Subgroups — C₂₉×#23020 #20317920

Order 7424.

874 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2933	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1929	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1871	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1866	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×#131	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#525	C₂²	1	2	yes	—
17	C₂₉×#470	C₄	1	2	yes	complemented
18	C₂₉×#469	C₄	1	2	yes	complemented
19	C₂₉×#468	C₄	1	2	yes	complemented
20	C₂₉×#468	C₄	1	2	yes	complemented
21	C₂₉×#443	—	2	4	no	—
22	C₂₉×#436	—	2	2	no	—
23	C₂₉×#435	—	2	2	no	—
24	C₂₉×#435	—	2	2	no	—
25	C₈×D₄×C₂₉	—	2	2	no	—
26	C₂₉×#430	—	2	4	no	—
27	C₂×C₂₉×#108	C₂²	1	2	yes	—
28	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
30	C₂₉×#427	C₂²	1	1	yes	characteristic
31	C₂₉×#424	C₂²	1	2	yes	—
32	C₂×C₂₉×#104	C₂²	1	2	yes	—
33	C₂×C₂₉×#104	C₂²	1	2	yes	—
34	C₂₉×#416	C₂²	1	2	yes	—
35	C₂₉×#408	C₂²	1	2	yes	—
36	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂₉×#405	C₂²	1	2	yes	—
38	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
41	C₂₉×#339	C₂²	1	2	yes	—
42	C₂₉×#339	C₂²	1	2	yes	—
43	C₂₉×#336	C₂²	1	1	yes	characteristic
44	C₂₉×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₂₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
47	C₂₉×#135	—	2	2	no	—
48	C₂₉×#135	—	2	2	no	—
49	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₂₉	C₂×C₄	1	2	yes	—
51	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₂₉×#131	—	2	4	no	—
53	C₂₉×#131	—	4	2	no	—
54	C₂×M₁₆×C₂₉	—	2	2	no	—
55	C₂×M₁₆×C₂₉	—	2	2	no	—
56	C₂×M₁₆×C₂₉	—	2	2	no	—
57	C₂×M₁₆×C₂₉	—	2	2	no	—
58	C₂×M₁₆×C₂₉	—	2	4	no	—
59	C₂×M₁₆×C₂₉	—	4	2	no	—
60	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
63	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₂₉	—	2	2	no	—
65	C₂²×C₈×C₂₉	—	2	2	no	—
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂₉×#123	—	2	2	no	—
71	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
73	C₂₉×#121	C₂×C₄	1	2	yes	—
74	C₂₉×#121	C₂×C₄	1	2	yes	—
75	C₂₉×#120	—	2	2	no	—
76	C₄×D₄×C₂₉	—	2	2	no	—
77	C₄×D₄×C₂₉	—	2	2	no	—
78	C₂₉×#117	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
82	C₂₉×#108	—	2	4	no	—
83	C₂₉×#108	—	2	2	no	—
84	C₂₉×#108	D₄	1	4	yes	complemented
85	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
86	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
87	C₂₉×#106	C₂×C₄	1	2	yes	—
88	C₂₉×C₄⋊C₈	—	2	2	no	—
89	C₂₉×C₄⋊C₈	—	2	2	no	—
90	C₂₉×#104	—	2	4	no	—
91	C₂₉×#104	—	4	2	no	—
92	C₂₉×#103	C₂×C₄	1	2	yes	—
93	C₂₉×#103	C₂×C₄	1	2	yes	—
94	C₂₉×#102	C₂×C₄	1	2	yes	—
95	C₂₉×#102	C₂×C₄	1	2	yes	—
96	C₂₉×C₂²⋊C₈	—	2	2	no	—
97	C₂₉×C₂²⋊C₈	—	2	2	no	—
98	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
99	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
100	C₂₉×#97	—	2	2	no	—
101	C₂₉×#97	—	2	2	no	—
102	C₄×C₈×C₂₉	—	2	2	no	—
103	C₄×C₈×C₂₉	—	2	2	no	—
104	C₂₉×#95	—	2	1	no	—
105	C₂⁴×C₂₉	#41	1	1	yes	characteristic
106	#41×C₂₉	—	2	2	no	—
107	#41×C₂₉	—	2	2	no	—
108	#41×C₂₉	—	2	2	no	—
109	#41×C₂₉	—	2	2	no	—
110	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₂₉	—	2	2	no	—
112	C₂×D₄×C₂₉	—	2	2	no	—
113	C₂×D₄×C₂₉	—	2	2	no	—
114	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₂₉	—	2	1	no	—
116	C₂²×C₄×C₂₉	—	2	1	no	—
117	C₂²×C₄×C₂₉	—	2	1	no	—
118	C₂²×C₄×C₂₉	—	2	1	no	—
119	C₂²×C₄×C₂₉	—	2	1	no	—
120	C₂²×C₄×C₂₉	—	2	2	no	—
121	C₂²×C₄×C₂₉	—	2	1	no	—
122	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₂₉	—	2	2	no	—
127	SD₁₆×C₂₉	—	2	4	no	—
128	D₈×C₂₉	—	2	2	no	—
129	M₁₆×C₂₉	—	2	2	no	—
130	M₁₆×C₂₉	—	2	4	no	—
131	M₁₆×C₂₉	—	2	4	no	—
132	M₁₆×C₂₉	—	2	2	no	—
133	M₁₆×C₂₉	—	2	2	no	—
134	M₁₆×C₂₉	—	4	4	no	—
135	M₁₆×C₂₉	—	4	4	no	—
136	M₁₆×C₂₉	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₂₉	—	2	1	no	—
138	C₂×C₈×C₂₉	—	2	1	no	—
139	C₂×C₈×C₂₉	—	2	2	no	—
140	C₂×C₈×C₂₉	—	2	1	no	—
141	C₂×C₈×C₂₉	—	2	1	no	—
142	C₂×C₈×C₂₉	—	2	1	no	—
143	C₂×C₈×C₂₉	—	2	1	no	—
144	C₂×C₈×C₂₉	—	2	2	no	—
145	C₂×C₈×C₂₉	—	4	4	no	—
146	C₂×C₈×C₂₉	—	4	4	no	—
147	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₂₉	#41	1	2	yes	—
155	C₄⋊C₄×C₂₉	—	2	2	no	—
156	C₄⋊C₄×C₂₉	—	2	2	no	—
157	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
158	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
159	C₂²⋊C₄×C₂₉	—	2	2	no	—
160	C₂²⋊C₄×C₂₉	—	2	2	no	—
161	C₂²⋊C₄×C₂₉	—	2	2	no	—
162	C₂²⋊C₄×C₂₉	—	2	2	no	—
163	C₂²⋊C₄×C₂₉	—	2	2	no	—
164	C₂²⋊C₄×C₂₉	—	4	2	no	—
165	C₄²×C₂₉	—	2	2	no	—
166	C₄²×C₂₉	—	2	1	no	—
167	C₄²×C₂₉	—	2	1	no	—
168	C₄²×C₂₉	—	2	1	no	—
169	C₄²×C₂₉	—	2	1	no	—
170	#23020	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₂₉	—	2	1	no	—
172	C₂³×C₂₉	—	2	1	no	—
173	C₂³×C₂₉	—	2	2	no	—
174	C₂³×C₂₉	—	4	1	no	—
175	C₂³×C₂₉	—	4	1	no	—
176	C₂³×C₂₉	C₄×D₄	1	2	yes	—
177	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
178	Q₈×C₂₉	—	2	2	no	—
179	Q₈×C₂₉	—	2	2	no	—
180	D₄×C₂₉	—	2	2	no	—
181	D₄×C₂₉	—	2	2	no	—
182	D₄×C₂₉	—	4	4	no	—
183	D₄×C₂₉	—	4	2	no	—
184	D₄×C₂₉	—	4	2	no	—
185	D₄×C₂₉	—	8	2	no	—
186	C₂×C₄×C₂₉	—	2	1	no	—
187	C₂×C₄×C₂₉	—	2	1	no	—
188	C₂×C₄×C₂₉	—	2	2	no	—
189	C₂×C₄×C₂₉	—	2	2	no	—
190	C₂×C₄×C₂₉	—	2	2	no	—
191	C₂×C₄×C₂₉	—	2	2	no	—
192	C₂×C₄×C₂₉	—	2	2	no	—
193	C₂×C₄×C₂₉	—	2	2	no	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	2	no	—
196	C₂×C₄×C₂₉	—	4	1	no	—
197	C₂×C₄×C₂₉	—	4	1	no	—
198	C₂×C₄×C₂₉	—	4	2	no	—
199	C₂×C₄×C₂₉	—	4	2	no	—
200	C₂×C₄×C₂₉	—	4	1	no	—
201	C₂×C₄×C₂₉	—	4	1	no	—
202	C₂×C₄×C₂₉	—	4	1	no	—
203	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₂₉	—	2	2	no	—
211	C₈×C₂₉	—	2	1	no	—
212	C₈×C₂₉	—	2	1	no	—
213	C₈×C₂₉	—	2	4	no	—
214	C₈×C₂₉	—	2	2	no	—
215	C₈×C₂₉	—	4	2	no	—
216	C₈×C₂₉	C₄×D₄	1	2	yes	—
217	C₈×C₂₉	C₄×D₄	1	2	yes	—
218	#3054	C₂×C₂₉	1	1	yes	characteristic
219	C₂×#443	C₂×C₂₉	1	1	yes	characteristic, complemented
220	#2933	C₂×C₂₉	1	2	yes	complemented
221	C₂×#430	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#1975	C₂×C₂₉	1	1	yes	characteristic, complemented
223	#1945	C₂×C₂₉	1	1	yes	characteristic, complemented
224	#1929	C₂×C₂₉	1	2	yes	complemented
225	#1871	C₂×C₂₉	1	2	yes	complemented
226	#1866	C₂×C₂₉	1	2	yes	complemented
227	#1773	C₂×C₂₉	1	1	yes	characteristic, complemented
228	#1753	C₂×C₂₉	1	1	yes	characteristic, complemented
229	C₂²×C₂₉	—	2	1	no	—
230	C₂²×C₂₉	—	2	1	no	—
231	C₂²×C₂₉	—	2	2	no	—
232	C₂²×C₂₉	—	2	2	no	—
233	C₂²×C₂₉	—	2	2	no	—
234	C₂²×C₂₉	—	4	2	no	—
235	C₂²×C₂₉	—	4	2	no	—
236	C₂²×C₂₉	—	4	2	no	—
237	C₂²×C₂₉	—	8	1	no	—
238	C₂²×C₂₉	—	8	1	no	—
239	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₂₉	#548	1	1	yes	characteristic
241	C₂²×C₂₉	#553	1	1	yes	characteristic
242	C₄×C₂₉	—	2	2	no	—
243	C₄×C₂₉	—	4	2	no	—
244	C₄×C₂₉	—	4	2	no	—
245	C₄×C₂₉	—	4	2	no	—
246	C₄×C₂₉	—	4	2	no	—
247	C₄×C₂₉	—	8	1	no	—
248	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
249	C₄×C₂₉	#520	1	1	yes	characteristic
250	C₄×C₂₉	D₄²	1	1	yes	characteristic
251	C₄×C₂₉	#547	1	1	yes	characteristic
252	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
253	C₂×#131	C₂²×C₂₉	1	2	yes	—
254	C₂²×M₁₆	C₂²×C₂₉	1	2	yes	—
255	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
256	#525	C₂²×C₂₉	1	2	yes	—
257	#470	C₄×C₂₉	1	2	yes	complemented
258	#469	C₄×C₂₉	1	2	yes	complemented
259	#468	C₄×C₂₉	1	2	yes	complemented
260	#468	C₄×C₂₉	1	2	yes	complemented
261	#443	—	2	4	no	—
262	#436	—	2	2	no	—
263	#435	—	2	2	no	—
264	#435	—	2	2	no	—
265	C₈×D₄	—	2	2	no	—
266	#430	—	2	4	no	—
267	C₂×#108	C₂²×C₂₉	1	2	yes	—
268	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
269	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
270	#427	C₂²×C₂₉	1	1	yes	characteristic
271	#424	C₂²×C₂₉	1	2	yes	—
272	C₂×#104	C₂²×C₂₉	1	2	yes	—
273	C₂×#104	C₂²×C₂₉	1	2	yes	—
274	#416	C₂²×C₂₉	1	2	yes	—
275	#408	C₂²×C₂₉	1	2	yes	—
276	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
277	#405	C₂²×C₂₉	1	2	yes	—
278	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
281	#339	C₂²×C₂₉	1	2	yes	—
282	#339	C₂²×C₂₉	1	2	yes	—
283	#336	C₂²×C₂₉	1	1	yes	characteristic
284	#336	C₂²×C₂₉	1	1	yes	characteristic
285	C₂×C₂₉	—	2	1	no	—
286	C₂×C₂₉	—	2	1	no	—
287	C₂×C₂₉	—	4	2	no	—
288	C₂×C₂₉	—	8	2	no	—
289	C₂×C₂₉	#2361	1	1	yes	characteristic
290	C₂×C₂₉	#2955	1	1	yes	characteristic
291	C₂×C₂₉	#2956	1	1	yes	characteristic
292	C₂×#41	C₂³×C₂₉	1	2	yes	—
293	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
294	#135	—	2	2	no	—
295	#135	—	2	2	no	—
296	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
297	C₂×SD₁₆	C₂×C₄×C₂₉	1	2	yes	—
298	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic
299	#131	—	2	4	no	—
300	#131	—	4	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	4	no	—
306	C₂×M₁₆	—	4	2	no	—
307	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
308	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
309	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
310	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
317	#123	—	2	2	no	—
318	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
319	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
320	#121	C₂×C₄×C₂₉	1	2	yes	—
321	#121	C₂×C₄×C₂₉	1	2	yes	—
322	#120	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	#117	C₂³×C₂₉	1	2	yes	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
329	#108	—	2	4	no	—
330	#108	—	2	2	no	—
331	#108	D₄×C₂₉	1	4	yes	complemented
332	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
333	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
334	#106	C₂×C₄×C₂₉	1	2	yes	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	#104	—	2	4	no	—
338	#104	—	4	2	no	—
339	#103	C₂×C₄×C₂₉	1	2	yes	—
340	#103	C₂×C₄×C₂₉	1	2	yes	—
341	#102	C₂×C₄×C₂₉	1	2	yes	—
342	#102	C₂×C₄×C₂₉	1	2	yes	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
346	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
347	#97	—	2	2	no	—
348	#97	—	2	2	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	#95	—	2	1	no	—
352	C₂₉	#23020	1	1	yes	characteristic, direct product factor, Sylow
353	C₂⁴	#41×C₂₉	1	1	yes	characteristic
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
372	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
374	Q₁₆	—	2	2	no	—
375	SD₁₆	—	2	4	no	—
376	D₈	—	2	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	4	4	no	—
383	M₁₆	—	4	4	no	—
384	M₁₆	C₂×D₄×C₂₉	1	4	yes	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	4	4	no	—
394	C₂×C₈	—	4	4	no	—
395	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
396	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
397	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
398	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
400	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
401	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
402	C₂×C₈	#41×C₂₉	1	2	yes	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
406	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₄×D₄×C₂₉	1	2	yes	—
424	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
455	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	2	1	no	—
459	C₈	—	2	1	no	—
460	C₈	—	2	4	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	C₄×D₄×C₂₉	1	2	yes	—
464	C₈	C₄×D₄×C₂₉	1	2	yes	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
476	C₂²	C₂₉×#548	1	1	yes	characteristic
477	C₂²	C₂₉×#553	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
485	C₄	C₂₉×#520	1	1	yes	characteristic
486	C₄	D₄²×C₂₉	1	1	yes	characteristic
487	C₄	C₂₉×#547	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	2	no	—
492	C₂	C₂₉×#2361	1	1	yes	characteristic
493	C₂	C₂₉×#2955	1	1	yes	characteristic
494	C₂	C₂₉×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂₉×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₂₉×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#443	C₂	semidirect
3. C₂₉×#2933	C₂	semidirect
4. C₂×C₂₉×#430	C₂	semidirect
5. C₂₉×#1975	C₂	semidirect
6. C₂₉×#1945	C₂	semidirect
7. C₂₉×#1929	C₂	semidirect
8. C₂₉×#1871	C₂	semidirect
9. C₂₉×#1866	C₂	semidirect
10. C₂₉×#1773	C₂	semidirect
11. C₂₉×#1753	C₂	semidirect
17. C₂₉×#470	C₄	semidirect
18. C₂₉×#469	C₄	semidirect
19. C₂₉×#468	C₄	semidirect
20. C₂₉×#468	C₄	semidirect
84. C₂₉×#108	D₄	semidirect
170. #23020	C₂₉	direct (N × H)
219. C₂×#443	C₂×C₂₉	semidirect
220. #2933	C₂×C₂₉	semidirect
221. C₂×#430	C₂×C₂₉	semidirect
222. #1975	C₂×C₂₉	semidirect
223. #1945	C₂×C₂₉	semidirect
224. #1929	C₂×C₂₉	semidirect
225. #1871	C₂×C₂₉	semidirect
226. #1866	C₂×C₂₉	semidirect
227. #1773	C₂×C₂₉	semidirect
228. #1753	C₂×C₂₉	semidirect
257. #470	C₄×C₂₉	semidirect
258. #469	C₄×C₂₉	semidirect
259. #468	C₄×C₂₉	semidirect
260. #468	C₄×C₂₉	semidirect
331. #108	D₄×C₂₉	semidirect
352. C₂₉	#23020	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×#3054	2
C₂×C₂₉×#443	2
C₂₉×#2933	2
C₂×C₂₉×#430	2
C₂₉×#1975	2
C₂₉×#1945	2
C₂₉×#1929	2
C₂₉×#1871	2
C₂₉×#1866	2
C₂₉×#1773	2
C₂₉×#1753	2
#23020	29

Subgroups — C29×#23020 #20317920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23020 #20317920