Subgroups — C₁₃×#33666 #15720005

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2234	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2227	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×D₁₆	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₁₃×#532	—	2	1	no	—
14	C₄×C₁₃×#41	—	2	1	no	—
15	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
17	C₁₃×#500	C₂²	1	1	yes	characteristic
18	C₁₃×#493	C₂²	1	1	yes	characteristic
19	C₁₃×#486	—	2	1	no	—
20	C₁₃×#466	—	2	1	no	—
21	C₁₃×#466	C₂²	1	2	yes	—
22	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×SD₁₆	—	2	1	no	—
25	C₄×C₁₃×SD₁₆	—	2	1	no	—
26	C₄×C₁₃×D₈	—	2	1	no	—
27	C₄×C₁₃×D₈	C₂²	1	2	yes	—
28	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₁₃×#416	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#367	C₂²	1	2	yes	—
34	C₁₃×#366	C₂²	1	2	yes	—
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#357	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	4	1	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×D₈	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂³	1	2	yes	—
51	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×#127	—	2	1	no	—
56	C₁₃×#124	—	4	1	no	—
57	C₁₃×#121	—	2	2	no	—
58	C₁₃×#121	—	4	1	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×Q₈×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	4	1	no	—
65	C₄×D₄×C₁₃	—	4	1	no	—
66	C₄×D₄×C₁₃	—	4	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	—	4	1	no	—
69	C₂×C₄²×C₁₃	—	4	1	no	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₁₃×SD₃₂	—	2	4	no	—
72	C₁₃×D₁₆	—	2	4	no	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
75	C₁₃×#107	—	2	1	no	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	1	yes	characteristic
78	C₁₃×#107	C₂³	1	2	yes	—
79	C₁₃×#106	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#103	—	2	1	no	—
82	C₁₃×#102	—	2	1	no	—
83	C₁₃×#102	—	2	1	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	#33666	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₁₃×#41	—	8	4	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	1	no	—
110	C₁₃×Q₁₆	#41	1	2	yes	complemented
111	C₁₃×SD₁₆	—	2	4	no	—
112	C₁₃×D₈	—	2	1	no	—
113	C₁₃×D₈	—	2	2	no	—
114	C₁₃×D₈	—	2	2	no	—
115	C₁₃×D₈	—	4	2	no	—
116	C₁₃×D₈	#41	1	2	yes	complemented
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	4	1	no	—
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	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	1	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₄²×C₁₃	—	4	1	no	—
136	C₄²×C₁₃	—	4	1	no	—
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	D₈	1	1	yes	characteristic
139	C₄²×C₁₃	D₈	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×C₁₆	—	2	2	no	—
143	C₁₃×C₁₆	—	2	2	no	—
144	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2234	C₂×C₁₃	1	2	yes	complemented
147	#2227	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2226	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2186	C₂×C₁₃	1	2	yes	complemented
152	C₄×SD₃₂	C₂×C₁₃	1	2	yes	complemented
153	C₄×D₁₆	C₂×C₁₃	1	2	yes	complemented
154	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	8	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	1	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	8	2	no	—
167	D₄×C₁₃	—	8	4	no	—
168	D₄×C₁₃	—	8	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	8	2	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	8	4	no	—
181	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₁₃	—	2	1	no	—
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	—	2	1	no	—
190	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
193	#532	—	2	1	no	—
194	C₄×#41	—	2	1	no	—
195	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
196	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
197	#500	C₂²×C₁₃	1	1	yes	characteristic
198	#493	C₂²×C₁₃	1	1	yes	characteristic
199	#486	—	2	1	no	—
200	#466	—	2	1	no	—
201	#466	C₂²×C₁₃	1	2	yes	—
202	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×SD₁₆	—	2	1	no	—
205	C₄×SD₁₆	—	2	1	no	—
206	C₄×D₈	—	2	1	no	—
207	C₄×D₈	C₂²×C₁₃	1	2	yes	—
208	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
210	#427	C₂²×C₁₃	1	1	yes	characteristic
211	#416	—	2	1	no	—
212	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
213	#367	C₂²×C₁₃	1	2	yes	—
214	#366	C₂²×C₁₃	1	2	yes	—
215	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	#358	C₂²×C₁₃	1	2	yes	—
218	#357	C₂²×C₁₃	1	2	yes	—
219	#357	C₂²×C₁₃	1	2	yes	—
220	#357	C₂²×C₁₃	1	2	yes	—
221	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
222	C₄×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	—	4	2	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	8	1	no	—
238	C₄×C₁₃	—	8	1	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	#508	1	2	yes	—
241	C₄×C₁₃	#509	1	2	yes	—
242	C₄×C₁₃	#525	1	1	yes	characteristic
243	C₄×C₁₃	#575	1	1	yes	characteristic
244	C₂×#41	—	2	1	no	—
245	C₂×#41	—	4	1	no	—
246	#135	—	2	2	no	—
247	#135	—	2	2	no	—
248	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	C₂³×C₁₃	1	2	yes	—
252	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₄⋊Q₈	—	2	1	no	—
256	#127	—	2	1	no	—
257	#124	—	4	1	no	—
258	#121	—	2	2	no	—
259	#121	—	4	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	—	4	1	no	—
267	C₄×D₄	—	4	1	no	—
268	#117	—	2	1	no	—
269	#117	—	4	1	no	—
270	C₂×C₄²	—	4	1	no	—
271	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
272	SD₃₂	—	2	4	no	—
273	D₁₆	—	2	4	no	—
274	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
275	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
276	#107	—	2	1	no	—
277	#107	C₂³×C₁₃	1	1	yes	characteristic
278	#107	C₂³×C₁₃	1	1	yes	characteristic
279	#107	C₂³×C₁₃	1	2	yes	—
280	#106	—	2	1	no	—
281	#103	—	2	1	no	—
282	#103	—	2	1	no	—
283	#102	—	2	1	no	—
284	#102	—	2	1	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
288	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₁₃	—	4	1	no	—
292	C₂×C₁₃	—	8	2	no	—
293	C₂×C₁₃	—	16	2	no	—
294	C₂×C₁₃	#3100	1	1	yes	characteristic
295	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
296	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
297	#41	—	2	4	no	—
298	#41	—	4	2	no	—
299	#41	—	8	4	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
313	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	Q₁₆	—	2	1	no	—
316	Q₁₆	C₁₃×#41	1	2	yes	complemented
317	SD₁₆	—	2	4	no	—
318	D₈	—	2	1	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	2	no	—
322	D₈	C₁₃×#41	1	2	yes	complemented
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₁₃×D₈	1	1	yes	characteristic
345	C₄²	C₁₃×D₈	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	2	no	—
350	C₁₃	#33666	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	8	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	4	no	—
364	D₄	—	8	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	8	4	no	—
377	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
379	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
380	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
381	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
387	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	2	no	—
405	C₄	C₁₃×#508	1	2	yes	—
406	C₄	C₁₃×#509	1	2	yes	—
407	C₄	C₁₃×#525	1	1	yes	characteristic
408	C₄	C₁₃×#575	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	8	2	no	—
411	C₂	—	16	2	no	—
412	C₂	C₁₃×#3100	1	1	yes	characteristic
413	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
414	C₂	C₂×C₁₃×#509	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
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3169	C₂	semidirect
2. C₄×C₁₃×#135	C₂	semidirect
3. C₁₃×#2234	C₂	semidirect
4. C₁₃×#2227	C₂	semidirect
5. C₁₃×#2226	C₂	semidirect
6. C₁₃×#2207	C₂	semidirect
7. C₁₃×#2206	C₂	semidirect
8. C₁₃×#2186	C₂	semidirect
9. C₄×C₁₃×SD₃₂	C₂	semidirect
10. C₄×C₁₃×D₁₆	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
90. #33666	C₁₃	direct (N × H)
110. C₁₃×Q₁₆	#41	semidirect
116. C₁₃×D₈	#41	semidirect
144. #3169	C₂×C₁₃	semidirect
145. C₄×#135	C₂×C₁₃	semidirect
146. #2234	C₂×C₁₃	semidirect
147. #2227	C₂×C₁₃	semidirect
148. #2226	C₂×C₁₃	semidirect
149. #2207	C₂×C₁₃	semidirect
150. #2206	C₂×C₁₃	semidirect
151. #2186	C₂×C₁₃	semidirect
152. C₄×SD₃₂	C₂×C₁₃	semidirect
153. C₄×D₁₆	C₂×C₁₃	semidirect
154. #2162	C₂×C₁₃	semidirect
316. Q₁₆	C₁₃×#41	semidirect
322. D₈	C₁₃×#41	semidirect
350. C₁₃	#33666	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×#3169	2
C₄×C₁₃×#135	2
C₁₃×#2234	2
C₁₃×#2227	2
C₁₃×#2226	2
C₁₃×#2207	2
C₁₃×#2206	2
C₁₃×#2186	2
C₄×C₁₃×SD₃₂	2
C₄×C₁₃×D₁₆	2
C₁₃×#2162	2
#33666	13

Subgroups — C13×#33666 #15720005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33666 #15720005