Subgroups — C₂×C₂₉×#1922 #20315940

Order 7424.

854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#405	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1922	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₂₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×#339	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×C₂₉×#336	C₂	1	1	yes	maximal, characteristic
9	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#427	C₄	1	4	yes	complemented
17	C₂₉×#427	C₂²	1	4	yes	—
18	C₂×C₂₉×#107	C₄	1	1	yes	characteristic, complemented
19	C₂×C₂₉×#107	C₄	1	1	yes	characteristic, complemented
20	C₂×C₂₉×#106	C₄	1	1	yes	characteristic, complemented
21	C₂×C₂₉×#106	C₄	1	1	yes	characteristic, complemented
22	C₂₉×#424	—	2	2	no	—
23	C₂₉×#424	C₂²	1	4	yes	—
24	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
25	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
26	C₂₉×#405	—	2	2	no	—
27	C₂₉×#405	C₂²	1	4	yes	—
28	C₂×C₂₉×#97	—	2	1	no	—
29	C₂×C₄×C₈×C₂₉	—	2	1	no	—
30	C₂₉×#341	C₂²	1	4	yes	—
31	C₂₉×#339	C₂²	1	4	yes	—
32	C₂₉×#339	C₂²	1	4	yes	—
33	C₂₉×#336	C₂²	1	4	yes	—
34	C₂³×C₄×C₂₉	—	2	1	no	—
35	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₂₉	—	2	1	no	—
37	C₂×M₁₆×C₂₉	—	2	2	no	—
38	C₂×M₁₆×C₂₉	—	2	1	no	—
39	C₂×M₁₆×C₂₉	—	2	2	no	—
40	C₂×M₁₆×C₂₉	—	2	2	no	—
41	C₂×M₁₆×C₂₉	Q₈	1	4	yes	—
42	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
43	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₂₉	—	2	1	no	—
45	C₂²×C₈×C₂₉	—	2	2	no	—
46	C₂²×C₈×C₂₉	—	2	2	no	—
47	C₂²×C₈×C₂₉	—	2	2	no	—
48	C₂²×C₈×C₂₉	—	2	2	no	—
49	C₂²×C₈×C₂₉	—	2	1	no	—
50	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₂₉	D₄	1	2	yes	—
54	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
58	C₂₉×#117	—	2	1	no	—
59	C₂₉×#117	—	2	1	no	—
60	C₂₉×#117	—	2	1	no	—
61	C₂₉×#117	—	2	1	no	—
62	C₂₉×#117	C₂×C₄	1	2	yes	—
63	C₂₉×#117	C₂×C₄	1	2	yes	—
64	C₂₉×#117	C₂³	1	2	yes	—
65	C₂₉×#117	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
72	C₂×C₄²×C₂₉	—	2	1	no	—
73	C₂×C₄²×C₂₉	—	2	1	no	—
74	C₂×C₄²×C₂₉	—	2	2	no	—
75	C₂×C₄²×C₂₉	—	2	2	no	—
76	C₂×C₄²×C₂₉	—	2	1	no	—
77	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
78	C₂₉×#107	C₂×C₄	1	4	yes	complemented
79	C₂₉×#107	C₂×C₄	1	4	yes	complemented
80	C₂₉×#106	C₂×C₄	1	4	yes	complemented
81	C₂₉×#106	C₂×C₄	1	4	yes	complemented
82	C₂₉×C₄⋊C₈	—	2	4	no	—
83	C₂₉×C₄⋊C₈	—	2	4	no	—
84	C₂₉×#97	—	2	4	no	—
85	C₄×C₈×C₂₉	—	2	4	no	—
86	C₂⁴×C₂₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	—	2	4	no	—
88	C₂²×C₄×C₂₉	—	2	1	no	—
89	C₂²×C₄×C₂₉	—	2	1	no	—
90	C₂²×C₄×C₂₉	—	2	1	no	—
91	C₂²×C₄×C₂₉	—	2	1	no	—
92	C₂²×C₄×C₂₉	—	2	2	no	—
93	C₂²×C₄×C₂₉	—	4	2	no	—
94	C₂²×C₄×C₂₉	—	4	2	no	—
95	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₂₉	#41	1	2	yes	—
101	C₂²×C₄×C₂₉	#41	1	2	yes	—
102	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₂₉	#41	1	2	yes	—
104	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₂₉	—	2	4	no	—
106	M₁₆×C₂₉	—	2	2	no	—
107	M₁₆×C₂₉	—	2	2	no	—
108	M₁₆×C₂₉	—	2	2	no	—
109	M₁₆×C₂₉	—	4	2	no	—
110	M₁₆×C₂₉	C₂×Q₈	1	4	yes	—
111	C₂×C₈×C₂₉	—	2	2	no	—
112	C₂×C₈×C₂₉	—	2	2	no	—
113	C₂×C₈×C₂₉	—	2	4	no	—
114	C₂×C₈×C₂₉	—	2	4	no	—
115	C₂×C₈×C₂₉	—	2	2	no	—
116	C₂×C₈×C₂₉	—	2	2	no	—
117	C₂×C₈×C₂₉	—	2	4	no	—
118	C₂×C₈×C₂₉	—	2	2	no	—
119	C₂×C₈×C₂₉	—	2	2	no	—
120	C₂×C₈×C₂₉	—	2	2	no	—
121	C₂×C₈×C₂₉	—	2	2	no	—
122	C₂×C₈×C₂₉	—	2	2	no	—
123	C₂×C₈×C₂₉	—	2	2	no	—
124	C₂×C₈×C₂₉	—	4	2	no	—
125	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₂₉	—	2	1	no	—
130	C₄⋊C₄×C₂₉	—	2	1	no	—
131	C₄⋊C₄×C₂₉	—	2	1	no	—
132	C₄⋊C₄×C₂₉	—	2	1	no	—
133	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
137	C₂²⋊C₄×C₂₉	—	2	2	no	—
138	C₂²⋊C₄×C₂₉	—	2	2	no	—
139	C₂²⋊C₄×C₂₉	—	2	2	no	—
140	C₂²⋊C₄×C₂₉	—	2	2	no	—
141	C₄²×C₂₉	—	2	2	no	—
142	C₄²×C₂₉	—	2	2	no	—
143	C₄²×C₂₉	—	2	2	no	—
144	C₄²×C₂₉	—	2	2	no	—
145	C₄²×C₂₉	—	2	2	no	—
146	C₄²×C₂₉	—	2	2	no	—
147	C₄²×C₂₉	—	4	2	no	—
148	C₂×#1922	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₂₉	—	2	2	no	—
150	C₂³×C₂₉	—	2	2	no	—
151	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
153	C₂³×C₂₉	#125	1	2	yes	—
154	C₂³×C₂₉	#126	1	2	yes	—
155	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₂₉	—	2	4	no	—
157	C₂×C₄×C₂₉	—	2	2	no	—
158	C₂×C₄×C₂₉	—	2	2	no	—
159	C₂×C₄×C₂₉	—	2	2	no	—
160	C₂×C₄×C₂₉	—	2	2	no	—
161	C₂×C₄×C₂₉	—	4	8	no	—
162	C₂×C₄×C₂₉	—	4	2	no	—
163	C₂×C₄×C₂₉	—	4	2	no	—
164	C₂×C₄×C₂₉	—	4	2	no	—
165	C₂×C₄×C₂₉	—	4	2	no	—
166	C₂×C₄×C₂₉	—	4	2	no	—
167	C₂×C₄×C₂₉	—	4	2	no	—
168	C₂×C₄×C₂₉	#117	1	2	yes	—
169	C₂×C₄×C₂₉	#117	1	2	yes	—
170	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
173	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
174	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₂₉	#123	1	2	yes	—
177	C₂×C₄×C₂₉	#123	1	2	yes	—
178	C₂×C₄×C₂₉	#125	1	2	yes	—
179	C₂×C₄×C₂₉	#126	1	2	yes	—
180	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
186	C₈×C₂₉	—	2	2	no	—
187	C₈×C₂₉	—	2	2	no	—
188	C₈×C₂₉	—	2	4	no	—
189	C₈×C₂₉	—	2	2	no	—
190	C₈×C₂₉	—	2	2	no	—
191	C₈×C₂₉	—	4	2	no	—
192	C₂×#427	C₂×C₂₉	1	1	yes	characteristic
193	C₂×#424	C₂×C₂₉	1	1	yes	characteristic
194	C₂×#405	C₂×C₂₉	1	1	yes	characteristic
195	#1922	C₂×C₂₉	1	8	yes	direct product factor
196	C₂×#341	C₂×C₂₉	1	1	yes	characteristic
197	C₂×#339	C₂×C₂₉	1	1	yes	characteristic
198	C₂×#339	C₂×C₂₉	1	1	yes	characteristic
199	C₂×#336	C₂×C₂₉	1	1	yes	characteristic
200	C₂²×C₂₉	—	2	4	no	—
201	C₂²×C₂₉	—	2	4	no	—
202	C₂²×C₂₉	—	2	1	no	—
203	C₂²×C₂₉	—	2	1	no	—
204	C₂²×C₂₉	—	2	1	no	—
205	C₂²×C₂₉	—	2	1	no	—
206	C₂²×C₂₉	#387	1	2	yes	—
207	C₂²×C₂₉	#387	1	2	yes	—
208	C₂²×C₂₉	#443	1	2	yes	—
209	C₂²×C₂₉	#444	1	2	yes	—
210	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₂₉	C₂×#125	1	1	yes	characteristic
212	C₂²×C₂₉	C₂×#126	1	1	yes	characteristic
213	C₄×C₂₉	—	4	4	no	—
214	C₄×C₂₉	—	4	2	no	—
215	C₄×C₂₉	—	4	2	no	—
216	C₄×C₂₉	—	4	2	no	—
217	C₄×C₂₉	—	4	2	no	—
218	C₄×C₂₉	#387	1	2	yes	—
219	C₄×C₂₉	#387	1	2	yes	—
220	C₄×C₂₉	C₂×#117	1	1	yes	characteristic
221	C₄×C₂₉	C₂×C₄×Q₈	1	1	yes	characteristic
222	C₄×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₄×C₂₉	C₂×#123	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
227	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
228	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
229	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
230	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
231	#427	C₄×C₂₉	1	4	yes	complemented
232	#427	C₂²×C₂₉	1	4	yes	—
233	C₂×#107	C₄×C₂₉	1	1	yes	characteristic, complemented
234	C₂×#107	C₄×C₂₉	1	1	yes	characteristic, complemented
235	C₂×#106	C₄×C₂₉	1	1	yes	characteristic, complemented
236	C₂×#106	C₄×C₂₉	1	1	yes	characteristic, complemented
237	#424	—	2	2	no	—
238	#424	C₂²×C₂₉	1	4	yes	—
239	C₂×C₄⋊C₈	—	2	1	no	—
240	C₂×C₄⋊C₈	—	2	1	no	—
241	#405	—	2	2	no	—
242	#405	C₂²×C₂₉	1	4	yes	—
243	C₂×#97	—	2	1	no	—
244	C₂×C₄×C₈	—	2	1	no	—
245	#341	C₂²×C₂₉	1	4	yes	—
246	#339	C₂²×C₂₉	1	4	yes	—
247	#339	C₂²×C₂₉	1	4	yes	—
248	#336	C₂²×C₂₉	1	4	yes	—
249	C₂×C₂₉	—	2	1	no	—
250	C₂×C₂₉	—	2	1	no	—
251	C₂×C₂₉	—	2	2	no	—
252	C₂×C₂₉	#1922	1	4	yes	direct product factor
253	C₂×C₂₉	C₂×#387	1	1	yes	characteristic
254	C₂×C₂₉	C₂×#443	1	1	yes	characteristic
255	C₂×C₂₉	C₂×#444	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	Q₈×C₂₉	1	4	yes	—
264	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
265	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
275	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
277	C₂²×C₈	D₄×C₂₉	1	2	yes	—
278	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
279	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	C₂×C₄×C₂₉	1	2	yes	—
285	#117	C₂×C₄×C₂₉	1	2	yes	—
286	#117	C₂³×C₂₉	1	2	yes	—
287	#117	C₂³×C₂₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
300	#107	C₂×C₄×C₂₉	1	4	yes	complemented
301	#107	C₂×C₄×C₂₉	1	4	yes	complemented
302	#106	C₂×C₄×C₂₉	1	4	yes	complemented
303	#106	C₂×C₄×C₂₉	1	4	yes	complemented
304	C₄⋊C₈	—	2	4	no	—
305	C₄⋊C₈	—	2	4	no	—
306	#97	—	2	4	no	—
307	C₄×C₈	—	2	4	no	—
308	C₂₉	C₂×#1922	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	#41×C₂₉	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
323	C₂²×C₄	#41×C₂₉	1	2	yes	—
324	C₂²×C₄	#41×C₂₉	1	2	yes	—
325	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
326	C₂²×C₄	#41×C₂₉	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	C₂×Q₈×C₂₉	1	4	yes	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
357	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
358	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
359	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	4	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
374	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
375	C₂³	C₂₉×#125	1	2	yes	—
376	C₂³	C₂₉×#126	1	2	yes	—
377	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	C₂₉×#117	1	2	yes	—
391	C₂×C₄	C₂₉×#117	1	2	yes	—
392	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
393	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
394	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
395	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
396	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
397	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
398	C₂×C₄	C₂₉×#123	1	2	yes	—
399	C₂×C₄	C₂₉×#123	1	2	yes	—
400	C₂×C₄	C₂₉×#125	1	2	yes	—
401	C₂×C₄	C₂₉×#126	1	2	yes	—
402	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	4	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	C₂₉×#387	1	2	yes	—
421	C₂²	C₂₉×#387	1	2	yes	—
422	C₂²	C₂₉×#443	1	2	yes	—
423	C₂²	C₂₉×#444	1	2	yes	—
424	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
425	C₂²	C₂×C₂₉×#125	1	1	yes	characteristic
426	C₂²	C₂×C₂₉×#126	1	1	yes	characteristic
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	C₂₉×#387	1	2	yes	—
433	C₄	C₂₉×#387	1	2	yes	—
434	C₄	C₂×C₂₉×#117	1	1	yes	characteristic
435	C₄	C₂×C₄×Q₈×C₂₉	1	1	yes	characteristic
436	C₄	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
437	C₄	C₂×C₂₉×#123	1	1	yes	characteristic
438	C₂	—	2	1	no	—
439	C₂	—	2	1	no	—
440	C₂	—	2	2	no	—
441	C₂	C₂₉×#1922	1	4	yes	direct product factor
442	C₂	C₂×C₂₉×#387	1	1	yes	characteristic
443	C₂	C₂×C₂₉×#443	1	1	yes	characteristic
444	C₂	C₂×C₂₉×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₄×D₄
prime radical	C₂⁴×C₂₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1922	C₂	direct (N × H)
16. C₂₉×#427	C₄	semidirect
18. C₂×C₂₉×#107	C₄	semidirect
19. C₂×C₂₉×#107	C₄	semidirect
20. C₂×C₂₉×#106	C₄	semidirect
21. C₂×C₂₉×#106	C₄	semidirect
78. C₂₉×#107	C₂×C₄	semidirect
79. C₂₉×#107	C₂×C₄	semidirect
80. C₂₉×#106	C₂×C₄	semidirect
81. C₂₉×#106	C₂×C₄	semidirect
148. C₂×#1922	C₂₉	direct (N × H)
195. #1922	C₂×C₂₉	direct (N × H)
231. #427	C₄×C₂₉	semidirect
233. C₂×#107	C₄×C₂₉	semidirect
234. C₂×#107	C₄×C₂₉	semidirect
235. C₂×#106	C₄×C₂₉	semidirect
236. C₂×#106	C₄×C₂₉	semidirect
252. C₂×C₂₉	#1922	direct (N × H)
300. #107	C₂×C₄×C₂₉	semidirect
301. #107	C₂×C₄×C₂₉	semidirect
302. #106	C₂×C₄×C₂₉	semidirect
303. #106	C₂×C₄×C₂₉	semidirect
308. C₂₉	C₂×#1922	direct (N × H)
441. C₂	C₂₉×#1922	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×#427	2
C₂×C₂₉×#424	2
C₂×C₂₉×#405	2
C₂₉×#1922	2
C₂×C₂₉×#341	2
C₂×C₂₉×#339	2
C₂×C₂₉×#336	2
C₂×#1922	29

Subgroups — C2×C29×#1922 #20315940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1922 #20315940