Subgroups — C₂₉×#19212 #20314112

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#486	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1698	C₂	1	4	yes	maximal, complemented
6	C₂₉×#1678	C₂	1	4	yes	maximal, complemented
7	C₂₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1545	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#533	C₂²	1	1	yes	characteristic
11	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
13	C₂₉×#500	—	2	1	no	—
14	C₂₉×#492	—	2	1	no	—
15	C₂₉×#487	—	2	1	no	—
16	C₂₉×#486	—	2	1	no	—
17	C₂₉×#486	—	2	1	no	—
18	C₂₉×#486	—	2	1	no	—
19	C₂₉×#486	C₂²	1	2	yes	—
20	C₂₉×#486	C₂²	1	2	yes	—
21	C₂₉×#484	—	2	2	no	—
22	C₂₉×#477	C₂²	1	4	yes	complemented
23	C₂₉×#460	C₂²	1	4	yes	—
24	C₂₉×#450	—	2	2	no	—
25	C₂₉×#446	—	2	1	no	—
26	C₂₉×#446	C₂²	1	2	yes	complemented
27	C₈×Q₈×C₂₉	—	2	1	no	—
28	C₈×Q₈×C₂₉	C₂²	1	2	yes	complemented
29	C₂₉×#431	C₂²	1	1	yes	characteristic
30	C₂₉×#431	C₂²	1	1	yes	characteristic
31	C₂₉×#424	—	2	1	no	—
32	C₂₉×#423	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#102	—	2	1	no	—
34	C₂×C₂₉×#102	—	2	1	no	—
35	C₂₉×#405	—	2	1	no	—
36	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#335	C₂²	1	2	yes	complemented
38	C₂₉×#334	C₂²	1	2	yes	complemented
39	C₂₉×#333	C₂²	1	4	yes	complemented
40	C₂₉×#331	C₂²	1	4	yes	—
41	C₂²×Q₈×C₂₉	—	2	1	no	—
42	C₂²×D₄×C₂₉	—	2	1	no	—
43	C₂²×D₄×C₂₉	—	2	1	no	—
44	C₂²×D₄×C₂₉	—	2	1	no	—
45	C₂×SD₁₆×C₂₉	—	2	4	no	—
46	C₂×M₁₆×C₂₉	—	2	1	no	—
47	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
49	C₂₉×C₄⋊Q₈	—	2	1	no	—
50	C₂₉×C₄⋊Q₈	—	2	1	no	—
51	C₂₉×C₄⋊Q₈	—	2	1	no	—
52	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₂₉×#127	—	2	1	no	—
56	C₂₉×#127	—	2	1	no	—
57	C₂₉×#127	—	2	1	no	—
58	C₂₉×#127	C₂³	1	2	yes	—
59	C₂₉×#125	—	2	1	no	—
60	C₂₉×C₂²⋊Q₈	—	2	1	no	—
61	C₂₉×C₂²⋊Q₈	D₄	1	2	yes	—
62	C₄×Q₈×C₂₉	—	2	1	no	—
63	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
64	C₂₉×#117	—	2	1	no	—
65	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
67	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
68	C₂₉×#107	—	2	4	no	—
69	C₂₉×C₄⋊C₈	—	2	2	no	—
70	C₂₉×C₄⋊C₈	—	2	2	no	—
71	C₂₉×C₄⋊C₈	—	2	1	no	—
72	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
74	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
75	C₂₉×#103	—	2	4	no	—
76	C₂₉×#102	—	2	2	no	—
77	C₂₉×#102	—	2	2	no	—
78	C₂₉×#102	—	2	2	no	—
79	C₂₉×#102	—	2	2	no	—
80	C₂₉×#102	—	2	4	no	—
81	C₂₉×C₂²⋊C₈	—	2	1	no	—
82	C₂₉×C₂²⋊C₈	—	2	1	no	—
83	C₂₉×#97	—	2	2	no	—
84	C₄×C₈×C₂₉	—	2	2	no	—
85	C₄×C₈×C₂₉	—	2	1	no	—
86	C₄×C₈×C₂₉	—	2	1	no	—
87	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
88	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
89	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
91	C₂⁴×C₂₉	—	4	1	no	—
92	C₂×Q₈×C₂₉	—	2	1	no	—
93	C₂×Q₈×C₂₉	—	2	2	no	—
94	C₂×Q₈×C₂₉	—	4	1	no	—
95	C₂×Q₈×C₂₉	—	8	2	no	—
96	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₂₉	—	2	2	no	—
98	C₂×D₄×C₂₉	—	2	2	no	—
99	C₂×D₄×C₂₉	—	2	2	no	—
100	C₂×D₄×C₂₉	—	4	1	no	—
101	C₂×D₄×C₂₉	—	4	1	no	—
102	C₂×D₄×C₂₉	—	4	1	no	—
103	C₂×D₄×C₂₉	—	4	2	no	—
104	C₂×D₄×C₂₉	—	4	2	no	—
105	C₂×D₄×C₂₉	—	8	2	no	—
106	C₂×D₄×C₂₉	—	8	2	no	—
107	C₂²×C₄×C₂₉	—	4	1	no	—
108	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
111	SD₁₆×C₂₉	—	8	4	no	—
112	M₁₆×C₂₉	—	4	2	no	—
113	C₂×C₈×C₂₉	—	2	2	no	—
114	C₂×C₈×C₂₉	—	2	2	no	—
115	C₂×C₈×C₂₉	—	2	2	no	—
116	C₂×C₈×C₂₉	—	2	2	no	—
117	C₂×C₈×C₂₉	—	2	2	no	—
118	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₂₉	—	2	1	no	—
123	C₄⋊C₄×C₂₉	—	2	1	no	—
124	C₄⋊C₄×C₂₉	—	2	1	no	—
125	C₄⋊C₄×C₂₉	—	2	2	no	—
126	C₄⋊C₄×C₂₉	—	2	2	no	—
127	C₄⋊C₄×C₂₉	—	2	2	no	—
128	C₄⋊C₄×C₂₉	—	2	2	no	—
129	C₄⋊C₄×C₂₉	—	4	1	no	—
130	C₄⋊C₄×C₂₉	—	4	1	no	—
131	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
132	C₂²⋊C₄×C₂₉	—	2	2	no	—
133	C₄²×C₂₉	—	2	2	no	—
134	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₂₉	#41	1	1	yes	characteristic
137	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
138	#19212	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₂₉	—	4	2	no	—
140	C₂³×C₂₉	—	8	2	no	—
141	C₂³×C₂₉	—	8	2	no	—
142	C₂³×C₂₉	—	8	2	no	—
143	C₂³×C₂₉	#121	1	1	yes	characteristic
144	Q₈×C₂₉	—	2	4	no	—
145	Q₈×C₂₉	—	4	2	no	—
146	Q₈×C₂₉	—	8	2	no	—
147	Q₈×C₂₉	—	8	2	no	—
148	D₄×C₂₉	—	4	2	no	—
149	D₄×C₂₉	—	4	2	no	—
150	D₄×C₂₉	—	4	4	no	—
151	D₄×C₂₉	—	8	2	no	—
152	D₄×C₂₉	—	8	2	no	—
153	D₄×C₂₉	—	8	2	no	—
154	D₄×C₂₉	—	8	2	no	—
155	C₂×C₄×C₂₉	—	2	2	no	—
156	C₂×C₄×C₂₉	—	2	2	no	—
157	C₂×C₄×C₂₉	—	2	2	no	—
158	C₂×C₄×C₂₉	—	2	2	no	—
159	C₂×C₄×C₂₉	—	4	2	no	—
160	C₂×C₄×C₂₉	—	8	2	no	—
161	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₂₉	#135	1	2	yes	—
165	C₂×C₄×C₂₉	#137	1	2	yes	—
166	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
169	C₈×C₂₉	—	2	1	no	—
170	C₈×C₂₉	—	2	1	no	—
171	C₈×C₂₉	—	2	1	no	—
172	C₈×C₂₉	—	2	1	no	—
173	C₈×C₂₉	—	4	2	no	—
174	C₈×C₂₉	—	4	2	no	—
175	C₈×C₂₉	—	4	2	no	—
176	#3230	C₂×C₂₉	1	1	yes	characteristic, complemented
177	#3208	C₂×C₂₉	1	1	yes	characteristic
178	C₂×#486	C₂×C₂₉	1	1	yes	characteristic
179	#2960	C₂×C₂₉	1	1	yes	characteristic, complemented
180	#1698	C₂×C₂₉	1	4	yes	complemented
181	#1678	C₂×C₂₉	1	4	yes	complemented
182	#1564	C₂×C₂₉	1	1	yes	characteristic, complemented
183	#1548	C₂×C₂₉	1	1	yes	characteristic, complemented
184	#1545	C₂×C₂₉	1	1	yes	characteristic
185	C₂²×C₂₉	—	2	1	no	—
186	C₂²×C₂₉	—	2	1	no	—
187	C₂²×C₂₉	—	8	2	no	—
188	C₂²×C₂₉	—	8	2	no	—
189	C₂²×C₂₉	—	8	2	no	—
190	C₂²×C₂₉	—	16	4	no	—
191	C₂²×C₂₉	#464	1	2	yes	—
192	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
193	C₄×C₂₉	—	2	1	no	—
194	C₄×C₂₉	—	2	1	no	—
195	C₄×C₂₉	—	4	2	no	—
196	C₄×C₂₉	—	4	2	no	—
197	C₄×C₂₉	—	8	2	no	—
198	C₄×C₂₉	#464	1	2	yes	—
199	C₄×C₂₉	#472	1	2	yes	—
200	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
201	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
202	C₄×C₂₉	#577	1	2	yes	—
203	#533	C₂²×C₂₉	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
205	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
206	#500	—	2	1	no	—
207	#492	—	2	1	no	—
208	#487	—	2	1	no	—
209	#486	—	2	1	no	—
210	#486	—	2	1	no	—
211	#486	—	2	1	no	—
212	#486	C₂²×C₂₉	1	2	yes	—
213	#486	C₂²×C₂₉	1	2	yes	—
214	#484	—	2	2	no	—
215	#477	C₂²×C₂₉	1	4	yes	complemented
216	#460	C₂²×C₂₉	1	4	yes	—
217	#450	—	2	2	no	—
218	#446	—	2	1	no	—
219	#446	C₂²×C₂₉	1	2	yes	complemented
220	C₈×Q₈	—	2	1	no	—
221	C₈×Q₈	C₂²×C₂₉	1	2	yes	complemented
222	#431	C₂²×C₂₉	1	1	yes	characteristic
223	#431	C₂²×C₂₉	1	1	yes	characteristic
224	#424	—	2	1	no	—
225	#423	C₂²×C₂₉	1	1	yes	characteristic
226	C₂×#102	—	2	1	no	—
227	C₂×#102	—	2	1	no	—
228	#405	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
230	#335	C₂²×C₂₉	1	2	yes	complemented
231	#334	C₂²×C₂₉	1	2	yes	complemented
232	#333	C₂²×C₂₉	1	4	yes	complemented
233	#331	C₂²×C₂₉	1	4	yes	—
234	C₂×C₂₉	—	2	2	no	—
235	C₂×C₂₉	—	16	2	no	—
236	C₂×C₂₉	C₂×#464	1	1	yes	characteristic
237	C₂×C₂₉	#3057	1	1	yes	characteristic
238	C₂×C₂₉	C₂×#472	1	1	yes	characteristic
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂×SD₁₆	—	2	4	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
246	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
251	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	C₂³×C₂₉	1	2	yes	—
257	#125	—	2	1	no	—
258	C₂²⋊Q₈	—	2	1	no	—
259	C₂²⋊Q₈	D₄×C₂₉	1	2	yes	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
262	#117	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
266	#107	—	2	4	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
271	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
272	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
273	#103	—	2	4	no	—
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	4	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
286	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
289	C₂₉	#19212	1	1	yes	characteristic, direct product factor, Sylow
290	C₂⁴	—	4	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	8	2	no	—
295	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
309	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
310	SD₁₆	—	8	4	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
335	C₄²	#41×C₂₉	1	1	yes	characteristic
336	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
337	C₂³	—	4	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	—	8	2	no	—
341	C₂³	C₂₉×#121	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	2	no	—
345	Q₈	—	8	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	4	no	—
349	D₄	—	8	2	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
360	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
361	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
362	C₂×C₄	C₂₉×#135	1	2	yes	—
363	C₂×C₄	C₂₉×#137	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂₉×#464	1	2	yes	—
381	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₂₉×#464	1	2	yes	—
388	C₄	C₂₉×#472	1	2	yes	—
389	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
390	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
391	C₄	C₂₉×#577	1	2	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	16	2	no	—
394	C₂	C₂×C₂₉×#464	1	1	yes	characteristic
395	C₂	C₂₉×#3057	1	1	yes	characteristic
396	C₂	C₂×C₂₉×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3230	C₂	semidirect
4. C₂₉×#2960	C₂	semidirect
5. C₂₉×#1698	C₂	semidirect
6. C₂₉×#1678	C₂	semidirect
7. C₂₉×#1564	C₂	semidirect
8. C₂₉×#1548	C₂	semidirect
22. C₂₉×#477	C₂²	semidirect
26. C₂₉×#446	C₂²	semidirect
28. C₈×Q₈×C₂₉	C₂²	semidirect
37. C₂₉×#335	C₂²	semidirect
38. C₂₉×#334	C₂²	semidirect
39. C₂₉×#333	C₂²	semidirect
138. #19212	C₂₉	direct (N × H)
176. #3230	C₂×C₂₉	semidirect
179. #2960	C₂×C₂₉	semidirect
180. #1698	C₂×C₂₉	semidirect
181. #1678	C₂×C₂₉	semidirect
182. #1564	C₂×C₂₉	semidirect
183. #1548	C₂×C₂₉	semidirect
215. #477	C₂²×C₂₉	semidirect
219. #446	C₂²×C₂₉	semidirect
221. C₈×Q₈	C₂²×C₂₉	semidirect
230. #335	C₂²×C₂₉	semidirect
231. #334	C₂²×C₂₉	semidirect
232. #333	C₂²×C₂₉	semidirect
289. C₂₉	#19212	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#3230	2
C₂₉×#3208	2
C₂×C₂₉×#486	2
C₂₉×#2960	2
C₂₉×#1698	2
C₂₉×#1678	2
C₂₉×#1564	2
C₂₉×#1548	2
C₂₉×#1545	2
#19212	29

Subgroups — C29×#19212 #20314112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19212 #20314112