Subgroups — C₂×C₂₉×#1861 #20315766

Order 7424.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#421	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₂₉×#104	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1861	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₂₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
10	C₂₉×#568	—	2	2	no	—
11	C₂₉×#568	—	2	2	no	—
12	C₂₉×#568	—	2	2	no	—
13	C₂₉×#568	C₂²	1	4	yes	—
14	C₂×C₂₉×#131	—	2	2	no	—
15	C₂×C₂₉×#131	—	2	2	no	—
16	C₂²×M₁₆×C₂₉	—	2	2	no	—
17	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#430	—	2	2	no	—
24	C₂₉×#430	C₂²	1	4	yes	complemented
25	C₂×C₂₉×#108	—	2	2	no	—
26	C₂₉×#423	—	2	2	no	—
27	C₂₉×#423	C₂²	1	4	yes	complemented
28	C₂×C₂₉×C₄⋊C₈	—	2	2	no	—
29	C₂₉×#421	—	2	2	no	—
30	C₂₉×#421	C₂²	1	4	yes	—
31	C₂×C₂₉×#104	—	2	2	no	—
32	C₂×C₂₉×#104	C₄	1	2	yes	complemented
33	C₂×C₂₉×#104	C₄	1	4	yes	complemented
34	C₂×C₂₉×#104	C₄	1	2	yes	complemented
35	C₂×C₂₉×#104	C₂²	1	4	yes	—
36	C₂₉×#344	C₂²	1	4	yes	complemented
37	C₂₉×#339	C₂²	1	4	yes	complemented
38	C₂×#41×C₂₉	—	2	1	no	—
39	C₂×#41×C₂₉	—	2	1	no	—
40	C₂×#41×C₂₉	—	2	1	no	—
41	C₂×#41×C₂₉	—	2	1	no	—
42	C₂×#41×C₂₉	—	2	1	no	—
43	C₂×#41×C₂₉	—	2	1	no	—
44	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
45	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
46	C₂×#41×C₂₉	D₄	1	2	yes	—
47	C₂×#41×C₂₉	D₄	1	2	yes	—
48	C₂×#41×C₂₉	Q₈	1	2	yes	—
49	C₂×#41×C₂₉	C₂³	1	2	yes	—
50	C₂²×Q₈×C₂₉	Q₈	1	1	yes	characteristic
51	C₂²×D₄×C₂₉	—	2	1	no	—
52	C₂²×D₄×C₂₉	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₂₉	—	2	1	no	—
54	C₂³×C₄×C₂₉	—	2	1	no	—
55	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
56	C₂₉×#131	—	2	8	no	—
57	C₂₉×#131	—	2	8	no	—
58	C₂₉×#131	—	2	8	no	—
59	C₂₉×#131	—	2	8	no	—
60	C₂×M₁₆×C₂₉	—	2	4	no	—
61	C₂×M₁₆×C₂₉	—	2	8	no	—
62	C₂×M₁₆×C₂₉	—	2	1	no	—
63	C₂×M₁₆×C₂₉	—	2	1	no	—
64	C₂×M₁₆×C₂₉	—	2	1	no	—
65	C₂×M₁₆×C₂₉	—	2	1	no	—
66	C₂×M₁₆×C₂₉	—	2	1	no	—
67	C₂×M₁₆×C₂₉	—	2	1	no	—
68	C₂×M₁₆×C₂₉	—	2	1	no	—
69	C₂×M₁₆×C₂₉	—	2	1	no	—
70	C₂×M₁₆×C₂₉	—	2	1	no	—
71	C₂×M₁₆×C₂₉	—	2	1	no	—
72	C₂×M₁₆×C₂₉	—	2	8	no	—
73	C₂×M₁₆×C₂₉	—	2	1	no	—
74	C₂×M₁₆×C₂₉	—	2	1	no	—
75	C₂×M₁₆×C₂₉	—	2	1	no	—
76	C₂×M₁₆×C₂₉	—	2	1	no	—
77	C₂×M₁₆×C₂₉	—	2	1	no	—
78	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
79	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
80	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
81	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
82	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
83	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
84	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
85	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
86	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
87	C₂²×C₈×C₂₉	—	2	4	no	—
88	C₂²×C₈×C₂₉	—	2	1	no	—
89	C₂²×C₈×C₂₉	—	2	1	no	—
90	C₂²×C₈×C₂₉	—	2	1	no	—
91	C₂²×C₈×C₂₉	D₄	1	2	yes	—
92	C₂₉×#117	—	2	1	no	—
93	C₂₉×#117	—	2	1	no	—
94	C₂₉×#117	—	2	1	no	—
95	C₂₉×#117	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₄²×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	—	2	1	no	—
100	C₂×C₄²×C₂₉	—	2	1	no	—
101	C₂×C₄²×C₂₉	—	2	1	no	—
102	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
104	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
106	C₂₉×#108	—	2	8	no	—
107	C₂₉×C₄⋊C₈	—	2	8	no	—
108	C₂₉×#104	—	2	8	no	—
109	C₂₉×#104	C₂×C₄	1	8	yes	complemented
110	C₂₉×#104	C₂×C₄	1	8	yes	complemented
111	C₂⁴×C₂₉	—	2	1	no	—
112	C₂⁴×C₂₉	#41	1	1	yes	characteristic
113	#41×C₂₉	—	2	2	no	—
114	#41×C₂₉	—	2	2	no	—
115	#41×C₂₉	—	2	2	no	—
116	#41×C₂₉	—	2	2	no	—
117	#41×C₂₉	—	2	2	no	—
118	#41×C₂₉	—	2	2	no	—
119	#41×C₂₉	—	2	2	no	—
120	#41×C₂₉	—	2	2	no	—
121	#41×C₂₉	—	2	2	no	—
122	#41×C₂₉	—	2	2	no	—
123	#41×C₂₉	—	2	2	no	—
124	#41×C₂₉	—	2	2	no	—
125	#41×C₂₉	C₄⋊C₄	1	4	yes	—
126	#41×C₂₉	C₄⋊C₄	1	4	yes	—
127	#41×C₂₉	C₂²×C₄	1	4	yes	—
128	#41×C₂₉	C₂×D₄	1	4	yes	—
129	C₂×Q₈×C₂₉	—	2	1	no	—
130	C₂×Q₈×C₂₉	—	2	1	no	—
131	C₂×Q₈×C₂₉	—	2	1	no	—
132	C₂×Q₈×C₂₉	C₄⋊C₄	1	2	yes	—
133	C₂×Q₈×C₂₉	C₄⋊C₄	1	2	yes	—
134	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
135	C₂×D₄×C₂₉	—	2	2	no	—
136	C₂×D₄×C₂₉	—	2	2	no	—
137	C₂×D₄×C₂₉	—	2	2	no	—
138	C₂×D₄×C₂₉	—	2	2	no	—
139	C₂×D₄×C₂₉	—	2	2	no	—
140	C₂×D₄×C₂₉	—	2	2	no	—
141	C₂×D₄×C₂₉	—	2	1	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	C₄⋊C₄	1	2	yes	—
145	C₂×D₄×C₂₉	C₄⋊C₄	1	2	yes	—
146	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₂₉	—	2	1	no	—
148	C₂²×C₄×C₂₉	—	2	1	no	—
149	C₂²×C₄×C₂₉	—	2	2	no	—
150	C₂²×C₄×C₂₉	—	2	2	no	—
151	C₂²×C₄×C₂₉	—	2	2	no	—
152	C₂²×C₄×C₂₉	—	2	2	no	—
153	C₂²×C₄×C₂₉	—	2	2	no	—
154	C₂²×C₄×C₂₉	—	2	2	no	—
155	C₂²×C₄×C₂₉	—	2	2	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	2	2	no	—
158	C₂²×C₄×C₂₉	—	4	4	no	—
159	C₂²×C₄×C₂₉	—	4	1	no	—
160	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
170	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
172	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
173	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₂₉	—	2	16	no	—
175	M₁₆×C₂₉	—	2	2	no	—
176	M₁₆×C₂₉	—	2	2	no	—
177	M₁₆×C₂₉	—	2	2	no	—
178	M₁₆×C₂₉	—	2	2	no	—
179	M₁₆×C₂₉	—	2	2	no	—
180	M₁₆×C₂₉	—	2	2	no	—
181	M₁₆×C₂₉	—	2	2	no	—
182	M₁₆×C₂₉	—	2	2	no	—
183	M₁₆×C₂₉	—	2	2	no	—
184	M₁₆×C₂₉	—	2	2	no	—
185	M₁₆×C₂₉	—	2	2	no	—
186	M₁₆×C₂₉	—	2	2	no	—
187	M₁₆×C₂₉	—	4	1	no	—
188	M₁₆×C₂₉	—	4	1	no	—
189	M₁₆×C₂₉	C₂²×C₄	1	4	yes	—
190	M₁₆×C₂₉	C₂×D₄	1	4	yes	—
191	C₂×C₈×C₂₉	—	2	16	no	—
192	C₂×C₈×C₂₉	—	2	2	no	—
193	C₂×C₈×C₂₉	—	2	2	no	—
194	C₂×C₈×C₂₉	—	2	2	no	—
195	C₂×C₈×C₂₉	—	2	2	no	—
196	C₂×C₈×C₂₉	—	2	2	no	—
197	C₂×C₈×C₂₉	—	2	2	no	—
198	C₂×C₈×C₂₉	—	2	2	no	—
199	C₂×C₈×C₂₉	—	2	2	no	—
200	C₂×C₈×C₂₉	—	2	2	no	—
201	C₂×C₈×C₂₉	—	4	1	no	—
202	C₂×C₈×C₂₉	—	4	1	no	—
203	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
204	C₄⋊C₄×C₂₉	—	2	2	no	—
205	C₄⋊C₄×C₂₉	—	4	1	no	—
206	C₂²⋊C₄×C₂₉	—	2	2	no	—
207	C₂²⋊C₄×C₂₉	—	4	1	no	—
208	C₄²×C₂₉	—	2	1	no	—
209	C₄²×C₂₉	—	2	2	no	—
210	C₄²×C₂₉	—	2	1	no	—
211	C₄²×C₂₉	—	2	2	no	—
212	C₄²×C₂₉	—	2	2	no	—
213	C₄²×C₂₉	—	4	1	no	—
214	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
215	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
216	C₂×#1861	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₂₉	—	2	2	no	—
218	C₂³×C₂₉	—	2	2	no	—
219	C₂³×C₂₉	—	2	2	no	—
220	C₂³×C₂₉	—	4	2	no	—
221	C₂³×C₂₉	—	8	2	no	—
222	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
223	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
224	C₂³×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂³×C₂₉	#123	1	1	yes	characteristic
227	C₂³×C₂₉	#123	1	1	yes	characteristic
228	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
229	Q₈×C₂₉	—	2	2	no	—
230	Q₈×C₂₉	—	2	2	no	—
231	Q₈×C₂₉	—	2	2	no	—
232	Q₈×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
233	D₄×C₂₉	—	2	4	no	—
234	D₄×C₂₉	—	2	4	no	—
235	D₄×C₂₉	—	2	4	no	—
236	D₄×C₂₉	—	2	4	no	—
237	D₄×C₂₉	—	2	2	no	—
238	D₄×C₂₉	—	2	2	no	—
239	D₄×C₂₉	—	2	2	no	—
240	D₄×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
241	C₂×C₄×C₂₉	—	2	4	no	—
242	C₂×C₄×C₂₉	—	2	2	no	—
243	C₂×C₄×C₂₉	—	2	2	no	—
244	C₂×C₄×C₂₉	—	2	2	no	—
245	C₂×C₄×C₂₉	—	2	2	no	—
246	C₂×C₄×C₂₉	—	2	4	no	—
247	C₂×C₄×C₂₉	—	2	4	no	—
248	C₂×C₄×C₂₉	—	2	4	no	—
249	C₂×C₄×C₂₉	—	2	4	no	—
250	C₂×C₄×C₂₉	—	2	2	no	—
251	C₂×C₄×C₂₉	—	4	4	no	—
252	C₂×C₄×C₂₉	—	4	4	no	—
253	C₂×C₄×C₂₉	—	4	2	no	—
254	C₂×C₄×C₂₉	—	4	2	no	—
255	C₂×C₄×C₂₉	—	8	2	no	—
256	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
264	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
268	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
269	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
270	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
277	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
278	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
279	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
283	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
284	C₈×C₂₉	—	2	4	no	—
285	C₈×C₂₉	—	2	4	no	—
286	C₈×C₂₉	—	2	4	no	—
287	C₈×C₂₉	—	4	2	no	—
288	C₂×#568	C₂×C₂₉	1	1	yes	characteristic
289	C₂×#430	C₂×C₂₉	1	1	yes	characteristic, complemented
290	C₂×#423	C₂×C₂₉	1	1	yes	characteristic, complemented
291	C₂×#421	C₂×C₂₉	1	1	yes	characteristic
292	C₂²×#104	C₂×C₂₉	1	1	yes	characteristic
293	#1861	C₂×C₂₉	1	8	yes	direct product factor
294	C₂×#344	C₂×C₂₉	1	1	yes	characteristic, complemented
295	C₂×#339	C₂×C₂₉	1	1	yes	characteristic, complemented
296	C₂²×C₂₉	—	2	2	no	—
297	C₂²×C₂₉	—	2	2	no	—
298	C₂²×C₂₉	—	2	2	no	—
299	C₂²×C₂₉	—	2	4	no	—
300	C₂²×C₂₉	—	4	1	no	—
301	C₂²×C₂₉	—	4	1	no	—
302	C₂²×C₂₉	—	4	1	no	—
303	C₂²×C₂₉	—	4	1	no	—
304	C₂²×C₂₉	—	4	4	no	—
305	C₂²×C₂₉	—	8	2	no	—
306	C₂²×C₂₉	—	8	2	no	—
307	C₂²×C₂₉	#385	1	1	yes	characteristic
308	C₂²×C₂₉	#385	1	1	yes	characteristic
309	C₂²×C₂₉	#385	1	1	yes	characteristic
310	C₂²×C₂₉	#385	1	1	yes	characteristic
311	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
313	C₂²×C₂₉	C₂×#123	1	1	yes	characteristic
314	C₄×C₂₉	—	2	4	no	—
315	C₄×C₂₉	—	2	4	no	—
316	C₄×C₂₉	—	4	2	no	—
317	C₄×C₂₉	—	8	2	no	—
318	C₄×C₂₉	#385	1	1	yes	characteristic
319	C₄×C₂₉	#385	1	1	yes	characteristic
320	C₄×C₂₉	#385	1	1	yes	characteristic
321	C₄×C₂₉	#385	1	1	yes	characteristic
322	C₄×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
323	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
324	C₄×C₂₉	C₂×#120	1	1	yes	characteristic
325	C₄×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
327	#568	—	2	2	no	—
328	#568	—	2	2	no	—
329	#568	—	2	2	no	—
330	#568	C₂²×C₂₉	1	4	yes	—
331	C₂×#131	—	2	2	no	—
332	C₂×#131	—	2	2	no	—
333	C₂²×M₁₆	—	2	2	no	—
334	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
335	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
336	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
337	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
339	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
340	#430	—	2	2	no	—
341	#430	C₂²×C₂₉	1	4	yes	complemented
342	C₂×#108	—	2	2	no	—
343	#423	—	2	2	no	—
344	#423	C₂²×C₂₉	1	4	yes	complemented
345	C₂×C₄⋊C₈	—	2	2	no	—
346	#421	—	2	2	no	—
347	#421	C₂²×C₂₉	1	4	yes	—
348	C₂×#104	—	2	2	no	—
349	C₂×#104	C₄×C₂₉	1	2	yes	complemented
350	C₂×#104	C₄×C₂₉	1	4	yes	complemented
351	C₂×#104	C₄×C₂₉	1	2	yes	complemented
352	C₂×#104	C₂²×C₂₉	1	4	yes	—
353	#344	C₂²×C₂₉	1	4	yes	complemented
354	#339	C₂²×C₂₉	1	4	yes	complemented
355	C₂×C₂₉	—	2	1	no	—
356	C₂×C₂₉	—	2	1	no	—
357	C₂×C₂₉	—	2	1	no	—
358	C₂×C₂₉	—	2	1	no	—
359	C₂×C₂₉	—	2	1	no	—
360	C₂×C₂₉	—	2	1	no	—
361	C₂×C₂₉	—	4	4	no	—
362	C₂×C₂₉	#1861	1	2	yes	direct product factor
363	C₂×C₂₉	C₂×#385	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
371	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
372	C₂×#41	D₄×C₂₉	1	2	yes	—
373	C₂×#41	D₄×C₂₉	1	2	yes	—
374	C₂×#41	Q₈×C₂₉	1	2	yes	—
375	C₂×#41	C₂³×C₂₉	1	2	yes	—
376	C₂²×Q₈	Q₈×C₂₉	1	1	yes	characteristic
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	Q₈×C₂₉	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
382	#131	—	2	8	no	—
383	#131	—	2	8	no	—
384	#131	—	2	8	no	—
385	#131	—	2	8	no	—
386	C₂×M₁₆	—	2	4	no	—
387	C₂×M₁₆	—	2	8	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	8	no	—
399	C₂×M₁₆	—	2	1	no	—
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	1	no	—
403	C₂×M₁₆	—	2	1	no	—
404	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
405	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
406	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
407	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
408	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
409	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
410	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
411	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
412	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
413	C₂²×C₈	—	2	4	no	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	2	1	no	—
417	C₂²×C₈	D₄×C₂₉	1	2	yes	—
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	C₂³×C₂₉	1	2	yes	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
429	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
430	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
432	#108	—	2	8	no	—
433	C₄⋊C₈	—	2	8	no	—
434	#104	—	2	8	no	—
435	#104	C₂×C₄×C₂₉	1	8	yes	complemented
436	#104	C₂×C₄×C₂₉	1	8	yes	complemented
437	C₂₉	C₂×#1861	1	1	yes	characteristic, direct product factor, Sylow
438	C₂⁴	—	2	1	no	—
439	C₂⁴	#41×C₂₉	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	C₄⋊C₄×C₂₉	1	4	yes	—
453	#41	C₄⋊C₄×C₂₉	1	4	yes	—
454	#41	C₂²×C₄×C₂₉	1	4	yes	—
455	#41	C₂×D₄×C₂₉	1	4	yes	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	C₄⋊C₄×C₂₉	1	2	yes	—
460	C₂×Q₈	C₄⋊C₄×C₂₉	1	2	yes	—
461	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₄⋊C₄×C₂₉	1	2	yes	—
472	C₂×D₄	C₄⋊C₄×C₂₉	1	2	yes	—
473	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
497	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
498	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
499	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
501	M₁₆	—	2	16	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	2	2	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	—	2	2	no	—
510	M₁₆	—	2	2	no	—
511	M₁₆	—	2	2	no	—
512	M₁₆	—	2	2	no	—
513	M₁₆	—	2	2	no	—
514	M₁₆	—	4	1	no	—
515	M₁₆	—	4	1	no	—
516	M₁₆	C₂²×C₄×C₂₉	1	4	yes	—
517	M₁₆	C₂×D₄×C₂₉	1	4	yes	—
518	C₂×C₈	—	2	16	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	2	2	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	4	1	no	—
529	C₂×C₈	—	4	1	no	—
530	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	2	no	—
540	C₄²	—	4	1	no	—
541	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
542	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
549	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
550	C₂³	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
551	C₂³	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
552	C₂³	C₂₉×#123	1	1	yes	characteristic
553	C₂³	C₂₉×#123	1	1	yes	characteristic
554	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×C₄⋊C₄×C₂₉	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×C₄⋊C₄×C₂₉	1	4	yes	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
583	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
584	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
586	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
587	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
588	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
589	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
590	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
591	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
592	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
593	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
594	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
595	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
596	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
597	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
598	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
599	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
600	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
601	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
602	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
603	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
604	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
608	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	4	no	—
612	C₈	—	2	4	no	—
613	C₈	—	4	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	C₂₉×#385	1	1	yes	characteristic
626	C₂²	C₂₉×#385	1	1	yes	characteristic
627	C₂²	C₂₉×#385	1	1	yes	characteristic
628	C₂²	C₂₉×#385	1	1	yes	characteristic
629	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
630	C₂²	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
631	C₂²	C₂×C₂₉×#123	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	2	no	—
636	C₄	C₂₉×#385	1	1	yes	characteristic
637	C₄	C₂₉×#385	1	1	yes	characteristic
638	C₄	C₂₉×#385	1	1	yes	characteristic
639	C₄	C₂₉×#385	1	1	yes	characteristic
640	C₄	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
641	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
642	C₄	C₂×C₂₉×#120	1	1	yes	characteristic
643	C₄	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	C₂₉×#1861	1	2	yes	direct product factor
652	C₂	C₂×C₂₉×#385	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#120
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	#385
prime radical	C₂²×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#430	C₂	semidirect
3. C₂×C₂₉×#423	C₂	semidirect
6. C₂₉×#1861	C₂	direct (N × H)
7. C₂×C₂₉×#344	C₂	semidirect
8. C₂×C₂₉×#339	C₂	semidirect
24. C₂₉×#430	C₂²	semidirect
27. C₂₉×#423	C₂²	semidirect
32. C₂×C₂₉×#104	C₄	semidirect
33. C₂×C₂₉×#104	C₄	semidirect
34. C₂×C₂₉×#104	C₄	semidirect
36. C₂₉×#344	C₂²	semidirect
37. C₂₉×#339	C₂²	semidirect
109. C₂₉×#104	C₂×C₄	semidirect
110. C₂₉×#104	C₂×C₄	semidirect
216. C₂×#1861	C₂₉	direct (N × H)
289. C₂×#430	C₂×C₂₉	semidirect
290. C₂×#423	C₂×C₂₉	semidirect
293. #1861	C₂×C₂₉	direct (N × H)
294. C₂×#344	C₂×C₂₉	semidirect
295. C₂×#339	C₂×C₂₉	semidirect
341. #430	C₂²×C₂₉	semidirect
344. #423	C₂²×C₂₉	semidirect
349. C₂×#104	C₄×C₂₉	semidirect
350. C₂×#104	C₄×C₂₉	semidirect
351. C₂×#104	C₄×C₂₉	semidirect
353. #344	C₂²×C₂₉	semidirect
354. #339	C₂²×C₂₉	semidirect
362. C₂×C₂₉	#1861	direct (N × H)
435. #104	C₂×C₄×C₂₉	semidirect
436. #104	C₂×C₄×C₂₉	semidirect
437. C₂₉	C₂×#1861	direct (N × H)
651. C₂	C₂₉×#1861	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×#568	2
C₂×C₂₉×#430	2
C₂×C₂₉×#423	2
C₂×C₂₉×#421	2
C₂²×C₂₉×#104	2
C₂₉×#1861	2
C₂×C₂₉×#344	2
C₂×C₂₉×#339	2
C₂×#1861	29

Subgroups — C2×C29×#1861 #20315766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1861 #20315766