Subgroups — C₁₃×#61935 #15748274

Order 3328.

1746 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×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3392	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3372	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3360	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3221	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3126	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#562	—	2	2	no	—
13	C₁₃×#557	C₂²	1	4	yes	—
14	C₁₃×#556	C₂²	1	4	yes	—
15	C₁₃×#554	C₂²	1	4	yes	—
16	C₁₃×#552	—	2	4	no	—
17	C₁₃×#550	C₂²	1	4	yes	—
18	C₁₃×#547	—	2	2	no	—
19	C₁₃×#541	—	2	2	no	—
20	C₁₃×#540	C₂²	1	4	yes	—
21	C₁₃×#537	—	2	4	no	—
22	C₁₃×#536	C₂²	1	2	yes	—
23	C₁₃×#533	—	2	2	no	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#532	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₃×#519	C₂²	1	2	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#496	C₂²	1	4	yes	—
30	C₁₃×#492	C₂²	1	4	yes	—
31	C₁₃×#492	C₂²	1	4	yes	—
32	C₁₃×#491	C₂²	1	4	yes	—
33	C₁₃×#488	C₂²	1	4	yes	—
34	C₁₃×#487	C₂²	1	4	yes	—
35	C₁₃×#482	C₂²	1	4	yes	—
36	C₁₃×#479	C₂²	1	8	yes	—
37	C₁₃×#477	C₂²	1	2	yes	—
38	C₁₃×#476	C₂²	1	2	yes	—
39	C₁₃×#463	C₂²	1	8	yes	—
40	C₁₃×#461	C₂²	1	4	yes	—
41	C₁₃×#461	C₂²	1	8	yes	—
42	C₁₃×#461	C₂²	1	4	yes	—
43	C₁₃×#460	C₂²	1	2	yes	—
44	C₁₃×#460	C₂²	1	8	yes	—
45	C₁₃×#459	C₂²	1	2	yes	—
46	C₁₃×#449	C₂²	1	4	yes	—
47	C₁₃×#448	C₂²	1	8	yes	—
48	C₁₃×#446	C₂²	1	4	yes	—
49	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
50	C₁₃×#440	C₂²	1	8	yes	—
51	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
52	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
53	C₄×C₁₃×D₈	C₂²	1	4	yes	—
54	C₁₃×#433	C₂²	1	4	yes	—
55	C₁₃×#431	C₂²	1	2	yes	—
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	—	2	2	no	—
58	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
63	C₂×C₁₃×D₈	C₂³	1	4	yes	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×#127	C₂³	1	2	yes	—
71	C₁₃×#127	C₂³	1	4	yes	—
72	C₁₃×#126	—	2	8	no	—
73	C₁₃×#125	—	2	4	no	—
74	C₁₃×#125	—	2	8	no	—
75	C₁₃×#125	D₄	1	2	yes	—
76	C₁₃×#125	C₂³	1	4	yes	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	C₂³	1	4	yes	—
79	C₁₃×#123	—	2	8	no	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	4	no	—
88	C₁₃×#121	—	2	8	no	—
89	C₁₃×#121	—	2	8	no	—
90	C₁₃×#121	C₂³	1	4	yes	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	—	2	4	no	—
93	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	C₂³	1	2	yes	—
99	C₄×D₄×C₁₃	C₂³	1	4	yes	—
100	C₄×D₄×C₁₃	C₂³	1	8	yes	—
101	C₁₃×#117	—	2	4	no	—
102	C₁₃×#117	—	2	4	no	—
103	C₁₃×#117	—	2	1	no	—
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₁₃×#117	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#107	C₂³	1	4	yes	—
111	C₁₃×#106	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
115	C₁₃×#103	C₂³	1	8	yes	—
116	C₁₃×#103	C₂³	1	4	yes	—
117	C₁₃×#103	C₂³	1	8	yes	—
118	C₁₃×#102	C₂³	1	4	yes	—
119	C₁₃×#102	C₂³	1	4	yes	—
120	C₁₃×#102	C₂³	1	4	yes	—
121	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₁₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	#61935	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₁₃×#41	—	4	2	no	—
127	C₁₃×#41	—	8	4	no	—
128	C₁₃×#41	—	8	8	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	4	4	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
133	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
134	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	8	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×SD₁₆	—	4	8	no	—
150	C₁₃×SD₁₆	—	4	8	no	—
151	C₁₃×SD₁₆	—	4	4	no	—
152	C₁₃×D₈	—	4	4	no	—
153	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
154	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
167	C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂⁴	1	2	yes	—
180	C₄²×C₁₃	C₂⁴	1	4	yes	—
181	#3548	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3397	C₂×C₁₃	1	4	yes	complemented
184	#3392	C₂×C₁₃	1	4	yes	complemented
185	#3372	C₂×C₁₃	1	4	yes	complemented
186	#3360	C₂×C₁₃	1	4	yes	complemented
187	#3221	C₂×C₁₃	1	4	yes	complemented
188	#3206	C₂×C₁₃	1	2	yes	complemented
189	#3126	C₂×C₁₃	1	4	yes	complemented
190	#3106	C₂×C₁₃	1	2	yes	complemented
191	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₃	—	2	8	no	—
196	Q₈×C₁₃	—	2	8	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	Q₈×C₁₃	—	8	2	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	2	4	no	—
202	D₄×C₁₃	—	2	4	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	4	4	no	—
205	D₄×C₁₃	—	8	2	no	—
206	D₄×C₁₃	—	8	8	no	—
207	D₄×C₁₃	—	8	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	4	8	no	—
218	C₂×C₄×C₁₃	—	8	8	no	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
224	C₈×C₁₃	—	2	4	no	—
225	C₈×C₁₃	—	2	4	no	—
226	#562	—	2	2	no	—
227	#557	C₂²×C₁₃	1	4	yes	—
228	#556	C₂²×C₁₃	1	4	yes	—
229	#554	C₂²×C₁₃	1	4	yes	—
230	#552	—	2	4	no	—
231	#550	C₂²×C₁₃	1	4	yes	—
232	#547	—	2	2	no	—
233	#541	—	2	2	no	—
234	#540	C₂²×C₁₃	1	4	yes	—
235	#537	—	2	4	no	—
236	#536	C₂²×C₁₃	1	2	yes	—
237	#533	—	2	2	no	—
238	#533	C₂²×C₁₃	1	1	yes	characteristic
239	#532	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	#519	C₂²×C₁₃	1	2	yes	—
242	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
243	#496	C₂²×C₁₃	1	4	yes	—
244	#492	C₂²×C₁₃	1	4	yes	—
245	#492	C₂²×C₁₃	1	4	yes	—
246	#491	C₂²×C₁₃	1	4	yes	—
247	#488	C₂²×C₁₃	1	4	yes	—
248	#487	C₂²×C₁₃	1	4	yes	—
249	#482	C₂²×C₁₃	1	4	yes	—
250	#479	C₂²×C₁₃	1	8	yes	—
251	#477	C₂²×C₁₃	1	2	yes	—
252	#476	C₂²×C₁₃	1	2	yes	—
253	#463	C₂²×C₁₃	1	8	yes	—
254	#461	C₂²×C₁₃	1	4	yes	—
255	#461	C₂²×C₁₃	1	8	yes	—
256	#461	C₂²×C₁₃	1	4	yes	—
257	#460	C₂²×C₁₃	1	2	yes	—
258	#460	C₂²×C₁₃	1	8	yes	—
259	#459	C₂²×C₁₃	1	2	yes	—
260	#449	C₂²×C₁₃	1	4	yes	—
261	#448	C₂²×C₁₃	1	8	yes	—
262	#446	C₂²×C₁₃	1	4	yes	—
263	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
264	#440	C₂²×C₁₃	1	8	yes	—
265	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
266	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
267	C₄×D₈	C₂²×C₁₃	1	4	yes	—
268	#433	C₂²×C₁₃	1	4	yes	—
269	#431	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	4	no	—
277	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	8	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	#577	1	4	yes	—
286	C₄×C₁₃	#585	1	2	yes	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	—	2	2	no	—
289	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
291	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
292	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
293	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
294	C₂×D₈	C₂³×C₁₃	1	4	yes	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
298	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
299	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
300	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
301	#127	C₂³×C₁₃	1	2	yes	—
302	#127	C₂³×C₁₃	1	4	yes	—
303	#126	—	2	8	no	—
304	#125	—	2	4	no	—
305	#125	—	2	8	no	—
306	#125	D₄×C₁₃	1	2	yes	—
307	#125	C₂³×C₁₃	1	4	yes	—
308	#124	—	2	2	no	—
309	#124	C₂³×C₁₃	1	4	yes	—
310	#123	—	2	8	no	—
311	#123	—	2	4	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
317	#121	—	2	2	no	—
318	#121	—	2	4	no	—
319	#121	—	2	8	no	—
320	#121	—	2	8	no	—
321	#121	C₂³×C₁₃	1	4	yes	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	4	no	—
324	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
325	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
326	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	C₂³×C₁₃	1	2	yes	—
330	C₄×D₄	C₂³×C₁₃	1	4	yes	—
331	C₄×D₄	C₂³×C₁₃	1	8	yes	—
332	#117	—	2	4	no	—
333	#117	—	2	4	no	—
334	#117	—	2	1	no	—
335	#117	C₂³×C₁₃	1	1	yes	characteristic
336	#117	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	#107	C₂³×C₁₃	1	4	yes	—
342	#106	C₂³×C₁₃	1	4	yes	—
343	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
344	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
345	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
346	#103	C₂³×C₁₃	1	8	yes	—
347	#103	C₂³×C₁₃	1	4	yes	—
348	#103	C₂³×C₁₃	1	8	yes	—
349	#102	C₂³×C₁₃	1	4	yes	—
350	#102	C₂³×C₁₃	1	4	yes	—
351	#102	C₂³×C₁₃	1	4	yes	—
352	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
353	#97	C₂³×C₁₃	1	4	yes	—
354	C₄×C₈	C₂³×C₁₃	1	4	yes	—
355	C₄×C₈	C₂³×C₁₃	1	4	yes	—
356	C₂×C₁₃	—	4	1	no	—
357	C₂×C₁₃	—	8	1	no	—
358	C₂×C₁₃	—	8	4	no	—
359	C₂×C₁₃	#3487	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#577	1	2	yes	—
361	#41	—	4	2	no	—
362	#41	—	8	4	no	—
363	#41	—	8	8	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
368	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
369	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
376	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
384	SD₁₆	—	4	8	no	—
385	SD₁₆	—	4	8	no	—
386	SD₁₆	—	4	4	no	—
387	D₈	—	4	4	no	—
388	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
389	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
400	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	8	no	—
412	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₄²	C₂⁴×C₁₃	1	2	yes	—
415	C₄²	C₂⁴×C₁₃	1	4	yes	—
416	C₁₃	#61935	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	1	no	—
418	C₂³	—	2	4	no	—
419	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	Q₈	—	2	8	no	—
421	Q₈	—	2	8	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	8	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	8	no	—
432	D₄	—	8	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
448	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	2	4	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	4	no	—
458	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	8	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	4	no	—
466	C₄	C₁₃×#577	1	4	yes	—
467	C₄	C₁₃×#585	1	2	yes	—
468	C₂	—	4	1	no	—
469	C₂	—	8	4	no	—
470	C₂	—	8	1	no	—
471	C₂	C₁₃×#3487	1	1	yes	characteristic
472	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3548	C₂	semidirect
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3392	C₂	semidirect
5. C₁₃×#3372	C₂	semidirect
6. C₁₃×#3360	C₂	semidirect
7. C₁₃×#3221	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3126	C₂	semidirect
10. C₁₃×#3106	C₂	semidirect
11. C₁₃×#2986	C₂	semidirect
125. #61935	C₁₃	direct (N × H)
181. #3548	C₂×C₁₃	semidirect
182. #3509	C₂×C₁₃	semidirect
183. #3397	C₂×C₁₃	semidirect
184. #3392	C₂×C₁₃	semidirect
185. #3372	C₂×C₁₃	semidirect
186. #3360	C₂×C₁₃	semidirect
187. #3221	C₂×C₁₃	semidirect
188. #3206	C₂×C₁₃	semidirect
189. #3126	C₂×C₁₃	semidirect
190. #3106	C₂×C₁₃	semidirect
191. #2986	C₂×C₁₃	semidirect
416. C₁₃	#61935	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×#3548	2
C₁₃×#3509	2
C₁₃×#3397	2
C₁₃×#3392	2
C₁₃×#3372	2
C₁₃×#3360	2
C₁₃×#3221	2
C₁₃×#3206	2
C₁₃×#3126	2
C₁₃×#3106	2
C₁₃×#2986	2
#61935	13

Subgroups — C13×#61935 #15748274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61935 #15748274