Subgroups — C₂×C₁₃×#2191 #15719868

Order 3328.

1128 conjugacy classes of subgroups.

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

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#575	C₂
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
2. C₂×C₁₃×#510	C₂	semidirect
3. C₂×C₁₃×#470	C₂	semidirect
4. C₁₃×#2191	C₂	direct (N × H)
5. C₂×C₁₃×#360	C₂	semidirect
6. C₂×C₁₃×#349	C₂	semidirect
15. C₂²×C₁₃×Q₁₆	C₂²	semidirect
19. C₁₃×#510	C₂²	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
24. C₁₃×#470	C₂²	semidirect
25. C₂×C₁₃×#106	C₂²	semidirect
27. C₁₃×#360	C₂²	semidirect
28. C₁₃×#349	C₂²	semidirect
58. C₂×C₁₃×Q₁₆	C₂³	semidirect
77. C₁₃×M₃₂	C₂³	semidirect
80. C₁₃×#106	C₂³	semidirect
82. C₂×#2191	C₁₃	direct (N × H)
154. C₂×#510	C₂×C₁₃	semidirect
155. C₂×#470	C₂×C₁₃	semidirect
156. #2191	C₂×C₁₃	direct (N × H)
157. C₂×#360	C₂×C₁₃	semidirect
158. C₂×#349	C₂×C₁₃	semidirect
214. C₂²×Q₁₆	C₂²×C₁₃	semidirect
218. #510	C₂²×C₁₃	semidirect
221. C₂×M₃₂	C₂²×C₁₃	semidirect
223. #470	C₂²×C₁₃	semidirect
224. C₂×#106	C₂²×C₁₃	semidirect
226. #360	C₂²×C₁₃	semidirect
227. #349	C₂²×C₁₃	semidirect
276. C₂×Q₁₆	C₂³×C₁₃	semidirect
295. M₃₂	C₂³×C₁₃	semidirect
298. #106	C₂³×C₁₃	semidirect
304. C₂×C₁₃	#2191	direct (N × H)
376. C₁₃	C₂×#2191	direct (N × H)
447. C₂	C₁₃×#2191	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×#510	2
C₂×C₁₃×#470	2
C₁₃×#2191	2
C₂×C₁₃×#360	2
C₂×C₁₃×#349	2
C₂×#2191	13

Subgroups — C2×C13×#2191 #15719868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2191 #15719868