	8	8	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
194	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₁₃	—	4	2	no	—
197	C₈×C₁₃	—	4	2	no	—
198	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
199	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
205	C₂×#103	C₂²×C₁₃	1	2	yes	—
206	C₂×#102	C₂²×C₁₃	1	2	yes	—
207	C₂×#102	C₂²×C₁₃	1	2	yes	—
208	C₂×#102	C₂²×C₁₃	1	2	yes	—
209	#397	—	2	2	no	—
210	#394	—	2	2	no	—
211	#394	—	2	2	no	—
212	#393	—	2	2	no	—
213	#391	C₂²×C₁₃	1	1	yes	characteristic
214	#391	C₂²×C₁₃	1	1	yes	characteristic
215	#390	C₂²×C₁₃	1	1	yes	characteristic
216	#390	C₂²×C₁₃	1	2	yes	—
217	#390	C₂²×C₁₃	1	1	yes	characteristic
218	#390	C₂²×C₁₃	1	2	yes	—
219	#376	C₂²×C₁₃	1	1	yes	characteristic
220	#340	C₂²×C₁₃	1	2	yes	—
221	#340	C₂²×C₁₃	1	2	yes	—
222	#336	C₂²×C₁₃	1	1	yes	characteristic
223	#336	C₂²×C₁₃	1	2	yes	—
224	#336	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₁₃	—	8	1	no	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	—	8	1	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	—	8	2	no	—
234	C₂²×C₁₃	—	8	2	no	—
235	C₂²×C₁₃	—	8	2	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	#535	1	1	yes	characteristic
238	C₂²×C₁₃	#535	1	1	yes	characteristic
239	C₂²×C₁₃	#537	1	1	yes	characteristic
240	C₂²×C₁₃	#576	1	2	yes	—
241	C₂²×C₁₃	#577	1	2	yes	—
242	C₄×C₁₃	—	4	1	no	—
243	C₄×C₁₃	—	4	1	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	8	1	no	—
247	C₄×C₁₃	—	8	1	no	—
248	C₄×C₁₃	—	8	1	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	H(3,𝔽₄)	1	2	yes	—
251	C₄×C₁₃	#562	1	2	yes	—
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
257	C₂×SD₁₆	—	4	2	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×SD₁₆	—	4	2	no	—
260	C₂×D₈	—	4	2	no	—
261	C₂×D₈	—	4	2	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₄⋊Q₈	—	4	2	no	—
266	#127	—	4	2	no	—
267	#125	—	4	2	no	—
268	#124	—	4	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
285	C₄⋊C₈	—	4	2	no	—
286	#103	—	4	2	no	—
287	#102	—	4	2	no	—
288	#102	—	4	2	no	—
289	#102	—	4	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₁₃	1	2	yes	—
293	#95	D₄×C₁₃	1	2	yes	—
294	C₂×C₁₃	—	16	2	no	—
295	C₂×C₁₃	—	16	1	no	—
296	C₂×C₁₃	#2819	1	1	yes	characteristic
297	C₂×C₁₃	#3220	1	1	yes	characteristic
298	C₂×C₁₃	#3221	1	1	yes	characteristic
299	C₂×C₁₃	#3224	1	2	yes	—
300	C₂×C₁₃	#3257	1	2	yes	—
301	C₂⁴	—	2	1	no	—
302	C₂⁴	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	—	8	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	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
331	SD₁₆	—	4	8	no	—
332	D₈	—	4	8	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₂²⋊C₄	—	8	2	no	—
350	C₂²⋊C₄	—	8	2	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	8	2	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	1	no	—
357	C₁₃	#32812	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	4	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	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	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	8	4	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	8	8	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
404	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	C₁₃×#535	1	1	yes	characteristic
420	C₂²	C₁₃×#535	1	1	yes	characteristic
421	C₂²	C₁₃×#537	1	1	yes	characteristic
422	C₂²	C₁₃×#576	1	2	yes	—
423	C₂²	C₁₃×#577	1	2	yes	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	C₁₃×H(3,𝔽₄)	1	2	yes	—
433	C₄	C₁₃×#562	1	2	yes	—
434	C₂	—	16	2	no	—
435	C₂	—	16	1	no	—
436	C₂	C₁₃×#2819	1	1	yes	characteristic
437	C₂	C₁₃×#3220	1	1	yes	characteristic
438	C₂	C₁₃×#3221	1	1	yes	characteristic
439	C₂	C₁₃×#3224	1	2	yes	—
440	C₂	C₁₃×#3257	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2011	C₂
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×#2641	C₂	semidirect
2. C₁₃×#2640	C₂	semidirect
3. C₁₃×#2055	C₂	semidirect
4. C₁₃×#2054	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
7. C₁₃×#2023	C₂	semidirect
8. C₁₃×#2014	C₂	semidirect
9. C₁₃×#2012	C₂	semidirect
11. C₁₃×#1832	C₂	semidirect
81. #32812	C₁₃	direct (N × H)
138. #2641	C₂×C₁₃	semidirect
139. #2640	C₂×C₁₃	semidirect
140. #2055	C₂×C₁₃	semidirect
141. #2054	C₂×C₁₃	semidirect
142. #2026	C₂×C₁₃	semidirect
143. #2025	C₂×C₁₃	semidirect
144. #2023	C₂×C₁₃	semidirect
145. #2014	C₂×C₁₃	semidirect
146. #2012	C₂×C₁₃	semidirect
148. #1832	C₂×C₁₃	semidirect
357. C₁₃	#32812	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×#2641	2
C₁₃×#2640	2
C₁₃×#2055	2
C₁₃×#2054	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#2023	2
C₁₃×#2014	2
C₁₃×#2012	2
C₁₃×#2011	2
C₁₃×#1832	2
#32812	13

Subgroups — C13×#32812 #15719151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32812 #15719151