Subgroups — C₁₃×#33838 #15720177

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 414 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	2	yes	maximal, complemented
2	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₁₃×#547	—	2	1	no	—
15	D₄²×C₁₃	—	2	1	no	—
16	C₁₃×#509	—	2	8	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
23	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#493	C₂²	1	1	yes	characteristic
25	C₁₃×#467	C₂²	1	2	yes	complemented
26	C₁₃×#466	C₂²	1	2	yes	—
27	C₁₃×#461	—	2	1	no	—
28	C₁₃×#459	—	2	1	no	—
29	C₁₃×#452	—	2	2	no	—
30	C₁₃×#447	—	2	2	no	—
31	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#358	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	1	yes	characteristic
38	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#357	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	4	1	no	—
45	C₁₃×#135	—	2	4	no	—
46	C₁₃×#135	—	4	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	1	no	—
53	C₂×C₁₃×D₈	—	4	2	no	—
54	C₂×C₁₃×D₈	C₂³	1	2	yes	—
55	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#123	—	4	2	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₁₃×#121	—	4	1	no	—
64	C₁₃×#121	—	4	1	no	—
65	C₁₃×#120	—	4	2	no	—
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
70	C₁₃×SD₃₂	—	2	4	no	—
71	C₁₃×SD₃₂	—	2	4	no	—
72	C₁₃×SD₃₂	—	4	2	no	—
73	C₁₃×D₁₆	—	2	4	no	—
74	C₁₃×D₁₆	D₄	1	4	yes	complemented
75	C₁₃×M₃₂	—	2	4	no	—
76	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂³	1	1	yes	characteristic
80	C₁₃×#107	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₃×#103	—	2	2	no	—
83	C₁₃×#102	—	2	1	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	#33838	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	4	2	no	—
90	C₁₃×#41	—	4	4	no	—
91	C₁₃×#41	—	8	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	4	4	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂×D₄×C₁₃	—	8	2	no	—
103	C₂×D₄×C₁₃	—	8	4	no	—
104	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×Q₁₆	—	2	2	no	—
111	C₁₃×Q₁₆	—	8	1	no	—
112	C₁₃×SD₁₆	—	4	4	no	—
113	C₁₃×D₈	—	2	2	no	—
114	C₁₃×D₈	—	2	1	no	—
115	C₁₃×D₈	—	2	1	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	4	4	no	—
118	C₁₃×D₈	—	8	1	no	—
119	C₁₃×D₈	C₂×D₄	1	2	yes	—
120	C₁₃×D₈	C₂×D₄	1	2	yes	complemented
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	1	no	—
140	C₁₃×C₁₆	C₂×D₄	1	2	yes	complemented
141	C₂×#509	C₂×C₁₃	1	2	yes	complemented
142	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
143	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2248	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2220	C₂×C₁₃	1	2	yes	complemented
146	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2187	C₂×C₁₃	1	2	yes	complemented
149	#2186	C₂×C₁₃	1	2	yes	complemented
150	C₄×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2169	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	8	4	no	—
156	C₂³×C₁₃	—	8	4	no	—
157	C₂³×C₁₃	—	16	2	no	—
158	C₂³×C₁₃	C₂×D₈	1	2	yes	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	8	4	no	—
169	D₄×C₁₃	—	8	4	no	—
170	D₄×C₁₃	—	8	4	no	—
171	D₄×C₁₃	—	8	2	no	—
172	D₄×C₁₃	—	16	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	8	4	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	2	1	no	—
187	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
190	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
191	#547	—	2	1	no	—
192	D₄²	—	2	1	no	—
193	#509	—	2	8	no	—
194	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
195	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
196	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
197	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
199	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
200	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
201	#493	C₂²×C₁₃	1	1	yes	characteristic
202	#467	C₂²×C₁₃	1	2	yes	complemented
203	#466	C₂²×C₁₃	1	2	yes	—
204	#461	—	2	1	no	—
205	#459	—	2	1	no	—
206	#452	—	2	2	no	—
207	#447	—	2	2	no	—
208	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
210	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
212	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
213	#358	C₂²×C₁₃	1	2	yes	complemented
214	#357	C₂²×C₁₃	1	1	yes	characteristic
215	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	#357	C₂²×C₁₃	1	2	yes	complemented
217	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
218	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	4	2	no	—
223	C₂²×C₁₃	—	4	2	no	—
224	C₂²×C₁₃	—	8	1	no	—
225	C₂²×C₁₃	—	8	1	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	—	16	8	no	—
232	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	8	1	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	—	8	2	no	—
238	C₄×C₁₃	#509	1	2	yes	complemented
239	C₄×C₁₃	D₄²	1	1	yes	characteristic
240	C₄×C₁₃	#576	1	1	yes	characteristic
241	C₂×#41	—	2	2	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	4	1	no	—
244	#135	—	2	4	no	—
245	#135	—	4	2	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×D₈	—	2	4	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	4	2	no	—
253	C₂×D₈	C₂³×C₁₃	1	2	yes	—
254	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
257	C₄⋊Q₈	—	2	1	no	—
258	#127	—	2	1	no	—
259	#123	—	4	2	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	#121	—	2	2	no	—
262	#121	—	4	1	no	—
263	#121	—	4	1	no	—
264	#120	—	4	2	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	—	4	1	no	—
269	SD₃₂	—	2	4	no	—
270	SD₃₂	—	2	4	no	—
271	SD₃₂	—	4	2	no	—
272	D₁₆	—	2	4	no	—
273	D₁₆	D₄×C₁₃	1	4	yes	complemented
274	M₃₂	—	2	4	no	—
275	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
277	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
278	#107	C₂³×C₁₃	1	1	yes	characteristic
279	#107	C₂³×C₁₃	1	1	yes	characteristic
280	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
281	#103	—	2	2	no	—
282	#102	—	2	1	no	—
283	#102	—	2	1	no	—
284	#102	—	2	2	no	—
285	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
286	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₁₃	—	4	2	no	—
288	C₂×C₁₃	—	8	2	no	—
289	C₂×C₁₃	—	8	2	no	—
290	C₂×C₁₃	—	16	2	no	—
291	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
292	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
293	C₂×C₁₃	#3416	1	1	yes	characteristic
294	C₂⁴	—	4	2	no	—
295	#41	—	4	4	no	—
296	#41	—	8	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	8	2	no	—
308	C₂×D₄	—	8	4	no	—
309	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	Q₁₆	—	2	2	no	—
315	Q₁₆	—	2	2	no	—
316	Q₁₆	—	8	1	no	—
317	SD₁₆	—	4	4	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	1	no	—
320	D₈	—	2	1	no	—
321	D₈	—	2	2	no	—
322	D₈	—	4	4	no	—
323	D₈	—	8	1	no	—
324	D₈	C₂×D₄×C₁₃	1	2	yes	—
325	D₈	C₂×D₄×C₁₃	1	2	yes	complemented
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
342	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₁₆	—	2	2	no	—
344	C₁₆	—	2	1	no	—
345	C₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
346	C₁₃	#33838	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	8	4	no	—
351	C₂³	—	8	4	no	—
352	C₂³	—	16	2	no	—
353	C₂³	C₂×C₁₃×D₈	1	2	yes	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	4	no	—
364	D₄	—	8	4	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	16	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	4	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
378	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	2	1	no	—
382	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	16	8	no	—
397	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	C₁₃×#509	1	2	yes	complemented
404	C₄	D₄²×C₁₃	1	1	yes	characteristic
405	C₄	C₁₃×#576	1	1	yes	characteristic
406	C₂	—	4	2	no	—
407	C₂	—	8	2	no	—
408	C₂	—	8	2	no	—
409	C₂	—	16	2	no	—
410	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
411	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
412	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 ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#509	C₂	semidirect
2. C₁₃×#3283	C₂	semidirect
3. D₄×C₁₃×D₈	C₂	semidirect
4. C₁₃×#2248	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2208	C₂	semidirect
7. C₁₃×#2206	C₂	semidirect
8. C₁₃×#2187	C₂	semidirect
9. C₁₃×#2186	C₂	semidirect
10. C₄×C₁₃×D₁₆	C₂	semidirect
11. C₁₃×#2169	C₂	semidirect
12. C₂×C₁₃×#135	C₂²	semidirect
18. C₂×C₁₃×SD₃₂	C₂²	semidirect
19. C₂×C₁₃×SD₃₂	C₂²	semidirect
21. C₂×C₁₃×D₁₆	C₂²	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
23. C₁₃×#494	C₂²	semidirect
25. C₁₃×#467	C₂²	semidirect
32. C₄×C₁₃×D₈	C₂²	semidirect
34. C₁₃×#366	C₂²	semidirect
35. C₁₃×C₄⋊C₁₆	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
38. C₁₃×#357	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
40. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₁₃×C₁₆	C₂²	semidirect
74. C₁₃×D₁₆	D₄	semidirect
88. #33838	C₁₃	direct (N × H)
120. C₁₃×D₈	C₂×D₄	semidirect
140. C₁₃×C₁₆	C₂×D₄	semidirect
141. C₂×#509	C₂×C₁₃	semidirect
142. #3283	C₂×C₁₃	semidirect
143. D₄×D₈	C₂×C₁₃	semidirect
144. #2248	C₂×C₁₃	semidirect
145. #2220	C₂×C₁₃	semidirect
146. #2208	C₂×C₁₃	semidirect
147. #2206	C₂×C₁₃	semidirect
148. #2187	C₂×C₁₃	semidirect
149. #2186	C₂×C₁₃	semidirect
150. C₄×D₁₆	C₂×C₁₃	semidirect
151. #2169	C₂×C₁₃	semidirect
189. C₂×#135	C₂²×C₁₃	semidirect
195. C₂×SD₃₂	C₂²×C₁₃	semidirect
196. C₂×SD₃₂	C₂²×C₁₃	semidirect
198. C₂×D₁₆	C₂²×C₁₃	semidirect
199. C₂×M₃₂	C₂²×C₁₃	semidirect
200. #494	C₂²×C₁₃	semidirect
202. #467	C₂²×C₁₃	semidirect
209. C₄×D₈	C₂²×C₁₃	semidirect
211. #366	C₂²×C₁₃	semidirect
212. C₄⋊C₁₆	C₂²×C₁₃	semidirect
213. #358	C₂²×C₁₃	semidirect
215. #357	C₂²×C₁₃	semidirect
216. #357	C₂²×C₁₃	semidirect
217. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
218. C₄×C₁₆	C₂²×C₁₃	semidirect
238. C₄×C₁₃	#509	semidirect
273. D₁₆	D₄×C₁₃	semidirect
325. D₈	C₂×D₄×C₁₃	semidirect
345. C₁₆	C₂×D₄×C₁₃	semidirect
346. C₁₃	#33838	direct (N × H)
403. C₄	C₁₃×#509	semidirect

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
C₁₃×#3283	2
D₄×C₁₃×D₈	2
C₁₃×#2248	2
C₁₃×#2220	2
C₁₃×#2208	2
C₁₃×#2206	2
C₁₃×#2187	2
C₁₃×#2186	2
C₄×C₁₃×D₁₆	2
C₁₃×#2169	2
#33838	13

Subgroups — C13×#33838 #15720177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33838 #15720177