Subgroups — C₁₃×#61936 #15748275

Order 3328.

1634 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3398	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3395	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3374	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3364	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3223	C₂	1	4	yes	maximal
8	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3127	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3107	C₂	1	2	yes	maximal
11	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#564	—	2	2	no	—
13	C₁₃×#557	—	2	2	no	—
14	C₁₃×#557	C₂²	1	4	yes	—
15	C₁₃×#557	C₂²	1	4	yes	—
16	C₁₃×#557	C₂²	1	4	yes	—
17	C₁₃×#556	C₂²	1	4	yes	—
18	C₁₃×#552	—	2	4	no	—
19	C₁₃×#541	—	2	2	no	—
20	C₁₃×#541	—	2	4	no	—
21	C₁₃×#541	C₂²	1	4	yes	—
22	C₁₃×#536	C₂²	1	2	yes	—
23	C₁₃×#533	—	2	2	no	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#533	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₃×#519	C₂²	1	2	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#497	C₂²	1	4	yes	—
30	C₁₃×#494	C₂²	1	4	yes	—
31	C₁₃×#494	C₂²	1	4	yes	—
32	C₁₃×#491	C₂²	1	4	yes	—
33	C₁₃×#488	C₂²	1	4	yes	—
34	C₁₃×#487	C₂²	1	4	yes	—
35	C₁₃×#485	C₂²	1	4	yes	—
36	C₁₃×#479	C₂²	1	8	yes	—
37	C₁₃×#475	C₂²	1	2	yes	—
38	C₁₃×#474	C₂²	1	2	yes	—
39	C₁₃×#464	C₂²	1	8	yes	—
40	C₁₃×#462	C₂²	1	2	yes	—
41	C₁₃×#462	C₂²	1	4	yes	—
42	C₁₃×#462	C₂²	1	8	yes	—
43	C₁₃×#462	C₂²	1	4	yes	—
44	C₁₃×#462	C₂²	1	8	yes	—
45	C₁₃×#461	C₂²	1	2	yes	—
46	C₁₃×#452	C₂²	1	4	yes	—
47	C₁₃×#451	C₂²	1	8	yes	—
48	C₁₃×#446	C₂²	1	4	yes	—
49	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
50	C₁₃×#441	C₂²	1	8	yes	—
51	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
52	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	—
53	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
54	C₁₃×#433	C₂²	1	4	yes	—
55	C₁₃×#431	C₂²	1	2	yes	—
56	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
59	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
60	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
62	C₁₃×C₄⋊Q₈	—	2	4	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×#126	—	2	8	no	—
72	C₁₃×#126	—	2	8	no	—
73	C₁₃×#125	—	2	4	no	—
74	C₁₃×#125	—	2	8	no	—
75	C₁₃×#125	—	2	4	no	—
76	C₁₃×#125	—	2	8	no	—
77	C₁₃×#125	—	2	8	no	—
78	C₁₃×#125	—	2	8	no	—
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	D₄	1	2	yes	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#124	C₂³	1	4	yes	—
83	C₁₃×#123	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	4	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₄×Q₈×C₁₃	—	2	4	no	—
90	C₄×Q₈×C₁₃	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	—	2	4	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
97	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#117	—	2	2	no	—
102	C₁₃×#117	—	2	4	no	—
103	C₁₃×#117	—	2	4	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	C₂³	1	1	yes	characteristic
106	C₁₃×#117	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#107	C₂³	1	4	yes	—
111	C₁₃×#106	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
115	C₁₃×#103	C₂³	1	4	yes	—
116	C₁₃×#103	C₂³	1	4	yes	—
117	C₁₃×#103	C₂³	1	8	yes	—
118	C₁₃×#103	C₂³	1	4	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	4	yes	—
121	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₁₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	#61936	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₁₃×#41	—	4	2	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	4	4	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
131	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
132	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×Q₁₆	—	4	8	no	—
142	C₁₃×Q₁₆	—	4	8	no	—
143	C₁₃×Q₁₆	—	4	4	no	—
144	C₁₃×SD₁₆	—	4	4	no	—
145	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
146	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
163	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
165	C₁₃×C₂²⋊C₄	—	2	1	no	—
166	C₁₃×C₂²⋊C₄	—	2	4	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	—	2	4	no	—
174	C₄²×C₁₃	—	2	8	no	—
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂⁴	1	2	yes	—
178	C₄²×C₁₃	C₂⁴	1	4	yes	—
179	#3556	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#3509	C₂×C₁₃	1	1	yes	characteristic
181	#3398	C₂×C₁₃	1	4	yes	complemented
182	#3395	C₂×C₁₃	1	4	yes	complemented
183	#3374	C₂×C₁₃	1	4	yes	complemented
184	#3364	C₂×C₁₃	1	4	yes	complemented
185	#3223	C₂×C₁₃	1	4	yes	—
186	#3209	C₂×C₁₃	1	2	yes	complemented
187	#3127	C₂×C₁₃	1	4	yes	complemented
188	#3107	C₂×C₁₃	1	2	yes	—
189	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	8	no	—
193	Q₈×C₁₃	—	2	4	no	—
194	Q₈×C₁₃	—	2	4	no	—
195	Q₈×C₁₃	—	2	8	no	—
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	4	4	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	D₄×C₁₃	—	2	2	no	—
200	D₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
216	C₈×C₁₃	—	2	4	no	—
217	C₈×C₁₃	—	2	4	no	—
218	#564	—	2	2	no	—
219	#557	—	2	2	no	—
220	#557	C₂²×C₁₃	1	4	yes	—
221	#557	C₂²×C₁₃	1	4	yes	—
222	#557	C₂²×C₁₃	1	4	yes	—
223	#556	C₂²×C₁₃	1	4	yes	—
224	#552	—	2	4	no	—
225	#541	—	2	2	no	—
226	#541	—	2	4	no	—
227	#541	C₂²×C₁₃	1	4	yes	—
228	#536	C₂²×C₁₃	1	2	yes	—
229	#533	—	2	2	no	—
230	#533	C₂²×C₁₃	1	2	yes	—
231	#533	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	#519	C₂²×C₁₃	1	2	yes	—
234	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
235	#497	C₂²×C₁₃	1	4	yes	—
236	#494	C₂²×C₁₃	1	4	yes	—
237	#494	C₂²×C₁₃	1	4	yes	—
238	#491	C₂²×C₁₃	1	4	yes	—
239	#488	C₂²×C₁₃	1	4	yes	—
240	#487	C₂²×C₁₃	1	4	yes	—
241	#485	C₂²×C₁₃	1	4	yes	—
242	#479	C₂²×C₁₃	1	8	yes	—
243	#475	C₂²×C₁₃	1	2	yes	—
244	#474	C₂²×C₁₃	1	2	yes	—
245	#464	C₂²×C₁₃	1	8	yes	—
246	#462	C₂²×C₁₃	1	2	yes	—
247	#462	C₂²×C₁₃	1	4	yes	—
248	#462	C₂²×C₁₃	1	8	yes	—
249	#462	C₂²×C₁₃	1	4	yes	—
250	#462	C₂²×C₁₃	1	8	yes	—
251	#461	C₂²×C₁₃	1	2	yes	—
252	#452	C₂²×C₁₃	1	4	yes	—
253	#451	C₂²×C₁₃	1	8	yes	—
254	#446	C₂²×C₁₃	1	4	yes	—
255	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
256	#441	C₂²×C₁₃	1	8	yes	—
257	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
258	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	—
259	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
260	#433	C₂²×C₁₃	1	4	yes	—
261	#431	C₂²×C₁₃	1	2	yes	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	4	1	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	8	no	—
270	C₄×C₁₃	—	4	1	no	—
271	C₄×C₁₃	—	4	4	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	4	no	—
275	C₄×C₁₃	#578	1	4	yes	—
276	C₄×C₁₃	#585	1	2	yes	—
277	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
279	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
280	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
281	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
282	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
288	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
290	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
291	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
292	#126	—	2	8	no	—
293	#126	—	2	8	no	—
294	#125	—	2	4	no	—
295	#125	—	2	8	no	—
296	#125	—	2	4	no	—
297	#125	—	2	8	no	—
298	#125	—	2	8	no	—
299	#125	—	2	8	no	—
300	#125	—	2	2	no	—
301	#125	D₄×C₁₃	1	2	yes	—
302	#125	C₂³×C₁₃	1	4	yes	—
303	#124	C₂³×C₁₃	1	4	yes	—
304	#123	—	2	4	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
309	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
310	C₄×Q₈	—	2	4	no	—
311	C₄×Q₈	—	2	4	no	—
312	C₄×Q₈	—	2	4	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
316	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
317	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
318	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
319	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	C₂³×C₁₃	1	2	yes	—
322	#117	—	2	2	no	—
323	#117	—	2	4	no	—
324	#117	—	2	4	no	—
325	#117	—	2	1	no	—
326	#117	C₂³×C₁₃	1	1	yes	characteristic
327	#117	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	#107	C₂³×C₁₃	1	4	yes	—
332	#106	C₂³×C₁₃	1	4	yes	—
333	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
334	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
335	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
336	#103	C₂³×C₁₃	1	4	yes	—
337	#103	C₂³×C₁₃	1	4	yes	—
338	#103	C₂³×C₁₃	1	8	yes	—
339	#103	C₂³×C₁₃	1	4	yes	—
340	#103	C₂³×C₁₃	1	8	yes	—
341	#102	C₂³×C₁₃	1	4	yes	—
342	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
343	#97	C₂³×C₁₃	1	4	yes	—
344	C₄×C₈	C₂³×C₁₃	1	4	yes	—
345	C₄×C₈	C₂³×C₁₃	1	4	yes	—
346	C₂×C₁₃	—	4	1	no	—
347	C₂×C₁₃	—	8	1	no	—
348	C₂×C₁₃	#3487	1	1	yes	characteristic
349	C₂×C₁₃	C₂×#578	1	2	yes	—
350	#41	—	4	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
355	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
356	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
357	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
365	Q₁₆	—	4	8	no	—
366	Q₁₆	—	4	8	no	—
367	Q₁₆	—	4	4	no	—
368	SD₁₆	—	4	4	no	—
369	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
370	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
386	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
387	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
388	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	8	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	8	no	—
399	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₄²	C₂⁴×C₁₃	1	2	yes	—
402	C₄²	C₂⁴×C₁₃	1	4	yes	—
403	C₁₃	#61936	1	1	yes	characteristic, direct product factor, Sylow
404	C₂³	—	2	1	no	—
405	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	2	8	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
429	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	C₁₃×#578	1	4	yes	—
446	C₄	C₁₃×#585	1	2	yes	—
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	C₁₃×#3487	1	1	yes	characteristic
450	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3556	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3395	C₂	semidirect
5. C₁₃×#3374	C₂	semidirect
6. C₁₃×#3364	C₂	semidirect
8. C₁₃×#3209	C₂	semidirect
9. C₁₃×#3127	C₂	semidirect
11. C₁₃×#2986	C₂	semidirect
125. #61936	C₁₃	direct (N × H)
179. #3556	C₂×C₁₃	semidirect
181. #3398	C₂×C₁₃	semidirect
182. #3395	C₂×C₁₃	semidirect
183. #3374	C₂×C₁₃	semidirect
184. #3364	C₂×C₁₃	semidirect
186. #3209	C₂×C₁₃	semidirect
187. #3127	C₂×C₁₃	semidirect
189. #2986	C₂×C₁₃	semidirect
403. C₁₃	#61936	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×#3556	2
C₁₃×#3509	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3374	2
C₁₃×#3364	2
C₁₃×#3223	2
C₁₃×#3209	2
C₁₃×#3127	2
C₁₃×#3107	2
C₁₃×#2986	2
#61936	13

Subgroups — C13×#61936 #15748275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61936 #15748275