Subgroups — C₁₃×#33612 #15719951

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2218	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2215	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₁₃×#537	—	2	1	no	—
16	C₁₃×#535	—	2	1	no	—
17	C₁₃×#509	—	2	4	no	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
20	C₁₃×#504	—	2	4	no	—
21	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
25	C₁₃×#469	—	2	2	no	—
26	C₁₃×#468	—	2	2	no	—
27	C₁₃×#467	C₂²	1	2	yes	complemented
28	C₁₃×#466	C₂²	1	2	yes	—
29	C₁₃×#466	C₂²	1	2	yes	—
30	C₁₃×#466	C₂²	1	2	yes	complemented
31	C₁₃×#427	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₁₃×#418	—	2	1	no	—
34	C₁₃×#417	—	2	1	no	—
35	C₁₃×#367	C₂²	1	2	yes	complemented
36	C₁₃×#366	C₂²	1	2	yes	complemented
37	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	1	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	C₂³	1	2	yes	—
54	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
55	C₁₃×#131	—	2	2	no	—
56	C₁₃×#131	—	2	2	no	—
57	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#127	—	4	1	no	—
62	C₁₃×#124	—	4	1	no	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₁₃×C₂²⋊Q₈	—	4	1	no	—
65	C₁₃×#121	—	2	2	no	—
66	C₁₃×#121	—	2	2	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#121	—	4	1	no	—
69	C₁₃×#121	—	4	2	no	—
70	C₁₃×#120	—	4	2	no	—
71	C₁₃×#117	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₁₃×SD₃₂	—	2	4	no	—
74	C₁₃×D₁₆	—	2	4	no	—
75	C₁₃×M₃₂	—	2	4	no	—
76	C₁₃×M₃₂	D₄	1	4	yes	complemented
77	C₂×C₁₃×C₁₆	—	2	2	no	—
78	C₂×C₁₃×C₁₆	—	2	4	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
82	C₁₃×#107	—	2	1	no	—
83	C₁₃×#107	C₂³	1	2	yes	—
84	C₁₃×#107	C₂³	1	1	yes	characteristic
85	C₁₃×#107	C₂³	1	1	yes	characteristic
86	C₁₃×#106	—	2	1	no	—
87	C₁₃×#103	—	2	2	no	—
88	C₁₃×#102	—	2	2	no	—
89	C₁₃×#102	—	2	2	no	—
90	C₁₃×#102	—	2	2	no	—
91	#33612	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	4	1	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₁₃×#41	—	2	2	no	—
95	C₁₃×#41	—	4	2	no	—
96	C₁₃×#41	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	1	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	D₈	1	2	yes	—
109	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₁₃×Q₁₆	—	2	1	no	—
115	C₁₃×Q₁₆	—	2	1	no	—
116	C₁₃×SD₁₆	—	4	2	no	—
117	C₁₃×D₈	—	2	1	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	—	2	2	no	—
120	C₁₃×D₈	—	2	1	no	—
121	C₁₃×D₈	—	4	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	C₁₃×C₁₆	—	2	1	no	—
143	C₁₃×C₁₆	—	2	1	no	—
144	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
145	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2220	C₂×C₁₃	1	2	yes	complemented
150	#2218	C₂×C₁₃	1	2	yes	complemented
151	#2217	C₂×C₁₃	1	2	yes	complemented
152	#2215	C₂×C₁₃	1	2	yes	complemented
153	#2159	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	8	2	no	—
159	C₂³×C₁₃	—	16	1	no	—
160	C₂³×C₁₃	—	16	1	no	—
161	C₂³×C₁₃	C₂×D₈	1	2	yes	—
162	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	—	4	1	no	—
165	Q₈×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	1	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	1	no	—
172	D₄×C₁₃	—	8	2	no	—
173	D₄×C₁₃	—	8	2	no	—
174	D₄×C₁₃	—	16	2	no	—
175	D₄×C₁₃	—	16	2	no	—
176	D₄×C₁₃	—	16	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	8	2	no	—
184	C₂×C₄×C₁₃	—	16	1	no	—
185	C₂×C₄×C₁₃	#121	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#135	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	#121	1	2	yes	—
192	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
195	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
197	#537	—	2	1	no	—
198	#535	—	2	1	no	—
199	#509	—	2	4	no	—
200	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
201	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
202	#504	—	2	4	no	—
203	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
205	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
207	#469	—	2	2	no	—
208	#468	—	2	2	no	—
209	#467	C₂²×C₁₃	1	2	yes	complemented
210	#466	C₂²×C₁₃	1	2	yes	—
211	#466	C₂²×C₁₃	1	2	yes	—
212	#466	C₂²×C₁₃	1	2	yes	complemented
213	#427	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
215	#418	—	2	1	no	—
216	#417	—	2	1	no	—
217	#367	C₂²×C₁₃	1	2	yes	complemented
218	#366	C₂²×C₁₃	1	2	yes	complemented
219	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
221	#357	C₂²×C₁₃	1	2	yes	—
222	#357	C₂²×C₁₃	1	2	yes	—
223	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
224	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	8	1	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	8	1	no	—
235	C₂²×C₁₃	—	8	2	no	—
236	C₂²×C₁₃	—	16	4	no	—
237	C₂²×C₁₃	#466	1	2	yes	—
238	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	—	8	1	no	—
242	C₄×C₁₃	—	8	1	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	#466	1	2	yes	—
245	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
246	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
247	C₂×#41	—	2	1	no	—
248	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
249	C₂²×D₄	—	2	1	no	—
250	#135	—	2	2	no	—
251	#135	—	2	2	no	—
252	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×D₈	—	2	2	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	C₂³×C₁₃	1	2	yes	—
258	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
259	#131	—	2	2	no	—
260	#131	—	2	2	no	—
261	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
262	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	#127	—	4	1	no	—
266	#124	—	4	1	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂²⋊Q₈	—	4	1	no	—
269	#121	—	2	2	no	—
270	#121	—	2	2	no	—
271	#121	—	2	2	no	—
272	#121	—	4	1	no	—
273	#121	—	4	2	no	—
274	#120	—	4	2	no	—
275	#117	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	SD₃₂	—	2	4	no	—
278	D₁₆	—	2	4	no	—
279	M₃₂	—	2	4	no	—
280	M₃₂	D₄×C₁₃	1	4	yes	complemented
281	C₂×C₁₆	—	2	2	no	—
282	C₂×C₁₆	—	2	4	no	—
283	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
286	#107	—	2	1	no	—
287	#107	C₂³×C₁₃	1	2	yes	—
288	#107	C₂³×C₁₃	1	1	yes	characteristic
289	#107	C₂³×C₁₃	1	1	yes	characteristic
290	#106	—	2	1	no	—
291	#103	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	C₂×C₁₃	—	2	2	no	—
296	C₂×C₁₃	—	4	2	no	—
297	C₂×C₁₃	—	16	1	no	—
298	C₂×C₁₃	—	16	2	no	—
299	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
300	C₂×C₁₃	#3415	1	1	yes	characteristic
301	C₂×C₁₃	#3416	1	1	yes	characteristic
302	C₂⁴	—	4	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	4	2	no	—
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	C₁₃×D₈	1	2	yes	—
319	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	Q₁₆	—	2	1	no	—
325	Q₁₆	—	2	1	no	—
326	SD₁₆	—	4	2	no	—
327	D₈	—	2	1	no	—
328	D₈	—	2	2	no	—
329	D₈	—	2	2	no	—
330	D₈	—	2	1	no	—
331	D₈	—	4	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
337	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
339	C₂×C₈	C₁₃×#41	1	2	yes	—
340	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₄²	—	4	1	no	—
352	C₁₆	—	2	1	no	—
353	C₁₆	—	2	1	no	—
354	C₁₆	C₂×D₄×C₁₃	1	4	yes	—
355	C₁₃	#33612	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	16	1	no	—
360	C₂³	—	16	1	no	—
361	C₂³	C₂×C₁₃×D₈	1	2	yes	—
362	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	16	2	no	—
375	D₄	—	16	2	no	—
376	D₄	—	16	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	16	1	no	—
385	C₂×C₄	C₁₃×#121	1	2	yes	—
386	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
387	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
388	C₂×C₄	C₁₃×#135	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	C₁₃×#121	1	2	yes	—
392	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	16	4	no	—
406	C₂²	C₁₃×#466	1	2	yes	—
407	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₁₃×#466	1	2	yes	—
414	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
415	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	16	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
421	C₂	C₁₃×#3415	1	1	yes	characteristic
422	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#509	C₂	semidirect
2. C₂×C₁₃×#504	C₂	semidirect
3. C₁₃×#3061	C₂	semidirect
4. C₁₃×#3058	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2218	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2215	C₂	semidirect
9. C₁₃×#2159	C₂	semidirect
10. C₁₃×#2138	C₂	semidirect
11. C₂×C₁₃×#357	C₂	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
24. C₂²×C₁₃×C₁₆	C₂²	semidirect
27. C₁₃×#467	C₂²	semidirect
30. C₁₃×#466	C₂²	semidirect
35. C₁₃×#367	C₂²	semidirect
36. C₁₃×#366	C₂²	semidirect
37. C₁₃×#358	C₂²	semidirect
38. C₁₃×#358	C₂²	semidirect
41. C₁₃×#357	C₂²	semidirect
42. C₁₃×#357	C₂²	semidirect
76. C₁₃×M₃₂	D₄	semidirect
91. #33612	C₁₃	direct (N × H)
145. C₂×#509	C₂×C₁₃	semidirect
146. C₂×#504	C₂×C₁₃	semidirect
147. #3061	C₂×C₁₃	semidirect
148. #3058	C₂×C₁₃	semidirect
149. #2220	C₂×C₁₃	semidirect
150. #2218	C₂×C₁₃	semidirect
151. #2217	C₂×C₁₃	semidirect
152. #2215	C₂×C₁₃	semidirect
153. #2159	C₂×C₁₃	semidirect
154. #2138	C₂×C₁₃	semidirect
155. C₂×#357	C₂×C₁₃	semidirect
204. C₂×M₃₂	C₂²×C₁₃	semidirect
206. C₂²×C₁₆	C₂²×C₁₃	semidirect
209. #467	C₂²×C₁₃	semidirect
212. #466	C₂²×C₁₃	semidirect
217. #367	C₂²×C₁₃	semidirect
218. #366	C₂²×C₁₃	semidirect
219. #358	C₂²×C₁₃	semidirect
220. #358	C₂²×C₁₃	semidirect
223. #357	C₂²×C₁₃	semidirect
224. #357	C₂²×C₁₃	semidirect
280. M₃₂	D₄×C₁₃	semidirect
355. C₁₃	#33612	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×#509	2
C₂×C₁₃×#504	2
C₁₃×#3061	2
C₁₃×#3058	2
C₁₃×#2220	2
C₁₃×#2218	2
C₁₃×#2217	2
C₁₃×#2215	2
C₁₃×#2159	2
C₁₃×#2138	2
C₂×C₁₃×#357	2
#33612	13

Subgroups — C13×#33612 #15719951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33612 #15719951