Subgroups — C₁₃×#61906 #15748245

Order 3328.

1748 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3372	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3218	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3206	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3112	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3108	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#559	C₂²	1	3	yes	—
13	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#557	—	2	3	no	—
16	C₁₃×#557	C₂²	1	2	yes	—
17	C₁₃×#557	C₂²	1	6	yes	—
18	C₁₃×#554	C₂²	1	3	yes	—
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#547	—	2	3	no	—
22	C₁₃×#542	—	2	3	no	—
23	C₁₃×#532	C₂²	1	3	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₁₃×#529	C₂²	1	3	yes	—
26	C₂×C₁₃×#125	—	2	3	no	—
27	C₁₃×#520	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#497	C₂²	1	6	yes	—
32	C₁₃×#492	C₂²	1	6	yes	—
33	C₁₃×#491	C₂²	1	6	yes	—
34	C₁₃×#487	C₂²	1	6	yes	—
35	C₁₃×#483	C₂²	1	1	yes	characteristic
36	C₁₃×#480	C₂²	1	3	yes	—
37	C₁₃×#479	C₂²	1	6	yes	—
38	C₁₃×#477	C₂²	1	6	yes	—
39	C₁₃×#464	C₂²	1	6	yes	—
40	C₁₃×#462	C₂²	1	6	yes	—
41	C₁₃×#461	C₂²	1	6	yes	—
42	C₁₃×#461	C₂²	1	12	yes	—
43	C₁₃×#460	C₂²	1	6	yes	—
44	C₁₃×#451	C₂²	1	3	yes	—
45	C₁₃×#448	C₂²	1	3	yes	—
46	C₁₃×#448	C₂²	1	6	yes	—
47	C₁₃×#446	C₂²	1	6	yes	—
48	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
49	C₁₃×#440	C₂²	1	12	yes	—
50	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
51	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
52	C₁₃×#432	C₂²	1	3	yes	—
53	C₁₃×#431	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	3	no	—
56	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
58	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
59	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
61	C₁₃×C₄⋊Q₈	—	2	3	no	—
62	C₁₃×C₄⋊Q₈	—	2	3	no	—
63	C₁₃×C₄⋊Q₈	—	2	3	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₃×#127	C₂³	1	3	yes	—
68	C₁₃×#126	—	2	3	no	—
69	C₁₃×#125	—	2	6	no	—
70	C₁₃×#125	—	2	6	no	—
71	C₁₃×#125	—	2	12	no	—
72	C₁₃×#125	C₂³	1	3	yes	—
73	C₁₃×#124	—	2	3	no	—
74	C₁₃×#124	—	2	3	no	—
75	C₁₃×#124	C₂³	1	3	yes	—
76	C₁₃×#123	—	2	3	no	—
77	C₁₃×#123	—	2	6	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×C₂²⋊Q₈	—	2	6	no	—
80	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×#121	—	2	3	no	—
82	C₁₃×#121	—	2	3	no	—
83	C₁₃×#121	C₂³	1	3	yes	—
84	C₄×Q₈×C₁₃	—	2	6	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	3	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	D₄	1	3	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	C₂³	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	6	yes	—
101	C₁₃×#117	—	2	3	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	—	2	3	no	—
109	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
110	C₁₃×#107	C₂³	1	6	yes	—
111	C₁₃×#106	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₃×#103	C₂³	1	6	yes	—
115	C₁₃×#103	C₂³	1	2	yes	—
116	C₁₃×#103	C₂³	1	6	yes	—
117	C₁₃×#103	C₂³	1	12	yes	—
118	C₁₃×#102	C₂³	1	6	yes	—
119	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
121	C₁₃×#97	C₂³	1	6	yes	—
122	C₄×C₈×C₁₃	C₂³	1	6	yes	—
123	#61906	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₁₃×#41	—	4	4	no	—
125	C₁₃×#41	—	8	6	no	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	3	no	—
128	C₂×Q₈×C₁₃	—	2	3	no	—
129	C₂×Q₈×C₁₃	—	4	6	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
133	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₁₃	—	2	3	no	—
135	C₂×D₄×C₁₃	—	2	3	no	—
136	C₂×D₄×C₁₃	—	2	3	no	—
137	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	3	no	—
140	C₂²×C₄×C₁₃	—	2	3	no	—
141	C₂²×C₄×C₁₃	—	2	6	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₁₃×Q₁₆	—	4	6	no	—
146	C₁₃×SD₁₆	—	4	6	no	—
147	C₁₃×SD₁₆	—	4	12	no	—
148	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
149	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
150	C₁₃×C₄⋊C₄	—	2	3	no	—
151	C₁₃×C₄⋊C₄	—	2	3	no	—
152	C₁₃×C₄⋊C₄	—	2	6	no	—
153	C₁₃×C₄⋊C₄	—	2	6	no	—
154	C₁₃×C₄⋊C₄	—	2	6	no	—
155	C₁₃×C₄⋊C₄	—	2	6	no	—
156	C₁₃×C₄⋊C₄	—	2	6	no	—
157	C₁₃×C₄⋊C₄	—	2	6	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	3	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
168	C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₁₃×C₂²⋊C₄	—	2	3	no	—
170	C₁₃×C₂²⋊C₄	—	2	3	no	—
171	C₁₃×C₂²⋊C₄	—	2	3	no	—
172	C₁₃×C₂²⋊C₄	—	2	3	no	—
173	C₁₃×C₂²⋊C₄	—	2	6	no	—
174	C₄²×C₁₃	—	2	6	no	—
175	C₄²×C₁₃	—	2	6	no	—
176	C₄²×C₁₃	—	2	3	no	—
177	C₄²×C₁₃	C₂×D₄	1	3	yes	—
178	C₄²×C₁₃	C₂×D₄	1	3	yes	—
179	C₄²×C₁₃	C₂⁴	1	3	yes	—
180	C₄²×C₁₃	C₂⁴	1	3	yes	—
181	#3522	C₂×C₁₃	1	1	yes	characteristic
182	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3400	C₂×C₁₃	1	6	yes	complemented
184	#3392	C₂×C₁₃	1	2	yes	complemented
185	#3372	C₂×C₁₃	1	6	yes	complemented
186	#3363	C₂×C₁₃	1	2	yes	complemented
187	#3218	C₂×C₁₃	1	3	yes	complemented
188	#3206	C₂×C₁₃	1	3	yes	complemented
189	#3112	C₂×C₁₃	1	3	yes	complemented
190	#3108	C₂×C₁₃	1	3	yes	complemented
191	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	3	no	—
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	6	no	—
195	Q₈×C₁₃	—	2	6	no	—
196	Q₈×C₁₃	—	2	6	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	4	6	no	—
199	Q₈×C₁₃	—	8	3	no	—
200	Q₈×C₁₃	#137	1	4	yes	—
201	D₄×C₁₃	—	2	6	no	—
202	D₄×C₁₃	—	4	6	no	—
203	D₄×C₁₃	—	4	6	no	—
204	D₄×C₁₃	—	8	3	no	—
205	C₂×C₄×C₁₃	—	2	6	no	—
206	C₂×C₄×C₁₃	—	2	6	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	6	no	—
211	C₂×C₄×C₁₃	—	2	3	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	4	6	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	6	no	—
216	C₂×C₄×C₁₃	—	8	6	no	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
222	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
223	C₈×C₁₃	—	2	2	no	—
224	C₈×C₁₃	—	2	6	no	—
225	#559	C₂²×C₁₃	1	3	yes	—
226	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
227	#557	—	2	1	no	—
228	#557	—	2	3	no	—
229	#557	C₂²×C₁₃	1	2	yes	—
230	#557	C₂²×C₁₃	1	6	yes	—
231	#554	C₂²×C₁₃	1	3	yes	—
232	#550	C₂²×C₁₃	1	1	yes	characteristic
233	#548	—	2	1	no	—
234	#547	—	2	3	no	—
235	#542	—	2	3	no	—
236	#532	C₂²×C₁₃	1	3	yes	—
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
238	#529	C₂²×C₁₃	1	3	yes	—
239	C₂×#125	—	2	3	no	—
240	#520	—	2	1	no	—
241	C₂×C₄×Q₈	—	2	1	no	—
242	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	#497	C₂²×C₁₃	1	6	yes	—
245	#492	C₂²×C₁₃	1	6	yes	—
246	#491	C₂²×C₁₃	1	6	yes	—
247	#487	C₂²×C₁₃	1	6	yes	—
248	#483	C₂²×C₁₃	1	1	yes	characteristic
249	#480	C₂²×C₁₃	1	3	yes	—
250	#479	C₂²×C₁₃	1	6	yes	—
251	#477	C₂²×C₁₃	1	6	yes	—
252	#464	C₂²×C₁₃	1	6	yes	—
253	#462	C₂²×C₁₃	1	6	yes	—
254	#461	C₂²×C₁₃	1	6	yes	—
255	#461	C₂²×C₁₃	1	12	yes	—
256	#460	C₂²×C₁₃	1	6	yes	—
257	#451	C₂²×C₁₃	1	3	yes	—
258	#448	C₂²×C₁₃	1	3	yes	—
259	#448	C₂²×C₁₃	1	6	yes	—
260	#446	C₂²×C₁₃	1	6	yes	—
261	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
262	#440	C₂²×C₁₃	1	12	yes	—
263	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
264	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
265	#432	C₂²×C₁₃	1	3	yes	—
266	#431	C₂²×C₁₃	1	3	yes	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	4	3	no	—
270	C₂²×C₁₃	—	4	3	no	—
271	C₂²×C₁₃	—	4	3	no	—
272	C₂²×C₁₃	#577	1	2	yes	—
273	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	2	3	no	—
276	C₄×C₁₃	—	2	3	no	—
277	C₄×C₁₃	—	2	3	no	—
278	C₄×C₁₃	—	4	6	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	3	no	—
283	C₄×C₁₃	C₂×#137	1	6	yes	—
284	C₄×C₁₃	#585	1	2	yes	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	3	no	—
287	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
289	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
290	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
291	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
292	C₄⋊Q₈	—	2	3	no	—
293	C₄⋊Q₈	—	2	3	no	—
294	C₄⋊Q₈	—	2	3	no	—
295	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
296	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
297	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
298	#127	C₂³×C₁₃	1	3	yes	—
299	#126	—	2	3	no	—
300	#125	—	2	6	no	—
301	#125	—	2	6	no	—
302	#125	—	2	12	no	—
303	#125	C₂³×C₁₃	1	3	yes	—
304	#124	—	2	3	no	—
305	#124	—	2	3	no	—
306	#124	C₂³×C₁₃	1	3	yes	—
307	#123	—	2	3	no	—
308	#123	—	2	6	no	—
309	C₂²⋊Q₈	—	2	3	no	—
310	C₂²⋊Q₈	—	2	6	no	—
311	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
312	#121	—	2	3	no	—
313	#121	—	2	3	no	—
314	#121	C₂³×C₁₃	1	3	yes	—
315	C₄×Q₈	—	2	6	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	3	no	—
319	C₄×Q₈	—	2	3	no	—
320	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
321	C₄×Q₈	D₄×C₁₃	1	3	yes	—
322	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
323	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
324	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
325	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
326	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
327	C₄×D₄	—	2	3	no	—
328	C₄×D₄	—	2	3	no	—
329	C₄×D₄	—	2	3	no	—
330	C₄×D₄	C₂³×C₁₃	1	3	yes	—
331	C₄×D₄	C₂³×C₁₃	1	6	yes	—
332	#117	—	2	3	no	—
333	C₂×C₄⋊C₄	—	2	3	no	—
334	C₂×C₄⋊C₄	—	2	3	no	—
335	C₂×C₄⋊C₄	—	2	3	no	—
336	C₂×C₄⋊C₄	—	2	3	no	—
337	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	—	2	3	no	—
340	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
341	#107	C₂³×C₁₃	1	6	yes	—
342	#106	C₂³×C₁₃	1	2	yes	—
343	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
344	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
345	#103	C₂³×C₁₃	1	6	yes	—
346	#103	C₂³×C₁₃	1	2	yes	—
347	#103	C₂³×C₁₃	1	6	yes	—
348	#103	C₂³×C₁₃	1	12	yes	—
349	#102	C₂³×C₁₃	1	6	yes	—
350	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
352	#97	C₂³×C₁₃	1	6	yes	—
353	C₄×C₈	C₂³×C₁₃	1	6	yes	—
354	C₂×C₁₃	—	2	2	no	—
355	C₂×C₁₃	—	8	3	no	—
356	C₂×C₁₃	#3487	1	1	yes	characteristic
357	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
358	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
359	#41	—	4	4	no	—
360	#41	—	8	6	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	3	no	—
363	C₂×Q₈	—	2	3	no	—
364	C₂×Q₈	—	4	6	no	—
365	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
366	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
368	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
369	C₂×D₄	—	2	3	no	—
370	C₂×D₄	—	2	3	no	—
371	C₂×D₄	—	2	3	no	—
372	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	3	no	—
375	C₂²×C₄	—	2	3	no	—
376	C₂²×C₄	—	2	6	no	—
377	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
380	Q₁₆	—	4	6	no	—
381	SD₁₆	—	4	6	no	—
382	SD₁₆	—	4	12	no	—
383	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
384	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
385	C₄⋊C₄	—	2	3	no	—
386	C₄⋊C₄	—	2	3	no	—
387	C₄⋊C₄	—	2	6	no	—
388	C₄⋊C₄	—	2	6	no	—
389	C₄⋊C₄	—	2	6	no	—
390	C₄⋊C₄	—	2	6	no	—
391	C₄⋊C₄	—	2	6	no	—
392	C₄⋊C₄	—	2	6	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	3	no	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
400	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	3	no	—
405	C₂²⋊C₄	—	2	3	no	—
406	C₂²⋊C₄	—	2	3	no	—
407	C₂²⋊C₄	—	2	3	no	—
408	C₂²⋊C₄	—	2	6	no	—
409	C₄²	—	2	6	no	—
410	C₄²	—	2	6	no	—
411	C₄²	—	2	3	no	—
412	C₄²	C₂×D₄×C₁₃	1	3	yes	—
413	C₄²	C₂×D₄×C₁₃	1	3	yes	—
414	C₄²	C₂⁴×C₁₃	1	3	yes	—
415	C₄²	C₂⁴×C₁₃	1	3	yes	—
416	C₁₃	#61906	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	3	no	—
418	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	Q₈	—	2	6	no	—
420	Q₈	—	2	6	no	—
421	Q₈	—	2	6	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	4	6	no	—
424	Q₈	—	8	3	no	—
425	Q₈	C₁₃×#137	1	4	yes	—
426	D₄	—	2	6	no	—
427	D₄	—	4	6	no	—
428	D₄	—	4	6	no	—
429	D₄	—	8	3	no	—
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	2	6	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	6	no	—
436	C₂×C₄	—	2	3	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	6	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	6	no	—
441	C₂×C₄	—	8	6	no	—
442	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
447	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	6	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	4	3	no	—
453	C₂²	—	4	3	no	—
454	C₂²	—	4	3	no	—
455	C₂²	C₁₃×#577	1	2	yes	—
456	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
457	C₄	—	2	3	no	—
458	C₄	—	2	3	no	—
459	C₄	—	2	3	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	3	no	—
464	C₄	—	4	6	no	—
465	C₄	—	4	1	no	—
466	C₄	C₂×C₁₃×#137	1	6	yes	—
467	C₄	C₁₃×#585	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	8	3	no	—
470	C₂	C₁₃×#3487	1	1	yes	characteristic
471	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
472	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3392	C₂	semidirect
5. C₁₃×#3372	C₂	semidirect
6. C₁₃×#3363	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3112	C₂	semidirect
10. C₁₃×#3108	C₂	semidirect
11. C₁₃×#2984	C₂	semidirect
123. #61906	C₁₃	direct (N × H)
182. C₂×#557	C₂×C₁₃	semidirect
183. #3400	C₂×C₁₃	semidirect
184. #3392	C₂×C₁₃	semidirect
185. #3372	C₂×C₁₃	semidirect
186. #3363	C₂×C₁₃	semidirect
187. #3218	C₂×C₁₃	semidirect
188. #3206	C₂×C₁₃	semidirect
189. #3112	C₂×C₁₃	semidirect
190. #3108	C₂×C₁₃	semidirect
191. #2984	C₂×C₁₃	semidirect
416. C₁₃	#61906	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×#3522	2
C₂×C₁₃×#557	2
C₁₃×#3400	2
C₁₃×#3392	2
C₁₃×#3372	2
C₁₃×#3363	2
C₁₃×#3218	2
C₁₃×#3206	2
C₁₃×#3112	2
C₁₃×#3108	2
C₁₃×#2984	2
#61906	13

Subgroups — C13×#61906 #15748245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61906 #15748245