Subgroups — C₂₉×#33630 #20328530

Order 7424.

542 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₉×#135	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2229	C₂	1	4	yes	maximal, complemented
4	C₂₉×#2228	C₂	1	4	yes	maximal, complemented
5	C₂₉×#2159	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2139	C₂	1	2	yes	maximal
8	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
9	C₂×C₂₉×#125	—	2	1	no	—
10	C₄×#41×C₂₉	—	2	1	no	—
11	C₂×C₂₉×M₃₂	C₂²	1	2	yes	—
12	C₂₉×#499	—	2	2	no	—
13	C₂₉×#499	C₂²	1	4	yes	—
14	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	—
15	C₄×SD₁₆×C₂₉	—	2	2	no	—
16	C₄×D₈×C₂₉	C₂²	1	2	yes	—
17	C₂₉×#427	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#107	C₂²	1	2	yes	—
19	C₂×C₂₉×#106	—	2	1	no	—
20	C₂₉×#416	—	2	1	no	—
21	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂₉×#367	C₂²	1	4	yes	—
23	C₂₉×#366	C₂²	1	4	yes	—
24	C₂₉×C₄⋊C₁₆	C₂²	1	4	yes	—
25	C₂₉×#358	C₂²	1	4	yes	—
26	C₂₉×#357	C₂²	1	4	yes	—
27	C₂×#41×C₂₉	—	2	1	no	—
28	C₂₉×#135	—	2	2	no	—
29	C₂₉×#135	Q₈	1	4	yes	—
30	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
31	C₂×SD₁₆×C₂₉	—	2	1	no	—
32	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
35	C₂₉×#125	—	2	4	no	—
36	C₂₉×#125	—	4	1	no	—
37	C₂₉×#125	—	4	1	no	—
38	C₄×Q₈×C₂₉	—	2	2	no	—
39	C₄×D₄×C₂₉	—	2	2	no	—
40	C₄×D₄×C₂₉	—	4	2	no	—
41	C₂₉×#117	—	2	1	no	—
42	C₂₉×#117	—	4	1	no	—
43	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₂₉	—	4	2	no	—
45	C₂×C₄²×C₂₉	—	4	1	no	—
46	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
47	C₂₉×M₃₂	—	2	4	no	—
48	C₂×C₁₆×C₂₉	C₂³	1	4	yes	—
49	C₂₉×#107	—	2	2	no	—
50	C₂₉×#107	C₂³	1	4	yes	—
51	C₂₉×#107	C₂³	1	2	yes	—
52	C₂₉×#106	—	2	4	no	—
53	C₂₉×#106	—	2	1	no	—
54	C₂₉×#103	—	2	2	no	—
55	C₂₉×#102	—	2	2	no	—
56	C₄×C₈×C₂₉	D₄	1	2	yes	—
57	C₄×C₈×C₂₉	C₂³	1	2	yes	—
58	#41×C₂₉	—	2	4	no	—
59	#41×C₂₉	—	4	2	no	—
60	C₂×Q₈×C₂₉	—	2	1	no	—
61	C₂×D₄×C₂₉	—	2	1	no	—
62	C₂×D₄×C₂₉	—	4	1	no	—
63	C₂²×C₄×C₂₉	—	4	1	no	—
64	C₂²×C₄×C₂₉	—	4	2	no	—
65	C₂²×C₄×C₂₉	—	4	2	no	—
66	C₂²×C₄×C₂₉	D₈	1	2	yes	—
67	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
68	Q₁₆×C₂₉	—	2	1	no	—
69	Q₁₆×C₂₉	C₂×Q₈	1	2	yes	—
70	SD₁₆×C₂₉	—	2	4	no	—
71	D₈×C₂₉	—	2	1	no	—
72	D₈×C₂₉	C₂×Q₈	1	2	yes	—
73	C₂×C₈×C₂₉	—	2	2	no	—
74	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
77	C₂×C₈×C₂₉	#41	1	2	yes	—
78	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
79	C₄⋊C₄×C₂₉	—	2	4	no	—
80	C₄⋊C₄×C₂₉	—	2	2	no	—
81	C₄⋊C₄×C₂₉	—	4	2	no	—
82	C₄⋊C₄×C₂₉	—	4	4	no	—
83	C₄⋊C₄×C₂₉	—	4	4	no	—
84	C₄⋊C₄×C₂₉	—	4	2	no	—
85	C₂²⋊C₄×C₂₉	—	4	1	no	—
86	C₂²⋊C₄×C₂₉	—	4	2	no	—
87	C₄²×C₂₉	—	4	1	no	—
88	C₄²×C₂₉	—	4	2	no	—
89	C₄²×C₂₉	D₈	1	1	yes	characteristic
90	C₄²×C₂₉	D₈	1	1	yes	characteristic
91	C₄²×C₂₉	C₂×D₄	1	2	yes	—
92	C₁₆×C₂₉	—	2	4	no	—
93	#33630	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂³×C₂₉	—	4	1	no	—
95	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
96	Q₈×C₂₉	—	2	2	no	—
97	Q₈×C₂₉	—	4	1	no	—
98	D₄×C₂₉	—	2	2	no	—
99	D₄×C₂₉	—	4	4	no	—
100	D₄×C₂₉	—	4	1	no	—
101	C₂×C₄×C₂₉	—	4	2	no	—
102	C₂×C₄×C₂₉	—	4	1	no	—
103	C₂×C₄×C₂₉	—	4	4	no	—
104	C₂×C₄×C₂₉	—	4	2	no	—
105	C₂×C₄×C₂₉	—	4	4	no	—
106	C₂×C₄×C₂₉	—	8	4	no	—
107	C₂×C₄×C₂₉	—	8	4	no	—
108	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
109	C₂×C₄×C₂₉	C₂×D₈	1	2	yes	—
110	C₂×C₄×C₂₉	C₂×D₈	1	2	yes	—
111	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₂₉	#137	1	2	yes	—
113	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
114	C₈×C₂₉	—	2	2	no	—
115	C₈×C₂₉	C₂²⋊Q₈	1	2	yes	—
116	C₈×C₂₉	C₂²×Q₈	1	1	yes	characteristic
117	C₈×C₂₉	C₂×#41	1	1	yes	characteristic
118	C₂×#499	C₂×C₂₉	1	1	yes	characteristic, complemented
119	C₄×#135	C₂×C₂₉	1	1	yes	characteristic
120	#2229	C₂×C₂₉	1	4	yes	complemented
121	#2228	C₂×C₂₉	1	4	yes	complemented
122	#2159	C₂×C₂₉	1	2	yes	complemented
123	#2150	C₂×C₂₉	1	1	yes	characteristic, complemented
124	#2139	C₂×C₂₉	1	2	yes	—
125	C₂²×C₂₉	—	2	2	no	—
126	C₂²×C₂₉	—	4	2	no	—
127	C₂²×C₂₉	—	8	2	no	—
128	C₂²×C₂₉	#474	1	2	yes	—
129	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
130	C₄×C₂₉	—	2	2	no	—
131	C₄×C₂₉	—	2	2	no	—
132	C₄×C₂₉	—	4	2	no	—
133	C₄×C₂₉	—	8	2	no	—
134	C₄×C₂₉	—	8	4	no	—
135	C₄×C₂₉	#474	1	2	yes	—
136	C₄×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
137	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
138	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
139	C₂×#125	—	2	1	no	—
140	C₄×#41	—	2	1	no	—
141	C₂×M₃₂	C₂²×C₂₉	1	2	yes	—
142	#499	—	2	2	no	—
143	#499	C₂²×C₂₉	1	4	yes	—
144	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	—
145	C₄×SD₁₆	—	2	2	no	—
146	C₄×D₈	C₂²×C₂₉	1	2	yes	—
147	#427	C₂²×C₂₉	1	1	yes	characteristic
148	C₂×#107	C₂²×C₂₉	1	2	yes	—
149	C₂×#106	—	2	1	no	—
150	#416	—	2	1	no	—
151	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
152	#367	C₂²×C₂₉	1	4	yes	—
153	#366	C₂²×C₂₉	1	4	yes	—
154	C₄⋊C₁₆	C₂²×C₂₉	1	4	yes	—
155	#358	C₂²×C₂₉	1	4	yes	—
156	#357	C₂²×C₂₉	1	4	yes	—
157	C₂×C₂₉	—	2	2	no	—
158	C₂×C₂₉	—	8	2	no	—
159	C₂×C₂₉	C₂×#474	1	1	yes	characteristic
160	C₂×C₂₉	#3414	1	2	yes	—
161	C₂×#41	—	2	1	no	—
162	#135	—	2	2	no	—
163	#135	Q₈×C₂₉	1	4	yes	—
164	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
165	C₂×SD₁₆	—	2	1	no	—
166	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
167	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
168	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
169	#125	—	2	4	no	—
170	#125	—	4	1	no	—
171	#125	—	4	1	no	—
172	C₄×Q₈	—	2	2	no	—
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	4	2	no	—
175	#117	—	2	1	no	—
176	#117	—	4	1	no	—
177	C₂×C₄⋊C₄	—	2	2	no	—
178	C₂×C₄⋊C₄	—	4	2	no	—
179	C₂×C₄²	—	4	1	no	—
180	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
181	M₃₂	—	2	4	no	—
182	C₂×C₁₆	C₂³×C₂₉	1	4	yes	—
183	#107	—	2	2	no	—
184	#107	C₂³×C₂₉	1	4	yes	—
185	#107	C₂³×C₂₉	1	2	yes	—
186	#106	—	2	4	no	—
187	#106	—	2	1	no	—
188	#103	—	2	2	no	—
189	#102	—	2	2	no	—
190	C₄×C₈	D₄×C₂₉	1	2	yes	—
191	C₄×C₈	C₂³×C₂₉	1	2	yes	—
192	C₂₉	#33630	1	1	yes	characteristic, direct product factor, Sylow
193	#41	—	2	4	no	—
194	#41	—	4	2	no	—
195	C₂×Q₈	—	2	1	no	—
196	C₂×D₄	—	2	1	no	—
197	C₂×D₄	—	4	1	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	—	4	2	no	—
200	C₂²×C₄	—	4	2	no	—
201	C₂²×C₄	D₈×C₂₉	1	2	yes	—
202	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
203	Q₁₆	—	2	1	no	—
204	Q₁₆	C₂×Q₈×C₂₉	1	2	yes	—
205	SD₁₆	—	2	4	no	—
206	D₈	—	2	1	no	—
207	D₈	C₂×Q₈×C₂₉	1	2	yes	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
210	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
211	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
212	C₂×C₈	#41×C₂₉	1	2	yes	—
213	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	2	4	no	—
216	C₄⋊C₄	—	4	2	no	—
217	C₄⋊C₄	—	4	4	no	—
218	C₄⋊C₄	—	4	4	no	—
219	C₄⋊C₄	—	4	2	no	—
220	C₂²⋊C₄	—	4	1	no	—
221	C₂²⋊C₄	—	4	2	no	—
222	C₄²	—	4	1	no	—
223	C₄²	—	4	2	no	—
224	C₄²	D₈×C₂₉	1	1	yes	characteristic
225	C₄²	D₈×C₂₉	1	1	yes	characteristic
226	C₄²	C₂×D₄×C₂₉	1	2	yes	—
227	C₁₆	—	2	4	no	—
228	C₂³	—	4	1	no	—
229	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
230	Q₈	—	2	2	no	—
231	Q₈	—	4	1	no	—
232	D₄	—	2	2	no	—
233	D₄	—	4	4	no	—
234	D₄	—	4	1	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	—	8	4	no	—
241	C₂×C₄	—	8	4	no	—
242	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
243	C₂×C₄	C₂×D₈×C₂₉	1	2	yes	—
244	C₂×C₄	C₂×D₈×C₂₉	1	2	yes	—
245	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
246	C₂×C₄	C₂₉×#137	1	2	yes	—
247	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	C₂₉×C₂²⋊Q₈	1	2	yes	—
250	C₈	C₂²×Q₈×C₂₉	1	1	yes	characteristic
251	C₈	C₂×#41×C₂₉	1	1	yes	characteristic
252	C₂²	—	2	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	—	8	2	no	—
255	C₂²	C₂₉×#474	1	2	yes	—
256	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	4	2	no	—
260	C₄	—	8	2	no	—
261	C₄	—	8	4	no	—
262	C₄	C₂₉×#474	1	2	yes	—
263	C₄	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
264	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
265	C₂	—	2	2	no	—
266	C₂	—	8	2	no	—
267	C₂	C₂×C₂₉×#474	1	1	yes	characteristic
268	C₂	C₂₉×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#499	C₂	semidirect
3. C₂₉×#2229	C₂	semidirect
4. C₂₉×#2228	C₂	semidirect
5. C₂₉×#2159	C₂	semidirect
6. C₂₉×#2150	C₂	semidirect
93. #33630	C₂₉	direct (N × H)
118. C₂×#499	C₂×C₂₉	semidirect
120. #2229	C₂×C₂₉	semidirect
121. #2228	C₂×C₂₉	semidirect
122. #2159	C₂×C₂₉	semidirect
123. #2150	C₂×C₂₉	semidirect
192. C₂₉	#33630	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×C₂₉×#499	2
C₄×C₂₉×#135	2
C₂₉×#2229	2
C₂₉×#2228	2
C₂₉×#2159	2
C₂₉×#2150	2
C₂₉×#2139	2
#33630	29

Subgroups — C29×#33630 #20328530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33630 #20328530