Subgroups — C₁₃×#26271 #15712610

Order 3328.

752 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2052	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2038	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1974	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×#536	C₂²	1	2	yes	—
16	C₁₃×#520	C₂²	1	2	yes	—
17	C₁₃×#497	—	2	2	no	—
18	C₁₃×#495	—	2	1	no	—
19	C₁₃×#494	—	2	1	no	—
20	C₁₃×#485	—	2	2	no	—
21	C₁₃×#485	—	2	2	no	—
22	C₁₃×#484	—	2	2	no	—
23	C₁₃×#483	—	2	2	no	—
24	C₁₃×#440	—	2	2	no	—
25	C₄×C₁₃×Q₁₆	—	2	1	no	—
26	C₄×C₁₃×D₈	—	2	1	no	—
27	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#419	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₂×C₁₃×#103	C₂²	1	2	yes	—
36	C₂×C₁₃×#101	C₂²	1	2	yes	—
37	C₁₃×#408	C₂²	1	2	yes	—
38	C₁₃×#405	C₂²	1	1	yes	characteristic
39	C₁₃×#405	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#339	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₁₃×#137	—	2	4	no	—
48	C₁₃×#137	—	4	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×Q₁₆	—	2	1	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
59	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#123	—	4	2	no	—
68	C₁₃×C₂²⋊Q₈	—	2	2	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	C₂³	1	1	yes	characteristic
75	C₁₃×#117	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#108	—	2	2	no	—
80	C₁₃×#108	—	2	2	no	—
81	C₁₃×#107	—	2	1	no	—
82	C₁₃×#107	—	2	1	no	—
83	C₁₃×#107	—	2	2	no	—
84	C₁₃×#107	D₄	1	1	yes	characteristic
85	C₁₃×#107	D₄	1	1	yes	characteristic
86	C₁₃×#106	—	2	2	no	—
87	C₁₃×#106	D₄	1	1	yes	characteristic
88	C₁₃×#106	D₄	1	1	yes	characteristic
89	C₁₃×#104	—	4	2	no	—
90	C₁₃×#103	—	2	2	no	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	—	2	2	no	—
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#101	—	4	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	C₁₃×C₂²⋊C₈	—	2	2	no	—
99	C₁₃×#97	—	2	1	no	—
100	C₁₃×#97	—	2	1	no	—
101	C₄×C₈×C₁₃	—	2	1	no	—
102	C₄×C₈×C₁₃	—	2	1	no	—
103	C₄×C₈×C₁₃	—	2	2	no	—
104	C₁₃×#95	—	4	2	no	—
105	#26271	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×Q₁₆	—	2	2	no	—
126	C₁₃×Q₁₆	—	4	4	no	—
127	C₁₃×Q₁₆	—	4	2	no	—
128	C₁₃×Q₁₆	—	4	2	no	—
129	C₁₃×SD₁₆	—	2	4	no	—
130	C₁₃×SD₁₆	—	4	4	no	—
131	C₁₃×D₈	—	2	2	no	—
132	C₁₃×M₁₆	—	2	1	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	—	2	1	no	—
136	C₁₃×M₁₆	—	2	2	no	—
137	C₁₃×M₁₆	#41	1	2	yes	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	#41	1	2	yes	—
148	C₂×C₈×C₁₃	#41	1	2	yes	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₁₃×C₂²⋊C₄	—	4	2	no	—
161	C₁₃×C₂²⋊C₄	—	4	2	no	—
162	C₁₃×C₂²⋊C₄	—	4	2	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	4	2	no	—
168	#3156	C₂×C₁₃	1	1	yes	characteristic
169	#3097	C₂×C₁₃	1	2	yes	complemented
170	#2951	C₂×C₁₃	1	1	yes	characteristic
171	#2052	C₂×C₁₃	1	2	yes	complemented
172	#2038	C₂×C₁₃	1	2	yes	complemented
173	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1974	C₂×C₁₃	1	1	yes	characteristic
175	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1882	C₂×C₁₃	1	2	yes	complemented
178	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	2	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	8	2	no	—
206	C₂×C₄×C₁₃	—	16	2	no	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	—	2	1	no	—
215	C₈×C₁₃	—	2	2	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₈×C₁₃	—	4	2	no	—
218	C₈×C₁₃	#123	1	2	yes	—
219	C₈×C₁₃	#123	1	2	yes	—
220	C₂×#137	C₂²×C₁₃	1	2	yes	—
221	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	#536	C₂²×C₁₃	1	2	yes	—
224	#520	C₂²×C₁₃	1	2	yes	—
225	#497	—	2	2	no	—
226	#495	—	2	1	no	—
227	#494	—	2	1	no	—
228	#485	—	2	2	no	—
229	#485	—	2	2	no	—
230	#484	—	2	2	no	—
231	#483	—	2	2	no	—
232	#440	—	2	2	no	—
233	C₄×Q₁₆	—	2	1	no	—
234	C₄×D₈	—	2	1	no	—
235	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
237	#428	C₂²×C₁₃	1	2	yes	—
238	#427	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#104	C₂²×C₁₃	1	2	yes	—
241	#419	C₂²×C₁₃	1	2	yes	—
242	#417	C₂²×C₁₃	1	2	yes	—
243	C₂×#103	C₂²×C₁₃	1	2	yes	—
244	C₂×#101	C₂²×C₁₃	1	2	yes	—
245	#408	C₂²×C₁₃	1	2	yes	—
246	#405	C₂²×C₁₃	1	1	yes	characteristic
247	#405	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
249	#391	C₂²×C₁₃	1	2	yes	—
250	#343	C₂²×C₁₃	1	2	yes	—
251	#339	C₂²×C₁₃	1	1	yes	characteristic
252	#339	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	#540	1	1	yes	characteristic
259	C₂²×C₁₃	D₄²	1	1	yes	characteristic
260	C₂²×C₁₃	#559	1	1	yes	characteristic
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	1	no	—
264	C₄×C₁₃	—	4	1	no	—
265	C₄×C₁₃	—	4	1	no	—
266	C₄×C₁₃	—	4	1	no	—
267	C₄×C₁₃	—	8	2	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
270	C₄×C₁₃	#532	1	1	yes	characteristic
271	C₄×C₁₃	#546	1	1	yes	characteristic
272	C₄×C₁₃	#550	1	1	yes	characteristic
273	C₂×#41	C₂³×C₁₃	1	2	yes	—
274	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
275	#137	—	2	4	no	—
276	#137	—	4	2	no	—
277	#135	—	2	2	no	—
278	#135	—	2	2	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×Q₁₆	—	2	1	no	—
281	C₂×Q₁₆	—	2	1	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
287	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
288	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₄⋊Q₈	—	2	2	no	—
294	#124	—	2	2	no	—
295	#123	—	4	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	4	2	no	—
301	#117	—	2	2	no	—
302	#117	C₂³×C₁₃	1	1	yes	characteristic
303	#117	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
307	#108	—	2	2	no	—
308	#108	—	2	2	no	—
309	#107	—	2	1	no	—
310	#107	—	2	1	no	—
311	#107	—	2	2	no	—
312	#107	D₄×C₁₃	1	1	yes	characteristic
313	#107	D₄×C₁₃	1	1	yes	characteristic
314	#106	—	2	2	no	—
315	#106	D₄×C₁₃	1	1	yes	characteristic
316	#106	D₄×C₁₃	1	1	yes	characteristic
317	#104	—	4	2	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#102	—	2	2	no	—
324	#101	—	4	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	#97	—	2	1	no	—
328	#97	—	2	1	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	2	2	no	—
332	#95	—	4	2	no	—
333	C₂×C₁₃	—	2	1	no	—
334	C₂×C₁₃	—	2	1	no	—
335	C₂×C₁₃	—	8	2	no	—
336	C₂×C₁₃	#2445	1	1	yes	characteristic
337	C₂×C₁₃	#3290	1	1	yes	characteristic
338	C₂×C₁₃	#3293	1	1	yes	characteristic
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	—	2	2	no	—
342	#41	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
358	Q₁₆	—	2	2	no	—
359	Q₁₆	—	4	4	no	—
360	Q₁₆	—	4	2	no	—
361	Q₁₆	—	4	2	no	—
362	SD₁₆	—	2	4	no	—
363	SD₁₆	—	4	4	no	—
364	D₈	—	2	2	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	C₁₃×#41	1	2	yes	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₈	C₁₃×#41	1	2	yes	—
381	C₂×C₈	C₁₃×#41	1	2	yes	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	2	no	—
401	C₁₃	#26271	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³	—	2	2	no	—
403	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	16	2	no	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
435	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	C₁₃×#123	1	2	yes	—
442	C₈	C₁₃×#123	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	C₁₃×#540	1	1	yes	characteristic
449	C₂²	D₄²×C₁₃	1	1	yes	characteristic
450	C₂²	C₁₃×#559	1	1	yes	characteristic
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	2	no	—
459	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
460	C₄	C₁₃×#532	1	1	yes	characteristic
461	C₄	C₁₃×#546	1	1	yes	characteristic
462	C₄	C₁₃×#550	1	1	yes	characteristic
463	C₂	—	2	1	no	—
464	C₂	—	2	1	no	—
465	C₂	—	8	2	no	—
466	C₂	C₁₃×#2445	1	1	yes	characteristic
467	C₂	C₁₃×#3290	1	1	yes	characteristic
468	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3097	C₂	semidirect
4. C₁₃×#2052	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
6. C₁₃×#1979	C₂	semidirect
8. C₁₃×#1969	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1882	C₂	semidirect
11. C₁₃×#1772	C₂	semidirect
105. #26271	C₁₃	direct (N × H)
169. #3097	C₂×C₁₃	semidirect
171. #2052	C₂×C₁₃	semidirect
172. #2038	C₂×C₁₃	semidirect
173. #1979	C₂×C₁₃	semidirect
175. #1969	C₂×C₁₃	semidirect
176. #1952	C₂×C₁₃	semidirect
177. #1882	C₂×C₁₃	semidirect
178. #1772	C₂×C₁₃	semidirect
401. C₁₃	#26271	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×#3156	2
C₁₃×#3097	2
C₁₃×#2951	2
C₁₃×#2052	2
C₁₃×#2038	2
C₁₃×#1979	2
C₁₃×#1974	2
C₁₃×#1969	2
C₁₃×#1952	2
C₁₃×#1882	2
C₁₃×#1772	2
#26271	13

Subgroups — C13×#26271 #15712610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26271 #15712610