Subgroups — C₂×C₁₃×#2212 #15719930

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2212	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#364	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×#135	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×SD₁₆	—	2	1	no	—
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	—	2	1	no	—
14	C₂×C₁₃×#124	—	2	1	no	—
15	C₁₃×#510	—	2	2	no	—
16	C₁₃×#510	C₂²	1	4	yes	complemented
17	C₁₃×#509	—	2	2	no	—
18	C₁₃×#509	C₂²	1	4	yes	—
19	C₂×C₁₃×Q₃₂	—	2	1	no	—
20	C₂×C₁₃×SD₃₂	—	2	1	no	—
21	C₂×C₁₃×SD₃₂	—	2	1	no	—
22	C₂×C₁₃×D₁₆	—	2	1	no	—
23	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
25	C₁₃×#495	—	2	2	no	—
26	C₁₃×#495	C₂²	1	4	yes	complemented
27	C₁₃×#443	—	2	2	no	—
28	C₁₃×#443	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#104	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#364	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	—	2	1	no	—
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₁₃×#135	—	2	1	no	—
39	C₁₃×#135	—	2	1	no	—
40	C₁₃×#135	D₄	1	2	yes	—
41	C₁₃×#135	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
48	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	4	1	no	—
52	C₂×C₁₃×SD₁₆	—	4	1	no	—
53	C₂×C₁₃×SD₁₆	—	4	2	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	—	2	1	no	—
59	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
60	C₂×C₁₃×D₈	C₂³	1	2	yes	—
61	C₁₃×#131	—	2	4	no	—
62	C₁₃×#131	—	4	2	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	4	1	no	—
65	C₂²×C₈×C₁₃	—	4	1	no	—
66	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#124	—	2	4	no	—
69	C₁₃×#124	—	4	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₁₃×Q₃₂	—	2	4	no	—
73	C₁₃×SD₃₂	—	2	4	no	—
74	C₁₃×SD₃₂	—	2	4	no	—
75	C₁₃×D₁₆	—	2	4	no	—
76	C₁₃×M₃₂	—	2	1	no	—
77	C₁₃×M₃₂	—	2	1	no	—
78	C₁₃×M₃₂	C₂³	1	2	yes	—
79	C₁₃×M₃₂	C₂³	1	2	yes	—
80	C₂×C₁₃×C₁₆	—	2	1	no	—
81	C₂×C₁₃×C₁₆	—	2	1	no	—
82	C₁₃×#108	—	2	1	no	—
83	C₁₃×#108	C₂³	1	2	yes	—
84	C₁₃×#104	—	2	4	no	—
85	C₄×C₈×C₁₃	D₄	1	2	yes	—
86	C₄×C₈×C₁₃	C₂³	1	2	yes	—
87	C₂×#2212	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	4	1	no	—
89	C₁₃×#41	—	2	2	no	—
90	C₁₃×#41	—	2	2	no	—
91	C₁₃×#41	—	4	1	no	—
92	C₁₃×#41	—	4	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	4	1	no	—
96	C₂×Q₈×C₁₃	—	4	1	no	—
97	C₂×Q₈×C₁₃	—	4	1	no	—
98	C₂×Q₈×C₁₃	—	4	1	no	—
99	C₂×Q₈×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	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	—	4	1	no	—
106	C₂×D₄×C₁₃	—	4	1	no	—
107	C₂×D₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₁₃×Q₁₆	—	2	1	no	—
113	C₁₃×Q₁₆	—	2	2	no	—
114	C₁₃×Q₁₆	—	2	2	no	—
115	C₁₃×Q₁₆	—	4	1	no	—
116	C₁₃×Q₁₆	—	4	1	no	—
117	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
118	C₁₃×SD₁₆	—	2	2	no	—
119	C₁₃×SD₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	4	4	no	—
121	C₁₃×SD₁₆	—	4	4	no	—
122	C₁₃×D₈	—	2	1	no	—
123	C₁₃×D₈	—	2	2	no	—
124	C₁₃×D₈	—	2	2	no	—
125	C₁₃×D₈	—	4	1	no	—
126	C₁₃×D₈	—	4	1	no	—
127	C₁₃×D₈	C₂×D₄	1	2	yes	—
128	C₁₃×M₁₆	—	2	2	no	—
129	C₁₃×M₁₆	—	4	1	no	—
130	C₁₃×M₁₆	—	4	4	no	—
131	C₂×C₈×C₁₃	—	4	1	no	—
132	C₂×C₈×C₁₃	—	4	4	no	—
133	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
134	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
135	C₂×C₈×C₁₃	D₈	1	2	yes	—
136	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
141	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	4	8	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₁₃×C₁₆	—	2	2	no	—
147	C₁₃×C₁₆	—	2	2	no	—
148	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#509	C₂×C₁₃	1	1	yes	characteristic
150	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂×#443	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2212	C₂×C₁₃	1	8	yes	direct product factor
153	C₂×#364	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂×#362	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#361	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	8	4	no	—
159	C₂³×C₁₃	—	8	1	no	—
160	C₂³×C₁₃	—	8	1	no	—
161	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	4	1	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	8	1	no	—
167	Q₈×C₁₃	—	8	1	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	1	no	—
174	D₄×C₁₃	—	8	1	no	—
175	D₄×C₁₃	—	8	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	8	1	no	—
183	C₂×C₄×C₁₃	—	8	1	no	—
184	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	—	4	2	no	—
191	C₈×C₁₃	#121	1	1	yes	characteristic
192	C₈×C₁₃	#121	1	1	yes	characteristic
193	C₈×C₁₃	C₂×D₈	1	2	yes	—
194	C₈×C₁₃	C₂×D₈	1	2	yes	—
195	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
198	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
199	C₂²×SD₁₆	—	2	1	no	—
200	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#131	—	2	1	no	—
202	C₂×#124	—	2	1	no	—
203	#510	—	2	2	no	—
204	#510	C₂²×C₁₃	1	4	yes	complemented
205	#509	—	2	2	no	—
206	#509	C₂²×C₁₃	1	4	yes	—
207	C₂×Q₃₂	—	2	1	no	—
208	C₂×SD₃₂	—	2	1	no	—
209	C₂×SD₃₂	—	2	1	no	—
210	C₂×D₁₆	—	2	1	no	—
211	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
213	#495	—	2	2	no	—
214	#495	C₂²×C₁₃	1	4	yes	complemented
215	#443	—	2	2	no	—
216	#443	C₂²×C₁₃	1	4	yes	complemented
217	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#104	—	2	1	no	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#364	C₂²×C₁₃	1	4	yes	complemented
221	#362	C₂²×C₁₃	1	4	yes	complemented
222	#361	C₂²×C₁₃	1	4	yes	complemented
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	8	4	no	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	16	2	no	—
229	C₂²×C₁₃	—	16	2	no	—
230	C₂²×C₁₃	#459	1	1	yes	characteristic
231	C₂²×C₁₃	#459	1	1	yes	characteristic
232	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	#459	1	1	yes	characteristic
237	C₄×C₁₃	#459	1	1	yes	characteristic
238	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
239	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
240	C₂×#41	—	2	1	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	#135	—	2	1	no	—
244	#135	—	2	1	no	—
245	#135	D₄×C₁₃	1	2	yes	—
246	#135	C₂³×C₁₃	1	2	yes	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
253	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×SD₁₆	—	4	1	no	—
257	C₂×SD₁₆	—	4	1	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	2	1	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	1	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
265	C₂×D₈	C₂³×C₁₃	1	2	yes	—
266	#131	—	2	4	no	—
267	#131	—	4	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	4	1	no	—
270	C₂²×C₈	—	4	1	no	—
271	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	#124	—	2	4	no	—
274	#124	—	4	2	no	—
275	C₂×C₂²⋊C₄	—	4	2	no	—
276	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
277	Q₃₂	—	2	4	no	—
278	SD₃₂	—	2	4	no	—
279	SD₃₂	—	2	4	no	—
280	D₁₆	—	2	4	no	—
281	M₃₂	—	2	1	no	—
282	M₃₂	—	2	1	no	—
283	M₃₂	C₂³×C₁₃	1	2	yes	—
284	M₃₂	C₂³×C₁₃	1	2	yes	—
285	C₂×C₁₆	—	2	1	no	—
286	C₂×C₁₆	—	2	1	no	—
287	#108	—	2	1	no	—
288	#108	C₂³×C₁₃	1	2	yes	—
289	#104	—	2	4	no	—
290	C₄×C₈	D₄×C₁₃	1	2	yes	—
291	C₄×C₈	C₂³×C₁₃	1	2	yes	—
292	C₂×C₁₃	—	2	1	no	—
293	C₂×C₁₃	—	2	1	no	—
294	C₂×C₁₃	—	8	2	no	—
295	C₂×C₁₃	—	16	2	no	—
296	C₂×C₁₃	#2212	1	2	yes	direct product factor
297	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
298	C₂⁴	—	4	1	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	4	1	no	—
302	#41	—	4	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	2	2	no	—
324	Q₁₆	—	2	2	no	—
325	Q₁₆	—	4	1	no	—
326	Q₁₆	—	4	1	no	—
327	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	4	4	no	—
331	SD₁₆	—	4	4	no	—
332	D₈	—	2	1	no	—
333	D₈	—	2	2	no	—
334	D₈	—	2	2	no	—
335	D₈	—	4	1	no	—
336	D₈	—	4	1	no	—
337	D₈	C₂×D₄×C₁₃	1	2	yes	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	4	1	no	—
340	M₁₆	—	4	4	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	4	no	—
343	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
344	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
345	C₂×C₈	C₁₃×D₈	1	2	yes	—
346	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
350	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
351	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
352	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₂²⋊C₄	—	4	8	no	—
354	C₄²	—	2	1	no	—
355	C₄²	C₂×D₄×C₁₃	1	2	yes	—
356	C₁₆	—	2	2	no	—
357	C₁₆	—	2	2	no	—
358	C₁₃	C₂×#2212	1	1	yes	characteristic, direct product factor, Sylow
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	8	4	no	—
362	C₂³	—	8	1	no	—
363	C₂³	—	8	1	no	—
364	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	8	1	no	—
370	Q₈	—	8	1	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
388	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
390	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
391	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	C₁₃×#121	1	1	yes	characteristic
395	C₈	C₁₃×#121	1	1	yes	characteristic
396	C₈	C₂×C₁₃×D₈	1	2	yes	—
397	C₈	C₂×C₁₃×D₈	1	2	yes	—
398	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	16	2	no	—
406	C₂²	—	16	2	no	—
407	C₂²	C₁₃×#459	1	1	yes	characteristic
408	C₂²	C₁₃×#459	1	1	yes	characteristic
409	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₁₃×#459	1	1	yes	characteristic
414	C₄	C₁₃×#459	1	1	yes	characteristic
415	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
416	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	8	2	no	—
420	C₂	—	16	2	no	—
421	C₂	C₁₃×#2212	1	2	yes	direct product factor
422	C₂	C₂×C₁₃×#459	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
3. C₂×C₁₃×#495	C₂	semidirect
4. C₂×C₁₃×#443	C₂	semidirect
5. C₁₃×#2212	C₂	direct (N × H)
6. C₂×C₁₃×#364	C₂	semidirect
7. C₂×C₁₃×#362	C₂	semidirect
8. C₂×C₁₃×#361	C₂	semidirect
16. C₁₃×#510	C₂²	semidirect
26. C₁₃×#495	C₂²	semidirect
28. C₁₃×#443	C₂²	semidirect
32. C₁₃×#364	C₂²	semidirect
33. C₁₃×#362	C₂²	semidirect
34. C₁₃×#361	C₂²	semidirect
87. C₂×#2212	C₁₃	direct (N × H)
148. C₂×#510	C₂×C₁₃	semidirect
150. C₂×#495	C₂×C₁₃	semidirect
151. C₂×#443	C₂×C₁₃	semidirect
152. #2212	C₂×C₁₃	direct (N × H)
153. C₂×#364	C₂×C₁₃	semidirect
154. C₂×#362	C₂×C₁₃	semidirect
155. C₂×#361	C₂×C₁₃	semidirect
204. #510	C₂²×C₁₃	semidirect
214. #495	C₂²×C₁₃	semidirect
216. #443	C₂²×C₁₃	semidirect
220. #364	C₂²×C₁₃	semidirect
221. #362	C₂²×C₁₃	semidirect
222. #361	C₂²×C₁₃	semidirect
296. C₂×C₁₃	#2212	direct (N × H)
358. C₁₃	C₂×#2212	direct (N × H)
421. C₂	C₁₃×#2212	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×#510	2
C₂×C₁₃×#509	2
C₂×C₁₃×#495	2
C₂×C₁₃×#443	2
C₁₃×#2212	2
C₂×C₁₃×#364	2
C₂×C₁₃×#362	2
C₂×C₁₃×#361	2
C₂×#2212	13

Subgroups — C2×C13×#2212 #15719930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2212 #15719930