Subgroups — C₁₃×#61436 #15747775

Order 3328.

1960 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×#3483	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3341	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3305	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3287	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3169	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3106	C₂	1	6	yes	maximal, complemented
10	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#135	C₂²	1	3	yes	—
13	Q₈²×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#555	—	2	6	no	—
15	C₁₃×#555	C₂²	1	6	yes	—
16	C₁₃×#550	—	2	2	no	—
17	C₁₃×#550	C₂²	1	6	yes	—
18	C₁₃×#550	C₂²	1	2	yes	—
19	C₁₃×#532	—	2	6	no	—
20	C₁₃×#532	C₂²	1	6	yes	—
21	C₄×C₁₃×#41	—	2	2	no	—
22	C₄×C₁₃×#41	C₂²	1	6	yes	—
23	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
24	C₁₃×#500	C₂²	1	3	yes	—
25	C₁₃×#493	C₂²	1	3	yes	—
26	C₁₃×#486	C₂²	1	6	yes	—
27	C₁₃×#482	C₂²	1	12	yes	—
28	C₁₃×#477	C₂²	1	6	yes	—
29	C₁₃×#476	C₂²	1	6	yes	—
30	C₁₃×#466	C₂²	1	6	yes	—
31	C₁₃×#466	C₂²	1	6	yes	—
32	C₁₃×#460	C₂²	1	6	yes	—
33	C₁₃×#459	C₂²	1	6	yes	—
34	C₁₃×#449	C₂²	1	12	yes	—
35	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
38	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
40	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
41	C₄×C₁₃×D₈	C₂²	1	3	yes	—
42	C₄×C₁₃×D₈	C₂²	1	6	yes	—
43	C₄×C₁₃×D₈	C₂²	1	3	yes	—
44	C₈×D₄×C₁₃	C₂²	1	3	yes	—
45	C₈×D₄×C₁₃	C₂²	1	3	yes	—
46	C₁₃×#431	C₂²	1	3	yes	—
47	C₁₃×#427	C₂²	1	3	yes	—
48	C₁₃×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	2	6	no	—
52	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
53	C₂×C₁₃×#41	C₂³	1	6	yes	—
54	C₁₃×#135	—	2	12	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
57	C₂×C₁₃×D₈	C₂³	1	3	yes	—
58	C₂×C₁₃×D₈	C₂³	1	6	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
61	C₁₃×C₄⋊Q₈	—	2	6	no	—
62	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
63	C₁₃×#127	—	2	6	no	—
64	C₁₃×#127	C₂³	1	6	yes	—
65	C₁₃×#124	—	2	12	no	—
66	C₁₃×#124	—	2	6	no	—
67	C₁₃×#121	—	2	6	no	—
68	C₁₃×#121	—	2	6	no	—
69	C₁₃×#121	—	2	6	no	—
70	C₁₃×#121	—	2	12	no	—
71	C₁₃×#121	C₂³	1	12	yes	—
72	C₄×Q₈×C₁₃	—	2	2	no	—
73	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
76	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₁₃	—	2	6	no	—
78	C₄×D₄×C₁₃	—	2	6	no	—
79	C₄×D₄×C₁₃	—	2	6	no	—
80	C₄×D₄×C₁₃	—	2	6	no	—
81	C₄×D₄×C₁₃	D₄	1	3	yes	—
82	C₄×D₄×C₁₃	C₂³	1	6	yes	—
83	C₄×D₄×C₁₃	C₂³	1	6	yes	—
84	C₄×D₄×C₁₃	C₂³	1	3	yes	—
85	C₁₃×#117	—	2	6	no	—
86	C₁₃×#117	—	2	6	no	—
87	C₁₃×#117	D₄	1	3	yes	—
88	C₁₃×#117	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₃	—	2	6	no	—
90	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
91	C₁₃×#107	C₂³	1	1	yes	characteristic
92	C₁₃×#107	C₂³	1	3	yes	—
93	C₁₃×#107	C₂³	1	6	yes	—
94	C₁₃×#106	C₂³	1	6	yes	—
95	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₃×#103	C₂³	1	2	yes	—
98	C₁₃×#103	C₂³	1	6	yes	—
99	C₁₃×#102	C₂³	1	6	yes	—
100	C₁₃×#102	C₂³	1	6	yes	—
101	C₁₃×#102	C₂³	1	12	yes	—
102	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×C₈×C₁₃	C₂³	1	3	yes	—
105	C₄×C₈×C₁₃	C₂³	1	3	yes	—
106	C₄×C₈×C₁₃	C₂³	1	3	yes	—
107	#61436	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	—	2	12	no	—
110	C₁₃×#41	—	4	6	no	—
111	C₁₃×#41	—	4	8	no	—
112	C₁₃×#41	—	8	12	no	—
113	C₂×Q₈×C₁₃	—	2	6	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
116	C₂×D₄×C₁₃	—	2	6	no	—
117	C₂×D₄×C₁₃	—	2	12	no	—
118	C₂×D₄×C₁₃	—	2	6	no	—
119	C₂×D₄×C₁₃	—	2	6	no	—
120	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
121	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₁₃	—	2	6	no	—
123	C₂²×C₄×C₁₃	—	2	6	no	—
124	C₂²×C₄×C₁₃	—	2	6	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
128	C₁₃×Q₁₆	#41	1	4	yes	complemented
129	C₁₃×SD₁₆	—	2	12	no	—
130	C₁₃×D₈	—	2	6	no	—
131	C₁₃×D₈	—	4	6	no	—
132	C₂×C₈×C₁₃	—	2	6	no	—
133	C₂×C₈×C₁₃	—	4	3	no	—
134	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
136	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
137	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	6	no	—
140	C₁₃×C₄⋊C₄	—	2	6	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
145	C₁₃×C₂²⋊C₄	—	2	6	no	—
146	C₁₃×C₂²⋊C₄	—	2	12	no	—
147	C₁₃×C₂²⋊C₄	—	2	6	no	—
148	C₁₃×C₂²⋊C₄	—	2	6	no	—
149	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
150	C₄²×C₁₃	—	2	6	no	—
151	C₄²×C₁₃	—	2	6	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	C₂×D₄	1	3	yes	—
154	C₄²×C₁₃	C₂×D₄	1	3	yes	—
155	C₄²×C₁₃	C₂⁴	1	3	yes	—
156	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
157	#3483	C₂×C₁₃	1	2	yes	complemented
158	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
159	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#3362	C₂×C₁₃	1	2	yes	complemented
161	#3341	C₂×C₁₃	1	3	yes	complemented
162	#3305	C₂×C₁₃	1	6	yes	complemented
163	#3287	C₂×C₁₃	1	3	yes	complemented
164	#3169	C₂×C₁₃	1	3	yes	complemented
165	#3106	C₂×C₁₃	1	6	yes	complemented
166	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₄×#135	C₂×C₁₃	1	3	yes	complemented
168	C₂³×C₁₃	—	2	6	no	—
169	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	8	6	no	—
172	Q₈×C₁₃	#135	1	4	yes	complemented
173	Q₈×C₁₃	C₂×#41	1	4	yes	—
174	D₄×C₁₃	—	2	6	no	—
175	D₄×C₁₃	—	2	6	no	—
176	D₄×C₁₃	—	2	6	no	—
177	D₄×C₁₃	—	4	12	no	—
178	D₄×C₁₃	—	4	12	no	—
179	D₄×C₁₃	—	8	6	no	—
180	D₄×C₁₃	—	8	12	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	6	no	—
183	C₂×C₄×C₁₃	—	2	6	no	—
184	C₂×C₄×C₁₃	—	2	3	no	—
185	C₂×C₄×C₁₃	—	2	3	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	6	no	—
188	C₂×C₄×C₁₃	—	4	12	no	—
189	C₂×C₄×C₁₃	—	4	12	no	—
190	C₂×C₄×C₁₃	—	4	12	no	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
197	C₈×C₁₃	—	2	3	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	3	no	—
200	C₈×C₁₃	C₂×#41	1	2	yes	—
201	C₂×#135	C₂²×C₁₃	1	3	yes	—
202	Q₈²	C₂²×C₁₃	1	2	yes	—
203	#555	—	2	6	no	—
204	#555	C₂²×C₁₃	1	6	yes	—
205	#550	—	2	2	no	—
206	#550	C₂²×C₁₃	1	6	yes	—
207	#550	C₂²×C₁₃	1	2	yes	—
208	#532	—	2	6	no	—
209	#532	C₂²×C₁₃	1	6	yes	—
210	C₄×#41	—	2	2	no	—
211	C₄×#41	C₂²×C₁₃	1	6	yes	—
212	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
213	#500	C₂²×C₁₃	1	3	yes	—
214	#493	C₂²×C₁₃	1	3	yes	—
215	#486	C₂²×C₁₃	1	6	yes	—
216	#482	C₂²×C₁₃	1	12	yes	—
217	#477	C₂²×C₁₃	1	6	yes	—
218	#476	C₂²×C₁₃	1	6	yes	—
219	#466	C₂²×C₁₃	1	6	yes	—
220	#466	C₂²×C₁₃	1	6	yes	—
221	#460	C₂²×C₁₃	1	6	yes	—
222	#459	C₂²×C₁₃	1	6	yes	—
223	#449	C₂²×C₁₃	1	12	yes	—
224	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
227	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
228	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
229	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
230	C₄×D₈	C₂²×C₁₃	1	3	yes	—
231	C₄×D₈	C₂²×C₁₃	1	6	yes	—
232	C₄×D₈	C₂²×C₁₃	1	3	yes	—
233	C₈×D₄	C₂²×C₁₃	1	3	yes	—
234	C₈×D₄	C₂²×C₁₃	1	3	yes	—
235	#431	C₂²×C₁₃	1	3	yes	—
236	#427	C₂²×C₁₃	1	3	yes	—
237	#416	C₂²×C₁₃	1	6	yes	—
238	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
239	C₂²×C₁₃	—	2	3	no	—
240	C₂²×C₁₃	—	2	3	no	—
241	C₂²×C₁₃	—	2	3	no	—
242	C₂²×C₁₃	—	4	6	no	—
243	C₂²×C₁₃	—	4	6	no	—
244	C₂²×C₁₃	—	4	6	no	—
245	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
246	C₄×C₁₃	—	2	3	no	—
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	3	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	6	no	—
252	C₄×C₁₃	C₂×#135	1	6	yes	—
253	C₄×C₁₃	#576	1	2	yes	—
254	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
255	C₄×C₁₃	#585	1	1	yes	characteristic
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	6	no	—
258	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
259	C₂×#41	C₂³×C₁₃	1	6	yes	—
260	#135	—	2	12	no	—
261	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
263	C₂×D₈	C₂³×C₁₃	1	3	yes	—
264	C₂×D₈	C₂³×C₁₃	1	6	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
266	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
267	C₄⋊Q₈	—	2	6	no	—
268	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
269	#127	—	2	6	no	—
270	#127	C₂³×C₁₃	1	6	yes	—
271	#124	—	2	12	no	—
272	#124	—	2	6	no	—
273	#121	—	2	6	no	—
274	#121	—	2	6	no	—
275	#121	—	2	6	no	—
276	#121	—	2	12	no	—
277	#121	C₂³×C₁₃	1	12	yes	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
280	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
281	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
282	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	6	no	—
284	C₄×D₄	—	2	6	no	—
285	C₄×D₄	—	2	6	no	—
286	C₄×D₄	—	2	6	no	—
287	C₄×D₄	D₄×C₁₃	1	3	yes	—
288	C₄×D₄	C₂³×C₁₃	1	6	yes	—
289	C₄×D₄	C₂³×C₁₃	1	6	yes	—
290	C₄×D₄	C₂³×C₁₃	1	3	yes	—
291	#117	—	2	6	no	—
292	#117	—	2	6	no	—
293	#117	D₄×C₁₃	1	3	yes	—
294	#117	C₂³×C₁₃	1	6	yes	—
295	C₂×C₄²	—	2	6	no	—
296	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
297	#107	C₂³×C₁₃	1	1	yes	characteristic
298	#107	C₂³×C₁₃	1	3	yes	—
299	#107	C₂³×C₁₃	1	6	yes	—
300	#106	C₂³×C₁₃	1	6	yes	—
301	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
302	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
303	#103	C₂³×C₁₃	1	2	yes	—
304	#103	C₂³×C₁₃	1	6	yes	—
305	#102	C₂³×C₁₃	1	6	yes	—
306	#102	C₂³×C₁₃	1	6	yes	—
307	#102	C₂³×C₁₃	1	12	yes	—
308	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
309	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂³×C₁₃	1	3	yes	—
311	C₄×C₈	C₂³×C₁₃	1	3	yes	—
312	C₄×C₈	C₂³×C₁₃	1	3	yes	—
313	C₂×C₁₃	—	4	3	no	—
314	C₂×C₁₃	—	8	6	no	—
315	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
316	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
317	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
318	#41	—	2	4	no	—
319	#41	—	2	12	no	—
320	#41	—	4	6	no	—
321	#41	—	4	8	no	—
322	#41	—	8	12	no	—
323	C₂×Q₈	—	2	6	no	—
324	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
326	C₂×D₄	—	2	6	no	—
327	C₂×D₄	—	2	12	no	—
328	C₂×D₄	—	2	6	no	—
329	C₂×D₄	—	2	6	no	—
330	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
331	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
332	C₂²×C₄	—	2	6	no	—
333	C₂²×C₄	—	2	6	no	—
334	C₂²×C₄	—	2	6	no	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
338	Q₁₆	C₁₃×#41	1	4	yes	complemented
339	SD₁₆	—	2	12	no	—
340	D₈	—	2	6	no	—
341	D₈	—	4	6	no	—
342	C₂×C₈	—	2	6	no	—
343	C₂×C₈	—	4	3	no	—
344	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
345	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
346	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
347	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	6	no	—
350	C₄⋊C₄	—	2	6	no	—
351	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
353	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
354	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
355	C₂²⋊C₄	—	2	6	no	—
356	C₂²⋊C₄	—	2	12	no	—
357	C₂²⋊C₄	—	2	6	no	—
358	C₂²⋊C₄	—	2	6	no	—
359	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	6	no	—
362	C₄²	—	2	6	no	—
363	C₄²	C₂×D₄×C₁₃	1	3	yes	—
364	C₄²	C₂×D₄×C₁₃	1	3	yes	—
365	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
366	C₄²	C₂⁴×C₁₃	1	3	yes	—
367	C₁₃	#61436	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	2	6	no	—
369	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
370	Q₈	—	2	2	no	—
371	Q₈	—	8	6	no	—
372	Q₈	C₁₃×#135	1	4	yes	complemented
373	Q₈	C₂×C₁₃×#41	1	4	yes	—
374	D₄	—	2	6	no	—
375	D₄	—	2	6	no	—
376	D₄	—	2	6	no	—
377	D₄	—	4	12	no	—
378	D₄	—	4	12	no	—
379	D₄	—	8	6	no	—
380	D₄	—	8	12	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	3	no	—
385	C₂×C₄	—	2	3	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	4	12	no	—
389	C₂×C₄	—	4	12	no	—
390	C₂×C₄	—	4	12	no	—
391	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
395	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	3	no	—
400	C₈	C₂×C₁₃×#41	1	2	yes	—
401	C₂²	—	2	3	no	—
402	C₂²	—	2	3	no	—
403	C₂²	—	2	3	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	6	no	—
406	C₂²	—	4	6	no	—
407	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	3	no	—
410	C₄	—	2	3	no	—
411	C₄	—	2	4	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	6	no	—
414	C₄	C₂×C₁₃×#135	1	6	yes	—
415	C₄	C₁₃×#576	1	2	yes	—
416	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
417	C₄	C₁₃×#585	1	1	yes	characteristic
418	C₂	—	4	3	no	—
419	C₂	—	8	6	no	—
420	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
421	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
422	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3483	C₂	semidirect
2. C₁₃×#3391	C₂	semidirect
3. Q₈×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#3362	C₂	semidirect
5. C₁₃×#3341	C₂	semidirect
6. C₁₃×#3305	C₂	semidirect
7. C₁₃×#3287	C₂	semidirect
8. C₁₃×#3169	C₂	semidirect
9. C₁₃×#3106	C₂	semidirect
10. C₈×C₁₃×#41	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
107. #61436	C₁₃	direct (N × H)
128. C₁₃×Q₁₆	#41	semidirect
157. #3483	C₂×C₁₃	semidirect
158. #3391	C₂×C₁₃	semidirect
159. Q₈×Q₁₆	C₂×C₁₃	semidirect
160. #3362	C₂×C₁₃	semidirect
161. #3341	C₂×C₁₃	semidirect
162. #3305	C₂×C₁₃	semidirect
163. #3287	C₂×C₁₃	semidirect
164. #3169	C₂×C₁₃	semidirect
165. #3106	C₂×C₁₃	semidirect
166. C₈×#41	C₂×C₁₃	semidirect
167. C₄×#135	C₂×C₁₃	semidirect
172. Q₈×C₁₃	#135	semidirect
338. Q₁₆	C₁₃×#41	semidirect
367. C₁₃	#61436	direct (N × H)
372. Q₈	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3483	2
C₁₃×#3391	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3362	2
C₁₃×#3341	2
C₁₃×#3305	2
C₁₃×#3287	2
C₁₃×#3169	2
C₁₃×#3106	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
#61436	13

Subgroups — C13×#61436 #15747775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61436 #15747775