Subgroups — C₁₃×#33762 #15720101

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 446 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
2	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2237	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2219	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2185	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#525	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
20	C₁₃×#467	—	2	1	no	—
21	C₁₃×#467	—	2	1	no	—
22	C₁₃×#467	C₂²	1	2	yes	—
23	C₁₃×#467	C₂²	1	2	yes	—
24	C₁₃×#467	C₂²	1	1	yes	characteristic
25	C₁₃×#467	C₂²	1	1	yes	characteristic
26	C₁₃×#466	C₂²	1	1	yes	characteristic
27	C₁₃×#466	C₂²	1	1	yes	characteristic
28	C₁₃×#465	—	2	1	no	—
29	C₁₃×#465	—	2	1	no	—
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₁₃×#416	—	2	1	no	—
33	C₂×C₁₃×#103	—	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×#358	C₂²	1	2	yes	complemented
38	C₁₃×#358	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	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₁₃×#135	—	4	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	—	4	2	no	—
49	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×SD₁₆	—	2	1	no	—
52	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	—	4	2	no	—
54	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#123	—	4	1	no	—
61	C₁₃×C₂²⋊Q₈	—	2	1	no	—
62	C₁₃×C₂²⋊Q₈	—	2	1	no	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	4	1	no	—
66	C₁₃×C₂²⋊Q₈	—	4	1	no	—
67	C₁₃×#121	—	2	1	no	—
68	C₁₃×#121	—	2	1	no	—
69	C₁₃×#120	—	4	1	no	—
70	C₄×D₄×C₁₃	—	4	1	no	—
71	C₄×D₄×C₁₃	—	4	1	no	—
72	C₁₃×#117	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
76	C₁₃×Q₃₂	—	4	2	no	—
77	C₁₃×SD₃₂	—	4	2	no	—
78	C₁₃×M₃₂	—	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	2	no	—
87	C₁₃×#103	—	2	2	no	—
88	C₁₃×#103	—	2	1	no	—
89	C₁₃×#103	—	2	1	no	—
90	C₁₃×#102	—	2	1	no	—
91	C₁₃×#102	—	2	1	no	—
92	#33762	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
94	C₁₃×#41	—	4	2	no	—
95	C₁₃×#41	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₁₃×Q₁₆	—	2	2	no	—
117	C₁₃×Q₁₆	—	2	2	no	—
118	C₁₃×Q₁₆	—	2	2	no	—
119	C₁₃×Q₁₆	—	4	2	no	—
120	C₁₃×SD₁₆	—	4	2	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
126	C₂×C₈×C₁₃	—	4	1	no	—
127	C₂×C₈×C₁₃	—	4	1	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	1	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	1	no	—
139	C₁₃×C₄⋊C₄	—	4	1	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	4	1	no	—
143	C₁₃×C₂²⋊C₄	—	4	1	no	—
144	C₁₃×C₂²⋊C₄	—	4	1	no	—
145	C₁₃×C₂²⋊C₄	—	4	1	no	—
146	C₁₃×C₂²⋊C₄	—	4	1	no	—
147	C₄²×C₁₃	—	4	1	no	—
148	C₁₃×C₁₆	—	2	2	no	—
149	C₁₃×C₁₆	—	2	2	no	—
150	#3050	C₂×C₁₃	1	1	yes	characteristic
151	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2237	C₂×C₁₃	1	2	yes	complemented
153	#2236	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2233	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2220	C₂×C₁₃	1	2	yes	complemented
156	#2219	C₂×C₁₃	1	2	yes	complemented
157	#2189	C₂×C₁₃	1	2	yes	complemented
158	#2188	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2185	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
168	Q₈×C₁₃	—	4	1	no	—
169	Q₈×C₁₃	—	4	2	no	—
170	Q₈×C₁₃	—	4	2	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	Q₈×C₁₃	—	8	2	no	—
173	D₄×C₁₃	—	4	1	no	—
174	D₄×C₁₃	—	4	1	no	—
175	D₄×C₁₃	—	8	2	no	—
176	D₄×C₁₃	—	8	2	no	—
177	D₄×C₁₃	—	8	2	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	8	2	no	—
193	C₂×C₄×C₁₃	—	8	2	no	—
194	C₂×C₄×C₁₃	—	8	2	no	—
195	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	—	2	1	no	—
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
203	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
206	#525	—	2	1	no	—
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
209	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
210	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
211	#467	—	2	1	no	—
212	#467	—	2	1	no	—
213	#467	C₂²×C₁₃	1	1	yes	characteristic
214	#467	C₂²×C₁₃	1	2	yes	—
215	#467	C₂²×C₁₃	1	1	yes	characteristic
216	#467	C₂²×C₁₃	1	2	yes	—
217	#466	C₂²×C₁₃	1	1	yes	characteristic
218	#466	C₂²×C₁₃	1	1	yes	characteristic
219	#465	—	2	1	no	—
220	#465	—	2	1	no	—
221	#427	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
223	#416	—	2	1	no	—
224	C₂×#103	—	2	1	no	—
225	#367	C₂²×C₁₃	1	2	yes	complemented
226	#366	C₂²×C₁₃	1	2	yes	complemented
227	#358	C₂²×C₁₃	1	2	yes	complemented
228	#358	C₂²×C₁₃	1	2	yes	complemented
229	#358	C₂²×C₁₃	1	2	yes	complemented
230	#357	C₂²×C₁₃	1	2	yes	complemented
231	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
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	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	8	1	no	—
244	C₂²×C₁₃	—	8	1	no	—
245	C₂²×C₁₃	—	8	1	no	—
246	C₂²×C₁₃	#510	1	2	yes	—
247	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	—	8	1	no	—
254	C₄×C₁₃	—	8	1	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	#534	1	1	yes	characteristic
257	C₄×C₁₃	#575	1	1	yes	characteristic
258	C₂×#41	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
261	#135	—	4	2	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×Q₁₆	—	4	2	no	—
264	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	—	4	2	no	—
269	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
271	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	#123	—	4	1	no	—
276	C₂²⋊Q₈	—	2	2	no	—
277	C₂²⋊Q₈	—	2	2	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	4	1	no	—
281	C₂²⋊Q₈	—	4	1	no	—
282	#121	—	2	1	no	—
283	#121	—	2	1	no	—
284	#120	—	4	1	no	—
285	C₄×D₄	—	4	1	no	—
286	C₄×D₄	—	4	1	no	—
287	#117	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	4	1	no	—
290	C₂×C₂²⋊C₄	—	4	1	no	—
291	Q₃₂	—	4	2	no	—
292	SD₃₂	—	4	2	no	—
293	M₃₂	—	4	2	no	—
294	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
295	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
296	#107	—	2	1	no	—
297	#107	C₂³×C₁₃	1	2	yes	—
298	#107	C₂³×C₁₃	1	1	yes	characteristic
299	#107	C₂³×C₁₃	1	1	yes	characteristic
300	#106	—	2	1	no	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	1	no	—
304	#103	—	2	1	no	—
305	#102	—	2	1	no	—
306	#102	—	2	1	no	—
307	C₂×C₁₃	—	2	2	no	—
308	C₂×C₁₃	—	4	1	no	—
309	C₂×C₁₃	—	4	1	no	—
310	C₂×C₁₃	—	16	1	no	—
311	C₂×C₁₃	#3186	1	1	yes	characteristic
312	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
313	C₂×C₁₃	#3414	1	1	yes	characteristic
314	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
332	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
333	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	Q₁₆	—	2	2	no	—
338	Q₁₆	—	2	2	no	—
339	Q₁₆	—	2	2	no	—
340	Q₁₆	—	4	2	no	—
341	SD₁₆	—	4	2	no	—
342	D₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₄²	—	4	1	no	—
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	2	no	—
371	C₁₃	#33762	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
377	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
378	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
379	Q₈	—	4	1	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	8	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
407	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₁₃×#510	1	2	yes	—
427	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₁₃×#534	1	1	yes	characteristic
437	C₄	C₁₃×#575	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	4	1	no	—
440	C₂	—	4	1	no	—
441	C₂	—	16	1	no	—
442	C₂	C₁₃×#3186	1	1	yes	characteristic
443	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
444	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	C₁₃×#3050	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×#467	C₂	semidirect
3. C₁₃×#2237	C₂	semidirect
4. C₁₃×#2236	C₂	semidirect
5. C₁₃×#2233	C₂	semidirect
6. C₁₃×#2220	C₂	semidirect
7. C₁₃×#2219	C₂	semidirect
8. C₁₃×#2189	C₂	semidirect
9. C₁₃×#2188	C₂	semidirect
10. C₁₃×#2185	C₂	semidirect
11. C₁₃×#2112	C₂	semidirect
17. C₂×C₁₃×Q₃₂	C₂²	semidirect
18. C₂×C₁₃×SD₃₂	C₂²	semidirect
34. C₁₃×#367	C₂²	semidirect
35. C₁₃×#366	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
37. C₁₃×#358	C₂²	semidirect
38. C₁₃×#358	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
92. #33762	C₁₃	direct (N × H)
151. C₂×#467	C₂×C₁₃	semidirect
152. #2237	C₂×C₁₃	semidirect
153. #2236	C₂×C₁₃	semidirect
154. #2233	C₂×C₁₃	semidirect
155. #2220	C₂×C₁₃	semidirect
156. #2219	C₂×C₁₃	semidirect
157. #2189	C₂×C₁₃	semidirect
158. #2188	C₂×C₁₃	semidirect
159. #2185	C₂×C₁₃	semidirect
160. #2112	C₂×C₁₃	semidirect
208. C₂×Q₃₂	C₂²×C₁₃	semidirect
209. C₂×SD₃₂	C₂²×C₁₃	semidirect
225. #367	C₂²×C₁₃	semidirect
226. #366	C₂²×C₁₃	semidirect
227. #358	C₂²×C₁₃	semidirect
228. #358	C₂²×C₁₃	semidirect
229. #358	C₂²×C₁₃	semidirect
230. #357	C₂²×C₁₃	semidirect
371. C₁₃	#33762	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×#467	2
C₁₃×#2237	2
C₁₃×#2236	2
C₁₃×#2233	2
C₁₃×#2220	2
C₁₃×#2219	2
C₁₃×#2189	2
C₁₃×#2188	2
C₁₃×#2185	2
C₁₃×#2112	2
#33762	13

Subgroups — C13×#33762 #15720101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33762 #15720101