Subgroups — C₁₃×#33645 #15719984

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2237	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2234	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2233	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2232	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2158	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2138	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#525	—	2	1	no	—
15	C₂×C₁₃×#117	—	2	1	no	—
16	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
17	C₁₃×#467	C₂²	1	1	yes	characteristic
18	C₁₃×#467	C₂²	1	1	yes	characteristic
19	C₁₃×#466	C₂²	1	1	yes	characteristic
20	C₁₃×#466	C₂²	1	1	yes	characteristic
21	C₁₃×#465	—	2	1	no	—
22	C₁₃×#465	—	2	1	no	—
23	C₁₃×#427	—	2	1	no	—
24	C₁₃×#427	—	2	1	no	—
25	C₁₃×#427	C₂²	1	1	yes	characteristic
26	C₁₃×#427	C₂²	1	2	yes	—
27	C₁₃×#427	C₂²	1	2	yes	—
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	—	2	1	no	—
31	C₁₃×#416	—	2	1	no	—
32	C₁₃×#367	C₂²	1	2	yes	complemented
33	C₁₃×#367	C₂²	1	2	yes	complemented
34	C₁₃×#366	C₂²	1	2	yes	complemented
35	C₁₃×#366	C₂²	1	2	yes	complemented
36	C₁₃×#358	C₂²	1	2	yes	complemented
37	C₁₃×#358	C₂²	1	2	yes	complemented
38	C₁₃×#357	C₂²	1	2	yes	complemented
39	C₁₃×#357	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₁₃×#135	—	2	4	no	—
46	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×SD₁₆	—	2	1	no	—
48	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#123	—	4	1	no	—
57	C₁₃×C₂²⋊Q₈	—	2	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×#121	—	2	1	no	—
60	C₁₃×#121	—	2	1	no	—
61	C₁₃×#120	—	4	1	no	—
62	C₄×D₄×C₁₃	—	4	1	no	—
63	C₄×D₄×C₁₃	—	4	1	no	—
64	C₁₃×#117	—	2	1	no	—
65	C₁₃×#117	—	2	2	no	—
66	C₁₃×#117	—	2	2	no	—
67	C₁₃×#117	—	4	1	no	—
68	C₁₃×#117	—	4	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
72	C₂×C₄²×C₁₃	—	4	1	no	—
73	C₂×C₁₃×C₁₆	—	2	4	no	—
74	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
75	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
76	C₁₃×#107	—	2	1	no	—
77	C₁₃×#107	—	2	1	no	—
78	C₁₃×#107	C₂³	1	2	yes	—
79	C₁₃×#107	C₂³	1	2	yes	—
80	C₁₃×#107	C₂³	1	1	yes	characteristic
81	C₁₃×#107	C₂³	1	1	yes	characteristic
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×#106	—	2	2	no	—
84	C₁₃×#106	—	2	1	no	—
85	C₁₃×#103	—	2	1	no	—
86	C₁₃×#103	—	2	1	no	—
87	C₁₃×#102	—	2	1	no	—
88	C₁₃×#102	—	2	1	no	—
89	#33645	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
91	C₁₃×#41	—	4	2	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	D₈	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	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	4	2	no	—
111	C₁₃×D₈	—	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	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	#41	1	4	yes	—
121	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₄⋊C₄	—	4	1	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	1	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₄²×C₁₃	—	4	2	no	—
138	C₄²×C₁₃	—	4	2	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	C₁₃×C₁₆	—	2	2	no	—
141	C₁₃×C₁₆	—	2	2	no	—
142	#3050	C₂×C₁₃	1	1	yes	characteristic
143	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2237	C₂×C₁₃	1	2	yes	complemented
145	#2236	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2235	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2234	C₂×C₁₃	1	2	yes	complemented
148	#2233	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2232	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2158	C₂×C₁₃	1	2	yes	complemented
151	#2138	C₂×C₁₃	1	2	yes	complemented
152	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
158	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
159	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
160	Q₈×C₁₃	—	4	1	no	—
161	Q₈×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	8	2	no	—
165	D₄×C₁₃	—	8	2	no	—
166	D₄×C₁₃	—	8	2	no	—
167	C₂×C₄×C₁₃	—	2	2	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	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	—	8	2	no	—
182	C₂×C₄×C₁₃	#123	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#137	1	2	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	—	2	1	no	—
190	C₈×C₁₃	#123	1	2	yes	—
191	C₈×C₁₃	C₂×#41	1	2	yes	—
192	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	#525	—	2	1	no	—
195	C₂×#117	—	2	1	no	—
196	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
197	#467	C₂²×C₁₃	1	1	yes	characteristic
198	#467	C₂²×C₁₃	1	1	yes	characteristic
199	#466	C₂²×C₁₃	1	1	yes	characteristic
200	#466	C₂²×C₁₃	1	1	yes	characteristic
201	#465	—	2	1	no	—
202	#465	—	2	1	no	—
203	#427	—	2	1	no	—
204	#427	—	2	1	no	—
205	#427	C₂²×C₁₃	1	2	yes	—
206	#427	C₂²×C₁₃	1	2	yes	—
207	#427	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#106	—	2	1	no	—
211	#416	—	2	1	no	—
212	#367	C₂²×C₁₃	1	2	yes	complemented
213	#367	C₂²×C₁₃	1	2	yes	complemented
214	#366	C₂²×C₁₃	1	2	yes	complemented
215	#366	C₂²×C₁₃	1	2	yes	complemented
216	#358	C₂²×C₁₃	1	2	yes	complemented
217	#358	C₂²×C₁₃	1	2	yes	complemented
218	#357	C₂²×C₁₃	1	2	yes	complemented
219	#357	C₂²×C₁₃	1	2	yes	complemented
220	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	8	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	#480	1	2	yes	—
235	C₂²×C₁₃	#508	1	2	yes	—
236	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	8	1	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	—	8	1	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	#480	1	2	yes	—
245	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
246	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
247	C₂×#41	—	2	1	no	—
248	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
249	#135	—	2	4	no	—
250	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×SD₁₆	—	2	1	no	—
252	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
255	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	#123	—	4	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	#121	—	2	1	no	—
264	#121	—	2	1	no	—
265	#120	—	4	1	no	—
266	C₄×D₄	—	4	1	no	—
267	C₄×D₄	—	4	1	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	—	2	1	no	—
271	#117	—	4	1	no	—
272	#117	—	4	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	4	1	no	—
276	C₂×C₄²	—	4	1	no	—
277	C₂×C₁₆	—	2	4	no	—
278	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
279	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
280	#107	—	2	1	no	—
281	#107	—	2	1	no	—
282	#107	C₂³×C₁₃	1	2	yes	—
283	#107	C₂³×C₁₃	1	2	yes	—
284	#107	C₂³×C₁₃	1	1	yes	characteristic
285	#107	C₂³×C₁₃	1	1	yes	characteristic
286	#106	—	2	2	no	—
287	#106	—	2	2	no	—
288	#106	—	2	1	no	—
289	#103	—	2	1	no	—
290	#103	—	2	1	no	—
291	#102	—	2	1	no	—
292	#102	—	2	1	no	—
293	C₂×C₁₃	—	2	2	no	—
294	C₂×C₁₃	—	2	2	no	—
295	C₂×C₁₃	—	4	1	no	—
296	C₂×C₁₃	—	16	1	no	—
297	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
298	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
299	C₂×C₁₃	#3414	1	1	yes	characteristic
300	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
314	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
315	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	Q₁₆	—	2	2	no	—
320	SD₁₆	—	4	2	no	—
321	D₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₈	C₁₃×#41	1	4	yes	—
331	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	4	2	no	—
348	C₄²	—	4	2	no	—
349	C₄²	—	4	1	no	—
350	C₁₆	—	2	2	no	—
351	C₁₆	—	2	2	no	—
352	C₁₃	#33645	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
358	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
359	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	C₁₃×#123	1	2	yes	—
383	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
386	C₂×C₄	C₁₃×#137	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₁₃×#123	1	2	yes	—
391	C₈	C₂×C₁₃×#41	1	2	yes	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	C₁₃×#480	1	2	yes	—
404	C₂²	C₁₃×#508	1	2	yes	—
405	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	1	no	—
413	C₄	C₁₃×#480	1	2	yes	—
414	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
415	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	2	2	no	—
418	C₂	—	4	1	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
421	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
422	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₁₃×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#427	C₂	semidirect
3. C₁₃×#2237	C₂	semidirect
4. C₁₃×#2236	C₂	semidirect
5. C₁₃×#2235	C₂	semidirect
6. C₁₃×#2234	C₂	semidirect
7. C₁₃×#2233	C₂	semidirect
8. C₁₃×#2232	C₂	semidirect
9. C₁₃×#2158	C₂	semidirect
10. C₁₃×#2138	C₂	semidirect
11. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
32. C₁₃×#367	C₂²	semidirect
33. C₁₃×#367	C₂²	semidirect
34. C₁₃×#366	C₂²	semidirect
35. C₁₃×#366	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
37. C₁₃×#358	C₂²	semidirect
38. C₁₃×#357	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
89. #33645	C₁₃	direct (N × H)
143. C₂×#427	C₂×C₁₃	semidirect
144. #2237	C₂×C₁₃	semidirect
145. #2236	C₂×C₁₃	semidirect
146. #2235	C₂×C₁₃	semidirect
147. #2234	C₂×C₁₃	semidirect
148. #2233	C₂×C₁₃	semidirect
149. #2232	C₂×C₁₃	semidirect
150. #2158	C₂×C₁₃	semidirect
151. #2138	C₂×C₁₃	semidirect
152. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
212. #367	C₂²×C₁₃	semidirect
213. #367	C₂²×C₁₃	semidirect
214. #366	C₂²×C₁₃	semidirect
215. #366	C₂²×C₁₃	semidirect
216. #358	C₂²×C₁₃	semidirect
217. #358	C₂²×C₁₃	semidirect
218. #357	C₂²×C₁₃	semidirect
219. #357	C₂²×C₁₃	semidirect
352. C₁₃	#33645	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×#3050	2
C₂×C₁₃×#427	2
C₁₃×#2237	2
C₁₃×#2236	2
C₁₃×#2235	2
C₁₃×#2234	2
C₁₃×#2233	2
C₁₃×#2232	2
C₁₃×#2158	2
C₁₃×#2138	2
C₂×C₁₃×C₂²⋊C₁₆	2
#33645	13

Subgroups — C13×#33645 #15719984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33645 #15719984