Subgroups — C₁₃×#32669 #15719008

Order 3328.

816 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2014	C₂	1	2	yes	maximal
5	C₁₃×#2013	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
11	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#400	—	2	1	no	—
24	C₁₃×#400	—	2	1	no	—
25	C₁₃×#394	—	2	1	no	—
26	C₁₃×#394	—	2	1	no	—
27	C₁₃×#391	—	2	1	no	—
28	C₁₃×#391	C₂²	1	2	yes	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#390	—	2	1	no	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#382	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂×C₁₃×SD₁₆	—	2	4	no	—
45	C₂×C₁₃×SD₁₆	—	4	2	no	—
46	C₂×C₁₃×SD₁₆	—	4	2	no	—
47	C₂×C₁₃×SD₁₆	—	4	2	no	—
48	C₂×C₁₃×SD₁₆	—	4	2	no	—
49	C₂×C₁₃×SD₁₆	—	4	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	4	1	no	—
53	C₁₃×C₄⋊Q₈	—	4	1	no	—
54	C₁₃×#127	—	4	1	no	—
55	C₁₃×#127	—	4	1	no	—
56	C₁₃×#124	—	4	4	no	—
57	C₄×Q₈×C₁₃	—	4	1	no	—
58	C₄×Q₈×C₁₃	—	4	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#106	—	4	2	no	—
76	C₁₃×C₄⋊C₈	—	4	1	no	—
77	C₁₃×#103	—	2	4	no	—
78	C₁₃×#103	—	4	2	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	4	2	no	—
81	C₄×C₈×C₁₃	—	4	1	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	#32669	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	4	1	no	—
97	C₂×Q₈×C₁₃	—	4	1	no	—
98	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×SD₁₆	—	4	8	no	—
121	C₁₃×SD₁₆	—	4	8	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	#41	1	4	yes	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	—	8	2	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2548	C₂×C₁₃	1	1	yes	characteristic
151	#2055	C₂×C₁₃	1	2	yes	complemented
152	#2014	C₂×C₁₃	1	2	yes	—
153	#2013	C₂×C₁₃	1	2	yes	complemented
154	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1968	C₂×C₁₃	1	2	yes	complemented
156	#1927	C₂×C₁₃	1	2	yes	complemented
157	#1926	C₂×C₁₃	1	2	yes	complemented
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	4	4	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	4	2	no	—
170	Q₈×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	8	4	no	—
176	D₄×C₁₃	—	8	4	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	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	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
204	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₈×C₁₃	—	2	4	no	—
206	C₈×C₁₃	—	4	2	no	—
207	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
208	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#106	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#103	C₂²×C₁₃	1	2	yes	—
216	C₂×#103	C₂²×C₁₃	1	2	yes	—
217	C₂×#102	C₂²×C₁₃	1	2	yes	—
218	C₂×#102	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#400	—	2	1	no	—
221	#400	—	2	1	no	—
222	#394	—	2	1	no	—
223	#394	—	2	1	no	—
224	#391	—	2	1	no	—
225	#391	C₂²×C₁₃	1	2	yes	—
226	#391	C₂²×C₁₃	1	2	yes	—
227	#390	—	2	1	no	—
228	#390	C₂²×C₁₃	1	2	yes	—
229	#390	C₂²×C₁₃	1	2	yes	—
230	#382	—	2	1	no	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#336	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	#534	1	1	yes	characteristic
244	C₂²×C₁₃	#550	1	2	yes	—
245	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
246	C₂²×C₁₃	#575	1	1	yes	characteristic
247	C₂²×C₁₃	#577	1	2	yes	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	—	4	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	#538	1	2	yes	—
258	C₄×C₁₃	#555	1	1	yes	characteristic
259	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
260	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×SD₁₆	—	4	2	no	—
267	C₂×SD₁₆	—	4	2	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂×SD₁₆	—	4	2	no	—
270	C₂×SD₁₆	—	4	2	no	—
271	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₄⋊Q₈	—	4	1	no	—
274	C₄⋊Q₈	—	4	1	no	—
275	#127	—	4	1	no	—
276	#127	—	4	1	no	—
277	#124	—	4	4	no	—
278	C₄×Q₈	—	4	1	no	—
279	C₄×Q₈	—	4	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	#106	—	4	2	no	—
297	C₄⋊C₈	—	4	1	no	—
298	#103	—	2	4	no	—
299	#103	—	4	2	no	—
300	#102	—	2	4	no	—
301	#102	—	4	2	no	—
302	C₄×C₈	—	4	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	C₂×C₁₃	—	16	2	no	—
310	C₂×C₁₃	#2733	1	1	yes	characteristic
311	C₂×C₁₃	#3187	1	1	yes	characteristic
312	C₂×C₁₃	#3200	1	1	yes	characteristic
313	C₂×C₁₃	#3392	1	2	yes	—
314	C₂×C₁₃	#3401	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	complemented
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
346	SD₁₆	—	4	8	no	—
347	SD₁₆	—	4	8	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	C₁₃×#41	1	4	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	4	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	4	2	no	—
374	C₄²	—	4	2	no	—
375	C₁₃	#32669	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	4	no	—
394	D₄	—	8	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
417	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
418	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
419	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
420	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₁₃×#534	1	1	yes	characteristic
433	C₂²	C₁₃×#550	1	2	yes	—
434	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
435	C₂²	C₁₃×#575	1	1	yes	characteristic
436	C₂²	C₁₃×#577	1	2	yes	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	2	no	—
446	C₄	C₁₃×#538	1	2	yes	—
447	C₄	C₁₃×#555	1	1	yes	characteristic
448	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
449	C₂	—	16	2	no	—
450	C₂	C₁₃×#2733	1	1	yes	characteristic
451	C₂	C₁₃×#3187	1	1	yes	characteristic
452	C₂	C₁₃×#3200	1	1	yes	characteristic
453	C₂	C₁₃×#3392	1	2	yes	—
454	C₂	C₁₃×#3401	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
1. C₁₃×#2568	C₂	semidirect
3. C₁₃×#2055	C₂	semidirect
5. C₁₃×#2013	C₂	semidirect
6. C₁₃×#1984	C₂	semidirect
7. C₁₃×#1968	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
9. C₁₃×#1926	C₂	semidirect
88. #32669	C₁₃	direct (N × H)
98. C₂×Q₈×C₁₃	SD₁₆	semidirect
149. #2568	C₂×C₁₃	semidirect
151. #2055	C₂×C₁₃	semidirect
153. #2013	C₂×C₁₃	semidirect
154. #1984	C₂×C₁₃	semidirect
155. #1968	C₂×C₁₃	semidirect
156. #1927	C₂×C₁₃	semidirect
157. #1926	C₂×C₁₃	semidirect
324. C₂×Q₈	C₁₃×SD₁₆	semidirect
375. C₁₃	#32669	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×#2568	2
C₁₃×#2548	2
C₁₃×#2055	2
C₁₃×#2014	2
C₁₃×#2013	2
C₁₃×#1984	2
C₁₃×#1968	2
C₁₃×#1927	2
C₁₃×#1926	2
#32669	13

Subgroups — C13×#32669 #15719008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32669 #15719008