Subgroups — C₂×C₁₃×#2190 #15719867

Order 3328.

1180 conjugacy classes of subgroups.

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

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₂×C₁₃×#509	C₂	semidirect
3. C₂×C₁₃×#469	C₂	semidirect
4. C₁₃×#2190	C₂	direct (N × H)
5. C₂×C₁₃×#360	C₂	semidirect
6. C₂×C₁₃×#349	C₂	semidirect
10. C₁₃×#575	C₂²	semidirect
15. C₂²×C₁₃×D₈	C₂²	semidirect
19. C₁₃×#509	C₂²	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
24. C₁₃×#469	C₂²	semidirect
25. C₂×C₁₃×#106	C₂²	semidirect
27. C₁₃×#360	C₂²	semidirect
28. C₁₃×#349	C₂²	semidirect
52. C₁₃×#135	D₄	semidirect
55. C₂×C₁₃×Q₁₆	D₄	semidirect
62. C₂×C₁₃×D₈	D₄	semidirect
63. C₂×C₁₃×D₈	C₂³	semidirect
77. C₁₃×M₃₂	C₂³	semidirect
80. C₁₃×#106	C₂³	semidirect
82. C₂×#2190	C₁₃	direct (N × H)
132. C₁₃×Q₁₆	C₂×D₄	semidirect
140. C₁₃×D₈	C₂×D₄	semidirect
154. C₂×#575	C₂×C₁₃	semidirect
155. C₂×#509	C₂×C₁₃	semidirect
156. C₂×#469	C₂×C₁₃	semidirect
157. #2190	C₂×C₁₃	direct (N × H)
158. C₂×#360	C₂×C₁₃	semidirect
159. C₂×#349	C₂×C₁₃	semidirect
213. #575	C₂²×C₁₃	semidirect
218. C₂²×D₈	C₂²×C₁₃	semidirect
222. #509	C₂²×C₁₃	semidirect
225. C₂×M₃₂	C₂²×C₁₃	semidirect
227. #469	C₂²×C₁₃	semidirect
228. C₂×#106	C₂²×C₁₃	semidirect
230. #360	C₂²×C₁₃	semidirect
231. #349	C₂²×C₁₃	semidirect
278. #135	D₄×C₁₃	semidirect
281. C₂×Q₁₆	D₄×C₁₃	semidirect
288. C₂×D₈	D₄×C₁₃	semidirect
289. C₂×D₈	C₂³×C₁₃	semidirect
303. M₃₂	C₂³×C₁₃	semidirect
306. #106	C₂³×C₁₃	semidirect
313. C₂×C₁₃	#2190	direct (N × H)
364. Q₁₆	C₂×D₄×C₁₃	semidirect
372. D₈	C₂×D₄×C₁₃	semidirect
386. C₁₃	C₂×#2190	direct (N × H)
465. C₂	C₁₃×#2190	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
C₂×C₁₃×#509	2
C₂×C₁₃×#469	2
C₁₃×#2190	2
C₂×C₁₃×#360	2
C₂×C₁₃×#349	2
C₂×#2190	13

Subgroups — C2×C13×#2190 #15719867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2190 #15719867