Subgroups — C₁₃×#17922 #15704261

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1586	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1581	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1580	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#480	C₄	1	2	yes	—
15	C₁₃×#474	C₄	1	2	yes	—
16	C₁₃×#459	C₄	1	2	yes	—
17	C₁₃×#447	C₄	1	2	yes	—
18	C₄×C₁₃×D₈	C₂²	1	2	yes	—
19	C₄×C₁₃×D₈	C₂²	1	2	yes	—
20	C₁₃×#436	C₂²	1	2	yes	complemented
21	C₁₃×#435	—	2	2	no	—
22	C₈×D₄×C₁₃	—	2	2	no	—
23	C₈×D₄×C₁₃	C₂²	1	2	yes	—
24	C₈×D₄×C₁₃	C₂²	1	2	yes	—
25	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#432	C₂²	1	1	yes	characteristic
27	C₁₃×#431	C₂²	1	1	yes	characteristic
28	C₁₃×#431	C₂²	1	1	yes	characteristic
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#408	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#335	C₂²	1	2	yes	complemented
34	C₁₃×#334	C₂²	1	2	yes	complemented
35	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
36	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
37	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
38	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
39	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#124	—	2	1	no	—
56	C₁₃×#121	—	2	1	no	—
57	C₁₃×#121	C₂×C₄	1	2	yes	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₁₃	C₂³	1	2	yes	—
63	C₄×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#107	C₂×C₄	1	2	yes	—
68	C₁₃×#107	C₂×C₄	1	2	yes	—
69	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×#102	C₂×C₄	1	2	yes	—
74	C₁₃×#102	C₂×C₄	1	2	yes	—
75	C₁₃×#102	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	—	2	2	no	—
81	C₁₃×C₂²⋊C₈	—	2	2	no	—
82	C₁₃×C₂²⋊C₈	—	2	2	no	—
83	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
84	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
85	C₁₃×#97	—	2	1	no	—
86	C₁₃×#97	—	2	1	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	#17922	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₁₃×#41	—	8	2	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₁₃×D₈	—	2	4	no	—
114	C₁₃×D₈	—	2	4	no	—
115	C₁₃×M₁₆	—	4	2	no	—
116	C₁₃×M₁₆	—	8	2	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	8	2	no	—
122	C₂×C₈×C₁₃	—	8	2	no	—
123	C₂×C₈×C₁₃	—	8	2	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₁₃×C₂²⋊C₄	—	2	2	no	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	#3100	C₂×C₁₃	1	1	yes	characteristic
141	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1586	C₂×C₁₃	1	2	yes	complemented
144	#1581	C₂×C₁₃	1	2	yes	complemented
145	#1580	C₂×C₁₃	1	2	yes	complemented
146	C₈×D₈	C₂×C₁₃	1	2	yes	complemented
147	#1572	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1490	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1484	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	2	4	no	—
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	8	1	no	—
155	C₂³×C₁₃	—	8	1	no	—
156	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
157	Q₈×C₁₃	—	8	1	no	—
158	D₄×C₁₃	—	2	4	no	—
159	D₄×C₁₃	—	2	2	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	8	1	no	—
163	D₄×C₁₃	—	8	1	no	—
164	D₄×C₁₃	—	8	2	no	—
165	D₄×C₁₃	#131	1	4	yes	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	—	8	1	no	—
177	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	—	4	1	no	—
189	C₈×C₁₃	—	4	2	no	—
190	C₈×C₁₃	—	4	2	no	—
191	#532	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
193	#480	C₄×C₁₃	1	2	yes	—
194	#474	C₄×C₁₃	1	2	yes	—
195	#459	C₄×C₁₃	1	2	yes	—
196	#447	C₄×C₁₃	1	2	yes	—
197	C₄×D₈	C₂²×C₁₃	1	2	yes	—
198	C₄×D₈	C₂²×C₁₃	1	2	yes	—
199	#436	C₂²×C₁₃	1	2	yes	complemented
200	#435	—	2	2	no	—
201	C₈×D₄	—	2	2	no	—
202	C₈×D₄	C₂²×C₁₃	1	2	yes	—
203	C₈×D₄	C₂²×C₁₃	1	2	yes	—
204	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
205	#432	C₂²×C₁₃	1	1	yes	characteristic
206	#431	C₂²×C₁₃	1	1	yes	characteristic
207	#431	C₂²×C₁₃	1	1	yes	characteristic
208	#431	C₂²×C₁₃	1	1	yes	characteristic
209	#408	—	2	2	no	—
210	C₂×C₂²⋊C₈	—	2	2	no	—
211	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	#335	C₂²×C₁₃	1	2	yes	complemented
213	#334	C₂²×C₁₃	1	2	yes	complemented
214	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
215	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
216	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
217	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
218	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
221	C₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	—	8	4	no	—
232	C₂²×C₁₃	C₂×C₄×D₄	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	—	2	1	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	C₂×#131	1	2	yes	—
240	C₄×C₁₃	#576	1	2	yes	—
241	C₂×#41	—	2	1	no	—
242	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
245	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
252	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
253	#124	—	2	1	no	—
254	#121	—	2	1	no	—
255	#121	C₂×C₄×C₁₃	1	2	yes	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
260	C₄×D₄	C₂³×C₁₃	1	2	yes	—
261	C₄×D₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
265	#107	C₂×C₄×C₁₃	1	2	yes	—
266	#107	C₂×C₄×C₁₃	1	2	yes	—
267	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
268	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
270	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
271	#102	C₂×C₄×C₁₃	1	2	yes	—
272	#102	C₂×C₄×C₁₃	1	2	yes	—
273	#102	C₂×C₄×C₁₃	1	2	yes	—
274	#102	C₂×C₄×C₁₃	1	2	yes	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
282	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
283	#97	—	2	1	no	—
284	#97	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₁₃	—	4	1	no	—
293	C₂×C₁₃	—	4	4	no	—
294	C₂×C₁₃	—	8	2	no	—
295	C₂×C₁₃	#2929	1	1	yes	characteristic
296	C₂×C₁₃	#2948	1	1	yes	characteristic
297	C₂×C₁₃	#2956	1	1	yes	characteristic
298	C₂⁴	—	2	1	no	—
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
307	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
316	D₈	—	2	4	no	—
317	D₈	—	2	4	no	—
318	M₁₆	—	4	2	no	—
319	M₁₆	—	8	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	8	2	no	—
325	C₂×C₈	—	8	2	no	—
326	C₂×C₈	—	8	2	no	—
327	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
334	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₄²	C₁₃×#41	1	1	yes	characteristic
342	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
343	C₁₃	#17922	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
350	Q₈	—	8	1	no	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	2	no	—
358	D₄	C₁₃×#131	1	4	yes	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	4	no	—
394	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₂×C₁₃×#131	1	2	yes	—
402	C₄	C₁₃×#576	1	2	yes	—
403	C₂	—	4	1	no	—
404	C₂	—	4	4	no	—
405	C₂	—	8	2	no	—
406	C₂	C₁₃×#2929	1	1	yes	characteristic
407	C₂	C₁₃×#2948	1	1	yes	characteristic
408	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2981	C₂	semidirect
3. C₁₃×#2972	C₂	semidirect
4. C₁₃×#1586	C₂	semidirect
5. C₁₃×#1581	C₂	semidirect
6. C₁₃×#1580	C₂	semidirect
7. C₈×C₁₃×D₈	C₂	semidirect
8. C₁₃×#1572	C₂	semidirect
9. C₁₃×#1490	C₂	semidirect
10. C₁₃×#1484	C₂	semidirect
11. C₁₃×#1453	C₂	semidirect
20. C₁₃×#436	C₂²	semidirect
25. C₈×D₄×C₁₃	C₂²	semidirect
33. C₁₃×#335	C₂²	semidirect
34. C₁₃×#334	C₂²	semidirect
37. C₁₃×D₄⋊C₈	C₂²	semidirect
38. C₁₃×D₄⋊C₈	C₂²	semidirect
39. C₁₃×#322	C₂²	semidirect
40. C₁₃×#322	C₂²	semidirect
41. C₁₃×#322	C₂²	semidirect
42. C₈²×C₁₃	C₂²	semidirect
94. #17922	C₁₃	direct (N × H)
141. #2981	C₂×C₁₃	semidirect
142. #2972	C₂×C₁₃	semidirect
143. #1586	C₂×C₁₃	semidirect
144. #1581	C₂×C₁₃	semidirect
145. #1580	C₂×C₁₃	semidirect
146. C₈×D₈	C₂×C₁₃	semidirect
147. #1572	C₂×C₁₃	semidirect
148. #1490	C₂×C₁₃	semidirect
149. #1484	C₂×C₁₃	semidirect
150. #1453	C₂×C₁₃	semidirect
199. #436	C₂²×C₁₃	semidirect
204. C₈×D₄	C₂²×C₁₃	semidirect
212. #335	C₂²×C₁₃	semidirect
213. #334	C₂²×C₁₃	semidirect
216. D₄⋊C₈	C₂²×C₁₃	semidirect
217. D₄⋊C₈	C₂²×C₁₃	semidirect
218. #322	C₂²×C₁₃	semidirect
219. #322	C₂²×C₁₃	semidirect
220. #322	C₂²×C₁₃	semidirect
221. C₈²	C₂²×C₁₃	semidirect
343. C₁₃	#17922	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×#3100	2
C₁₃×#2981	2
C₁₃×#2972	2
C₁₃×#1586	2
C₁₃×#1581	2
C₁₃×#1580	2
C₈×C₁₃×D₈	2
C₁₃×#1572	2
C₁₃×#1490	2
C₁₃×#1484	2
C₁₃×#1453	2
#17922	13

Subgroups — C13×#17922 #15704261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17922 #15704261