Subgroups — C₂₉×#19991 #20314891

Order 7424.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1711	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1646	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1642	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#555	C₂²	1	1	yes	characteristic
17	C₂₉×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#547	C₂²	1	1	yes	characteristic
20	C₂₉×#487	C₂²	1	1	yes	characteristic
21	C₂₉×#487	C₂²	1	1	yes	characteristic
22	C₂₉×#487	C₂²	1	1	yes	characteristic
23	C₂₉×#486	—	2	1	no	—
24	C₂₉×#486	C₂²	1	1	yes	characteristic
25	C₂₉×#486	C₂²	1	1	yes	characteristic
26	C₂₉×#486	C₂²	1	1	yes	characteristic
27	C₂₉×#485	—	2	1	no	—
28	C₂₉×#483	—	2	1	no	—
29	C₂₉×#482	—	2	1	no	—
30	C₂₉×#477	C₂²	1	1	yes	characteristic
31	C₂₉×#476	C₂²	1	1	yes	characteristic
32	C₂₉×#475	C₂²	1	1	yes	characteristic
33	C₂₉×#474	—	2	1	no	—
34	C₂₉×#474	C₂²	1	1	yes	characteristic
35	C₂₉×#466	—	2	1	no	—
36	C₂₉×#465	—	2	1	no	—
37	C₂₉×#465	—	2	1	no	—
38	C₂₉×#461	C₂²	1	1	yes	characteristic
39	C₂₉×#461	C₂²	1	1	yes	characteristic
40	C₂₉×#459	—	2	1	no	—
41	C₂₉×#459	C₂²	1	1	yes	characteristic
42	C₂₉×#459	C₂²	1	1	yes	characteristic
43	C₂₉×#449	—	2	1	no	—
44	C₂₉×#449	—	2	1	no	—
45	C₂₉×#448	—	2	1	no	—
46	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
47	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×D₈×C₂₉	—	2	1	no	—
49	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
50	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#416	—	2	1	no	—
54	C₂₉×#416	—	2	1	no	—
55	C₂×C₂₉×#103	—	2	1	no	—
56	C₂₉×#335	C₂²	1	1	yes	characteristic
57	C₂₉×#334	C₂²	1	1	yes	characteristic
58	C₂₉×#333	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#331	C₂²	1	1	yes	characteristic
62	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₂₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂×#41×C₂₉	—	2	1	no	—
69	C₂²×Q₈×C₂₉	—	2	1	no	—
70	C₂×SD₁₆×C₂₉	—	2	1	no	—
71	C₂×SD₁₆×C₂₉	—	2	1	no	—
72	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
73	C₂×D₈×C₂₉	—	2	1	no	—
74	C₂×D₈×C₂₉	—	2	1	no	—
75	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₂₉	—	2	1	no	—
77	C₂²×C₈×C₂₉	—	2	1	no	—
78	C₂²×C₈×C₂₉	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	—	2	1	no	—
80	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₂₉×#127	—	2	1	no	—
84	C₂₉×#127	C₂³	1	1	yes	characteristic
85	C₂₉×#124	—	4	1	no	—
86	C₂₉×#123	—	4	1	no	—
87	C₂₉×C₂²⋊Q₈	—	2	1	no	—
88	C₂₉×C₂²⋊Q₈	—	2	1	no	—
89	C₂₉×C₂²⋊Q₈	—	4	1	no	—
90	C₂₉×#121	—	2	1	no	—
91	C₂₉×#121	—	2	1	no	—
92	C₂₉×#121	—	2	1	no	—
93	C₂₉×#121	—	2	1	no	—
94	C₂₉×#121	—	4	1	no	—
95	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₂₉	—	2	1	no	—
97	C₄×D₄×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂₉×#117	—	2	1	no	—
102	C₂₉×#117	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
104	C₂₉×#107	—	2	1	no	—
105	C₂₉×#107	—	2	1	no	—
106	C₂₉×#107	D₄	1	1	yes	characteristic
107	C₂₉×#106	—	2	1	no	—
108	C₂₉×#106	—	2	1	no	—
109	C₂₉×#106	D₄	1	1	yes	characteristic
110	C₂₉×C₄⋊C₈	—	2	1	no	—
111	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₂₉×#103	—	2	1	no	—
116	C₂₉×#103	—	2	1	no	—
117	C₂₉×#103	—	2	1	no	—
118	C₂₉×#103	—	2	1	no	—
119	C₂₉×#103	—	2	1	no	—
120	C₂₉×#103	—	2	1	no	—
121	C₂₉×#103	—	2	1	no	—
122	C₂₉×#103	—	2	1	no	—
123	C₂₉×#103	—	4	1	no	—
124	C₂₉×#103	D₄	1	1	yes	characteristic
125	C₂₉×#102	—	2	1	no	—
126	C₂₉×#102	—	2	1	no	—
127	C₂₉×#102	—	2	1	no	—
128	C₂₉×#102	—	2	1	no	—
129	C₂₉×#102	—	2	1	no	—
130	C₂₉×#102	—	2	1	no	—
131	C₂₉×#102	—	2	1	no	—
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	4	1	no	—
134	C₂₉×#102	D₄	1	1	yes	characteristic
135	C₂₉×#102	D₄	1	1	yes	characteristic
136	C₂₉×#102	D₄	1	1	yes	characteristic
137	C₂₉×C₂²⋊C₈	—	2	1	no	—
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₂₉	—	2	1	no	—
141	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	#41×C₂₉	—	4	2	no	—
145	#41×C₂₉	—	4	2	no	—
146	#41×C₂₉	—	8	1	no	—
147	#41×C₂₉	—	8	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	—	4	1	no	—
152	C₂×Q₈×C₂₉	—	4	2	no	—
153	C₂×Q₈×C₂₉	—	8	1	no	—
154	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₂₉	—	2	1	no	—
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	4	1	no	—
159	C₂×D₄×C₂₉	—	4	1	no	—
160	C₂×D₄×C₂₉	—	4	1	no	—
161	C₂×D₄×C₂₉	—	4	1	no	—
162	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₂₉	—	2	1	no	—
166	C₂²×C₄×C₂₉	—	2	1	no	—
167	C₂²×C₄×C₂₉	—	2	1	no	—
168	C₂²×C₄×C₂₉	—	4	1	no	—
169	C₂²×C₄×C₂₉	—	4	1	no	—
170	C₂²×C₄×C₂₉	—	4	1	no	—
171	SD₁₆×C₂₉	—	2	2	no	—
172	SD₁₆×C₂₉	—	8	1	no	—
173	SD₁₆×C₂₉	—	8	1	no	—
174	D₈×C₂₉	—	2	2	no	—
175	D₈×C₂₉	—	4	2	no	—
176	D₈×C₂₉	—	8	1	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	—	2	1	no	—
180	C₂×C₈×C₂₉	—	2	1	no	—
181	C₂×C₈×C₂₉	—	2	1	no	—
182	C₂×C₈×C₂₉	—	8	1	no	—
183	C₂×C₈×C₂₉	—	8	1	no	—
184	C₂×C₈×C₂₉	—	8	1	no	—
185	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₂₉	—	2	1	no	—
190	C₄⋊C₄×C₂₉	—	2	1	no	—
191	C₄⋊C₄×C₂₉	—	2	1	no	—
192	C₄⋊C₄×C₂₉	—	2	1	no	—
193	C₄⋊C₄×C₂₉	—	2	1	no	—
194	C₄⋊C₄×C₂₉	—	2	1	no	—
195	C₄⋊C₄×C₂₉	—	2	1	no	—
196	C₄⋊C₄×C₂₉	—	4	1	no	—
197	C₄⋊C₄×C₂₉	—	4	1	no	—
198	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₂₉	—	2	1	no	—
203	C₂²⋊C₄×C₂₉	—	2	1	no	—
204	C₂²⋊C₄×C₂₉	—	2	1	no	—
205	C₂²⋊C₄×C₂₉	—	4	1	no	—
206	C₂²⋊C₄×C₂₉	—	4	1	no	—
207	C₂²⋊C₄×C₂₉	—	4	1	no	—
208	C₂²⋊C₄×C₂₉	—	4	1	no	—
209	C₂²⋊C₄×C₂₉	—	4	1	no	—
210	C₄²×C₂₉	—	2	1	no	—
211	C₄²×C₂₉	—	4	1	no	—
212	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
213	#19991	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₂₉	—	2	1	no	—
215	C₂³×C₂₉	—	2	1	no	—
216	C₂³×C₂₉	—	2	1	no	—
217	C₂³×C₂₉	—	4	1	no	—
218	Q₈×C₂₉	—	2	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	4	1	no	—
223	Q₈×C₂₉	—	8	2	no	—
224	Q₈×C₂₉	—	8	1	no	—
225	Q₈×C₂₉	#135	1	2	yes	—
226	D₄×C₂₉	—	2	1	no	—
227	D₄×C₂₉	—	2	1	no	—
228	D₄×C₂₉	—	2	1	no	—
229	D₄×C₂₉	—	2	1	no	—
230	D₄×C₂₉	—	2	1	no	—
231	D₄×C₂₉	—	4	1	no	—
232	D₄×C₂₉	—	4	1	no	—
233	D₄×C₂₉	—	4	1	no	—
234	D₄×C₂₉	—	4	1	no	—
235	D₄×C₂₉	—	8	2	no	—
236	D₄×C₂₉	—	8	1	no	—
237	D₄×C₂₉	—	8	2	no	—
238	D₄×C₂₉	—	16	1	no	—
239	D₄×C₂₉	—	16	1	no	—
240	D₄×C₂₉	#135	1	2	yes	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	4	1	no	—
252	C₂×C₄×C₂₉	—	4	1	no	—
253	C₂×C₄×C₂₉	—	4	1	no	—
254	C₂×C₄×C₂₉	—	4	1	no	—
255	C₂×C₄×C₂₉	—	8	2	no	—
256	C₂×C₄×C₂₉	—	8	2	no	—
257	C₂×C₄×C₂₉	—	8	2	no	—
258	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
261	C₈×C₂₉	—	2	1	no	—
262	C₈×C₂₉	—	2	1	no	—
263	C₈×C₂₉	—	2	1	no	—
264	C₈×C₂₉	—	2	1	no	—
265	C₈×C₂₉	—	4	1	no	—
266	C₈×C₂₉	—	4	1	no	—
267	C₈×C₂₉	—	4	1	no	—
268	C₈×C₂₉	—	4	1	no	—
269	C₈×C₂₉	—	4	1	no	—
270	#3358	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#3305	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#3303	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#3298	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1711	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1684	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1681	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#1679	C₂×C₂₉	1	1	yes	characteristic, complemented
278	#1677	C₂×C₂₉	1	1	yes	characteristic, complemented
279	#1646	C₂×C₂₉	1	1	yes	characteristic, complemented
280	#1642	C₂×C₂₉	1	1	yes	characteristic, complemented
281	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
283	C₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
284	C₈×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
285	C₂²×C₂₉	—	2	2	no	—
286	C₂²×C₂₉	—	4	1	no	—
287	C₂²×C₂₉	—	4	1	no	—
288	C₂²×C₂₉	—	4	1	no	—
289	C₂²×C₂₉	—	4	1	no	—
290	C₂²×C₂₉	—	4	1	no	—
291	C₂²×C₂₉	—	4	1	no	—
292	C₂²×C₂₉	—	4	1	no	—
293	C₂²×C₂₉	—	4	1	no	—
294	C₂²×C₂₉	—	8	1	no	—
295	C₂²×C₂₉	—	8	1	no	—
296	C₂²×C₂₉	—	8	1	no	—
297	C₂²×C₂₉	D₄²	1	1	yes	characteristic
298	C₄×C₂₉	—	2	2	no	—
299	C₄×C₂₉	—	2	1	no	—
300	C₄×C₂₉	—	4	1	no	—
301	C₄×C₂₉	—	4	1	no	—
302	C₄×C₂₉	—	4	1	no	—
303	C₄×C₂₉	—	4	1	no	—
304	C₄×C₂₉	—	8	1	no	—
305	C₄×C₂₉	—	8	1	no	—
306	C₄×C₂₉	—	8	1	no	—
307	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
308	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
309	C₄×C₂₉	#576	1	1	yes	characteristic
310	C₄×C₂₉	#577	1	1	yes	characteristic
311	#555	C₂²×C₂₉	1	1	yes	characteristic
312	#550	C₂²×C₂₉	1	1	yes	characteristic
313	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
314	#547	C₂²×C₂₉	1	1	yes	characteristic
315	#487	C₂²×C₂₉	1	1	yes	characteristic
316	#487	C₂²×C₂₉	1	1	yes	characteristic
317	#487	C₂²×C₂₉	1	1	yes	characteristic
318	#486	—	2	1	no	—
319	#486	C₂²×C₂₉	1	1	yes	characteristic
320	#486	C₂²×C₂₉	1	1	yes	characteristic
321	#486	C₂²×C₂₉	1	1	yes	characteristic
322	#485	—	2	1	no	—
323	#483	—	2	1	no	—
324	#482	—	2	1	no	—
325	#477	C₂²×C₂₉	1	1	yes	characteristic
326	#476	C₂²×C₂₉	1	1	yes	characteristic
327	#475	C₂²×C₂₉	1	1	yes	characteristic
328	#474	—	2	1	no	—
329	#474	C₂²×C₂₉	1	1	yes	characteristic
330	#466	—	2	1	no	—
331	#465	—	2	1	no	—
332	#465	—	2	1	no	—
333	#461	C₂²×C₂₉	1	1	yes	characteristic
334	#461	C₂²×C₂₉	1	1	yes	characteristic
335	#459	—	2	1	no	—
336	#459	C₂²×C₂₉	1	1	yes	characteristic
337	#459	C₂²×C₂₉	1	1	yes	characteristic
338	#449	—	2	1	no	—
339	#449	—	2	1	no	—
340	#448	—	2	1	no	—
341	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
342	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
343	C₄×D₈	—	2	1	no	—
344	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
345	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
346	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
347	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
348	#416	—	2	1	no	—
349	#416	—	2	1	no	—
350	C₂×#103	—	2	1	no	—
351	#335	C₂²×C₂₉	1	1	yes	characteristic
352	#334	C₂²×C₂₉	1	1	yes	characteristic
353	#333	C₂²×C₂₉	1	1	yes	characteristic
354	#332	C₂²×C₂₉	1	1	yes	characteristic
355	#332	C₂²×C₂₉	1	1	yes	characteristic
356	#331	C₂²×C₂₉	1	1	yes	characteristic
357	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
358	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
359	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
360	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
361	C₈²	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×C₂₉	—	4	2	no	—
363	C₂×C₂₉	—	8	1	no	—
364	C₂×C₂₉	—	8	1	no	—
365	C₂×C₂₉	—	16	1	no	—
366	C₂×C₂₉	#3280	1	1	yes	characteristic
367	C₂×C₂₉	#3282	1	1	yes	characteristic
368	C₂×C₂₉	#3290	1	1	yes	characteristic
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂²×Q₈	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
375	C₂×D₈	—	2	1	no	—
376	C₂×D₈	—	2	1	no	—
377	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
383	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
384	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
385	#127	—	2	1	no	—
386	#127	C₂³×C₂₉	1	1	yes	characteristic
387	#124	—	4	1	no	—
388	#123	—	4	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	4	1	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	4	1	no	—
397	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
401	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
402	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	#107	—	2	1	no	—
407	#107	—	2	1	no	—
408	#107	D₄×C₂₉	1	1	yes	characteristic
409	#106	—	2	1	no	—
410	#106	—	2	1	no	—
411	#106	D₄×C₂₉	1	1	yes	characteristic
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	4	1	no	—
426	#103	D₄×C₂₉	1	1	yes	characteristic
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	4	1	no	—
436	#102	D₄×C₂₉	1	1	yes	characteristic
437	#102	D₄×C₂₉	1	1	yes	characteristic
438	#102	D₄×C₂₉	1	1	yes	characteristic
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₂²⋊C₈	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
446	C₂₉	#19991	1	1	yes	characteristic, direct product factor, Sylow
447	#41	—	4	2	no	—
448	#41	—	4	2	no	—
449	#41	—	8	1	no	—
450	#41	—	8	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	8	1	no	—
457	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
467	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	SD₁₆	—	2	2	no	—
475	SD₁₆	—	8	1	no	—
476	SD₁₆	—	8	1	no	—
477	D₈	—	2	2	no	—
478	D₈	—	4	2	no	—
479	D₈	—	8	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	8	1	no	—
486	C₂×C₈	—	8	1	no	—
487	C₂×C₈	—	8	1	no	—
488	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	4	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	8	2	no	—
526	Q₈	—	8	1	no	—
527	Q₈	C₂₉×#135	1	2	yes	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	2	no	—
540	D₄	—	16	1	no	—
541	D₄	—	16	1	no	—
542	D₄	C₂₉×#135	1	2	yes	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
562	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	D₄²×C₂₉	1	1	yes	characteristic
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
595	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
596	C₄	C₂₉×#576	1	1	yes	characteristic
597	C₄	C₂₉×#577	1	1	yes	characteristic
598	C₂	—	4	2	no	—
599	C₂	—	8	1	no	—
600	C₂	—	8	1	no	—
601	C₂	—	16	1	no	—
602	C₂	C₂₉×#3280	1	1	yes	characteristic
603	C₂	C₂₉×#3282	1	1	yes	characteristic
604	C₂	C₂₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3358	C₂	semidirect
2. C₂₉×#3305	C₂	semidirect
3. C₂₉×#3303	C₂	semidirect
4. C₂₉×#3298	C₂	semidirect
5. C₂₉×#1711	C₂	semidirect
6. C₂₉×#1684	C₂	semidirect
7. C₂₉×#1681	C₂	semidirect
8. C₂₉×#1679	C₂	semidirect
9. C₂₉×#1677	C₂	semidirect
10. C₂₉×#1646	C₂	semidirect
11. C₂₉×#1642	C₂	semidirect
12. C₂₉×#1637	C₂	semidirect
13. C₂₉×#1625	C₂	semidirect
14. C₈×SD₁₆×C₂₉	C₂	semidirect
15. C₈×D₈×C₂₉	C₂	semidirect
213. #19991	C₂₉	direct (N × H)
270. #3358	C₂×C₂₉	semidirect
271. #3305	C₂×C₂₉	semidirect
272. #3303	C₂×C₂₉	semidirect
273. #3298	C₂×C₂₉	semidirect
274. #1711	C₂×C₂₉	semidirect
275. #1684	C₂×C₂₉	semidirect
276. #1681	C₂×C₂₉	semidirect
277. #1679	C₂×C₂₉	semidirect
278. #1677	C₂×C₂₉	semidirect
279. #1646	C₂×C₂₉	semidirect
280. #1642	C₂×C₂₉	semidirect
281. #1637	C₂×C₂₉	semidirect
282. #1625	C₂×C₂₉	semidirect
283. C₈×SD₁₆	C₂×C₂₉	semidirect
284. C₈×D₈	C₂×C₂₉	semidirect
446. C₂₉	#19991	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×#3358	2
C₂₉×#3305	2
C₂₉×#3303	2
C₂₉×#3298	2
C₂₉×#1711	2
C₂₉×#1684	2
C₂₉×#1681	2
C₂₉×#1679	2
C₂₉×#1677	2
C₂₉×#1646	2
C₂₉×#1642	2
C₂₉×#1637	2
C₂₉×#1625	2
C₈×SD₁₆×C₂₉	2
C₈×D₈×C₂₉	2
#19991	29

Subgroups — C29×#19991 #20314891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19991 #20314891