Subgroups — C₁₃×#32946 #15719285

Order 3328.

1294 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#473	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3007	C₂	1	2	yes	maximal
5	C₁₃×#1908	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1901	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1815	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#137	C₂²	1	4	yes	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
12	C₁₃×#568	—	2	8	no	—
13	C₂×C₁₃×#131	—	2	2	no	—
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	—	2	2	no	—
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₁₃×#473	—	2	8	no	—
21	C₁₃×#470	—	2	2	no	—
22	C₁₃×#470	—	2	2	no	—
23	C₁₃×#452	—	2	4	no	—
24	C₁₃×#451	—	2	2	no	—
25	C₁₃×#450	—	2	2	no	—
26	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#417	C₂²	1	4	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#101	C₂²	1	4	yes	complemented
31	C₁₃×#407	C₂²	1	2	yes	—
32	C₁₃×#343	C₂²	1	4	yes	complemented
33	C₁₃×#341	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	4	no	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	D₄	1	2	yes	—
39	C₂×C₁₃×#41	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×#137	—	2	8	no	—
47	C₁₃×#137	—	2	8	no	—
48	C₂×C₁₃×Q₁₆	—	2	4	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	2	4	no	—
51	C₂×C₁₃×SD₁₆	—	2	4	no	—
52	C₁₃×#131	—	2	16	no	—
53	C₁₃×#131	—	2	4	no	—
54	C₁₃×#131	—	2	4	no	—
55	C₁₃×#131	—	2	4	no	—
56	C₁₃×#131	D₄	1	8	yes	—
57	C₂×C₁₃×M₁₆	—	2	16	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	4	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	2	4	no	—
63	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
64	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	—	2	1	no	—
68	C₂²×C₈×C₁₃	—	2	2	no	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₁₃×#108	—	2	4	no	—
80	C₁₃×#106	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#101	—	2	8	no	—
85	C₁₃×C₂²⋊C₈	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	—	2	2	no	—
87	#32946	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	1	no	—
89	C₂⁴×C₁₃	#41	1	1	yes	characteristic
90	C₁₃×#41	—	2	4	no	—
91	C₁₃×#41	—	2	8	no	—
92	C₁₃×#41	—	2	4	no	—
93	C₁₃×#41	—	2	4	no	—
94	C₁₃×#41	—	2	4	no	—
95	C₁₃×#41	—	2	2	no	—
96	C₁₃×#41	—	2	2	no	—
97	C₁₃×#41	C₂×D₄	1	4	yes	—
98	C₁₃×#41	#41	1	4	yes	—
99	C₂×Q₈×C₁₃	—	2	4	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	4	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₃	—	2	8	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	4	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×Q₁₆	—	4	8	no	—
128	C₁₃×Q₁₆	—	4	4	no	—
129	C₁₃×SD₁₆	—	4	8	no	—
130	C₁₃×M₁₆	—	2	4	no	—
131	C₁₃×M₁₆	—	2	8	no	—
132	C₁₃×M₁₆	—	2	2	no	—
133	C₁₃×M₁₆	—	2	4	no	—
134	C₁₃×M₁₆	—	2	8	no	—
135	C₁₃×M₁₆	—	2	4	no	—
136	C₁₃×M₁₆	—	2	4	no	—
137	C₁₃×M₁₆	—	2	4	no	—
138	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
139	C₂×C₈×C₁₃	—	2	4	no	—
140	C₂×C₈×C₁₃	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	8	no	—
144	C₂×C₈×C₁₃	—	2	4	no	—
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	2	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₂×#568	C₂×C₁₃	1	1	yes	characteristic
155	C₂×#473	C₂×C₁₃	1	2	yes	complemented
156	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#3007	C₂×C₁₃	1	2	yes	—
158	#1908	C₂×C₁₃	1	4	yes	complemented
159	#1901	C₂×C₁₃	1	2	yes	complemented
160	#1815	C₂×C₁₃	1	2	yes	complemented
161	#1811	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	8	2	no	—
167	C₂³×C₁₃	#121	1	1	yes	characteristic
168	C₂³×C₁₃	#121	1	1	yes	characteristic
169	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	4	no	—
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	Q₈×C₁₃	—	4	4	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	#121	1	4	yes	—
176	D₄×C₁₃	—	2	8	no	—
177	D₄×C₁₃	—	2	4	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	#121	1	4	yes	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	8	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	8	2	no	—
198	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
204	C₈×C₁₃	—	2	4	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	4	4	no	—
207	C₈×C₁₃	#120	1	4	yes	—
208	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#137	C₂²×C₁₃	1	4	yes	—
210	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	#568	—	2	8	no	—
212	C₂×#131	—	2	2	no	—
213	C₂×#131	C₂²×C₁₃	1	2	yes	—
214	C₂×#131	C₂²×C₁₃	1	2	yes	—
215	C₂²×M₁₆	—	2	2	no	—
216	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
219	#473	—	2	8	no	—
220	#470	—	2	2	no	—
221	#470	—	2	2	no	—
222	#452	—	2	4	no	—
223	#451	—	2	2	no	—
224	#450	—	2	2	no	—
225	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
226	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
227	#417	C₂²×C₁₃	1	4	yes	—
228	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
229	C₂×#101	C₂²×C₁₃	1	4	yes	complemented
230	#407	C₂²×C₁₃	1	2	yes	—
231	#343	C₂²×C₁₃	1	4	yes	complemented
232	#341	C₂²×C₁₃	1	2	yes	complemented
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	8	4	no	—
242	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
243	C₂²×C₁₃	#525	1	2	yes	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	8	2	no	—
248	C₄×C₁₃	—	8	2	no	—
249	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
250	C₄×C₁₃	C₂×#121	1	2	yes	—
251	C₄×C₁₃	#525	1	1	yes	characteristic
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	2	1	no	—
255	C₂×#41	—	2	1	no	—
256	C₂×#41	D₄×C₁₃	1	2	yes	—
257	C₂×#41	C₂³×C₁₃	1	2	yes	—
258	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
259	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
264	#137	—	2	8	no	—
265	#137	—	2	8	no	—
266	C₂×Q₁₆	—	2	4	no	—
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	—	2	4	no	—
269	C₂×SD₁₆	—	2	4	no	—
270	#131	—	2	16	no	—
271	#131	—	2	4	no	—
272	#131	—	2	4	no	—
273	#131	—	2	4	no	—
274	#131	D₄×C₁₃	1	8	yes	—
275	C₂×M₁₆	—	2	16	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	4	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
282	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
283	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
284	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	#108	—	2	4	no	—
298	#106	—	2	2	no	—
299	#103	—	2	4	no	—
300	#103	—	2	4	no	—
301	#102	—	2	4	no	—
302	#101	—	2	8	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂×C₁₃	—	2	2	no	—
306	C₂×C₁₃	—	4	1	no	—
307	C₂×C₁₃	—	4	1	no	—
308	C₂×C₁₃	—	4	4	no	—
309	C₂×C₁₃	#2847	1	1	yes	characteristic
310	C₂×C₁₃	#3069	1	2	yes	—
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₁₃×#41	1	1	yes	characteristic
313	#41	—	2	4	no	—
314	#41	—	2	8	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	2	4	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	C₂×D₄×C₁₃	1	4	yes	—
321	#41	C₁₃×#41	1	4	yes	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
350	Q₁₆	—	4	8	no	—
351	Q₁₆	—	4	4	no	—
352	SD₁₆	—	4	8	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	8	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	4	no	—
357	M₁₆	—	2	8	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	8	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₁₃	#32946	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	8	2	no	—
383	C₂³	C₁₃×#121	1	1	yes	characteristic
384	C₂³	C₁₃×#121	1	1	yes	characteristic
385	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
386	Q₈	—	2	4	no	—
387	Q₈	—	2	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	4	no	—
390	Q₈	—	4	2	no	—
391	Q₈	C₁₃×#121	1	4	yes	—
392	D₄	—	2	8	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	C₁₃×#121	1	4	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
415	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
420	C₈	—	2	4	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	4	no	—
423	C₈	C₁₃×#120	1	4	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	4	no	—
433	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
434	C₂²	C₁₃×#525	1	2	yes	—
435	C₄	—	2	1	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	2	no	—
440	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
441	C₄	C₂×C₁₃×#121	1	2	yes	—
442	C₄	C₁₃×#525	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	4	1	no	—
445	C₂	—	4	1	no	—
446	C₂	—	4	4	no	—
447	C₂	C₁₃×#2847	1	1	yes	characteristic
448	C₂	C₁₃×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#473	C₂	semidirect
3. C₂×C₁₃×#470	C₂	semidirect
5. C₁₃×#1908	C₂	semidirect
6. C₁₃×#1901	C₂	semidirect
7. C₁₃×#1815	C₂	semidirect
8. C₁₃×#1811	C₂	semidirect
11. C₂²×C₁₃×Q₁₆	C₂²	semidirect
26. C₂×C₁₃×#108	C₂²	semidirect
27. C₂×C₁₃×#106	C₂²	semidirect
29. C₂×C₁₃×#103	C₂²	semidirect
30. C₂×C₁₃×#101	C₂²	semidirect
32. C₁₃×#343	C₂²	semidirect
33. C₁₃×#341	C₂²	semidirect
87. #32946	C₁₃	direct (N × H)
155. C₂×#473	C₂×C₁₃	semidirect
156. C₂×#470	C₂×C₁₃	semidirect
158. #1908	C₂×C₁₃	semidirect
159. #1901	C₂×C₁₃	semidirect
160. #1815	C₂×C₁₃	semidirect
161. #1811	C₂×C₁₃	semidirect
210. C₂²×Q₁₆	C₂²×C₁₃	semidirect
225. C₂×#108	C₂²×C₁₃	semidirect
226. C₂×#106	C₂²×C₁₃	semidirect
228. C₂×#103	C₂²×C₁₃	semidirect
229. C₂×#101	C₂²×C₁₃	semidirect
231. #343	C₂²×C₁₃	semidirect
232. #341	C₂²×C₁₃	semidirect
377. C₁₃	#32946	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#568	2
C₂×C₁₃×#473	2
C₂×C₁₃×#470	2
C₁₃×#3007	2
C₁₃×#1908	2
C₁₃×#1901	2
C₁₃×#1815	2
C₁₃×#1811	2
#32946	13

Subgroups — C13×#32946 #15719285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32946 #15719285