Subgroups — C₁₃×#33754 #15720093

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2234	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2215	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2184	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#525	—	2	1	no	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
20	C₁₃×#467	C₂²	1	1	yes	characteristic
21	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#466	—	2	1	no	—
23	C₁₃×#466	—	2	1	no	—
24	C₁₃×#466	C₂²	1	2	yes	—
25	C₁₃×#466	C₂²	1	2	yes	—
26	C₁₃×#466	C₂²	1	1	yes	characteristic
27	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#465	—	2	1	no	—
29	C₁₃×#465	—	2	1	no	—
30	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₁₃×#416	—	2	1	no	—
33	C₂×C₁₃×#102	—	2	1	no	—
34	C₁₃×#367	C₂²	1	2	yes	complemented
35	C₁₃×#366	C₂²	1	2	yes	complemented
36	C₁₃×#358	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	complemented
38	C₁₃×#357	C₂²	1	2	yes	complemented
39	C₁₃×#357	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	4	1	no	—
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₁₃×#135	—	4	2	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	—	2	1	no	—
51	C₂×C₁₃×D₈	—	4	2	no	—
52	C₂×C₁₃×D₈	C₂³	1	2	yes	—
53	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	—	4	2	no	—
55	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#123	—	4	1	no	—
62	C₁₃×C₂²⋊Q₈	—	2	1	no	—
63	C₁₃×C₂²⋊Q₈	—	2	1	no	—
64	C₁₃×#121	—	2	1	no	—
65	C₁₃×#121	—	2	1	no	—
66	C₁₃×#121	—	2	2	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#121	—	4	1	no	—
69	C₁₃×#121	—	4	1	no	—
70	C₁₃×#120	—	4	1	no	—
71	C₄×D₄×C₁₃	—	4	1	no	—
72	C₄×D₄×C₁₃	—	4	1	no	—
73	C₁₃×#117	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
76	C₁₃×SD₃₂	—	4	2	no	—
77	C₁₃×D₁₆	—	4	2	no	—
78	C₂×C₁₃×C₁₆	—	4	2	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₁₃×#107	—	2	1	no	—
82	C₁₃×#107	C₂³	1	2	yes	—
83	C₁₃×#107	C₂³	1	1	yes	characteristic
84	C₁₃×#107	C₂³	1	1	yes	characteristic
85	C₁₃×#106	—	2	1	no	—
86	C₁₃×#103	—	2	1	no	—
87	C₁₃×#103	—	2	1	no	—
88	C₁₃×#102	—	2	2	no	—
89	C₁₃×#102	—	2	2	no	—
90	C₁₃×#102	—	2	1	no	—
91	C₁₃×#102	—	2	1	no	—
92	#33754	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	4	1	no	—
94	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
95	C₁₃×#41	—	4	2	no	—
96	C₁₃×#41	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	4	2	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	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	1	no	—
108	C₂×D₄×C₁₃	—	8	4	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₁₃×Q₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	4	2	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×D₈	—	2	2	no	—
123	C₁₃×D₈	—	2	2	no	—
124	C₁₃×D₈	—	4	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₂×C₈×C₁₃	—	4	1	no	—
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	4	1	no	—
139	C₁₃×C₄⋊C₄	—	4	1	no	—
140	C₁₃×C₄⋊C₄	—	4	1	no	—
141	C₁₃×C₂²⋊C₄	—	4	1	no	—
142	C₁₃×C₂²⋊C₄	—	4	1	no	—
143	C₁₃×C₂²⋊C₄	—	4	1	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₁₃×C₂²⋊C₄	—	4	1	no	—
147	C₁₃×C₂²⋊C₄	—	4	1	no	—
148	C₄²×C₁₃	—	4	1	no	—
149	C₁₃×C₁₆	—	2	2	no	—
150	C₁₃×C₁₆	—	2	2	no	—
151	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2236	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2234	C₂×C₁₃	1	2	yes	complemented
155	#2233	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2217	C₂×C₁₃	1	2	yes	complemented
157	#2215	C₂×C₁₃	1	2	yes	complemented
158	#2187	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2186	C₂×C₁₃	1	2	yes	complemented
160	#2184	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	8	2	no	—
168	C₂³×C₁₃	—	8	2	no	—
169	C₂³×C₁₃	—	8	2	no	—
170	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
171	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
173	Q₈×C₁₃	—	4	1	no	—
174	Q₈×C₁₃	—	4	1	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	1	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	1	no	—
179	D₄×C₁₃	—	8	2	no	—
180	D₄×C₁₃	—	8	4	no	—
181	D₄×C₁₃	—	8	2	no	—
182	D₄×C₁₃	—	8	2	no	—
183	D₄×C₁₃	—	8	2	no	—
184	D₄×C₁₃	—	8	4	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	8	2	no	—
200	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₁₃	—	2	1	no	—
205	C₈×C₁₃	—	2	1	no	—
206	C₈×C₁₃	—	2	1	no	—
207	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
208	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
209	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	#525	—	2	1	no	—
212	C₂×#121	—	2	1	no	—
213	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
214	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
215	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
216	#467	C₂²×C₁₃	1	1	yes	characteristic
217	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
218	#466	—	2	1	no	—
219	#466	—	2	1	no	—
220	#466	C₂²×C₁₃	1	1	yes	characteristic
221	#466	C₂²×C₁₃	1	2	yes	—
222	#466	C₂²×C₁₃	1	2	yes	—
223	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
224	#465	—	2	1	no	—
225	#465	—	2	1	no	—
226	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
227	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
228	#416	—	2	1	no	—
229	C₂×#102	—	2	1	no	—
230	#367	C₂²×C₁₃	1	2	yes	complemented
231	#366	C₂²×C₁₃	1	2	yes	complemented
232	#358	C₂²×C₁₃	1	2	yes	complemented
233	#357	C₂²×C₁₃	1	2	yes	complemented
234	#357	C₂²×C₁₃	1	2	yes	complemented
235	#357	C₂²×C₁₃	1	2	yes	complemented
236	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	8	1	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	8	1	no	—
251	C₂²×C₁₃	—	8	1	no	—
252	C₂²×C₁₃	—	8	2	no	—
253	C₂²×C₁₃	—	16	4	no	—
254	C₂²×C₁₃	#508	1	2	yes	—
255	C₂²×C₁₃	#509	1	2	yes	—
256	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	8	1	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	#534	1	1	yes	characteristic
265	C₄×C₁₃	#575	1	1	yes	characteristic
266	C₂×#41	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	4	1	no	—
269	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
270	#135	—	4	2	no	—
271	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×SD₁₆	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	4	2	no	—
275	C₂×D₈	C₂³×C₁₃	1	2	yes	—
276	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂²×C₈	—	4	2	no	—
278	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	#123	—	4	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	#121	—	2	2	no	—
288	#121	—	2	2	no	—
289	#121	—	2	1	no	—
290	#121	—	2	1	no	—
291	#121	—	4	1	no	—
292	#121	—	4	1	no	—
293	#120	—	4	1	no	—
294	C₄×D₄	—	4	1	no	—
295	C₄×D₄	—	4	1	no	—
296	#117	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	4	1	no	—
299	SD₃₂	—	4	2	no	—
300	D₁₆	—	4	2	no	—
301	C₂×C₁₆	—	4	2	no	—
302	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
303	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
304	#107	—	2	1	no	—
305	#107	C₂³×C₁₃	1	1	yes	characteristic
306	#107	C₂³×C₁₃	1	1	yes	characteristic
307	#107	C₂³×C₁₃	1	2	yes	—
308	#106	—	2	1	no	—
309	#103	—	2	1	no	—
310	#103	—	2	1	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	1	no	—
314	#102	—	2	1	no	—
315	C₂×C₁₃	—	2	2	no	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	4	1	no	—
318	C₂×C₁₃	—	16	1	no	—
319	C₂×C₁₃	—	16	2	no	—
320	C₂×C₁₃	#3186	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
322	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
323	C₂⁴	—	4	1	no	—
324	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	8	4	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
344	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
345	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	Q₁₆	—	2	2	no	—
350	SD₁₆	—	4	2	no	—
351	D₈	—	2	2	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	D₈	—	4	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₄²	—	4	1	no	—
379	C₁₆	—	2	2	no	—
380	C₁₆	—	2	2	no	—
381	C₁₃	#33754	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
391	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
392	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
393	Q₈	—	4	1	no	—
394	Q₈	—	4	1	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	4	no	—
404	D₄	—	8	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	16	4	no	—
443	C₂²	C₁₃×#508	1	2	yes	—
444	C₂²	C₁₃×#509	1	2	yes	—
445	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	C₁₃×#534	1	1	yes	characteristic
454	C₄	C₁₃×#575	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	2	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	16	2	no	—
459	C₂	—	16	1	no	—
460	C₂	C₁₃×#3186	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
462	C₂	C₂×C₁₃×#509	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 ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3050	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₁₃×#2236	C₂	semidirect
4. C₁₃×#2234	C₂	semidirect
5. C₁₃×#2233	C₂	semidirect
6. C₁₃×#2217	C₂	semidirect
7. C₁₃×#2215	C₂	semidirect
8. C₁₃×#2187	C₂	semidirect
9. C₁₃×#2186	C₂	semidirect
10. C₁₃×#2184	C₂	semidirect
11. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
12. C₂×C₁₃×#135	C₂²	semidirect
17. C₂×C₁₃×SD₃₂	C₂²	semidirect
18. C₂×C₁₃×D₁₆	C₂²	semidirect
19. C₂²×C₁₃×C₁₆	C₂²	semidirect
21. C₁₃×#467	C₂²	semidirect
27. C₁₃×#466	C₂²	semidirect
30. C₁₃×#427	C₂²	semidirect
34. C₁₃×#367	C₂²	semidirect
35. C₁₃×#366	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
37. C₁₃×#357	C₂²	semidirect
38. C₁₃×#357	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
42. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
92. #33754	C₁₃	direct (N × H)
151. #3050	C₂×C₁₃	semidirect
152. C₂×#466	C₂×C₁₃	semidirect
153. #2236	C₂×C₁₃	semidirect
154. #2234	C₂×C₁₃	semidirect
155. #2233	C₂×C₁₃	semidirect
156. #2217	C₂×C₁₃	semidirect
157. #2215	C₂×C₁₃	semidirect
158. #2187	C₂×C₁₃	semidirect
159. #2186	C₂×C₁₃	semidirect
160. #2184	C₂×C₁₃	semidirect
161. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
208. C₂×#135	C₂²×C₁₃	semidirect
213. C₂×SD₃₂	C₂²×C₁₃	semidirect
214. C₂×D₁₆	C₂²×C₁₃	semidirect
215. C₂²×C₁₆	C₂²×C₁₃	semidirect
217. #467	C₂²×C₁₃	semidirect
223. #466	C₂²×C₁₃	semidirect
226. #427	C₂²×C₁₃	semidirect
230. #367	C₂²×C₁₃	semidirect
231. #366	C₂²×C₁₃	semidirect
232. #358	C₂²×C₁₃	semidirect
233. #357	C₂²×C₁₃	semidirect
234. #357	C₂²×C₁₃	semidirect
235. #357	C₂²×C₁₃	semidirect
238. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
381. C₁₃	#33754	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3050	2
C₂×C₁₃×#466	2
C₁₃×#2236	2
C₁₃×#2234	2
C₁₃×#2233	2
C₁₃×#2217	2
C₁₃×#2215	2
C₁₃×#2187	2
C₁₃×#2186	2
C₁₃×#2184	2
C₂×C₁₃×C₂²⋊C₁₆	2
#33754	13

Subgroups — C13×#33754 #15720093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33754 #15720093