Subgroups — C₁₃×#21140 #15707479

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1929	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1922	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1876	C₂	1	2	yes	maximal
7	C₁₃×#1866	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×Q₁₆	C₄	1	2	yes	complemented
17	C₄×C₁₃×SD₁₆	C₄	1	2	yes	complemented
18	C₄×C₁₃×SD₁₆	C₄	1	2	yes	complemented
19	C₄×C₁₃×D₈	C₄	1	2	yes	complemented
20	C₁₃×#433	—	2	2	no	—
21	C₁₃×#432	—	2	1	no	—
22	C₁₃×#432	—	2	1	no	—
23	C₂×C₁₃×#108	C₂²	1	2	yes	—
24	C₁₃×#427	C₂²	1	1	yes	characteristic
25	C₁₃×#424	C₂²	1	2	yes	—
26	C₂×C₁₃×#104	C₂²	1	2	yes	—
27	C₂×C₁₃×#104	C₂²	1	2	yes	—
28	C₁₃×#416	C₂²	1	1	yes	characteristic
29	C₁₃×#416	C₂²	1	1	yes	characteristic
30	C₁₃×#408	C₂²	1	2	yes	—
31	C₁₃×#405	—	2	2	no	—
32	C₁₃×#405	C₂²	1	2	yes	—
33	C₄×C₁₃×M₁₆	—	2	1	no	—
34	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#97	—	2	1	no	—
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#376	C₂²	1	1	yes	characteristic
40	C₁₃×#341	C₂²	1	2	yes	—
41	C₁₃×#339	C₂²	1	2	yes	—
42	C₁₃×#339	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
47	C₁₃×#135	—	2	4	no	—
48	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×#131	—	2	4	no	—
53	C₁₃×#131	—	2	4	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	—	2	1	no	—
69	C₁₃×#117	C₂³	1	1	yes	characteristic
70	C₁₃×#117	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#108	—	2	4	no	—
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#104	—	2	4	no	—
81	C₁₃×#104	—	2	4	no	—
82	C₁₃×#103	C₂×C₄	1	2	yes	—
83	C₁₃×#103	C₂×C₄	1	2	yes	—
84	C₁₃×#102	C₂×C₄	1	2	yes	—
85	C₁₃×#102	C₂×C₄	1	2	yes	—
86	C₁₃×C₂²⋊C₈	—	2	2	no	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×#97	—	2	2	no	—
89	C₁₃×#97	—	2	1	no	—
90	C₁₃×#97	—	2	1	no	—
91	C₁₃×#97	D₄	1	1	yes	characteristic
92	C₁₃×#97	D₄	1	1	yes	characteristic
93	C₁₃×#97	D₄	1	2	yes	—
94	C₄×C₈×C₁₃	—	2	2	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	C₄×C₈×C₁₃	—	2	1	no	—
97	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
98	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
99	C₁₃×#95	—	2	2	no	—
100	#21140	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	#41	1	4	yes	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	#41	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×Q₁₆	—	2	2	no	—
119	C₁₃×SD₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	2	2	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×M₁₆	—	2	8	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	#41	1	4	yes	—
127	C₂×C₈×C₁₃	—	2	8	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	2	no	—
146	C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
157	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1929	C₂×C₁₃	1	2	yes	complemented
160	#1922	C₂×C₁₃	1	2	yes	complemented
161	#1876	C₂×C₁₃	1	2	yes	—
162	#1866	C₂×C₁₃	1	2	yes	complemented
163	C₄×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1759	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1759	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1746	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	1	no	—
171	Q₈×C₁₃	—	2	1	no	—
172	Q₈×C₁₃	—	2	1	no	—
173	Q₈×C₁₃	#117	1	2	yes	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	2	1	no	—
176	D₄×C₁₃	—	2	1	no	—
177	D₄×C₁₃	—	2	1	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	#117	1	2	yes	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	8	2	no	—
190	C₂×C₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
196	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	2	4	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	4	2	no	—
204	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#131	C₂²×C₁₃	1	2	yes	—
206	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
207	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
208	C₄×Q₁₆	C₄×C₁₃	1	2	yes	complemented
209	C₄×SD₁₆	C₄×C₁₃	1	2	yes	complemented
210	C₄×SD₁₆	C₄×C₁₃	1	2	yes	complemented
211	C₄×D₈	C₄×C₁₃	1	2	yes	complemented
212	#433	—	2	2	no	—
213	#432	—	2	1	no	—
214	#432	—	2	1	no	—
215	C₂×#108	C₂²×C₁₃	1	2	yes	—
216	#427	C₂²×C₁₃	1	1	yes	characteristic
217	#424	C₂²×C₁₃	1	2	yes	—
218	C₂×#104	C₂²×C₁₃	1	2	yes	—
219	C₂×#104	C₂²×C₁₃	1	2	yes	—
220	#416	C₂²×C₁₃	1	1	yes	characteristic
221	#416	C₂²×C₁₃	1	1	yes	characteristic
222	#408	C₂²×C₁₃	1	2	yes	—
223	#405	—	2	2	no	—
224	#405	C₂²×C₁₃	1	2	yes	—
225	C₄×M₁₆	—	2	1	no	—
226	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#97	—	2	1	no	—
229	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	#376	C₂²×C₁₃	1	1	yes	characteristic
232	#341	C₂²×C₁₃	1	2	yes	—
233	#339	C₂²×C₁₃	1	2	yes	—
234	#339	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	2	yes	—
236	#336	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₁₃	#529	1	2	yes	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
252	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
253	C₄×C₁₃	#525	1	2	yes	—
254	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
256	#135	—	2	4	no	—
257	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
259	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
261	#131	—	2	4	no	—
262	#131	—	2	4	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
271	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
275	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
276	#117	—	2	1	no	—
277	#117	—	2	1	no	—
278	#117	C₂³×C₁₃	1	1	yes	characteristic
279	#117	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
284	#108	—	2	4	no	—
285	#107	C₂×C₄×C₁₃	1	2	yes	—
286	#106	C₂×C₄×C₁₃	1	2	yes	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	#104	—	2	4	no	—
290	#104	—	2	4	no	—
291	#103	C₂×C₄×C₁₃	1	2	yes	—
292	#103	C₂×C₄×C₁₃	1	2	yes	—
293	#102	C₂×C₄×C₁₃	1	2	yes	—
294	#102	C₂×C₄×C₁₃	1	2	yes	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	#97	—	2	2	no	—
298	#97	—	2	1	no	—
299	#97	—	2	1	no	—
300	#97	D₄×C₁₃	1	1	yes	characteristic
301	#97	D₄×C₁₃	1	1	yes	characteristic
302	#97	D₄×C₁₃	1	2	yes	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
307	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
308	#95	—	2	2	no	—
309	C₂×C₁₃	—	2	2	no	—
310	C₂×C₁₃	—	4	2	no	—
311	C₂×C₁₃	—	8	1	no	—
312	C₂×C₁₃	#2290	1	1	yes	characteristic
313	C₂×C₁₃	#2957	1	2	yes	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	C₁₃×#41	1	4	yes	—
318	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
319	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
323	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₁₃×#41	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
331	Q₁₆	—	2	2	no	—
332	SD₁₆	—	2	2	no	—
333	SD₁₆	—	2	2	no	—
334	D₈	—	2	2	no	—
335	M₁₆	—	2	8	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	C₁₃×#41	1	4	yes	—
340	C₂×C₈	—	2	8	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
348	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
349	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
355	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
367	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₁₃	#21140	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	C₁₃×#117	1	2	yes	—
377	D₄	—	2	4	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	C₁₃×#117	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
395	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
399	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
400	C₈	—	2	1	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	2	no	—
403	C₈	—	2	2	no	—
404	C₈	—	2	4	no	—
405	C₈	—	2	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
413	C₂²	C₁₃×#529	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
422	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
423	C₄	C₁₃×#525	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	C₁₃×#2290	1	1	yes	characteristic
428	C₂	C₁₃×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2923	C₂	semidirect
3. C₁₃×#2875	C₂	semidirect
4. C₁₃×#1929	C₂	semidirect
5. C₁₃×#1922	C₂	semidirect
7. C₁₃×#1866	C₂	semidirect
8. C₄×C₁₃×#108	C₂	semidirect
9. C₁₃×#1759	C₂	semidirect
10. C₁₃×#1759	C₂	semidirect
11. C₁₃×#1746	C₂	semidirect
16. C₄×C₁₃×Q₁₆	C₄	semidirect
17. C₄×C₁₃×SD₁₆	C₄	semidirect
18. C₄×C₁₃×SD₁₆	C₄	semidirect
19. C₄×C₁₃×D₈	C₄	semidirect
100. #21140	C₁₃	direct (N × H)
157. #2923	C₂×C₁₃	semidirect
158. #2875	C₂×C₁₃	semidirect
159. #1929	C₂×C₁₃	semidirect
160. #1922	C₂×C₁₃	semidirect
162. #1866	C₂×C₁₃	semidirect
163. C₄×#108	C₂×C₁₃	semidirect
164. #1759	C₂×C₁₃	semidirect
165. #1759	C₂×C₁₃	semidirect
166. #1746	C₂×C₁₃	semidirect
208. C₄×Q₁₆	C₄×C₁₃	semidirect
209. C₄×SD₁₆	C₄×C₁₃	semidirect
210. C₄×SD₁₆	C₄×C₁₃	semidirect
211. C₄×D₈	C₄×C₁₃	semidirect
369. C₁₃	#21140	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#135	2
C₁₃×#2923	2
C₁₃×#2875	2
C₁₃×#1929	2
C₁₃×#1922	2
C₁₃×#1876	2
C₁₃×#1866	2
C₄×C₁₃×#108	2
C₁₃×#1759	2
C₁₃×#1746	2
#21140	13

Subgroups — C13×#21140 #15707479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21140 #15707479