Subgroups — C₁₃×#33674 #15720013

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2235	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2232	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2228	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2184	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2177	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2175	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₁₃×#529	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
17	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#488	—	2	1	no	—
20	C₁₃×#467	C₂²	1	1	yes	characteristic
21	C₁₃×#466	C₂²	1	1	yes	characteristic
22	C₁₃×#465	—	2	1	no	—
23	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₄×C₁₃×SD₁₆	—	2	1	no	—
25	C₄×C₁₃×D₈	—	2	1	no	—
26	C₄×C₁₃×D₈	—	2	1	no	—
27	C₄×C₁₃×D₈	C₂²	1	2	yes	—
28	C₄×C₁₃×D₈	C₂²	1	2	yes	—
29	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#367	C₂²	1	2	yes	complemented
34	C₁₃×#366	C₂²	1	2	yes	complemented
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₁₃×#358	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	—
38	C₁₃×#357	C₂²	1	2	yes	—
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×#346	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	4	1	no	—
45	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×SD₁₆	—	2	1	no	—
47	C₂×C₁₃×D₈	—	2	4	no	—
48	C₂×C₁₃×D₈	—	2	1	no	—
49	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×D₈	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#126	—	4	1	no	—
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×#124	—	2	1	no	—
56	C₁₃×#123	—	4	1	no	—
57	C₁₃×C₂²⋊Q₈	—	2	1	no	—
58	C₁₃×#121	—	2	1	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	4	1	no	—
64	C₄×D₄×C₁₃	—	4	1	no	—
65	C₄×D₄×C₁₃	—	4	1	no	—
66	C₁₃×#117	—	4	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₁₃×SD₃₂	—	2	4	no	—
71	C₁₃×D₁₆	—	2	4	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	C₂³	1	2	yes	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#103	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	2	no	—
83	C₁₃×#102	—	2	1	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33674	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	4	1	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	4	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	8	4	no	—
103	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×SD₁₆	—	4	2	no	—
108	C₁₃×D₈	—	2	4	no	—
109	C₁₃×D₈	—	2	2	no	—
110	C₁₃×D₈	—	2	2	no	—
111	C₁₃×D₈	#41	1	4	yes	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	4	1	no	—
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	2	no	—
128	C₁₃×C₂²⋊C₄	—	4	2	no	—
129	C₁₃×C₂²⋊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	C₄²×C₁₃	—	4	1	no	—
134	C₄²×C₁₃	D₈	1	1	yes	characteristic
135	C₄²×C₁₃	D₈	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	2	no	—
140	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2235	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2232	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2228	C₂×C₁₃	1	2	yes	complemented
145	#2210	C₂×C₁₃	1	2	yes	complemented
146	#2187	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2184	C₂×C₁₃	1	1	yes	characteristic
148	#2177	C₂×C₁₃	1	2	yes	complemented
149	#2175	C₂×C₁₃	1	2	yes	complemented
150	#2163	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	4	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	8	2	no	—
155	C₂³×C₁₃	—	8	2	no	—
156	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
157	Q₈×C₁₃	—	4	1	no	—
158	Q₈×C₁₃	—	4	1	no	—
159	D₄×C₁₃	—	2	4	no	—
160	D₄×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	8	2	no	—
174	C₂×C₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	—	8	2	no	—
177	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	—	2	1	no	—
186	C₈×C₁₃	C₂×#41	1	2	yes	—
187	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
188	#529	—	2	1	no	—
189	C₂×C₄×D₄	—	2	1	no	—
190	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
191	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
192	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
193	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
194	#488	—	2	1	no	—
195	#467	C₂²×C₁₃	1	1	yes	characteristic
196	#466	C₂²×C₁₃	1	1	yes	characteristic
197	#465	—	2	1	no	—
198	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
199	C₄×SD₁₆	—	2	1	no	—
200	C₄×D₈	—	2	1	no	—
201	C₄×D₈	—	2	1	no	—
202	C₄×D₈	C₂²×C₁₃	1	2	yes	—
203	C₄×D₈	C₂²×C₁₃	1	2	yes	—
204	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#102	—	2	1	no	—
207	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
208	#367	C₂²×C₁₃	1	2	yes	complemented
209	#366	C₂²×C₁₃	1	2	yes	complemented
210	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
211	#358	C₂²×C₁₃	1	2	yes	complemented
212	#357	C₂²×C₁₃	1	2	yes	—
213	#357	C₂²×C₁₃	1	2	yes	—
214	#357	C₂²×C₁₃	1	2	yes	complemented
215	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	#346	C₂²×C₁₃	1	2	yes	complemented
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	8	8	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	—	8	1	no	—
225	C₂²×C₁₃	—	8	1	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	#509	1	2	yes	—
228	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	—	8	1	no	—
238	C₄×C₁₃	#525	1	1	yes	characteristic
239	C₄×C₁₃	#575	1	1	yes	characteristic
240	C₂²×D₄	—	2	1	no	—
241	C₂³×C₄	—	4	1	no	—
242	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	—	2	4	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₂×D₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
250	#126	—	4	1	no	—
251	#125	—	2	1	no	—
252	#124	—	2	1	no	—
253	#123	—	4	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	#121	—	2	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	4	1	no	—
261	C₄×D₄	—	4	1	no	—
262	C₄×D₄	—	4	1	no	—
263	#117	—	4	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	4	1	no	—
266	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
267	SD₃₂	—	2	4	no	—
268	D₁₆	—	2	4	no	—
269	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
270	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
271	#107	—	2	1	no	—
272	#107	C₂³×C₁₃	1	1	yes	characteristic
273	#107	C₂³×C₁₃	1	1	yes	characteristic
274	#107	C₂³×C₁₃	1	2	yes	—
275	#106	—	2	1	no	—
276	#103	—	2	1	no	—
277	#103	—	2	1	no	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	—	2	1	no	—
281	#102	—	2	1	no	—
282	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
283	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₁₃	—	2	2	no	—
287	C₂×C₁₃	—	8	4	no	—
288	C₂×C₁₃	—	16	1	no	—
289	C₂×C₁₃	#3100	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
291	C₂×C₁₃	#3414	1	1	yes	characteristic
292	C₂⁴	—	4	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	8	4	no	—
305	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
306	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	Q₁₆	—	2	2	no	—
309	SD₁₆	—	4	2	no	—
310	D₈	—	2	4	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	C₁₃×#41	1	4	yes	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	C₁₃×D₈	1	1	yes	characteristic
337	C₄²	C₁₃×D₈	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	2	no	—
342	C₁₃	#33674	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	1	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	1	no	—
356	D₄	—	8	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
370	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₂×C₁₃×#41	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	8	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	C₁₃×#509	1	2	yes	—
389	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	1	no	—
399	C₄	C₁₃×#525	1	1	yes	characteristic
400	C₄	C₁₃×#575	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	16	1	no	—
404	C₂	C₁₃×#3100	1	1	yes	characteristic
405	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
406	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#2184	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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×#3168	C₂	semidirect
2. C₂×C₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2235	C₂	semidirect
4. C₁₃×#2232	C₂	semidirect
5. C₁₃×#2228	C₂	semidirect
6. C₁₃×#2210	C₂	semidirect
7. C₁₃×#2187	C₂	semidirect
9. C₁₃×#2177	C₂	semidirect
10. C₁₃×#2175	C₂	semidirect
11. C₁₃×#2163	C₂	semidirect
17. C₁₃×#499	C₂²	semidirect
18. C₁₃×#495	C₂²	semidirect
23. C₄×C₁₃×Q₁₆	C₂²	semidirect
29. C₄×C₁₃×D₈	C₂²	semidirect
33. C₁₃×#367	C₂²	semidirect
34. C₁₃×#366	C₂²	semidirect
35. C₁₃×C₄⋊C₁₆	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
42. C₁₃×#346	C₂²	semidirect
89. #33674	C₁₃	direct (N × H)
140. #3168	C₂×C₁₃	semidirect
141. C₂×C₄×D₈	C₂×C₁₃	semidirect
142. #2235	C₂×C₁₃	semidirect
143. #2232	C₂×C₁₃	semidirect
144. #2228	C₂×C₁₃	semidirect
145. #2210	C₂×C₁₃	semidirect
146. #2187	C₂×C₁₃	semidirect
148. #2177	C₂×C₁₃	semidirect
149. #2175	C₂×C₁₃	semidirect
150. #2163	C₂×C₁₃	semidirect
192. #499	C₂²×C₁₃	semidirect
193. #495	C₂²×C₁₃	semidirect
198. C₄×Q₁₆	C₂²×C₁₃	semidirect
204. C₄×D₈	C₂²×C₁₃	semidirect
208. #367	C₂²×C₁₃	semidirect
209. #366	C₂²×C₁₃	semidirect
210. C₄⋊C₁₆	C₂²×C₁₃	semidirect
211. #358	C₂²×C₁₃	semidirect
214. #357	C₂²×C₁₃	semidirect
217. #346	C₂²×C₁₃	semidirect
342. C₁₃	#33674	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×#3168	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2235	2
C₁₃×#2232	2
C₁₃×#2228	2
C₁₃×#2210	2
C₁₃×#2187	2
C₁₃×#2184	2
C₁₃×#2177	2
C₁₃×#2175	2
C₁₃×#2163	2
#33674	13

Subgroups — C13×#33674 #15720013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33674 #15720013