Subgroups — C₂×C₁₃×#2223 #15719955

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2223	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#361	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#137	—	2	1	no	—
10	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×SD₃₂	—	2	1	no	—
15	C₂×C₁₃×SD₃₂	—	2	1	no	—
16	C₂×C₁₃×SD₃₂	—	2	2	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
18	C₁₃×#504	—	2	2	no	—
19	C₁₃×#504	C₂²	1	4	yes	complemented
20	C₂×C₁₃×M₃₂	—	2	1	no	—
21	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₁₆	—	2	1	no	—
23	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
24	C₁₃×#473	—	2	2	no	—
25	C₁₃×#473	C₂²	1	4	yes	complemented
26	C₁₃×#472	—	2	2	no	—
27	C₁₃×#472	C₂²	1	4	yes	—
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#101	—	2	1	no	—
31	C₂×C₁₃×#100	—	2	1	no	—
32	C₁₃×#368	C₂²	1	4	yes	complemented
33	C₁₃×#362	C₂²	1	4	yes	complemented
34	C₁₃×#361	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₁₃×#137	—	2	4	no	—
39	C₁₃×#137	—	4	2	no	—
40	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
41	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
42	C₂×C₁₃×Q₁₆	—	2	1	no	—
43	C₂×C₁₃×Q₁₆	—	2	1	no	—
44	C₂×C₁₃×Q₁₆	—	2	1	no	—
45	C₂×C₁₃×Q₁₆	—	2	1	no	—
46	C₂×C₁₃×Q₁₆	—	2	1	no	—
47	C₂×C₁₃×Q₁₆	—	4	1	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×SD₁₆	—	4	1	no	—
50	C₂×C₁₃×SD₁₆	—	4	1	no	—
51	C₂×C₁₃×D₈	—	2	1	no	—
52	C₂×C₁₃×D₈	—	2	1	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	4	1	no	—
57	C₂×C₁₃×D₈	C₂³	1	2	yes	—
58	C₁₃×#131	—	2	1	no	—
59	C₁₃×#131	—	2	1	no	—
60	C₁₃×#131	D₄	1	2	yes	—
61	C₁₃×#131	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	—	2	1	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×SD₃₂	—	2	4	no	—
69	C₁₃×SD₃₂	—	2	4	no	—
70	C₁₃×M₃₂	—	2	1	no	—
71	C₁₃×M₃₂	—	2	4	no	—
72	C₁₃×M₃₂	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	—	2	1	no	—
74	C₂×C₁₃×C₁₆	—	2	4	no	—
75	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
78	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
79	C₁₃×#108	—	2	1	no	—
80	C₁₃×#108	—	2	1	no	—
81	C₁₃×#108	C₂³	1	2	yes	—
82	C₁₃×#108	C₂³	1	2	yes	—
83	C₁₃×#101	—	2	4	no	—
84	C₁₃×#100	—	2	4	no	—
85	C₂×#2223	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	4	1	no	—
87	C₁₃×#41	—	2	1	no	—
88	C₁₃×#41	—	2	1	no	—
89	C₁₃×#41	D₈	1	2	yes	—
90	C₁₃×#41	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	4	1	no	—
93	C₂×Q₈×C₁₃	—	4	1	no	—
94	C₂×Q₈×C₁₃	—	4	1	no	—
95	C₂×Q₈×C₁₃	—	4	1	no	—
96	C₂×Q₈×C₁₃	—	4	1	no	—
97	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
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	1	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	1	no	—
105	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×Q₁₆	—	2	2	no	—
111	C₁₃×Q₁₆	—	4	4	no	—
112	C₁₃×Q₁₆	—	4	1	no	—
113	C₁₃×Q₁₆	—	4	1	no	—
114	C₁₃×SD₁₆	—	4	4	no	—
115	C₁₃×SD₁₆	—	4	4	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	—	4	4	no	—
119	C₁₃×D₈	—	4	1	no	—
120	C₁₃×D₈	—	4	1	no	—
121	C₁₃×M₁₆	—	2	1	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	—	4	1	no	—
127	C₁₃×M₁₆	—	4	1	no	—
128	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	4	1	no	—
133	C₂×C₈×C₁₃	—	4	1	no	—
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
138	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×C₁₆	—	2	2	no	—
141	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
142	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
143	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂×#472	C₂×C₁₃	1	1	yes	characteristic
147	#2223	C₂×C₁₃	1	8	yes	direct product factor
148	C₂×#368	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#362	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂×#361	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	2	1	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	8	1	no	—
154	C₂³×C₁₃	—	8	1	no	—
155	C₂³×C₁₃	—	16	2	no	—
156	C₂³×C₁₃	#135	1	1	yes	characteristic
157	Q₈×C₁₃	—	2	1	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	8	1	no	—
161	Q₈×C₁₃	—	8	1	no	—
162	Q₈×C₁₃	C₂×D₈	1	2	yes	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	2	no	—
165	D₄×C₁₃	—	2	1	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	8	1	no	—
169	D₄×C₁₃	—	8	1	no	—
170	D₄×C₁₃	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	8	1	no	—
176	C₂×C₄×C₁₃	—	8	1	no	—
177	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	#121	1	1	yes	characteristic
187	C₈×C₁₃	#121	1	1	yes	characteristic
188	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×#137	—	2	1	no	—
191	C₂×AGL(1,ℤ/8)	—	2	1	no	—
192	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×SD₃₂	—	2	1	no	—
196	C₂×SD₃₂	—	2	1	no	—
197	C₂×SD₃₂	—	2	2	no	—
198	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
199	#504	—	2	2	no	—
200	#504	C₂²×C₁₃	1	4	yes	complemented
201	C₂×M₃₂	—	2	1	no	—
202	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²×C₁₆	—	2	1	no	—
204	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	#473	—	2	2	no	—
206	#473	C₂²×C₁₃	1	4	yes	complemented
207	#472	—	2	2	no	—
208	#472	C₂²×C₁₃	1	4	yes	—
209	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#101	—	2	1	no	—
212	C₂×#100	—	2	1	no	—
213	#368	C₂²×C₁₃	1	4	yes	complemented
214	#362	C₂²×C₁₃	1	4	yes	complemented
215	#361	C₂²×C₁₃	1	4	yes	complemented
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	16	2	no	—
221	C₂²×C₁₃	—	16	2	no	—
222	C₂²×C₁₃	—	16	2	no	—
223	C₂²×C₁₃	#466	1	1	yes	characteristic
224	C₂²×C₁₃	#466	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	#466	1	1	yes	characteristic
229	C₄×C₁₃	#466	1	1	yes	characteristic
230	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
231	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
232	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	#137	—	2	4	no	—
236	#137	—	4	2	no	—
237	AGL(1,ℤ/8)	—	2	4	no	—
238	AGL(1,ℤ/8)	—	4	2	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×Q₁₆	—	2	1	no	—
244	C₂×Q₁₆	—	4	1	no	—
245	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
246	C₂×SD₁₆	—	4	1	no	—
247	C₂×SD₁₆	—	4	1	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	4	1	no	—
254	C₂×D₈	C₂³×C₁₃	1	2	yes	—
255	#131	—	2	1	no	—
256	#131	—	2	1	no	—
257	#131	D₄×C₁₃	1	2	yes	—
258	#131	C₂³×C₁₃	1	2	yes	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	SD₃₂	—	2	4	no	—
266	SD₃₂	—	2	4	no	—
267	M₃₂	—	2	1	no	—
268	M₃₂	—	2	4	no	—
269	M₃₂	C₂³×C₁₃	1	2	yes	—
270	C₂×C₁₆	—	2	1	no	—
271	C₂×C₁₆	—	2	4	no	—
272	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
273	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
274	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
275	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
276	#108	—	2	1	no	—
277	#108	—	2	1	no	—
278	#108	C₂³×C₁₃	1	2	yes	—
279	#108	C₂³×C₁₃	1	2	yes	—
280	#101	—	2	4	no	—
281	#100	—	2	4	no	—
282	C₂×C₁₃	—	2	1	no	—
283	C₂×C₁₃	—	2	1	no	—
284	C₂×C₁₃	—	4	2	no	—
285	C₂×C₁₃	—	16	2	no	—
286	C₂×C₁₃	#2223	1	2	yes	direct product factor
287	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
288	C₂⁴	—	4	1	no	—
289	#41	—	2	1	no	—
290	#41	—	2	1	no	—
291	#41	C₁₃×D₈	1	2	yes	—
292	#41	C₂×D₄×C₁₃	1	2	yes	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	4	4	no	—
314	Q₁₆	—	4	1	no	—
315	Q₁₆	—	4	1	no	—
316	SD₁₆	—	4	4	no	—
317	SD₁₆	—	4	4	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	4	4	no	—
321	D₈	—	4	1	no	—
322	D₈	—	4	1	no	—
323	M₁₆	—	2	1	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
340	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
341	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₁₆	—	2	2	no	—
343	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
344	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
345	C₁₃	C₂×#2223	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	—	2	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	16	2	no	—
351	C₂³	C₁₃×#135	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	8	1	no	—
356	Q₈	—	8	1	no	—
357	Q₈	C₂×C₁₃×D₈	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	C₂×C₁₃×D₈	1	2	yes	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
373	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
376	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	C₁₃×#121	1	1	yes	characteristic
382	C₈	C₁₃×#121	1	1	yes	characteristic
383	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	—	16	2	no	—
392	C₂²	C₁₃×#466	1	1	yes	characteristic
393	C₂²	C₁₃×#466	1	1	yes	characteristic
394	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₁₃×#466	1	1	yes	characteristic
398	C₄	C₁₃×#466	1	1	yes	characteristic
399	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
400	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	16	2	no	—
405	C₂	C₁₃×#2223	1	2	yes	direct product factor
406	C₂	C₂×C₁₃×#466	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#472	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×SD₃₂	C₂	semidirect
2. C₂×C₁₃×#504	C₂	semidirect
3. C₂×C₁₃×#473	C₂	semidirect
5. C₁₃×#2223	C₂	direct (N × H)
6. C₂×C₁₃×#368	C₂	semidirect
7. C₂×C₁₃×#362	C₂	semidirect
8. C₂×C₁₃×#361	C₂	semidirect
17. C₂×C₁₃×SD₃₂	C₂²	semidirect
19. C₁₃×#504	C₂²	semidirect
25. C₁₃×#473	C₂²	semidirect
32. C₁₃×#368	C₂²	semidirect
33. C₁₃×#362	C₂²	semidirect
34. C₁₃×#361	C₂²	semidirect
85. C₂×#2223	C₁₃	direct (N × H)
143. C₂²×SD₃₂	C₂×C₁₃	semidirect
144. C₂×#504	C₂×C₁₃	semidirect
145. C₂×#473	C₂×C₁₃	semidirect
147. #2223	C₂×C₁₃	direct (N × H)
148. C₂×#368	C₂×C₁₃	semidirect
149. C₂×#362	C₂×C₁₃	semidirect
150. C₂×#361	C₂×C₁₃	semidirect
198. C₂×SD₃₂	C₂²×C₁₃	semidirect
200. #504	C₂²×C₁₃	semidirect
206. #473	C₂²×C₁₃	semidirect
213. #368	C₂²×C₁₃	semidirect
214. #362	C₂²×C₁₃	semidirect
215. #361	C₂²×C₁₃	semidirect
286. C₂×C₁₃	#2223	direct (N × H)
345. C₁₃	C₂×#2223	direct (N × H)
405. C₂	C₁₃×#2223	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×SD₃₂	2
C₂×C₁₃×#504	2
C₂×C₁₃×#473	2
C₂×C₁₃×#472	2
C₁₃×#2223	2
C₂×C₁₃×#368	2
C₂×C₁₃×#362	2
C₂×C₁₃×#361	2
C₂×#2223	13

Subgroups — C2×C13×#2223 #15719955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2223 #15719955