Subgroups — C₁₃×#18655 #15704994

Order 3328.

884 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1653	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1652	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#557	—	2	1	no	—
11	C₁₃×#557	C₂²	1	2	yes	—
12	C₁₃×#556	—	2	1	no	—
13	C₁₃×#556	C₂²	1	2	yes	—
14	C₁₃×#552	—	2	2	no	—
15	C₁₃×#552	—	2	2	no	—
16	C₁₃×#541	—	2	2	no	—
17	C₁₃×#536	—	2	1	no	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₃×#519	—	2	1	no	—
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#498	—	2	2	no	—
26	C₁₃×#498	C₂²	1	4	yes	—
27	C₁₃×#494	—	2	1	no	—
28	C₁₃×#487	—	2	1	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#475	C₂²	1	2	yes	—
32	C₁₃×#474	C₂²	1	2	yes	—
33	C₁₃×#462	C₂²	1	4	yes	—
34	C₁₃×#451	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#428	—	2	1	no	—
37	C₂×C₁₃×#106	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#417	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	—	2	4	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₃×#126	—	2	4	no	—
63	C₁₃×#126	—	2	4	no	—
64	C₁₃×#125	—	2	2	no	—
65	C₁₃×#125	—	2	4	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	—	2	4	no	—
68	C₁₃×#125	—	2	1	no	—
69	C₁₃×#124	—	2	2	no	—
70	C₁₃×#123	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×C₂²⋊Q₈	—	2	1	no	—
76	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
77	C₄×Q₈×C₁₃	—	2	2	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
90	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#117	—	2	4	no	—
92	C₁₃×#117	—	2	2	no	—
93	C₁₃×#117	—	2	1	no	—
94	C₁₃×#117	—	2	2	no	—
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	—	2	2	no	—
104	C₁₃×#106	—	2	8	no	—
105	C₁₃×#106	—	2	2	no	—
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	4	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×C₂²⋊C₈	—	2	1	no	—
113	C₄×C₈×C₁₃	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	#18655	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	4	1	no	—
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	—	8	2	no	—
127	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	4	1	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₁₃×Q₁₆	—	8	4	no	—
140	C₁₃×M₁₆	—	4	2	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	4	1	no	—
162	C₁₃×C₄⋊C₄	—	4	1	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	1	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₄²×C₁₃	—	2	4	no	—
174	C₄²×C₁₃	—	2	4	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
183	#3509	C₂×C₁₃	1	1	yes	characteristic
184	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3079	C₂×C₁₃	1	1	yes	characteristic
187	#1653	C₂×C₁₃	1	4	yes	complemented
188	#1652	C₂×C₁₃	1	4	yes	complemented
189	#1546	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1476	C₂×C₁₃	1	1	yes	characteristic
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	#120	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	1	no	—
195	Q₈×C₁₃	—	2	1	no	—
196	Q₈×C₁₃	—	2	4	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	Q₈×C₁₃	—	4	2	no	—
199	Q₈×C₁₃	—	4	4	no	—
200	Q₈×C₁₃	—	4	2	no	—
201	Q₈×C₁₃	—	4	4	no	—
202	Q₈×C₁₃	—	8	2	no	—
203	D₄×C₁₃	—	2	1	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	8	2	no	—
220	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#135	1	2	yes	—
224	C₂×C₄×C₁₃	#137	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₁₃	—	2	4	no	—
229	C₈×C₁₃	—	4	2	no	—
230	C₈×C₁₃	—	4	2	no	—
231	#557	—	2	1	no	—
232	#557	C₂²×C₁₃	1	2	yes	—
233	#556	—	2	1	no	—
234	#556	C₂²×C₁₃	1	2	yes	—
235	#552	—	2	2	no	—
236	#552	—	2	2	no	—
237	#541	—	2	2	no	—
238	#536	—	2	1	no	—
239	#533	—	2	1	no	—
240	#533	—	2	1	no	—
241	#533	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	#519	—	2	1	no	—
245	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
246	#498	—	2	2	no	—
247	#498	C₂²×C₁₃	1	4	yes	—
248	#494	—	2	1	no	—
249	#487	—	2	1	no	—
250	#477	—	2	1	no	—
251	#476	—	2	1	no	—
252	#475	C₂²×C₁₃	1	2	yes	—
253	#474	C₂²×C₁₃	1	2	yes	—
254	#462	C₂²×C₁₃	1	4	yes	—
255	#451	—	2	2	no	—
256	#431	C₂²×C₁₃	1	1	yes	characteristic
257	#428	—	2	1	no	—
258	C₂×#106	—	2	2	no	—
259	#423	C₂²×C₁₃	1	1	yes	characteristic
260	#417	—	2	1	no	—
261	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
262	#332	C₂²×C₁₃	1	4	yes	—
263	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
264	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
265	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	#452	1	2	yes	—
272	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	4	1	no	—
276	C₄×C₁₃	—	4	4	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	8	2	no	—
282	C₄×C₁₃	#452	1	2	yes	—
283	C₄×C₁₃	#456	1	2	yes	—
284	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
285	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
286	C₄×C₁₃	#577	1	2	yes	—
287	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂×Q₁₆	—	2	4	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
300	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
301	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
303	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
304	#126	—	2	4	no	—
305	#126	—	2	4	no	—
306	#125	—	2	2	no	—
307	#125	—	2	4	no	—
308	#125	—	2	2	no	—
309	#125	—	2	4	no	—
310	#125	—	2	1	no	—
311	#124	—	2	2	no	—
312	#123	—	2	4	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
327	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
332	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
333	#117	—	2	4	no	—
334	#117	—	2	2	no	—
335	#117	—	2	1	no	—
336	#117	—	2	2	no	—
337	#117	—	2	1	no	—
338	#117	D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
345	#107	—	2	2	no	—
346	#106	—	2	8	no	—
347	#106	—	2	2	no	—
348	C₄⋊C₈	—	2	1	no	—
349	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
350	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
351	#103	—	2	2	no	—
352	#103	—	2	4	no	—
353	#102	—	2	2	no	—
354	C₂²⋊C₈	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	C₂³×C₁₃	1	2	yes	—
358	C₂×C₁₃	—	2	2	no	—
359	C₂×C₁₃	—	8	1	no	—
360	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
361	C₂×C₁₃	#3010	1	1	yes	characteristic
362	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	1	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	—	8	2	no	—
373	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
385	Q₁₆	—	8	4	no	—
386	M₁₆	—	4	2	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
429	C₁₃	#18655	1	1	yes	characteristic, direct product factor, Sylow
430	C₂³	—	2	1	no	—
431	C₂³	C₁₃×#120	1	1	yes	characteristic
432	Q₈	—	2	1	no	—
433	Q₈	—	2	1	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	4	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	4	no	—
440	Q₈	—	8	2	no	—
441	D₄	—	2	1	no	—
442	D₄	—	2	1	no	—
443	D₄	—	4	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
459	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
460	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
461	C₂×C₄	C₁₃×#135	1	2	yes	—
462	C₂×C₄	C₁₃×#137	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	C₁₃×#452	1	2	yes	—
475	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	4	no	—
484	C₄	—	8	2	no	—
485	C₄	C₁₃×#452	1	2	yes	—
486	C₄	C₁₃×#456	1	2	yes	—
487	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
488	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
489	C₄	C₁₃×#577	1	2	yes	—
490	C₂	—	2	2	no	—
491	C₂	—	8	1	no	—
492	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
493	C₂	C₁₃×#3010	1	1	yes	characteristic
494	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3209	C₂	semidirect
3. C₂×C₁₃×#498	C₂	semidirect
5. C₁₃×#1653	C₂	semidirect
6. C₁₃×#1652	C₂	semidirect
7. C₁₃×#1546	C₂	semidirect
8. C₁₃×#1493	C₂	semidirect
116. #18655	C₁₃	direct (N × H)
184. #3209	C₂×C₁₃	semidirect
185. C₂×#498	C₂×C₁₃	semidirect
187. #1653	C₂×C₁₃	semidirect
188. #1652	C₂×C₁₃	semidirect
189. #1546	C₂×C₁₃	semidirect
190. #1493	C₂×C₁₃	semidirect
429. C₁₃	#18655	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×#3509	2
C₁₃×#3209	2
C₂×C₁₃×#498	2
C₁₃×#3079	2
C₁₃×#1653	2
C₁₃×#1652	2
C₁₃×#1546	2
C₁₃×#1493	2
C₁₃×#1476	2
#18655	13

Subgroups — C13×#18655 #15704994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18655 #15704994