Subgroups — C₁₃×#33530 #15719869

Order 3328.

1132 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3414	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2191	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2190	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2145	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#349	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#41	—	2	1	no	—
9	C₁₃×#575	—	2	4	no	—
10	C₁₃×#575	—	2	2	no	—
11	C₁₃×#575	C₂²	1	4	yes	—
12	C₂×C₁₃×#137	—	2	2	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
14	C₂×C₁₃×#135	—	2	1	no	—
15	C₂×C₁₃×#135	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#525	—	2	1	no	—
19	C₁₃×#510	—	2	2	no	—
20	C₁₃×#510	C₂²	1	4	yes	complemented
21	C₁₃×#509	—	2	2	no	—
22	C₁₃×#509	C₂²	1	4	yes	complemented
23	C₁₃×#508	—	2	4	no	—
24	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
25	C₁₃×#470	C₂²	1	2	yes	complemented
26	C₁₃×#469	C₂²	1	2	yes	complemented
27	C₁₃×#468	—	2	2	no	—
28	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#416	—	2	1	no	—
30	C₁₃×#360	C₂²	1	8	yes	complemented
31	C₁₃×#349	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#41	—	2	2	no	—
33	C₂×C₁₃×#41	—	2	4	no	—
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	4	1	no	—
38	C₂×C₁₃×#41	—	4	2	no	—
39	C₂×C₁₃×#41	—	4	2	no	—
40	C₂×C₁₃×#41	—	4	1	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	4	1	no	—
44	C₂³×C₄×C₁₃	—	4	1	no	—
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₁₃×#137	—	2	8	no	—
47	C₁₃×#137	—	2	8	no	—
48	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
49	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	4	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	—	2	2	no	—
54	C₁₃×#135	—	2	2	no	—
55	C₁₃×#135	—	2	2	no	—
56	C₁₃×#135	D₄	1	4	yes	complemented
57	C₁₃×#135	C₂³	1	4	yes	—
58	C₂×C₁₃×Q₁₆	—	2	1	no	—
59	C₂×C₁₃×Q₁₆	D₄	1	2	yes	complemented
60	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	1	no	—
64	C₂×C₁₃×D₈	—	2	1	no	—
65	C₂×C₁₃×D₈	D₄	1	2	yes	complemented
66	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic, complemented
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	—	2	2	no	—
69	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#123	—	4	1	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#120	—	4	1	no	—
77	C₄×D₄×C₁₃	—	4	2	no	—
78	C₁₃×#117	—	2	1	no	—
79	C₁₃×Q₃₂	—	2	4	no	—
80	C₁₃×SD₃₂	—	2	4	no	—
81	C₁₃×SD₃₂	—	2	4	no	—
82	C₁₃×D₁₆	—	2	4	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₁₃×M₃₂	C₂³	1	4	yes	complemented
85	C₂×C₁₃×C₁₆	—	2	2	no	—
86	C₁₃×#107	—	2	1	no	—
87	C₁₃×#106	C₂³	1	2	yes	complemented
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#102	—	2	2	no	—
90	#33530	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	4	1	no	—
92	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
93	C₁₃×#41	—	2	8	no	—
94	C₁₃×#41	—	2	4	no	—
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	4	4	no	—
97	C₁₃×#41	—	4	4	no	—
98	C₁₃×#41	—	4	4	no	—
99	C₁₃×#41	—	4	4	no	—
100	C₁₃×#41	—	4	4	no	—
101	C₁₃×#41	—	4	2	no	—
102	C₁₃×#41	—	4	2	no	—
103	C₁₃×#41	—	4	1	no	—
104	C₁₃×#41	—	4	1	no	—
105	C₁₃×#41	—	4	1	no	—
106	C₁₃×#41	—	4	1	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	4	1	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	4	1	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂×D₄×C₁₃	—	4	4	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	4	no	—
120	C₂×D₄×C₁₃	—	4	2	no	—
121	C₂×D₄×C₁₃	—	4	2	no	—
122	C₂×D₄×C₁₃	—	4	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	4	no	—
129	C₂²×C₄×C₁₃	—	4	4	no	—
130	C₂²×C₄×C₁₃	—	4	1	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	1	no	—
133	C₂²×C₄×C₁₃	D₈	1	2	yes	—
134	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₁₃×Q₁₆	—	2	4	no	—
138	C₁₃×Q₁₆	—	2	2	no	—
139	C₁₃×Q₁₆	—	2	2	no	—
140	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
141	C₁₃×SD₁₆	—	2	8	no	—
142	C₁₃×SD₁₆	—	2	4	no	—
143	C₁₃×SD₁₆	—	2	4	no	—
144	C₁₃×SD₁₆	—	4	2	no	—
145	C₁₃×D₈	—	2	4	no	—
146	C₁₃×D₈	—	2	2	no	—
147	C₁₃×D₈	—	2	2	no	—
148	C₁₃×D₈	C₂×D₄	1	4	yes	—
149	C₁₃×M₁₆	—	2	4	no	—
150	C₁₃×M₁₆	—	2	4	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₂²⋊C₄	—	4	1	no	—
161	C₁₃×C₂²⋊C₄	—	4	2	no	—
162	C₁₃×C₂²⋊C₄	—	4	2	no	—
163	C₄²×C₁₃	—	4	1	no	—
164	C₁₃×C₁₆	—	2	4	no	—
165	C₂×#575	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#3414	C₂×C₁₃	1	2	yes	complemented
167	#3054	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2191	C₂×C₁₃	1	4	yes	complemented
169	#2190	C₂×C₁₃	1	4	yes	complemented
170	#2145	C₂×C₁₃	1	2	yes	complemented
171	C₂×#349	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	4	4	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	8	1	no	—
178	C₂³×C₁₃	—	8	4	no	—
179	C₂³×C₁₃	C₂×D₈	1	2	yes	—
180	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	4	no	—
182	Q₈×C₁₃	—	4	4	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	1	no	—
185	Q₈×C₁₃	—	4	1	no	—
186	D₄×C₁₃	—	2	4	no	—
187	D₄×C₁₃	—	4	4	no	—
188	D₄×C₁₃	—	4	8	no	—
189	D₄×C₁₃	—	4	4	no	—
190	D₄×C₁₃	—	4	4	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	1	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	8	4	no	—
195	D₄×C₁₃	—	8	1	no	—
196	D₄×C₁₃	—	8	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	4	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	8	1	no	—
211	C₂×C₄×C₁₃	—	8	1	no	—
212	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	#120	1	2	yes	—
221	C₈×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂²×#41	—	2	1	no	—
223	#575	—	2	4	no	—
224	#575	—	2	2	no	—
225	#575	C₂²×C₁₃	1	4	yes	—
226	C₂×#137	—	2	2	no	—
227	C₂×AGL(1,ℤ/8)	—	2	2	no	—
228	C₂×#135	—	2	1	no	—
229	C₂×#135	C₂²×C₁₃	1	2	yes	—
230	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
231	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	#525	—	2	1	no	—
233	#510	—	2	2	no	—
234	#510	C₂²×C₁₃	1	4	yes	complemented
235	#509	—	2	2	no	—
236	#509	C₂²×C₁₃	1	4	yes	complemented
237	#508	—	2	4	no	—
238	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
239	#470	C₂²×C₁₃	1	2	yes	complemented
240	#469	C₂²×C₁₃	1	2	yes	complemented
241	#468	—	2	2	no	—
242	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	#416	—	2	1	no	—
244	#360	C₂²×C₁₃	1	8	yes	complemented
245	#349	C₂²×C₁₃	1	4	yes	complemented
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	8	1	no	—
252	C₂²×C₁₃	—	8	4	no	—
253	C₂²×C₁₃	—	8	2	no	—
254	C₂²×C₁₃	—	8	8	no	—
255	C₂²×C₁₃	—	8	1	no	—
256	C₂²×C₁₃	#447	1	1	yes	characteristic
257	C₂²×C₁₃	#447	1	1	yes	characteristic
258	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	#447	1	1	yes	characteristic
264	C₄×C₁₃	#447	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
266	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	2	1	no	—
272	C₂×#41	—	4	1	no	—
273	C₂×#41	—	4	2	no	—
274	C₂×#41	—	4	2	no	—
275	C₂×#41	—	4	1	no	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	4	1	no	—
279	C₂³×C₄	—	4	1	no	—
280	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
281	#137	—	2	8	no	—
282	#137	—	2	8	no	—
283	AGL(1,ℤ/8)	—	2	8	no	—
284	AGL(1,ℤ/8)	—	2	8	no	—
285	#135	—	2	4	no	—
286	#135	—	2	4	no	—
287	#135	—	2	2	no	—
288	#135	—	2	2	no	—
289	#135	—	2	2	no	—
290	#135	—	2	2	no	—
291	#135	D₄×C₁₃	1	4	yes	complemented
292	#135	C₂³×C₁₃	1	4	yes	—
293	C₂×Q₁₆	—	2	1	no	—
294	C₂×Q₁₆	D₄×C₁₃	1	2	yes	complemented
295	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	1	no	—
299	C₂×D₈	—	2	1	no	—
300	C₂×D₈	D₄×C₁₃	1	2	yes	complemented
301	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
305	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
306	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	#123	—	4	1	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	#121	—	2	2	no	—
311	#120	—	4	1	no	—
312	C₄×D₄	—	4	2	no	—
313	#117	—	2	1	no	—
314	Q₃₂	—	2	4	no	—
315	SD₃₂	—	2	4	no	—
316	SD₃₂	—	2	4	no	—
317	D₁₆	—	2	4	no	—
318	M₃₂	—	2	2	no	—
319	M₃₂	C₂³×C₁₃	1	4	yes	complemented
320	C₂×C₁₆	—	2	2	no	—
321	#107	—	2	1	no	—
322	#106	C₂³×C₁₃	1	2	yes	complemented
323	#103	—	2	2	no	—
324	#102	—	2	2	no	—
325	C₂×C₁₃	—	2	1	no	—
326	C₂×C₁₃	—	2	1	no	—
327	C₂×C₁₃	—	2	1	no	—
328	C₂×C₁₃	—	4	2	no	—
329	C₂×C₁₃	—	8	4	no	—
330	C₂×C₁₃	—	16	1	no	—
331	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
332	C₂⁴	—	4	1	no	—
333	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
334	#41	—	2	8	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	#41	—	4	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	1	no	—
345	#41	—	4	1	no	—
346	#41	—	4	1	no	—
347	#41	—	4	1	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	4	1	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	C₁₃×D₈	1	2	yes	—
375	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
378	Q₁₆	—	2	4	no	—
379	Q₁₆	—	2	2	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
382	SD₁₆	—	2	8	no	—
383	SD₁₆	—	2	4	no	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	4	2	no	—
386	D₈	—	2	4	no	—
387	D₈	—	2	2	no	—
388	D₈	—	2	2	no	—
389	D₈	C₂×D₄×C₁₃	1	4	yes	—
390	M₁₆	—	2	4	no	—
391	M₁₆	—	2	4	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
398	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₄²	—	4	1	no	—
405	C₁₆	—	2	4	no	—
406	C₁₃	#33530	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	4	no	—
414	C₂³	C₂×C₁₃×D₈	1	2	yes	—
415	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	4	4	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	8	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	1	no	—
428	D₄	—	4	1	no	—
429	D₄	—	8	4	no	—
430	D₄	—	8	1	no	—
431	D₄	—	8	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
448	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
449	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
450	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
451	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
452	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	C₁₃×#120	1	2	yes	—
456	C₈	C₂²×D₄×C₁₃	1	2	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	4	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	8	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₁₃×#447	1	1	yes	characteristic
468	C₂²	C₁₃×#447	1	1	yes	characteristic
469	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₁₃×#447	1	1	yes	characteristic
475	C₄	C₁₃×#447	1	1	yes	characteristic
476	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
477	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	4	2	no	—
482	C₂	—	8	4	no	—
483	C₂	—	16	1	no	—
484	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#447
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#575	C₂	semidirect
2. C₁₃×#3414	C₂	semidirect
3. C₁₃×#3054	C₂	semidirect
4. C₁₃×#2191	C₂	semidirect
5. C₁₃×#2190	C₂	semidirect
6. C₁₃×#2145	C₂	semidirect
7. C₂×C₁₃×#349	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
20. C₁₃×#510	C₂²	semidirect
22. C₁₃×#509	C₂²	semidirect
24. C₂×C₁₃×M₃₂	C₂²	semidirect
25. C₁₃×#470	C₂²	semidirect
26. C₁₃×#469	C₂²	semidirect
28. C₁₃×#427	C₂²	semidirect
30. C₁₃×#360	C₂²	semidirect
31. C₁₃×#349	C₂²	semidirect
56. C₁₃×#135	D₄	semidirect
59. C₂×C₁₃×Q₁₆	D₄	semidirect
60. C₂×C₁₃×Q₁₆	C₂³	semidirect
65. C₂×C₁₃×D₈	D₄	semidirect
66. C₂×C₁₃×D₈	C₂³	semidirect
84. C₁₃×M₃₂	C₂³	semidirect
87. C₁₃×#106	C₂³	semidirect
90. #33530	C₁₃	direct (N × H)
165. C₂×#575	C₂×C₁₃	semidirect
166. #3414	C₂×C₁₃	semidirect
167. #3054	C₂×C₁₃	semidirect
168. #2191	C₂×C₁₃	semidirect
169. #2190	C₂×C₁₃	semidirect
170. #2145	C₂×C₁₃	semidirect
171. C₂×#349	C₂×C₁₃	semidirect
230. C₂×#135	C₂²×C₁₃	semidirect
234. #510	C₂²×C₁₃	semidirect
236. #509	C₂²×C₁₃	semidirect
238. C₂×M₃₂	C₂²×C₁₃	semidirect
239. #470	C₂²×C₁₃	semidirect
240. #469	C₂²×C₁₃	semidirect
242. #427	C₂²×C₁₃	semidirect
244. #360	C₂²×C₁₃	semidirect
245. #349	C₂²×C₁₃	semidirect
291. #135	D₄×C₁₃	semidirect
294. C₂×Q₁₆	D₄×C₁₃	semidirect
295. C₂×Q₁₆	C₂³×C₁₃	semidirect
300. C₂×D₈	D₄×C₁₃	semidirect
301. C₂×D₈	C₂³×C₁₃	semidirect
319. M₃₂	C₂³×C₁₃	semidirect
322. #106	C₂³×C₁₃	semidirect
406. C₁₃	#33530	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#575	2
C₁₃×#3414	2
C₁₃×#3054	2
C₁₃×#2191	2
C₁₃×#2190	2
C₁₃×#2145	2
C₂×C₁₃×#349	2
#33530	13

Subgroups — C13×#33530 #15719869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33530 #15719869