Subgroups — C₁₃×#33840 #15720179

Order 3328.

748 conjugacy classes of subgroups.

The subgroup lattice has 418 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×#3287	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2218	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×SD₃₂	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×#550	—	2	1	no	—
15	D₄²×C₁₃	—	2	1	no	—
16	C₁₃×#509	—	2	8	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
20	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
21	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
23	C₁₃×#493	C₂²	1	1	yes	characteristic
24	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#466	C₂²	1	2	yes	—
26	C₁₃×#466	C₂²	1	2	yes	complemented
27	C₁₃×#460	—	2	1	no	—
28	C₁₃×#459	—	2	1	no	—
29	C₁₃×#449	—	2	2	no	—
30	C₁₃×#447	—	2	2	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#367	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#357	C₂²	1	1	yes	characteristic
38	C₁₃×#357	C₂²	1	2	yes	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	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	4	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	1	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	2	yes	—
56	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#127	—	2	1	no	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#127	—	4	1	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₁₃×#121	—	4	1	no	—
64	C₁₃×#121	—	4	2	no	—
65	C₁₃×#120	—	4	2	no	—
66	C₄×Q₈×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	—	4	1	no	—
69	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₁₃×SD₃₂	—	2	4	no	—
71	C₁₃×SD₃₂	D₄	1	4	yes	complemented
72	C₁₃×D₁₆	—	2	4	no	—
73	C₁₃×D₁₆	—	2	4	no	—
74	C₁₃×D₁₆	—	4	2	no	—
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	1	no	—
83	C₁₃×#102	—	2	1	no	—
84	C₁₃×#102	—	2	2	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	#33840	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	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	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	2	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	1	no	—
105	C₂×D₄×C₁₃	—	8	2	no	—
106	C₂×D₄×C₁₃	—	8	4	no	—
107	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₁₃×Q₁₆	—	2	1	no	—
112	C₁₃×Q₁₆	C₂×D₄	1	2	yes	complemented
113	C₁₃×SD₁₆	—	4	4	no	—
114	C₁₃×D₈	—	2	2	no	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	—	2	1	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	—	4	4	no	—
120	C₁₃×D₈	—	8	1	no	—
121	C₁₃×D₈	—	8	1	no	—
122	C₁₃×D₈	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
136	C₄²×C₁₃	—	4	1	no	—
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	#3287	C₂×C₁₃	1	1	yes	characteristic, complemented
143	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2246	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2218	C₂×C₁₃	1	2	yes	complemented
146	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2186	C₂×C₁₃	1	2	yes	complemented
149	#2184	C₂×C₁₃	1	2	yes	complemented
150	C₄×SD₃₂	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	2	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	—	2	2	no	—
160	Q₈×C₁₃	—	4	1	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	2	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	—	8	2	no	—
173	D₄×C₁₃	—	16	1	no	—
174	D₄×C₁₃	—	16	1	no	—
175	D₄×C₁₃	—	16	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	8	4	no	—
182	C₂×C₄×C₁₃	—	8	2	no	—
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
185	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
192	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
193	#550	—	2	1	no	—
194	D₄²	—	2	1	no	—
195	#509	—	2	8	no	—
196	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
198	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
199	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
200	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
201	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
202	#493	C₂²×C₁₃	1	1	yes	characteristic
203	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
204	#466	C₂²×C₁₃	1	2	yes	—
205	#466	C₂²×C₁₃	1	2	yes	complemented
206	#460	—	2	1	no	—
207	#459	—	2	1	no	—
208	#449	—	2	2	no	—
209	#447	—	2	2	no	—
210	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
213	#367	C₂²×C₁₃	1	1	yes	characteristic, complemented
214	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
215	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	#357	C₂²×C₁₃	1	1	yes	characteristic
217	#357	C₂²×C₁₃	1	2	yes	complemented
218	#357	C₂²×C₁₃	1	2	yes	complemented
219	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
220	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	8	1	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	—	16	8	no	—
234	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	8	1	no	—
239	C₄×C₁₃	—	8	1	no	—
240	C₄×C₁₃	#509	1	2	yes	complemented
241	C₄×C₁₃	D₄²	1	1	yes	characteristic
242	C₄×C₁₃	#576	1	1	yes	characteristic
243	C₂×#41	—	2	2	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	4	1	no	—
246	#135	—	2	4	no	—
247	#135	—	4	2	no	—
248	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×D₈	—	2	4	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	4	2	no	—
255	C₂×D₈	C₂³×C₁₃	1	2	yes	—
256	C₂×D₈	C₂³×C₁₃	1	2	yes	—
257	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	4	1	no	—
262	#121	—	2	2	no	—
263	#121	—	2	2	no	—
264	#121	—	4	1	no	—
265	#121	—	4	2	no	—
266	#120	—	4	2	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	4	1	no	—
270	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
271	SD₃₂	—	2	4	no	—
272	SD₃₂	D₄×C₁₃	1	4	yes	complemented
273	D₁₆	—	2	4	no	—
274	D₁₆	—	2	4	no	—
275	D₁₆	—	4	2	no	—
276	M₃₂	—	2	4	no	—
277	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
279	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
280	#107	C₂³×C₁₃	1	1	yes	characteristic
281	#107	C₂³×C₁₃	1	1	yes	characteristic
282	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
283	#103	—	2	1	no	—
284	#102	—	2	1	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
288	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₁₃	—	4	2	no	—
290	C₂×C₁₃	—	8	2	no	—
291	C₂×C₁₃	—	16	2	no	—
292	C₂×C₁₃	—	16	2	no	—
293	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
295	C₂×C₁₃	#3415	1	1	yes	characteristic
296	C₂⁴	—	4	2	no	—
297	#41	—	4	4	no	—
298	#41	—	8	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	—	8	4	no	—
314	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
318	Q₁₆	—	2	1	no	—
319	Q₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
320	SD₁₆	—	4	4	no	—
321	D₈	—	2	2	no	—
322	D₈	—	2	2	no	—
323	D₈	—	2	1	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	4	4	no	—
327	D₈	—	8	1	no	—
328	D₈	—	8	1	no	—
329	D₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
343	C₄²	—	4	1	no	—
344	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₁₆	—	2	2	no	—
346	C₁₆	—	2	1	no	—
347	C₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
348	C₁₃	#33840	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	4	1	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	8	4	no	—
353	C₂³	—	8	4	no	—
354	C₂³	—	16	2	no	—
355	C₂³	C₂×C₁₃×D₈	1	2	yes	—
356	Q₈	—	2	2	no	—
357	Q₈	—	4	1	no	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	4	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	16	1	no	—
371	D₄	—	16	1	no	—
372	D₄	—	16	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
381	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
382	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	1	no	—
386	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
387	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	16	8	no	—
401	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	C₁₃×#509	1	2	yes	complemented
408	C₄	D₄²×C₁₃	1	1	yes	characteristic
409	C₄	C₁₃×#576	1	1	yes	characteristic
410	C₂	—	4	2	no	—
411	C₂	—	8	2	no	—
412	C₂	—	16	2	no	—
413	C₂	—	16	2	no	—
414	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
415	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
416	C₂	C₁₃×#3415	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×#3287	C₂	semidirect
3. D₄×C₁₃×D₈	C₂	semidirect
4. C₁₃×#2246	C₂	semidirect
5. C₁₃×#2218	C₂	semidirect
6. C₁₃×#2207	C₂	semidirect
7. C₁₃×#2206	C₂	semidirect
8. C₁₃×#2186	C₂	semidirect
9. C₁₃×#2184	C₂	semidirect
10. C₄×C₁₃×SD₃₂	C₂	semidirect
11. C₁₃×#2169	C₂	semidirect
12. C₂×C₁₃×#135	C₂²	semidirect
18. C₂×C₁₃×SD₃₂	C₂²	semidirect
20. C₂×C₁₃×D₁₆	C₂²	semidirect
21. C₂×C₁₃×D₁₆	C₂²	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
24. C₁₃×#493	C₂²	semidirect
26. C₁₃×#466	C₂²	semidirect
31. C₄×C₁₃×Q₁₆	C₂²	semidirect
34. C₁₃×#367	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
71. C₁₃×SD₃₂	D₄	semidirect
88. #33840	C₁₃	direct (N × H)
112. C₁₃×Q₁₆	C₂×D₄	semidirect
140. C₁₃×C₁₆	C₂×D₄	semidirect
141. C₂×#509	C₂×C₁₃	semidirect
142. #3287	C₂×C₁₃	semidirect
143. D₄×D₈	C₂×C₁₃	semidirect
144. #2246	C₂×C₁₃	semidirect
145. #2218	C₂×C₁₃	semidirect
146. #2207	C₂×C₁₃	semidirect
147. #2206	C₂×C₁₃	semidirect
148. #2186	C₂×C₁₃	semidirect
149. #2184	C₂×C₁₃	semidirect
150. C₄×SD₃₂	C₂×C₁₃	semidirect
151. #2169	C₂×C₁₃	semidirect
191. C₂×#135	C₂²×C₁₃	semidirect
197. C₂×SD₃₂	C₂²×C₁₃	semidirect
199. C₂×D₁₆	C₂²×C₁₃	semidirect
200. C₂×D₁₆	C₂²×C₁₃	semidirect
201. C₂×M₃₂	C₂²×C₁₃	semidirect
203. #493	C₂²×C₁₃	semidirect
205. #466	C₂²×C₁₃	semidirect
210. C₄×Q₁₆	C₂²×C₁₃	semidirect
213. #367	C₂²×C₁₃	semidirect
214. C₄⋊C₁₆	C₂²×C₁₃	semidirect
215. #358	C₂²×C₁₃	semidirect
217. #357	C₂²×C₁₃	semidirect
218. #357	C₂²×C₁₃	semidirect
219. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
220. C₄×C₁₆	C₂²×C₁₃	semidirect
240. C₄×C₁₃	#509	semidirect
272. SD₃₂	D₄×C₁₃	semidirect
319. Q₁₆	C₂×D₄×C₁₃	semidirect
347. C₁₆	C₂×D₄×C₁₃	semidirect
348. C₁₃	#33840	direct (N × H)
407. 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×#3287	2
D₄×C₁₃×D₈	2
C₁₃×#2246	2
C₁₃×#2218	2
C₁₃×#2207	2
C₁₃×#2206	2
C₁₃×#2186	2
C₁₃×#2184	2
C₄×C₁₃×SD₃₂	2
C₁₃×#2169	2
#33840	13

Subgroups — C13×#33840 #15720179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33840 #15720179