Subgroups — C₁₃×#33521 #15719860

Order 3328.

1140 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#510	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2189	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2188	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2139	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂×C₁₃×#135	—	2	8	no	—
11	C₂×C₁₃×#135	—	2	1	no	—
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	2	yes	—
15	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₁₃×SD₁₆	—	2	1	no	—
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
21	C₁₃×#510	—	2	8	no	—
22	C₂×C₁₃×Q₃₂	C₂²	1	4	yes	complemented
23	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
24	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
25	C₁₃×#467	—	2	1	no	—
26	C₁₃×#467	—	2	1	no	—
27	C₁₃×#467	C₂²	1	2	yes	—
28	C₁₃×#467	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#103	—	2	1	no	—
31	C₁₃×#358	C₂²	1	4	yes	complemented
32	C₁₃×#357	C₂²	1	4	yes	complemented
33	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#41	—	2	8	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	—	4	4	no	—
39	C₂×C₁₃×#41	—	4	1	no	—
40	C₂×C₁₃×#41	—	4	1	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	4	1	no	—
45	C₂³×C₄×C₁₃	—	4	1	no	—
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₁₃×#135	—	2	8	no	—
48	C₁₃×#135	—	2	8	no	—
49	C₁₃×#135	—	2	4	no	—
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	4	no	—
52	C₁₃×#135	D₄	1	8	yes	—
53	C₂×C₁₃×Q₁₆	—	2	4	no	—
54	C₂×C₁₃×Q₁₆	—	2	1	no	—
55	C₂×C₁₃×Q₁₆	—	2	4	no	—
56	C₂×C₁₃×Q₁₆	—	2	1	no	—
57	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×SD₁₆	—	2	8	no	—
60	C₂×C₁₃×SD₁₆	—	2	2	no	—
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×D₈	—	2	4	no	—
63	C₂×C₁₃×D₈	—	2	1	no	—
64	C₂×C₁₃×D₈	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃	—	2	4	no	—
66	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
75	C₁₃×C₂²⋊Q₈	—	4	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
79	C₁₃×Q₃₂	—	2	8	no	—
80	C₁₃×SD₃₂	—	2	8	no	—
81	C₁₃×M₃₂	—	2	4	no	—
82	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
83	C₁₃×#107	—	2	1	no	—
84	C₁₃×#107	C₂³	1	2	yes	—
85	C₁₃×#103	—	2	2	no	—
86	C₁₃×#103	—	2	2	no	—
87	#33521	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	4	1	no	—
89	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
90	C₁₃×#41	—	2	8	no	—
91	C₁₃×#41	—	2	8	no	—
92	C₁₃×#41	—	4	8	no	—
93	C₁₃×#41	—	4	4	no	—
94	C₁₃×#41	—	4	8	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	1	no	—
101	C₂×Q₈×C₁₃	—	4	1	no	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	8	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	4	8	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	—	4	1	no	—
119	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	D₈	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	C₁₃×Q₁₆	—	2	4	no	—
126	C₁₃×Q₁₆	—	2	2	no	—
127	C₁₃×Q₁₆	—	2	4	no	—
128	C₁₃×Q₁₆	—	4	2	no	—
129	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
130	C₁₃×SD₁₆	—	2	8	no	—
131	C₁₃×SD₁₆	—	2	8	no	—
132	C₁₃×D₈	—	2	4	no	—
133	C₁₃×D₈	—	2	2	no	—
134	C₁₃×D₈	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	4	1	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	2	no	—
150	C₁₃×C₂²⋊C₄	—	4	2	no	—
151	C₁₃×C₁₆	—	2	4	no	—
152	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic
153	C₂×#510	C₂×C₁₃	1	2	yes	complemented
154	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2189	C₂×C₁₃	1	4	yes	complemented
156	#2188	C₂×C₁₃	1	2	yes	complemented
157	#2187	C₂×C₁₃	1	2	yes	complemented
158	#2139	C₂×C₁₃	1	2	yes	complemented
159	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	4	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	8	2	no	—
166	C₂³×C₁₃	—	8	2	no	—
167	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	4	no	—
171	Q₈×C₁₃	—	4	4	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	8	2	no	—
176	D₄×C₁₃	—	2	4	no	—
177	D₄×C₁₃	—	4	4	no	—
178	D₄×C₁₃	—	4	8	no	—
179	D₄×C₁₃	—	4	8	no	—
180	D₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	—	4	4	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	8	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	8	2	no	—
195	C₂×C₄×C₁₃	—	8	2	no	—
196	C₂×C₄×C₁₃	#120	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	#120	1	2	yes	—
205	C₈×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂²×#41	—	2	1	no	—
207	C₂×#135	—	2	8	no	—
208	C₂×#135	—	2	1	no	—
209	C₂×#135	—	2	1	no	—
210	C₂×#135	C₂²×C₁₃	1	2	yes	—
211	C₂×#135	C₂²×C₁₃	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
214	C₂²×SD₁₆	—	2	1	no	—
215	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	—	2	1	no	—
218	#510	—	2	8	no	—
219	C₂×Q₃₂	C₂²×C₁₃	1	4	yes	complemented
220	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
221	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
222	#467	—	2	1	no	—
223	#467	—	2	1	no	—
224	#467	C₂²×C₁₃	1	2	yes	—
225	#467	C₂²×C₁₃	1	2	yes	complemented
226	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
227	C₂×#103	—	2	1	no	—
228	#358	C₂²×C₁₃	1	4	yes	complemented
229	#357	C₂²×C₁₃	1	4	yes	complemented
230	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
231	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	8	8	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	#447	1	2	yes	—
245	C₂²×C₁₃	#510	1	2	yes	complemented
246	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	#447	1	2	yes	—
253	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
254	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂×#41	—	2	8	no	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	4	4	no	—
259	C₂×#41	—	4	1	no	—
260	C₂×#41	—	4	1	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	4	1	no	—
265	C₂³×C₄	—	4	1	no	—
266	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
267	#135	—	2	8	no	—
268	#135	—	2	8	no	—
269	#135	—	2	4	no	—
270	#135	—	2	4	no	—
271	#135	—	2	4	no	—
272	#135	D₄×C₁₃	1	8	yes	—
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	4	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
278	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
279	C₂×SD₁₆	—	2	8	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×D₈	—	2	4	no	—
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	C₂³×C₁₃	1	2	yes	—
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	4	1	no	—
295	C₂²⋊Q₈	—	4	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	4	1	no	—
298	C₂×C₂²⋊C₄	—	4	1	no	—
299	Q₃₂	—	2	8	no	—
300	SD₃₂	—	2	8	no	—
301	M₃₂	—	2	4	no	—
302	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
303	#107	—	2	1	no	—
304	#107	C₂³×C₁₃	1	2	yes	—
305	#103	—	2	2	no	—
306	#103	—	2	2	no	—
307	C₂×C₁₃	—	2	2	no	—
308	C₂×C₁₃	—	2	2	no	—
309	C₂×C₁₃	—	4	1	no	—
310	C₂×C₁₃	—	8	4	no	—
311	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
312	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
313	C₂×C₁₃	#3414	1	1	yes	characteristic
314	C₂⁴	—	4	1	no	—
315	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
316	#41	—	2	8	no	—
317	#41	—	2	8	no	—
318	#41	—	4	8	no	—
319	#41	—	4	8	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	1	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
346	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
347	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	Q₁₆	—	2	4	no	—
352	Q₁₆	—	2	2	no	—
353	Q₁₆	—	2	4	no	—
354	Q₁₆	—	4	2	no	—
355	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
356	SD₁₆	—	2	8	no	—
357	SD₁₆	—	2	8	no	—
358	D₈	—	2	4	no	—
359	D₈	—	2	2	no	—
360	D₈	C₂×D₄×C₁₃	1	4	yes	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
370	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	1	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	C₁₆	—	2	4	no	—
378	C₁₃	#33521	1	1	yes	characteristic, direct product factor, Sylow
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	2	no	—
386	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
387	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
388	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	8	2	no	—
395	D₄	—	2	4	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	8	no	—
398	D₄	—	4	8	no	—
399	D₄	—	4	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	C₁₃×#120	1	2	yes	—
416	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
417	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
419	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	C₁₃×#120	1	2	yes	—
424	C₈	C₂²×D₄×C₁₃	1	2	yes	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	8	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	C₁₃×#447	1	2	yes	—
438	C₂²	C₁₃×#510	1	2	yes	complemented
439	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	4	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	C₁₃×#447	1	2	yes	—
446	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
447	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	—	4	1	no	—
451	C₂	—	8	4	no	—
452	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
453	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
454	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#135	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#510	C₂	semidirect
3. C₂×C₁₃×#467	C₂	semidirect
4. C₁₃×#2189	C₂	semidirect
5. C₁₃×#2188	C₂	semidirect
6. C₁₃×#2187	C₂	semidirect
7. C₁₃×#2139	C₂	semidirect
8. C₁₃×#2112	C₂	semidirect
16. C₂²×C₁₃×Q₁₆	C₂²	semidirect
22. C₂×C₁₃×Q₃₂	C₂²	semidirect
23. C₂×C₁₃×SD₃₂	C₂²	semidirect
24. C₂×C₁₃×M₃₂	C₂²	semidirect
28. C₁₃×#467	C₂²	semidirect
29. C₂×C₁₃×#107	C₂²	semidirect
31. C₁₃×#358	C₂²	semidirect
32. C₁₃×#357	C₂²	semidirect
34. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
87. #33521	C₁₃	direct (N × H)
153. C₂×#510	C₂×C₁₃	semidirect
154. C₂×#467	C₂×C₁₃	semidirect
155. #2189	C₂×C₁₃	semidirect
156. #2188	C₂×C₁₃	semidirect
157. #2187	C₂×C₁₃	semidirect
158. #2139	C₂×C₁₃	semidirect
159. #2112	C₂×C₁₃	semidirect
213. C₂²×Q₁₆	C₂²×C₁₃	semidirect
219. C₂×Q₃₂	C₂²×C₁₃	semidirect
220. C₂×SD₃₂	C₂²×C₁₃	semidirect
221. C₂×M₃₂	C₂²×C₁₃	semidirect
225. #467	C₂²×C₁₃	semidirect
226. C₂×#107	C₂²×C₁₃	semidirect
228. #358	C₂²×C₁₃	semidirect
229. #357	C₂²×C₁₃	semidirect
231. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
245. C₂²×C₁₃	#510	semidirect
378. C₁₃	#33521	direct (N × H)
438. C₂²	C₁₃×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#510	2
C₂×C₁₃×#467	2
C₁₃×#2189	2
C₁₃×#2188	2
C₁₃×#2187	2
C₁₃×#2139	2
C₁₃×#2112	2
#33521	13

Subgroups — C13×#33521 #15719860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33521 #15719860