Subgroups — C₂×C₂₉×#3222 #20355692

Order 7424.

2214 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#535	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3222	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₉×#460	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₉×#452	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₉×#450	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
19	C₂₉×#541	—	2	4	no	—
20	C₂₉×#541	C₂²	1	8	yes	complemented
21	C₂₉×#535	—	2	4	no	—
22	C₂₉×#535	C₂²	1	8	yes	—
23	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#126	—	2	2	no	—
27	C₂×C₂₉×#125	—	2	2	no	—
28	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₂₉×#121	—	2	2	no	—
33	C₂×C₂₉×#120	—	2	2	no	—
34	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
35	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
36	C₂₉×#497	C₂²	1	8	yes	complemented
37	C₂₉×#492	C₂²	1	8	yes	complemented
38	C₂₉×#490	C₂²	1	8	yes	complemented
39	C₂₉×#488	C₂²	1	8	yes	complemented
40	C₂₉×#464	C₂²	1	16	yes	complemented
41	C₂₉×#460	C₂²	1	16	yes	complemented
42	C₂₉×#452	C₂²	1	16	yes	complemented
43	C₂₉×#450	C₂²	1	16	yes	complemented
44	C₂₉×#433	C₂²	1	8	yes	complemented
45	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
46	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
47	C₂×C₂₉×#102	C₂²	1	2	yes	—
48	C₂×C₂₉×#102	C₂²	1	2	yes	—
49	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
50	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
51	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₂₉	—	2	1	no	—
54	C₂×#41×C₂₉	—	2	2	no	—
55	C₂×#41×C₂₉	—	4	4	no	—
56	C₂×#41×C₂₉	C₂³	1	4	yes	—
57	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₂₉	—	2	1	no	—
60	C₂²×D₄×C₂₉	—	2	1	no	—
61	C₂²×D₄×C₂₉	—	2	2	no	—
62	C₂²×D₄×C₂₉	—	2	2	no	—
63	C₂²×D₄×C₂₉	—	2	2	no	—
64	C₂²×D₄×C₂₉	—	4	4	no	—
65	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
69	C₂³×C₄×C₂₉	—	2	1	no	—
70	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₂₉	—	4	4	no	—
72	C₂×Q₁₆×C₂₉	C₂³	1	8	yes	complemented
73	C₂×SD₁₆×C₂₉	—	4	4	no	—
74	C₂×SD₁₆×C₂₉	—	4	4	no	—
75	C₂×SD₁₆×C₂₉	—	4	4	no	—
76	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	—
77	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	—
78	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	complemented
79	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
80	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
81	C₂₉×C₄⋊Q₈	—	2	2	no	—
82	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	complemented
83	C₂₉×#127	—	2	2	no	—
84	C₂₉×#127	—	2	2	no	—
85	C₂₉×#127	C₂³	1	4	yes	—
86	C₂₉×#127	C₂³	1	4	yes	—
87	C₂₉×#126	—	2	16	no	—
88	C₂₉×#125	—	2	16	no	—
89	C₂₉×#125	—	2	2	no	—
90	C₂₉×#125	C₂³	1	4	yes	complemented
91	C₂₉×#124	—	2	2	no	—
92	C₂₉×#124	—	2	2	no	—
93	C₂₉×#124	C₂³	1	4	yes	—
94	C₂₉×#124	C₂³	1	4	yes	—
95	C₂₉×C₂²⋊Q₈	—	2	4	no	—
96	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
97	C₂₉×#121	—	2	16	no	—
98	C₂₉×#120	—	2	16	no	—
99	C₄×Q₈×C₂₉	—	2	4	no	—
100	C₄×Q₈×C₂₉	C₂³	1	8	yes	complemented
101	C₂₉×#117	D₄	1	4	yes	—
102	C₂₉×#117	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
106	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
108	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
113	C₂×C₄²×C₂₉	—	2	2	no	—
114	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
116	C₂₉×C₄⋊C₈	C₂³	1	8	yes	complemented
117	C₂₉×#103	C₂³	1	8	yes	complemented
118	C₂₉×#102	C₂³	1	8	yes	—
119	C₂₉×#102	C₂³	1	8	yes	—
120	C₂₉×#102	C₂³	1	8	yes	complemented
121	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₂₉×#97	C₂³	1	4	yes	complemented
123	C₄×C₈×C₂₉	C₂³	1	4	yes	complemented
124	C₂⁴×C₂₉	—	2	1	no	—
125	C₂⁴×C₂₉	—	2	1	no	—
126	C₂⁴×C₂₉	—	2	1	no	—
127	C₂⁴×C₂₉	—	2	4	no	—
128	C₂⁴×C₂₉	—	4	4	no	—
129	C₂⁴×C₂₉	—	8	4	no	—
130	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
131	#41×C₂₉	—	4	8	no	—
132	#41×C₂₉	—	4	8	no	—
133	C₂×Q₈×C₂₉	—	2	2	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	4	no	—
136	C₂×Q₈×C₂₉	—	2	4	no	—
137	C₂×Q₈×C₂₉	—	2	4	no	—
138	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
139	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
140	C₂×D₄×C₂₉	—	2	4	no	—
141	C₂×D₄×C₂₉	—	2	4	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	8	no	—
146	C₂×D₄×C₂₉	—	2	8	no	—
147	C₂×D₄×C₂₉	—	2	4	no	—
148	C₂×D₄×C₂₉	—	2	4	no	—
149	C₂×D₄×C₂₉	—	2	4	no	—
150	C₂×D₄×C₂₉	—	4	8	no	—
151	C₂×D₄×C₂₉	—	4	4	no	—
152	C₂×D₄×C₂₉	—	4	8	no	—
153	C₂×D₄×C₂₉	—	4	4	no	—
154	C₂×D₄×C₂₉	—	8	4	no	—
155	C₂×D₄×C₂₉	—	8	4	no	—
156	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
157	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
158	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₂₉	—	2	4	no	—
160	C₂²×C₄×C₂₉	—	2	2	no	—
161	C₂²×C₄×C₂₉	—	2	2	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	2	4	no	—
164	C₂²×C₄×C₂₉	—	4	4	no	—
165	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
171	Q₁₆×C₂₉	—	4	8	no	—
172	SD₁₆×C₂₉	—	4	8	no	—
173	SD₁₆×C₂₉	—	4	8	no	—
174	SD₁₆×C₂₉	—	4	8	no	—
175	C₂×C₈×C₂₉	—	2	4	no	—
176	C₂×C₈×C₂₉	—	2	4	no	—
177	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
178	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
179	C₄⋊C₄×C₂₉	—	2	8	no	—
180	C₄⋊C₄×C₂₉	—	2	8	no	—
181	C₄⋊C₄×C₂₉	—	2	8	no	—
182	C₄⋊C₄×C₂₉	—	2	8	no	—
183	C₄⋊C₄×C₂₉	—	2	2	no	—
184	C₄⋊C₄×C₂₉	C₂×D₄	1	8	yes	—
185	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
186	C₂²⋊C₄×C₂₉	—	2	8	no	—
187	C₂²⋊C₄×C₂₉	—	2	8	no	—
188	C₂²⋊C₄×C₂₉	—	2	8	no	—
189	C₂²⋊C₄×C₂₉	C₂×D₄	1	8	yes	—
190	C₄²×C₂₉	—	2	8	no	—
191	C₄²×C₂₉	C₂×D₄	1	2	yes	—
192	C₄²×C₂₉	C₂×D₄	1	2	yes	—
193	C₄²×C₂₉	C₂⁴	1	2	yes	—
194	C₄²×C₂₉	C₂⁴	1	2	yes	—
195	C₂×#3222	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₂₉	—	2	2	no	—
197	C₂³×C₂₉	—	2	4	no	—
198	C₂³×C₂₉	—	2	2	no	—
199	C₂³×C₂₉	—	2	2	no	—
200	C₂³×C₂₉	—	2	2	no	—
201	C₂³×C₂₉	—	4	8	no	—
202	C₂³×C₂₉	—	4	2	no	—
203	C₂³×C₂₉	—	4	2	no	—
204	C₂³×C₂₉	—	4	2	no	—
205	C₂³×C₂₉	—	4	4	no	—
206	C₂³×C₂₉	—	4	4	no	—
207	C₂³×C₂₉	—	4	4	no	—
208	C₂³×C₂₉	—	8	8	no	—
209	C₂³×C₂₉	—	8	16	no	—
210	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
211	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₂₉	—	2	4	no	—
213	Q₈×C₂₉	—	2	4	no	—
214	Q₈×C₂₉	—	2	4	no	—
215	Q₈×C₂₉	—	4	4	no	—
216	Q₈×C₂₉	—	4	2	no	—
217	D₄×C₂₉	—	2	4	no	—
218	D₄×C₂₉	—	2	4	no	—
219	D₄×C₂₉	—	2	4	no	—
220	D₄×C₂₉	—	4	8	no	—
221	D₄×C₂₉	—	4	8	no	—
222	D₄×C₂₉	—	4	2	no	—
223	D₄×C₂₉	—	4	2	no	—
224	D₄×C₂₉	—	4	2	no	—
225	D₄×C₂₉	—	8	8	no	—
226	D₄×C₂₉	—	8	8	no	—
227	C₂×C₄×C₂₉	—	2	2	no	—
228	C₂×C₄×C₂₉	—	2	4	no	—
229	C₂×C₄×C₂₉	—	2	4	no	—
230	C₂×C₄×C₂₉	—	2	4	no	—
231	C₂×C₄×C₂₉	—	2	4	no	—
232	C₂×C₄×C₂₉	—	2	4	no	—
233	C₂×C₄×C₂₉	—	2	4	no	—
234	C₂×C₄×C₂₉	—	2	2	no	—
235	C₂×C₄×C₂₉	—	4	8	no	—
236	C₂×C₄×C₂₉	—	4	2	no	—
237	C₂×C₄×C₂₉	—	4	4	no	—
238	C₂×C₄×C₂₉	—	4	4	no	—
239	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₂₉	H(5,𝔽₂)	1	4	yes	—
244	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
245	C₈×C₂₉	—	2	4	no	—
246	C₈×C₂₉	—	2	4	no	—
247	C₂×#541	C₂×C₂₉	1	1	yes	characteristic, complemented
248	C₂×#535	C₂×C₂₉	1	1	yes	characteristic
249	#3222	C₂×C₂₉	1	16	yes	direct product factor
250	C₂×#497	C₂×C₂₉	1	1	yes	characteristic, complemented
251	C₂×#492	C₂×C₂₉	1	1	yes	characteristic, complemented
252	C₂×#490	C₂×C₂₉	1	1	yes	characteristic, complemented
253	C₂×#488	C₂×C₂₉	1	1	yes	characteristic, complemented
254	C₂×#464	C₂×C₂₉	1	2	yes	complemented
255	C₂×#460	C₂×C₂₉	1	2	yes	complemented
256	C₂×#452	C₂×C₂₉	1	2	yes	complemented
257	C₂×#450	C₂×C₂₉	1	2	yes	complemented
258	C₂×#433	C₂×C₂₉	1	1	yes	characteristic, complemented
259	C₂²×C₂₉	—	2	2	no	—
260	C₂²×C₂₉	—	2	4	no	—
261	C₂²×C₂₉	—	4	4	no	—
262	C₂²×C₂₉	—	4	2	no	—
263	C₂²×C₂₉	—	4	2	no	—
264	C₂²×C₂₉	—	4	2	no	—
265	C₂²×C₂₉	—	4	4	no	—
266	C₂²×C₂₉	—	4	4	no	—
267	C₂²×C₂₉	—	4	4	no	—
268	C₂²×C₂₉	—	8	16	no	—
269	C₂²×C₂₉	—	8	4	no	—
270	C₂²×C₂₉	—	8	4	no	—
271	C₂²×C₂₉	—	8	4	no	—
272	C₂²×C₂₉	#535	1	2	yes	—
273	C₂²×C₂₉	#577	1	4	yes	—
274	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
275	C₄×C₂₉	—	2	2	no	—
276	C₄×C₂₉	—	2	4	no	—
277	C₄×C₂₉	—	2	4	no	—
278	C₄×C₂₉	—	4	2	no	—
279	C₄×C₂₉	—	4	4	no	—
280	C₄×C₂₉	—	4	4	no	—
281	C₄×C₂₉	#535	1	2	yes	—
282	C₄×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
283	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
284	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
285	C₂²×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
286	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
287	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
288	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
289	#541	—	2	4	no	—
290	#541	C₂²×C₂₉	1	8	yes	complemented
291	#535	—	2	4	no	—
292	#535	C₂²×C₂₉	1	8	yes	—
293	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
294	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
295	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
296	C₂×#126	—	2	2	no	—
297	C₂×#125	—	2	2	no	—
298	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic, complemented
299	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
300	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
301	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
302	C₂×#121	—	2	2	no	—
303	C₂×#120	—	2	2	no	—
304	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
305	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
306	#497	C₂²×C₂₉	1	8	yes	complemented
307	#492	C₂²×C₂₉	1	8	yes	complemented
308	#490	C₂²×C₂₉	1	8	yes	complemented
309	#488	C₂²×C₂₉	1	8	yes	complemented
310	#464	C₂²×C₂₉	1	16	yes	complemented
311	#460	C₂²×C₂₉	1	16	yes	complemented
312	#452	C₂²×C₂₉	1	16	yes	complemented
313	#450	C₂²×C₂₉	1	16	yes	complemented
314	#433	C₂²×C₂₉	1	8	yes	complemented
315	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
316	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
317	C₂×#102	C₂²×C₂₉	1	2	yes	—
318	C₂×#102	C₂²×C₂₉	1	2	yes	—
319	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
320	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
321	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic, complemented
322	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
323	C₂×C₂₉	—	4	2	no	—
324	C₂×C₂₉	—	8	2	no	—
325	C₂×C₂₉	—	8	2	no	—
326	C₂×C₂₉	—	8	2	no	—
327	C₂×C₂₉	#3222	1	4	yes	direct product factor
328	C₂×C₂₉	C₂×#535	1	1	yes	characteristic
329	C₂×C₂₉	C₂×#577	1	2	yes	—
330	C₂⁵	—	2	1	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	4	4	no	—
333	C₂×#41	C₂³×C₂₉	1	4	yes	—
334	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
335	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	4	4	no	—
342	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
348	C₂×Q₁₆	—	4	4	no	—
349	C₂×Q₁₆	C₂³×C₂₉	1	8	yes	complemented
350	C₂×SD₁₆	—	4	4	no	—
351	C₂×SD₁₆	—	4	4	no	—
352	C₂×SD₁₆	—	4	4	no	—
353	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	—
354	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	—
355	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	complemented
356	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
357	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
358	C₄⋊Q₈	—	2	2	no	—
359	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	complemented
360	#127	—	2	2	no	—
361	#127	—	2	2	no	—
362	#127	C₂³×C₂₉	1	4	yes	—
363	#127	C₂³×C₂₉	1	4	yes	—
364	#126	—	2	16	no	—
365	#125	—	2	16	no	—
366	#125	—	2	2	no	—
367	#125	C₂³×C₂₉	1	4	yes	complemented
368	#124	—	2	2	no	—
369	#124	—	2	2	no	—
370	#124	C₂³×C₂₉	1	4	yes	—
371	#124	C₂³×C₂₉	1	4	yes	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
374	#121	—	2	16	no	—
375	#120	—	2	16	no	—
376	C₄×Q₈	—	2	4	no	—
377	C₄×Q₈	C₂³×C₂₉	1	8	yes	complemented
378	#117	D₄×C₂₉	1	4	yes	—
379	#117	C₂³×C₂₉	1	4	yes	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₂₉	1	8	yes	complemented
394	#103	C₂³×C₂₉	1	8	yes	complemented
395	#102	C₂³×C₂₉	1	8	yes	—
396	#102	C₂³×C₂₉	1	8	yes	—
397	#102	C₂³×C₂₉	1	8	yes	complemented
398	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	—
399	#97	C₂³×C₂₉	1	4	yes	complemented
400	C₄×C₈	C₂³×C₂₉	1	4	yes	complemented
401	C₂₉	C₂×#3222	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	2	1	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	4	4	no	—
407	C₂⁴	—	8	4	no	—
408	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
409	#41	—	4	8	no	—
410	#41	—	4	8	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
417	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	8	4	no	—
433	C₂×D₄	—	8	4	no	—
434	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
435	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
436	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
449	Q₁₆	—	4	8	no	—
450	SD₁₆	—	4	8	no	—
451	SD₁₆	—	4	8	no	—
452	SD₁₆	—	4	8	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
456	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	C₂×D₄×C₂₉	1	8	yes	—
463	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	C₂×D₄×C₂₉	1	8	yes	—
468	C₄²	—	2	8	no	—
469	C₄²	C₂×D₄×C₂₉	1	2	yes	—
470	C₄²	C₂×D₄×C₂₉	1	2	yes	—
471	C₄²	C₂⁴×C₂₉	1	2	yes	—
472	C₄²	C₂⁴×C₂₉	1	2	yes	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	8	8	no	—
486	C₂³	—	8	16	no	—
487	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
488	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	4	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	4	no	—
497	D₄	—	4	8	no	—
498	D₄	—	4	8	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	8	no	—
503	D₄	—	8	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
517	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
518	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
520	C₂×C₄	C₂₉×H(5,𝔽₂)	1	4	yes	—
521	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
522	C₈	—	2	4	no	—
523	C₈	—	2	4	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	8	16	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	4	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₂₉×#535	1	2	yes	—
538	C₂²	C₂₉×#577	1	4	yes	—
539	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	4	no	—
542	C₄	—	2	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	4	no	—
546	C₄	C₂₉×#535	1	2	yes	—
547	C₄	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
548	C₂	—	4	2	no	—
549	C₂	—	8	2	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₂₉×#3222	1	4	yes	direct product factor
553	C₂	C₂×C₂₉×#535	1	1	yes	characteristic
554	C₂	C₂×C₂₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#541	C₂	semidirect
3. C₂₉×#3222	C₂	direct (N × H)
4. C₂×C₂₉×#497	C₂	semidirect
5. C₂×C₂₉×#492	C₂	semidirect
6. C₂×C₂₉×#490	C₂	semidirect
7. C₂×C₂₉×#488	C₂	semidirect
8. C₂×C₂₉×#464	C₂	semidirect
9. C₂×C₂₉×#460	C₂	semidirect
10. C₂×C₂₉×#452	C₂	semidirect
11. C₂×C₂₉×#450	C₂	semidirect
12. C₂×C₂₉×#433	C₂	semidirect
15. C₂²×Q₁₆×C₂₉	C₂²	semidirect
18. C₂²×SD₁₆×C₂₉	C₂²	semidirect
20. C₂₉×#541	C₂²	semidirect
23. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₂₉×#125	C₂²	semidirect
34. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
36. C₂₉×#497	C₂²	semidirect
37. C₂₉×#492	C₂²	semidirect
38. C₂₉×#490	C₂²	semidirect
39. C₂₉×#488	C₂²	semidirect
40. C₂₉×#464	C₂²	semidirect
41. C₂₉×#460	C₂²	semidirect
42. C₂₉×#452	C₂²	semidirect
43. C₂₉×#450	C₂²	semidirect
44. C₂₉×#433	C₂²	semidirect
45. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
46. C₂×C₂₉×#103	C₂²	semidirect
49. C₂×C₂₉×#102	C₂²	semidirect
51. C₂×C₂₉×#97	C₂²	semidirect
52. C₂×C₄×C₈×C₂₉	C₂²	semidirect
72. C₂×Q₁₆×C₂₉	C₂³	semidirect
78. C₂×SD₁₆×C₂₉	C₂³	semidirect
82. C₂₉×C₄⋊Q₈	C₂³	semidirect
90. C₂₉×#125	C₂³	semidirect
100. C₄×Q₈×C₂₉	C₂³	semidirect
116. C₂₉×C₄⋊C₈	C₂³	semidirect
117. C₂₉×#103	C₂³	semidirect
120. C₂₉×#102	C₂³	semidirect
122. C₂₉×#97	C₂³	semidirect
123. C₄×C₈×C₂₉	C₂³	semidirect
195. C₂×#3222	C₂₉	direct (N × H)
247. C₂×#541	C₂×C₂₉	semidirect
249. #3222	C₂×C₂₉	direct (N × H)
250. C₂×#497	C₂×C₂₉	semidirect
251. C₂×#492	C₂×C₂₉	semidirect
252. C₂×#490	C₂×C₂₉	semidirect
253. C₂×#488	C₂×C₂₉	semidirect
254. C₂×#464	C₂×C₂₉	semidirect
255. C₂×#460	C₂×C₂₉	semidirect
256. C₂×#452	C₂×C₂₉	semidirect
257. C₂×#450	C₂×C₂₉	semidirect
258. C₂×#433	C₂×C₂₉	semidirect
285. C₂²×Q₁₆	C₂²×C₂₉	semidirect
288. C₂²×SD₁₆	C₂²×C₂₉	semidirect
290. #541	C₂²×C₂₉	semidirect
293. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
298. C₂×#125	C₂²×C₂₉	semidirect
304. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
306. #497	C₂²×C₂₉	semidirect
307. #492	C₂²×C₂₉	semidirect
308. #490	C₂²×C₂₉	semidirect
309. #488	C₂²×C₂₉	semidirect
310. #464	C₂²×C₂₉	semidirect
311. #460	C₂²×C₂₉	semidirect
312. #452	C₂²×C₂₉	semidirect
313. #450	C₂²×C₂₉	semidirect
314. #433	C₂²×C₂₉	semidirect
315. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
316. C₂×#103	C₂²×C₂₉	semidirect
319. C₂×#102	C₂²×C₂₉	semidirect
321. C₂×#97	C₂²×C₂₉	semidirect
322. C₂×C₄×C₈	C₂²×C₂₉	semidirect
327. C₂×C₂₉	#3222	direct (N × H)
349. C₂×Q₁₆	C₂³×C₂₉	semidirect
355. C₂×SD₁₆	C₂³×C₂₉	semidirect
359. C₄⋊Q₈	C₂³×C₂₉	semidirect
367. #125	C₂³×C₂₉	semidirect
377. C₄×Q₈	C₂³×C₂₉	semidirect
393. C₄⋊C₈	C₂³×C₂₉	semidirect
394. #103	C₂³×C₂₉	semidirect
397. #102	C₂³×C₂₉	semidirect
399. #97	C₂³×C₂₉	semidirect
400. C₄×C₈	C₂³×C₂₉	semidirect
401. C₂₉	C₂×#3222	direct (N × H)
552. C₂	C₂₉×#3222	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×#541	2
C₂×C₂₉×#535	2
C₂₉×#3222	2
C₂×C₂₉×#497	2
C₂×C₂₉×#492	2
C₂×C₂₉×#490	2
C₂×C₂₉×#488	2
C₂×C₂₉×#464	2
C₂×C₂₉×#460	2
C₂×C₂₉×#452	2
C₂×C₂₉×#450	2
C₂×C₂₉×#433	2
C₂×#3222	29

Subgroups — C2×C29×#3222 #20355692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3222 #20355692