Subgroups — C₁₃×#24798 #15711137

Order 3328.

846 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3046	C₂	1	2	yes	maximal
4	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2038	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
17	C₁₃×#536	C₂²	1	2	yes	—
18	C₁₃×#520	C₂²	1	2	yes	—
19	C₁₃×#473	—	2	4	no	—
20	C₁₃×#470	—	2	2	no	—
21	C₁₃×#467	—	2	1	no	—
22	C₁₃×#467	—	2	1	no	—
23	C₁₃×#464	—	2	2	no	—
24	C₁₃×#463	—	2	2	no	—
25	C₁₃×#462	—	2	2	no	—
26	C₁₃×#461	—	2	2	no	—
27	C₁₃×#443	—	2	4	no	—
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
30	C₁₃×#428	—	2	2	no	—
31	C₁₃×#428	C₂²	1	2	yes	—
32	C₁₃×#427	—	2	1	no	—
33	C₁₃×#427	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	—	2	1	no	—
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₁₃×#424	C₂²	1	2	yes	—
37	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
39	C₁₃×#419	C₂²	1	2	yes	—
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₂×C₁₃×#103	C₂²	1	2	yes	—
42	C₂×C₁₃×#101	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#391	C₂²	1	2	yes	—
45	C₁₃×#343	C₂²	1	2	yes	—
46	C₁₃×#339	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×#137	—	2	4	no	—
51	C₁₃×#137	—	2	4	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	—	2	1	no	—
56	C₂×C₁₃×Q₁₆	—	2	1	no	—
57	C₂×C₁₃×Q₁₆	—	2	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
60	C₂×C₁₃×SD₁₆	—	2	2	no	—
61	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
62	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
63	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
64	C₁₃×#131	—	2	2	no	—
65	C₁₃×#131	—	2	2	no	—
66	C₁₃×#131	—	2	2	no	—
67	C₁₃×#131	D₄	1	4	yes	—
68	C₂×C₁₃×M₁₆	—	2	1	no	—
69	C₂×C₁₃×M₁₆	—	2	1	no	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#123	—	4	2	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	4	2	no	—
85	C₁₃×#117	—	2	2	no	—
86	C₁₃×#117	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#108	—	2	2	no	—
91	C₁₃×#108	—	2	2	no	—
92	C₁₃×#107	—	2	1	no	—
93	C₁₃×#107	—	2	1	no	—
94	C₁₃×#107	—	2	2	no	—
95	C₁₃×#107	D₄	1	1	yes	characteristic
96	C₁₃×#107	D₄	1	1	yes	characteristic
97	C₁₃×#106	—	2	2	no	—
98	C₁₃×#106	D₄	1	2	yes	—
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×#104	—	2	2	no	—
102	C₁₃×#104	—	2	2	no	—
103	C₁₃×#103	—	2	2	no	—
104	C₁₃×#103	—	2	2	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#101	—	2	4	no	—
110	C₄×C₈×C₁₃	—	2	2	no	—
111	C₁₃×#95	—	4	2	no	—
112	#24798	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₁₃×#41	—	2	1	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	—	2	1	no	—
119	C₁₃×#41	C₂×D₄	1	2	yes	—
120	C₁₃×#41	#41	1	2	yes	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×Q₁₆	—	2	2	no	—
141	C₁₃×Q₁₆	—	4	4	no	—
142	C₁₃×Q₁₆	—	4	2	no	—
143	C₁₃×Q₁₆	—	4	2	no	—
144	C₁₃×SD₁₆	—	2	2	no	—
145	C₁₃×SD₁₆	—	2	2	no	—
146	C₁₃×SD₁₆	—	4	4	no	—
147	C₁₃×D₈	—	2	2	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	—	2	4	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	1	no	—
152	C₁₃×M₁₆	—	2	1	no	—
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	4	2	no	—
155	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	4	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	4	2	no	—
163	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₃	#41	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	—	4	2	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	4	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	2	no	—
179	C₁₃×C₂²⋊C₄	—	4	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	4	2	no	—
184	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3046	C₂×C₁₃	1	2	yes	—
187	C₂×#443	C₂×C₁₃	1	1	yes	characteristic
188	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#2064	C₂×C₁₃	1	2	yes	complemented
190	#2038	C₂×C₁₃	1	2	yes	complemented
191	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1945	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1882	C₂×C₁₃	1	2	yes	complemented
194	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	Q₈×C₁₃	—	2	1	no	—
199	Q₈×C₁₃	—	2	1	no	—
200	Q₈×C₁₃	—	2	1	no	—
201	Q₈×C₁₃	—	4	2	no	—
202	Q₈×C₁₃	—	4	2	no	—
203	Q₈×C₁₃	—	4	2	no	—
204	Q₈×C₁₃	—	4	2	no	—
205	Q₈×C₁₃	#121	1	2	yes	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	—	2	1	no	—
210	D₄×C₁₃	—	2	1	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	1	no	—
213	D₄×C₁₃	#121	1	2	yes	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	8	2	no	—
230	C₂×C₄×C₁₃	—	16	2	no	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	1	no	—
239	C₈×C₁₃	—	2	1	no	—
240	C₈×C₁₃	—	4	1	no	—
241	C₈×C₁₃	—	4	2	no	—
242	C₈×C₁₃	#121	1	2	yes	—
243	C₈×C₁₃	#121	1	2	yes	—
244	C₂×#137	C₂²×C₁₃	1	2	yes	—
245	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
249	#536	C₂²×C₁₃	1	2	yes	—
250	#520	C₂²×C₁₃	1	2	yes	—
251	#473	—	2	4	no	—
252	#470	—	2	2	no	—
253	#467	—	2	1	no	—
254	#467	—	2	1	no	—
255	#464	—	2	2	no	—
256	#463	—	2	2	no	—
257	#462	—	2	2	no	—
258	#461	—	2	2	no	—
259	#443	—	2	4	no	—
260	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
262	#428	—	2	2	no	—
263	#428	C₂²×C₁₃	1	2	yes	—
264	#427	—	2	1	no	—
265	#427	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#107	—	2	1	no	—
267	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
268	#424	C₂²×C₁₃	1	2	yes	—
269	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
271	#419	C₂²×C₁₃	1	2	yes	—
272	#417	C₂²×C₁₃	1	2	yes	—
273	C₂×#103	C₂²×C₁₃	1	2	yes	—
274	C₂×#101	C₂²×C₁₃	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
276	#391	C₂²×C₁₃	1	2	yes	—
277	#343	C₂²×C₁₃	1	2	yes	—
278	#339	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	4	1	no	—
287	C₂²×C₁₃	#537	1	1	yes	characteristic
288	C₂²×C₁₃	D₄²	1	1	yes	characteristic
289	C₂²×C₁₃	#553	1	1	yes	characteristic
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	8	2	no	—
296	C₄×C₁₃	—	8	2	no	—
297	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
298	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
299	C₄×C₁₃	#547	1	1	yes	characteristic
300	C₄×C₁₃	#548	1	1	yes	characteristic
301	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
304	#137	—	2	4	no	—
305	#137	—	2	4	no	—
306	#135	—	2	2	no	—
307	#135	—	2	2	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	1	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
316	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
317	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
318	#131	—	2	2	no	—
319	#131	—	2	2	no	—
320	#131	—	2	2	no	—
321	#131	D₄×C₁₃	1	4	yes	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₄⋊Q₈	—	2	2	no	—
332	#124	—	2	2	no	—
333	#123	—	4	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	4	2	no	—
339	#117	—	2	2	no	—
340	#117	C₂³×C₁₃	1	2	yes	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	#108	—	2	2	no	—
345	#108	—	2	2	no	—
346	#107	—	2	1	no	—
347	#107	—	2	1	no	—
348	#107	—	2	2	no	—
349	#107	D₄×C₁₃	1	1	yes	characteristic
350	#107	D₄×C₁₃	1	1	yes	characteristic
351	#106	—	2	2	no	—
352	#106	D₄×C₁₃	1	2	yes	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	—	2	2	no	—
355	#104	—	2	2	no	—
356	#104	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	#102	—	2	2	no	—
363	#101	—	2	4	no	—
364	C₄×C₈	—	2	2	no	—
365	#95	—	4	2	no	—
366	C₂×C₁₃	—	2	1	no	—
367	C₂×C₁₃	—	2	1	no	—
368	C₂×C₁₃	—	4	2	no	—
369	C₂×C₁₃	—	8	1	no	—
370	C₂×C₁₃	#2416	1	1	yes	characteristic
371	C₂×C₁₃	#3290	1	1	yes	characteristic
372	C₂×C₁₃	#3293	1	1	yes	characteristic
373	#41	—	2	1	no	—
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	—	2	1	no	—
377	#41	—	2	1	no	—
378	#41	—	2	1	no	—
379	#41	C₂×D₄×C₁₃	1	2	yes	—
380	#41	C₁₃×#41	1	2	yes	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	Q₁₆	—	2	2	no	—
401	Q₁₆	—	4	4	no	—
402	Q₁₆	—	4	2	no	—
403	Q₁₆	—	4	2	no	—
404	SD₁₆	—	2	2	no	—
405	SD₁₆	—	2	2	no	—
406	SD₁₆	—	4	4	no	—
407	D₈	—	2	2	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	1	no	—
412	M₁₆	—	2	1	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	4	2	no	—
415	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
426	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₈	C₁₃×#41	1	2	yes	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	4	2	no	—
444	C₁₃	#24798	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	C₁₃×#121	1	2	yes	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	1	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	1	no	—
463	D₄	C₁₃×#121	1	2	yes	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	—	16	2	no	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
486	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	2	no	—
492	C₈	C₁₃×#121	1	2	yes	—
493	C₈	C₁₃×#121	1	2	yes	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	C₁₃×#537	1	1	yes	characteristic
503	C₂²	D₄²×C₁₃	1	1	yes	characteristic
504	C₂²	C₁₃×#553	1	1	yes	characteristic
505	C₄	—	2	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	8	2	no	—
511	C₄	—	8	2	no	—
512	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
513	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
514	C₄	C₁₃×#547	1	1	yes	characteristic
515	C₄	C₁₃×#548	1	1	yes	characteristic
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	4	2	no	—
519	C₂	—	8	1	no	—
520	C₂	C₁₃×#2416	1	1	yes	characteristic
521	C₂	C₁₃×#3290	1	1	yes	characteristic
522	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#473	C₂	semidirect
2. C₁₃×#3059	C₂	semidirect
5. C₁₃×#2913	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
7. C₁₃×#2038	C₂	semidirect
8. C₁₃×#1969	C₂	semidirect
9. C₁₃×#1945	C₂	semidirect
10. C₁₃×#1882	C₂	semidirect
11. C₁₃×#1816	C₂	semidirect
112. #24798	C₁₃	direct (N × H)
184. C₂×#473	C₂×C₁₃	semidirect
185. #3059	C₂×C₁₃	semidirect
188. #2913	C₂×C₁₃	semidirect
189. #2064	C₂×C₁₃	semidirect
190. #2038	C₂×C₁₃	semidirect
191. #1969	C₂×C₁₃	semidirect
192. #1945	C₂×C₁₃	semidirect
193. #1882	C₂×C₁₃	semidirect
194. #1816	C₂×C₁₃	semidirect
444. C₁₃	#24798	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×#473	2
C₁₃×#3059	2
C₁₃×#3046	2
C₂×C₁₃×#443	2
C₁₃×#2913	2
C₁₃×#2064	2
C₁₃×#2038	2
C₁₃×#1969	2
C₁₃×#1945	2
C₁₃×#1882	2
C₁₃×#1816	2
#24798	13

Subgroups — C13×#24798 #15711137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24798 #15711137