Subgroups — C₁₃×#33778 #15720117

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2249	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2242	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₁₃×#532	—	2	1	no	—
15	C₁₃×#529	—	2	1	no	—
16	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
20	C₁₃×#499	C₂²	1	1	yes	characteristic
21	C₁₃×#495	—	2	1	no	—
22	C₁₃×#495	C₂²	1	2	yes	—
23	C₁₃×#495	C₂²	1	1	yes	characteristic
24	C₁₃×#494	C₂²	1	1	yes	characteristic
25	C₁₃×#493	C₂²	1	1	yes	characteristic
26	C₁₃×#492	—	2	1	no	—
27	C₁₃×#488	—	2	1	no	—
28	C₁₃×#467	C₂²	1	1	yes	characteristic
29	C₁₃×#466	C₂²	1	1	yes	characteristic
30	C₁₃×#465	—	2	1	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×SD₁₆	—	2	1	no	—
33	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₁₃×#135	—	4	2	no	—
45	C₁₃×#135	—	4	2	no	—
46	C₁₃×#135	—	4	4	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	C₂³	1	2	yes	—
55	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#126	—	4	1	no	—
61	C₁₃×#125	—	2	1	no	—
62	C₁₃×#124	—	2	1	no	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#123	—	4	1	no	—
65	C₁₃×C₂²⋊Q₈	—	2	1	no	—
66	C₁₃×#121	—	2	1	no	—
67	C₁₃×#121	—	4	1	no	—
68	C₁₃×#121	—	4	1	no	—
69	C₄×Q₈×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	4	1	no	—
72	C₄×D₄×C₁₃	—	4	1	no	—
73	C₄×D₄×C₁₃	—	4	1	no	—
74	C₁₃×#117	—	4	1	no	—
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₁₃×Q₃₂	—	4	2	no	—
77	C₁₃×SD₃₂	—	4	2	no	—
78	C₁₃×SD₃₂	—	4	2	no	—
79	C₁₃×D₁₆	—	4	2	no	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
82	C₁₃×#107	C₂³	1	1	yes	characteristic
83	C₁₃×#107	C₂³	1	1	yes	characteristic
84	C₁₃×#106	—	2	1	no	—
85	C₁₃×#103	—	2	1	no	—
86	C₁₃×#103	—	2	1	no	—
87	C₁₃×#102	—	2	1	no	—
88	C₁₃×#102	—	2	1	no	—
89	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	#33778	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₁₃×#41	—	4	4	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	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	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	1	no	—
110	C₁₃×Q₁₆	—	2	2	no	—
111	C₁₃×Q₁₆	—	2	1	no	—
112	C₁₃×Q₁₆	—	2	2	no	—
113	C₁₃×Q₁₆	—	4	2	no	—
114	C₁₃×SD₁₆	—	4	4	no	—
115	C₁₃×SD₁₆	—	4	2	no	—
116	C₁₃×SD₁₆	—	4	4	no	—
117	C₁₃×D₈	—	2	1	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	—	2	1	no	—
120	C₁₃×D₈	—	2	2	no	—
121	C₁₃×D₈	—	4	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	1	no	—
136	C₁₃×C₄⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	1	no	—
139	C₁₃×C₂²⋊C₄	—	4	1	no	—
140	C₁₃×C₂²⋊C₄	—	4	1	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	4	2	no	—
143	C₁₃×C₂²⋊C₄	—	4	1	no	—
144	C₄²×C₁₃	—	4	1	no	—
145	C₄²×C₁₃	D₈	1	1	yes	characteristic
146	C₄²×C₁₃	D₈	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₁₃×C₁₆	—	2	2	no	—
150	C₁₃×C₁₆	—	2	2	no	—
151	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2249	C₂×C₁₃	1	2	yes	complemented
154	#2242	C₂×C₁₃	1	2	yes	complemented
155	#2209	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2189	C₂×C₁₃	1	2	yes	complemented
160	#2186	C₂×C₁₃	1	2	yes	complemented
161	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	1	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	1	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	1	no	—
173	D₄×C₁₃	—	8	2	no	—
174	D₄×C₁₃	—	8	2	no	—
175	D₄×C₁₃	—	8	4	no	—
176	D₄×C₁₃	—	8	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	8	4	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	2	1	no	—
195	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
196	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×#135	—	2	1	no	—
199	C₂×#135	C₂²×C₁₃	1	2	yes	—
200	#532	—	2	1	no	—
201	#529	—	2	1	no	—
202	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
203	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
204	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
205	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
206	#499	C₂²×C₁₃	1	1	yes	characteristic
207	#495	—	2	1	no	—
208	#495	C₂²×C₁₃	1	2	yes	—
209	#495	C₂²×C₁₃	1	1	yes	characteristic
210	#494	C₂²×C₁₃	1	1	yes	characteristic
211	#493	C₂²×C₁₃	1	1	yes	characteristic
212	#492	—	2	1	no	—
213	#488	—	2	1	no	—
214	#467	C₂²×C₁₃	1	1	yes	characteristic
215	#466	C₂²×C₁₃	1	1	yes	characteristic
216	#465	—	2	1	no	—
217	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
218	C₄×SD₁₆	—	2	1	no	—
219	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
222	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	#358	C₂²×C₁₃	1	2	yes	—
224	#358	C₂²×C₁₃	1	2	yes	—
225	#357	C₂²×C₁₃	1	2	yes	—
226	#357	C₂²×C₁₃	1	2	yes	—
227	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
228	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	2	no	—
234	C₂²×C₁₃	—	8	2	no	—
235	C₂²×C₁₃	—	8	1	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	—	8	1	no	—
245	C₄×C₁₃	—	8	2	no	—
246	C₄×C₁₃	—	8	1	no	—
247	C₄×C₁₃	#508	1	2	yes	—
248	C₄×C₁₃	#535	1	1	yes	characteristic
249	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂×#41	—	2	2	no	—
251	#135	—	4	2	no	—
252	#135	—	4	2	no	—
253	#135	—	4	4	no	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
256	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×SD₁₆	—	2	1	no	—
260	C₂×D₈	—	2	1	no	—
261	C₂×D₈	C₂³×C₁₃	1	2	yes	—
262	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	2	1	no	—
266	#127	—	2	1	no	—
267	#126	—	4	1	no	—
268	#125	—	2	1	no	—
269	#124	—	2	1	no	—
270	#124	—	2	2	no	—
271	#123	—	4	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	#121	—	2	1	no	—
274	#121	—	4	1	no	—
275	#121	—	4	1	no	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	4	1	no	—
279	C₄×D₄	—	4	1	no	—
280	C₄×D₄	—	4	1	no	—
281	#117	—	4	1	no	—
282	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
283	Q₃₂	—	4	2	no	—
284	SD₃₂	—	4	2	no	—
285	SD₃₂	—	4	2	no	—
286	D₁₆	—	4	2	no	—
287	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
288	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
289	#107	C₂³×C₁₃	1	1	yes	characteristic
290	#107	C₂³×C₁₃	1	1	yes	characteristic
291	#106	—	2	1	no	—
292	#103	—	2	1	no	—
293	#103	—	2	1	no	—
294	#102	—	2	1	no	—
295	#102	—	2	1	no	—
296	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
297	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₁₃	—	4	1	no	—
301	C₂×C₁₃	—	16	1	no	—
302	C₂×C₁₃	—	16	2	no	—
303	C₂×C₁₃	#3205	1	1	yes	characteristic
304	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
305	C₂×C₁₃	#3414	1	1	yes	characteristic
306	#41	—	4	4	no	—
307	#41	—	4	4	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
319	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	Q₁₆	—	2	1	no	—
322	Q₁₆	—	2	2	no	—
323	Q₁₆	—	2	1	no	—
324	Q₁₆	—	2	2	no	—
325	Q₁₆	—	4	2	no	—
326	SD₁₆	—	4	4	no	—
327	SD₁₆	—	4	4	no	—
328	SD₁₆	—	4	2	no	—
329	D₈	—	2	1	no	—
330	D₈	—	2	2	no	—
331	D₈	—	2	1	no	—
332	D₈	—	2	2	no	—
333	D₈	—	4	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	C₁₃×D₈	1	1	yes	characteristic
358	C₄²	C₁₃×D₈	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₁₆	—	2	2	no	—
362	C₁₆	—	2	2	no	—
363	C₁₃	#33778	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
367	Q₈	—	4	2	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	1	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	8	2	no	—
376	D₄	—	8	2	no	—
377	D₄	—	8	4	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
390	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
391	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
392	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
393	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
398	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
399	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	1	no	—
418	C₄	C₁₃×#508	1	2	yes	—
419	C₄	C₁₃×#535	1	1	yes	characteristic
420	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂	—	4	1	no	—
422	C₂	—	16	1	no	—
423	C₂	—	16	2	no	—
424	C₂	C₁₃×#3205	1	1	yes	characteristic
425	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
426	C₂	C₁₃×#3414	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 ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3168	C₂	semidirect
2. C₁₃×#3147	C₂	semidirect
3. C₁₃×#2249	C₂	semidirect
4. C₁₃×#2242	C₂	semidirect
5. C₁₃×#2209	C₂	semidirect
6. C₁₃×#2208	C₂	semidirect
7. C₁₃×#2207	C₂	semidirect
8. C₁₃×#2206	C₂	semidirect
9. C₁₃×#2189	C₂	semidirect
10. C₁₃×#2186	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
93. #33778	C₁₃	direct (N × H)
151. #3168	C₂×C₁₃	semidirect
152. #3147	C₂×C₁₃	semidirect
153. #2249	C₂×C₁₃	semidirect
154. #2242	C₂×C₁₃	semidirect
155. #2209	C₂×C₁₃	semidirect
156. #2208	C₂×C₁₃	semidirect
157. #2207	C₂×C₁₃	semidirect
158. #2206	C₂×C₁₃	semidirect
159. #2189	C₂×C₁₃	semidirect
160. #2186	C₂×C₁₃	semidirect
161. #2162	C₂×C₁₃	semidirect
363. C₁₃	#33778	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×#3168	2
C₁₃×#3147	2
C₁₃×#2249	2
C₁₃×#2242	2
C₁₃×#2209	2
C₁₃×#2208	2
C₁₃×#2207	2
C₁₃×#2206	2
C₁₃×#2189	2
C₁₃×#2186	2
C₁₃×#2162	2
#33778	13

Subgroups — C13×#33778 #15720117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33778 #15720117