Subgroups — C₁₃×#25846 #15712185

Order 3328.

964 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2584	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2059	C₂	1	2	yes	maximal
6	C₁₃×#2059	C₂	1	2	yes	maximal
7	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1865	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#557	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	—	2	2	no	—
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#501	—	2	4	no	—
24	C₁₃×#479	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	2	yes	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#398	—	2	1	no	—
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	2	8	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
54	C₁₃×#125	—	2	16	no	—
55	C₁₃×#125	—	2	4	no	—
56	C₁₃×#125	—	2	4	no	—
57	C₁₃×#125	—	2	2	no	—
58	C₁₃×#125	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	8	no	—
60	C₄×Q₈×C₁₃	—	2	4	no	—
61	C₄×Q₈×C₁₃	—	2	4	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	D₄	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#107	—	2	2	no	—
88	C₁₃×#107	—	2	4	no	—
89	C₁₃×#106	—	2	2	no	—
90	C₁₃×#106	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	Q₈	1	8	yes	complemented
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	#25846	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	4	4	no	—
106	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
126	C₁₃×C₄⋊C₄	—	2	8	no	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	4	4	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	8	2	no	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
147	C₄²×C₁₃	—	2	8	no	—
148	C₄²×C₁₃	—	2	4	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	8	1	no	—
152	C₄²×C₁₃	C₂×D₄	1	2	yes	—
153	C₄²×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×#557	C₂×C₁₃	1	1	yes	characteristic
155	C₂×#501	C₂×C₁₃	1	1	yes	characteristic
156	C₂×#479	C₂×C₁₃	1	1	yes	characteristic
157	#2584	C₂×C₁₃	1	1	yes	characteristic
158	#2059	C₂×C₁₃	1	2	yes	—
159	#2059	C₂×C₁₃	1	2	yes	—
160	#1987	C₂×C₁₃	1	1	yes	characteristic
161	#1985	C₂×C₁₃	1	1	yes	characteristic
162	#1865	C₂×C₁₃	1	2	yes	—
163	#1863	C₂×C₁₃	1	2	yes	—
164	#1763	C₂×C₁₃	1	1	yes	characteristic
165	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	4	no	—
168	Q₈×C₁₃	—	4	4	no	—
169	Q₈×C₁₃	—	4	8	no	—
170	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	#120	1	2	yes	—
196	C₂×C₄×C₁₃	#120	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
200	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
201	C₈×C₁₃	—	2	4	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	—	4	1	no	—
204	#557	—	2	4	no	—
205	#557	—	2	4	no	—
206	C₂×C₄⋊Q₈	—	2	1	no	—
207	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#125	—	2	2	no	—
209	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#125	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
215	#501	—	2	4	no	—
216	#479	—	2	4	no	—
217	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#107	C₂²×C₁₃	1	2	yes	—
219	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#106	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#103	C₂²×C₁₃	1	2	yes	—
225	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
226	#398	—	2	1	no	—
227	#395	—	2	1	no	—
228	#389	—	2	2	no	—
229	#389	C₂²×C₁₃	1	2	yes	—
230	#389	C₂²×C₁₃	1	2	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	#340	C₂²×C₁₃	1	2	yes	—
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	2	yes	—
236	#336	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
238	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
239	C₂²×C₁₃	#575	1	2	yes	—
240	C₂²×C₁₃	#577	1	1	yes	characteristic
241	C₂²×C₁₃	#578	1	1	yes	characteristic
242	C₄×C₁₃	—	2	4	no	—
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	8	1	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
253	C₄×C₁₃	#536	1	1	yes	characteristic
254	C₄×C₁₃	D₄×Q₈	1	2	yes	—
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
257	C₂²×Q₈	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	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
261	C₄⋊Q₈	—	2	8	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
264	#125	—	2	16	no	—
265	#125	—	2	4	no	—
266	#125	—	2	4	no	—
267	#125	—	2	2	no	—
268	#125	—	2	2	no	—
269	C₄×Q₈	—	2	8	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	D₄×C₁₃	1	4	yes	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	#107	—	2	2	no	—
298	#107	—	2	4	no	—
299	#106	—	2	2	no	—
300	#106	—	2	4	no	—
301	C₄⋊C₈	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	Q₈×C₁₃	1	8	yes	complemented
305	#97	—	2	2	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	C₂×C₁₃	#2434	1	1	yes	characteristic
310	C₂×C₁₃	#3005	1	1	yes	characteristic
311	C₂×C₁₃	#3013	1	1	yes	characteristic
312	C₂×C₁₃	#3388	1	2	yes	—
313	C₂×C₁₃	#3390	1	2	yes	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
321	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	8	2	no	—
358	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
359	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
361	C₄²	—	2	8	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	8	1	no	—
366	C₄²	C₂×D₄×C₁₃	1	2	yes	—
367	C₄²	C₂×D₄×C₁₃	1	2	yes	—
368	C₁₃	#25846	1	1	yes	characteristic, direct product factor, Sylow
369	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	4	no	—
373	Q₈	—	4	8	no	—
374	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	C₁₃×#120	1	2	yes	—
400	C₂×C₄	C₁₃×#120	1	2	yes	—
401	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
404	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
405	C₈	—	2	4	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
409	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
410	C₂²	C₁₃×#575	1	2	yes	—
411	C₂²	C₁₃×#577	1	1	yes	characteristic
412	C₂²	C₁₃×#578	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
424	C₄	C₁₃×#536	1	1	yes	characteristic
425	C₄	D₄×Q₈×C₁₃	1	2	yes	—
426	C₂	C₁₃×#2434	1	1	yes	characteristic
427	C₂	C₁₃×#3005	1	1	yes	characteristic
428	C₂	C₁₃×#3013	1	1	yes	characteristic
429	C₂	C₁₃×#3388	1	2	yes	—
430	C₂	C₁₃×#3390	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
94. C₁₃×#103	Q₈	semidirect
99. #25846	C₁₃	direct (N × H)
304. #103	Q₈×C₁₃	semidirect
368. C₁₃	#25846	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#557	2
C₂×C₁₃×#501	2
C₂×C₁₃×#479	2
C₁₃×#2584	2
C₁₃×#2059	2
C₁₃×#1987	2
C₁₃×#1985	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1763	2
#25846	13

Subgroups — C13×#25846 #15712185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25846 #15712185