Subgroups — C₂×C₂₉×#3224 #20355693

Order 7424.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3224	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
27	C₂₉×#542	—	2	4	no	—
28	C₂₉×#542	C₂²	1	8	yes	complemented
29	C₂₉×#535	—	2	4	no	—
30	C₂₉×#535	C₂²	1	8	yes	complemented
31	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#126	—	2	1	no	—
35	C₂×C₂₉×#124	—	2	1	no	—
36	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₉×#123	—	2	1	no	—
40	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
41	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#121	—	2	1	no	—
43	C₂×C₂₉×#121	—	2	1	no	—
44	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
45	C₂×C₂₉×#120	—	2	1	no	—
46	C₂×C₂₉×#120	—	2	1	no	—
47	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
50	C₂₉×#496	C₂²	1	8	yes	complemented
51	C₂₉×#495	C₂²	1	8	yes	complemented
52	C₂₉×#489	C₂²	1	8	yes	complemented
53	C₂₉×#486	C₂²	1	8	yes	complemented
54	C₂₉×#464	C₂²	1	8	yes	complemented
55	C₂₉×#463	C₂²	1	8	yes	complemented
56	C₂₉×#460	C₂²	1	8	yes	complemented
57	C₂₉×#459	C₂²	1	8	yes	complemented
58	C₂₉×#452	C₂²	1	8	yes	complemented
59	C₂₉×#450	C₂²	1	8	yes	complemented
60	C₂₉×#449	C₂²	1	8	yes	complemented
61	C₂₉×#447	C₂²	1	8	yes	complemented
62	C₂₉×#433	C₂²	1	8	yes	complemented
63	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
68	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
69	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
70	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
71	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₂₉	—	2	1	no	—
78	C₂×#41×C₂₉	—	2	2	no	—
79	C₂×#41×C₂₉	—	4	2	no	—
80	C₂×#41×C₂₉	—	4	2	no	—
81	C₂×#41×C₂₉	C₂³	1	4	yes	—
82	C₂²×Q₈×C₂₉	—	2	1	no	—
83	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₂₉	—	2	1	no	—
86	C₂²×D₄×C₂₉	—	2	1	no	—
87	C₂²×D₄×C₂₉	—	2	1	no	—
88	C₂²×D₄×C₂₉	—	2	2	no	—
89	C₂²×D₄×C₂₉	—	2	1	no	—
90	C₂²×D₄×C₂₉	—	2	1	no	—
91	C₂²×D₄×C₂₉	—	2	1	no	—
92	C₂²×D₄×C₂₉	—	2	1	no	—
93	C₂²×D₄×C₂₉	—	4	2	no	—
94	C₂²×D₄×C₂₉	—	4	2	no	—
95	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₂₉	—	2	1	no	—
101	C₂³×C₄×C₂₉	—	2	1	no	—
102	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₂×Q₁₆×C₂₉	—	4	2	no	—
104	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	complemented
105	C₂×SD₁₆×C₂₉	—	4	2	no	—
106	C₂×SD₁₆×C₂₉	—	4	2	no	—
107	C₂×SD₁₆×C₂₉	—	4	2	no	—
108	C₂×SD₁₆×C₂₉	—	4	2	no	—
109	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	complemented
112	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	complemented
113	C₂×D₈×C₂₉	—	4	2	no	—
114	C₂×D₈×C₂₉	—	4	2	no	—
115	C₂×D₈×C₂₉	—	4	2	no	—
116	C₂×D₈×C₂₉	C₂³	1	4	yes	—
117	C₂×D₈×C₂₉	C₂³	1	4	yes	—
118	C₂×D₈×C₂₉	C₂³	1	4	yes	complemented
119	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
123	C₂₉×C₄⋊Q₈	—	2	2	no	—
124	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	complemented
125	C₂₉×#127	—	2	2	no	—
126	C₂₉×#127	—	2	2	no	—
127	C₂₉×#127	C₂³	1	4	yes	—
128	C₂₉×#127	C₂³	1	4	yes	—
129	C₂₉×#126	—	2	8	no	—
130	C₂₉×#124	—	2	8	no	—
131	C₂₉×#124	—	2	2	no	—
132	C₂₉×#124	—	2	2	no	—
133	C₂₉×#124	—	2	2	no	—
134	C₂₉×#124	C₂³	1	4	yes	—
135	C₂₉×#124	C₂³	1	4	yes	—
136	C₂₉×#124	C₂³	1	4	yes	complemented
137	C₂₉×#123	—	2	8	no	—
138	C₂₉×C₂²⋊Q₈	—	2	2	no	—
139	C₂₉×C₂²⋊Q₈	—	2	8	no	—
140	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₂₉×#121	—	2	2	no	—
142	C₂₉×#121	—	2	8	no	—
143	C₂₉×#121	—	2	8	no	—
144	C₂₉×#121	C₂³	1	4	yes	—
145	C₂₉×#120	—	2	8	no	—
146	C₂₉×#120	—	2	8	no	—
147	C₄×Q₈×C₂₉	—	2	2	no	—
148	C₄×Q₈×C₂₉	C₂³	1	4	yes	complemented
149	C₄×D₄×C₂₉	—	2	2	no	—
150	C₄×D₄×C₂₉	C₂³	1	4	yes	complemented
151	C₂₉×#117	D₄	1	4	yes	—
152	C₂₉×#117	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
155	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
166	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
169	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₂₉	—	2	1	no	—
172	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
174	C₂₉×C₄⋊C₈	C₂³	1	4	yes	complemented
175	C₂₉×C₄⋊C₈	C₂³	1	4	yes	complemented
176	C₂₉×#103	C₂³	1	4	yes	complemented
177	C₂₉×#103	C₂³	1	4	yes	complemented
178	C₂₉×#102	C₂³	1	4	yes	—
179	C₂₉×#102	C₂³	1	4	yes	—
180	C₂₉×#102	C₂³	1	4	yes	—
181	C₂₉×#102	C₂³	1	4	yes	—
182	C₂₉×#102	C₂³	1	4	yes	complemented
183	C₂₉×#102	C₂³	1	4	yes	complemented
184	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₂₉×#97	C₂³	1	4	yes	complemented
187	C₄×C₈×C₂₉	C₂³	1	4	yes	complemented
188	C₂⁴×C₂₉	—	2	1	no	—
189	C₂⁴×C₂₉	—	2	1	no	—
190	C₂⁴×C₂₉	—	2	1	no	—
191	C₂⁴×C₂₉	—	2	1	no	—
192	C₂⁴×C₂₉	—	2	4	no	—
193	C₂⁴×C₂₉	—	4	4	no	—
194	C₂⁴×C₂₉	—	8	2	no	—
195	C₂⁴×C₂₉	—	8	2	no	—
196	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
197	#41×C₂₉	—	4	4	no	—
198	#41×C₂₉	—	4	4	no	—
199	#41×C₂₉	—	4	8	no	—
200	C₂×Q₈×C₂₉	—	2	1	no	—
201	C₂×Q₈×C₂₉	—	2	1	no	—
202	C₂×Q₈×C₂₉	—	2	4	no	—
203	C₂×Q₈×C₂₉	—	2	2	no	—
204	C₂×Q₈×C₂₉	—	2	2	no	—
205	C₂×Q₈×C₂₉	—	2	2	no	—
206	C₂×Q₈×C₂₉	—	2	2	no	—
207	C₂×Q₈×C₂₉	—	8	2	no	—
208	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
210	C₂×D₄×C₂₉	—	2	4	no	—
211	C₂×D₄×C₂₉	—	2	4	no	—
212	C₂×D₄×C₂₉	—	2	1	no	—
213	C₂×D₄×C₂₉	—	2	4	no	—
214	C₂×D₄×C₂₉	—	2	1	no	—
215	C₂×D₄×C₂₉	—	2	1	no	—
216	C₂×D₄×C₂₉	—	2	1	no	—
217	C₂×D₄×C₂₉	—	2	4	no	—
218	C₂×D₄×C₂₉	—	2	4	no	—
219	C₂×D₄×C₂₉	—	2	4	no	—
220	C₂×D₄×C₂₉	—	2	4	no	—
221	C₂×D₄×C₂₉	—	2	2	no	—
222	C₂×D₄×C₂₉	—	2	2	no	—
223	C₂×D₄×C₂₉	—	2	2	no	—
224	C₂×D₄×C₂₉	—	2	2	no	—
225	C₂×D₄×C₂₉	—	2	2	no	—
226	C₂×D₄×C₂₉	—	2	2	no	—
227	C₂×D₄×C₂₉	—	2	2	no	—
228	C₂×D₄×C₂₉	—	2	2	no	—
229	C₂×D₄×C₂₉	—	4	4	no	—
230	C₂×D₄×C₂₉	—	4	4	no	—
231	C₂×D₄×C₂₉	—	4	4	no	—
232	C₂×D₄×C₂₉	—	4	8	no	—
233	C₂×D₄×C₂₉	—	4	4	no	—
234	C₂×D₄×C₂₉	—	8	2	no	—
235	C₂×D₄×C₂₉	—	8	2	no	—
236	C₂×D₄×C₂₉	—	8	2	no	—
237	C₂×D₄×C₂₉	—	8	2	no	—
238	C₂×D₄×C₂₉	—	8	2	no	—
239	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
241	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
242	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₂₉	—	2	2	no	—
244	C₂²×C₄×C₂₉	—	2	2	no	—
245	C₂²×C₄×C₂₉	—	2	1	no	—
246	C₂²×C₄×C₂₉	—	2	1	no	—
247	C₂²×C₄×C₂₉	—	2	1	no	—
248	C₂²×C₄×C₂₉	—	2	1	no	—
249	C₂²×C₄×C₂₉	—	2	4	no	—
250	C₂²×C₄×C₂₉	—	2	4	no	—
251	C₂²×C₄×C₂₉	—	4	4	no	—
252	C₂²×C₄×C₂₉	—	8	2	no	—
253	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
261	Q₁₆×C₂₉	—	4	4	no	—
262	SD₁₆×C₂₉	—	4	4	no	—
263	SD₁₆×C₂₉	—	4	4	no	—
264	SD₁₆×C₂₉	—	4	4	no	—
265	SD₁₆×C₂₉	—	4	4	no	—
266	D₈×C₂₉	—	4	4	no	—
267	D₈×C₂₉	—	4	4	no	—
268	D₈×C₂₉	—	4	4	no	—
269	C₂×C₈×C₂₉	—	2	2	no	—
270	C₂×C₈×C₂₉	—	2	2	no	—
271	C₂×C₈×C₂₉	—	2	2	no	—
272	C₂×C₈×C₂₉	—	2	2	no	—
273	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
274	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₉	—	2	4	no	—
278	C₄⋊C₄×C₂₉	—	2	4	no	—
279	C₄⋊C₄×C₂₉	—	2	4	no	—
280	C₄⋊C₄×C₂₉	—	2	1	no	—
281	C₄⋊C₄×C₂₉	—	2	1	no	—
282	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
284	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₂₉	—	2	4	no	—
287	C₂²⋊C₄×C₂₉	—	2	4	no	—
288	C₂²⋊C₄×C₂₉	—	2	4	no	—
289	C₂²⋊C₄×C₂₉	—	2	4	no	—
290	C₂²⋊C₄×C₂₉	—	2	4	no	—
291	C₂²⋊C₄×C₂₉	—	2	4	no	—
292	C₂²⋊C₄×C₂₉	—	2	4	no	—
293	C₂²⋊C₄×C₂₉	—	2	4	no	—
294	C₂²⋊C₄×C₂₉	—	2	4	no	—
295	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
296	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
297	C₄²×C₂₉	—	2	4	no	—
298	C₄²×C₂₉	C₂×D₄	1	2	yes	—
299	C₄²×C₂₉	C₂×D₄	1	2	yes	—
300	C₄²×C₂₉	C₂⁴	1	2	yes	—
301	C₄²×C₂₉	C₂⁴	1	2	yes	—
302	C₂×#3224	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
303	C₂³×C₂₉	—	2	2	no	—
304	C₂³×C₂₉	—	2	2	no	—
305	C₂³×C₂₉	—	2	2	no	—
306	C₂³×C₂₉	—	2	2	no	—
307	C₂³×C₂₉	—	2	2	no	—
308	C₂³×C₂₉	—	2	2	no	—
309	C₂³×C₂₉	—	2	2	no	—
310	C₂³×C₂₉	—	4	8	no	—
311	C₂³×C₂₉	—	4	2	no	—
312	C₂³×C₂₉	—	4	2	no	—
313	C₂³×C₂₉	—	4	2	no	—
314	C₂³×C₂₉	—	4	2	no	—
315	C₂³×C₂₉	—	4	2	no	—
316	C₂³×C₂₉	—	4	2	no	—
317	C₂³×C₂₉	—	4	2	no	—
318	C₂³×C₂₉	—	4	2	no	—
319	C₂³×C₂₉	—	4	2	no	—
320	C₂³×C₂₉	—	4	2	no	—
321	C₂³×C₂₉	—	4	2	no	—
322	C₂³×C₂₉	—	4	2	no	—
323	C₂³×C₂₉	—	8	4	no	—
324	C₂³×C₂₉	—	8	4	no	—
325	C₂³×C₂₉	—	8	16	no	—
326	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
327	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₂₉	—	2	2	no	—
329	Q₈×C₂₉	—	2	2	no	—
330	Q₈×C₂₉	—	2	2	no	—
331	Q₈×C₂₉	—	2	2	no	—
332	Q₈×C₂₉	—	4	2	no	—
333	Q₈×C₂₉	—	4	2	no	—
334	Q₈×C₂₉	—	8	4	no	—
335	D₄×C₂₉	—	2	2	no	—
336	D₄×C₂₉	—	2	2	no	—
337	D₄×C₂₉	—	2	2	no	—
338	D₄×C₂₉	—	2	2	no	—
339	D₄×C₂₉	—	2	2	no	—
340	D₄×C₂₉	—	2	2	no	—
341	D₄×C₂₉	—	2	2	no	—
342	D₄×C₂₉	—	2	2	no	—
343	D₄×C₂₉	—	4	8	no	—
344	D₄×C₂₉	—	4	8	no	—
345	D₄×C₂₉	—	4	2	no	—
346	D₄×C₂₉	—	4	2	no	—
347	D₄×C₂₉	—	4	2	no	—
348	D₄×C₂₉	—	4	2	no	—
349	D₄×C₂₉	—	8	4	no	—
350	D₄×C₂₉	—	8	4	no	—
351	D₄×C₂₉	—	8	4	no	—
352	D₄×C₂₉	—	8	4	no	—
353	D₄×C₂₉	—	8	4	no	—
354	C₂×C₄×C₂₉	—	2	2	no	—
355	C₂×C₄×C₂₉	—	2	2	no	—
356	C₂×C₄×C₂₉	—	2	2	no	—
357	C₂×C₄×C₂₉	—	2	2	no	—
358	C₂×C₄×C₂₉	—	2	2	no	—
359	C₂×C₄×C₂₉	—	2	4	no	—
360	C₂×C₄×C₂₉	—	2	2	no	—
361	C₂×C₄×C₂₉	—	2	2	no	—
362	C₂×C₄×C₂₉	—	2	2	no	—
363	C₂×C₄×C₂₉	—	2	2	no	—
364	C₂×C₄×C₂₉	—	2	2	no	—
365	C₂×C₄×C₂₉	—	2	2	no	—
366	C₂×C₄×C₂₉	—	4	8	no	—
367	C₂×C₄×C₂₉	—	4	2	no	—
368	C₂×C₄×C₂₉	—	4	2	no	—
369	C₂×C₄×C₂₉	—	4	2	no	—
370	C₂×C₄×C₂₉	—	4	2	no	—
371	C₂×C₄×C₂₉	—	8	4	no	—
372	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
381	C₈×C₂₉	—	2	2	no	—
382	C₈×C₂₉	—	2	2	no	—
383	C₈×C₂₉	—	2	2	no	—
384	C₈×C₂₉	—	2	2	no	—
385	C₂×#542	C₂×C₂₉	1	1	yes	characteristic, complemented
386	C₂×#535	C₂×C₂₉	1	1	yes	characteristic, complemented
387	#3224	C₂×C₂₉	1	16	yes	direct product factor
388	C₂×#496	C₂×C₂₉	1	1	yes	characteristic, complemented
389	C₂×#495	C₂×C₂₉	1	1	yes	characteristic, complemented
390	C₂×#489	C₂×C₂₉	1	1	yes	characteristic, complemented
391	C₂×#486	C₂×C₂₉	1	1	yes	characteristic, complemented
392	C₂×#464	C₂×C₂₉	1	1	yes	characteristic, complemented
393	C₂×#460	C₂×C₂₉	1	1	yes	characteristic, complemented
394	C₂×#463	C₂×C₂₉	1	1	yes	characteristic, complemented
395	C₂×#459	C₂×C₂₉	1	1	yes	characteristic, complemented
396	C₂×#452	C₂×C₂₉	1	1	yes	characteristic, complemented
397	C₂×#449	C₂×C₂₉	1	1	yes	characteristic, complemented
398	C₂×#450	C₂×C₂₉	1	1	yes	characteristic, complemented
399	C₂×#447	C₂×C₂₉	1	1	yes	characteristic, complemented
400	C₂×#433	C₂×C₂₉	1	1	yes	characteristic, complemented
401	C₂²×C₂₉	—	2	2	no	—
402	C₂²×C₂₉	—	2	2	no	—
403	C₂²×C₂₉	—	2	2	no	—
404	C₂²×C₂₉	—	4	4	no	—
405	C₂²×C₂₉	—	4	2	no	—
406	C₂²×C₂₉	—	4	2	no	—
407	C₂²×C₂₉	—	4	2	no	—
408	C₂²×C₂₉	—	4	2	no	—
409	C₂²×C₂₉	—	4	2	no	—
410	C₂²×C₂₉	—	4	2	no	—
411	C₂²×C₂₉	—	4	2	no	—
412	C₂²×C₂₉	—	4	2	no	—
413	C₂²×C₂₉	—	4	2	no	—
414	C₂²×C₂₉	—	4	2	no	—
415	C₂²×C₂₉	—	4	2	no	—
416	C₂²×C₂₉	—	4	2	no	—
417	C₂²×C₂₉	—	8	16	no	—
418	C₂²×C₂₉	—	8	4	no	—
419	C₂²×C₂₉	—	8	4	no	—
420	C₂²×C₂₉	—	8	4	no	—
421	C₂²×C₂₉	—	8	4	no	—
422	C₂²×C₂₉	#535	1	2	yes	—
423	C₂²×C₂₉	#576	1	2	yes	—
424	C₂²×C₂₉	#577	1	2	yes	—
425	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₂₉	—	2	2	no	—
427	C₄×C₂₉	—	2	2	no	—
428	C₄×C₂₉	—	2	2	no	—
429	C₄×C₂₉	—	2	2	no	—
430	C₄×C₂₉	—	2	2	no	—
431	C₄×C₂₉	—	4	2	no	—
432	C₄×C₂₉	—	4	2	no	—
433	C₄×C₂₉	—	4	2	no	—
434	C₄×C₂₉	—	4	2	no	—
435	C₄×C₂₉	#535	1	2	yes	—
436	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
439	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
440	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
441	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
442	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
443	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
444	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
445	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
446	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
447	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
448	#542	—	2	4	no	—
449	#542	C₂²×C₂₉	1	8	yes	complemented
450	#535	—	2	4	no	—
451	#535	C₂²×C₂₉	1	8	yes	complemented
452	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
453	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
454	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
455	C₂×#126	—	2	1	no	—
456	C₂×#124	—	2	1	no	—
457	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
458	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
459	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic, complemented
460	C₂×#123	—	2	1	no	—
461	C₂×C₂²⋊Q₈	—	2	1	no	—
462	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
463	C₂×#121	—	2	1	no	—
464	C₂×#121	—	2	1	no	—
465	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
466	C₂×#120	—	2	1	no	—
467	C₂×#120	—	2	1	no	—
468	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
469	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
470	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
471	#496	C₂²×C₂₉	1	8	yes	complemented
472	#495	C₂²×C₂₉	1	8	yes	complemented
473	#489	C₂²×C₂₉	1	8	yes	complemented
474	#486	C₂²×C₂₉	1	8	yes	complemented
475	#464	C₂²×C₂₉	1	8	yes	complemented
476	#463	C₂²×C₂₉	1	8	yes	complemented
477	#460	C₂²×C₂₉	1	8	yes	complemented
478	#459	C₂²×C₂₉	1	8	yes	complemented
479	#452	C₂²×C₂₉	1	8	yes	complemented
480	#450	C₂²×C₂₉	1	8	yes	complemented
481	#449	C₂²×C₂₉	1	8	yes	complemented
482	#447	C₂²×C₂₉	1	8	yes	complemented
483	#433	C₂²×C₂₉	1	8	yes	complemented
484	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
485	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
486	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
487	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
488	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
489	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
490	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
491	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
492	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
493	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
494	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
495	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
496	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic, complemented
497	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
498	C₂×C₂₉	—	4	2	no	—
499	C₂×C₂₉	—	8	2	no	—
500	C₂×C₂₉	—	8	2	no	—
501	C₂×C₂₉	—	8	2	no	—
502	C₂×C₂₉	—	8	2	no	—
503	C₂×C₂₉	#3224	1	4	yes	direct product factor
504	C₂×C₂₉	C₂×#535	1	1	yes	characteristic
505	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
506	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
507	C₂⁵	—	2	1	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	4	2	no	—
510	C₂×#41	—	4	2	no	—
511	C₂×#41	C₂³×C₂₉	1	4	yes	—
512	C₂²×Q₈	—	2	1	no	—
513	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	4	2	no	—
524	C₂²×D₄	—	4	2	no	—
525	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
533	C₂×Q₁₆	—	4	2	no	—
534	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	complemented
535	C₂×SD₁₆	—	4	2	no	—
536	C₂×SD₁₆	—	4	2	no	—
537	C₂×SD₁₆	—	4	2	no	—
538	C₂×SD₁₆	—	4	2	no	—
539	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
540	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	complemented
542	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	complemented
543	C₂×D₈	—	4	2	no	—
544	C₂×D₈	—	4	2	no	—
545	C₂×D₈	—	4	2	no	—
546	C₂×D₈	C₂³×C₂₉	1	4	yes	—
547	C₂×D₈	C₂³×C₂₉	1	4	yes	—
548	C₂×D₈	C₂³×C₂₉	1	4	yes	complemented
549	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
552	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
553	C₄⋊Q₈	—	2	2	no	—
554	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	complemented
555	#127	—	2	2	no	—
556	#127	—	2	2	no	—
557	#127	C₂³×C₂₉	1	4	yes	—
558	#127	C₂³×C₂₉	1	4	yes	—
559	#126	—	2	8	no	—
560	#124	—	2	8	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	C₂³×C₂₉	1	4	yes	—
565	#124	C₂³×C₂₉	1	4	yes	—
566	#124	C₂³×C₂₉	1	4	yes	complemented
567	#123	—	2	8	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	8	no	—
570	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
571	#121	—	2	2	no	—
572	#121	—	2	8	no	—
573	#121	—	2	8	no	—
574	#121	C₂³×C₂₉	1	4	yes	—
575	#120	—	2	8	no	—
576	#120	—	2	8	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	C₂³×C₂₉	1	4	yes	complemented
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	C₂³×C₂₉	1	4	yes	complemented
581	#117	D₄×C₂₉	1	4	yes	—
582	#117	C₂³×C₂₉	1	4	yes	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
587	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
604	C₄⋊C₈	C₂³×C₂₉	1	4	yes	complemented
605	C₄⋊C₈	C₂³×C₂₉	1	4	yes	complemented
606	#103	C₂³×C₂₉	1	4	yes	complemented
607	#103	C₂³×C₂₉	1	4	yes	complemented
608	#102	C₂³×C₂₉	1	4	yes	—
609	#102	C₂³×C₂₉	1	4	yes	—
610	#102	C₂³×C₂₉	1	4	yes	—
611	#102	C₂³×C₂₉	1	4	yes	—
612	#102	C₂³×C₂₉	1	4	yes	complemented
613	#102	C₂³×C₂₉	1	4	yes	complemented
614	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
615	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
616	#97	C₂³×C₂₉	1	4	yes	complemented
617	C₄×C₈	C₂³×C₂₉	1	4	yes	complemented
618	C₂₉	C₂×#3224	1	1	yes	characteristic, direct product factor, Sylow
619	C₂⁴	—	2	1	no	—
620	C₂⁴	—	2	1	no	—
621	C₂⁴	—	2	1	no	—
622	C₂⁴	—	2	1	no	—
623	C₂⁴	—	2	4	no	—
624	C₂⁴	—	4	4	no	—
625	C₂⁴	—	8	2	no	—
626	C₂⁴	—	8	2	no	—
627	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
628	#41	—	4	4	no	—
629	#41	—	4	4	no	—
630	#41	—	4	8	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	4	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	8	2	no	—
639	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
640	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	4	4	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	8	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	8	2	no	—
666	C₂×D₄	—	8	2	no	—
667	C₂×D₄	—	8	2	no	—
668	C₂×D₄	—	8	2	no	—
669	C₂×D₄	—	8	2	no	—
670	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
671	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
672	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
673	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	4	4	no	—
683	C₂²×C₄	—	8	2	no	—
684	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
692	Q₁₆	—	4	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	4	no	—
696	SD₁₆	—	4	4	no	—
697	D₈	—	4	4	no	—
698	D₈	—	4	4	no	—
699	D₈	—	4	4	no	—
700	C₂×C₈	—	2	2	no	—
701	C₂×C₈	—	2	2	no	—
702	C₂×C₈	—	2	2	no	—
703	C₂×C₈	—	2	2	no	—
704	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
705	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
706	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
707	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
714	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
715	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
727	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
728	C₄²	—	2	4	no	—
729	C₄²	C₂×D₄×C₂₉	1	2	yes	—
730	C₄²	C₂×D₄×C₂₉	1	2	yes	—
731	C₄²	C₂⁴×C₂₉	1	2	yes	—
732	C₄²	C₂⁴×C₂₉	1	2	yes	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	4	2	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	8	4	no	—
754	C₂³	—	8	4	no	—
755	C₂³	—	8	16	no	—
756	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
757	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	8	4	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	2	no	—
779	D₄	—	8	4	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
808	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
810	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	8	16	no	—
832	C₂²	—	8	4	no	—
833	C₂²	—	8	4	no	—
834	C₂²	—	8	4	no	—
835	C₂²	—	8	4	no	—
836	C₂²	C₂₉×#535	1	2	yes	—
837	C₂²	C₂₉×#576	1	2	yes	—
838	C₂²	C₂₉×#577	1	2	yes	—
839	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	C₂₉×#535	1	2	yes	—
850	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
851	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
852	C₂	—	4	2	no	—
853	C₂	—	8	2	no	—
854	C₂	—	8	2	no	—
855	C₂	—	8	2	no	—
856	C₂	—	8	2	no	—
857	C₂	C₂₉×#3224	1	4	yes	direct product factor
858	C₂	C₂×C₂₉×#535	1	1	yes	characteristic
859	C₂	C₂×C₂₉×#576	1	1	yes	characteristic
860	C₂	C₂×C₂₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
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×#542	C₂	semidirect
2. C₂×C₂₉×#535	C₂	semidirect
3. C₂₉×#3224	C₂	direct (N × H)
4. C₂×C₂₉×#496	C₂	semidirect
5. C₂×C₂₉×#495	C₂	semidirect
6. C₂×C₂₉×#489	C₂	semidirect
7. C₂×C₂₉×#486	C₂	semidirect
8. C₂×C₂₉×#464	C₂	semidirect
9. C₂×C₂₉×#460	C₂	semidirect
10. C₂×C₂₉×#463	C₂	semidirect
11. C₂×C₂₉×#459	C₂	semidirect
12. C₂×C₂₉×#452	C₂	semidirect
13. C₂×C₂₉×#449	C₂	semidirect
14. C₂×C₂₉×#450	C₂	semidirect
15. C₂×C₂₉×#447	C₂	semidirect
16. C₂×C₂₉×#433	C₂	semidirect
19. C₂²×Q₁₆×C₂₉	C₂²	semidirect
22. C₂²×SD₁₆×C₂₉	C₂²	semidirect
23. C₂²×SD₁₆×C₂₉	C₂²	semidirect
26. C₂²×D₈×C₂₉	C₂²	semidirect
28. C₂₉×#542	C₂²	semidirect
30. C₂₉×#535	C₂²	semidirect
31. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₂₉×#124	C₂²	semidirect
47. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
48. C₂×C₄×D₄×C₂₉	C₂²	semidirect
50. C₂₉×#496	C₂²	semidirect
51. C₂₉×#495	C₂²	semidirect
52. C₂₉×#489	C₂²	semidirect
53. C₂₉×#486	C₂²	semidirect
54. C₂₉×#464	C₂²	semidirect
55. C₂₉×#463	C₂²	semidirect
56. C₂₉×#460	C₂²	semidirect
57. C₂₉×#459	C₂²	semidirect
58. C₂₉×#452	C₂²	semidirect
59. C₂₉×#450	C₂²	semidirect
60. C₂₉×#449	C₂²	semidirect
61. C₂₉×#447	C₂²	semidirect
62. C₂₉×#433	C₂²	semidirect
63. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
64. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
65. C₂×C₂₉×#103	C₂²	semidirect
66. C₂×C₂₉×#103	C₂²	semidirect
71. C₂×C₂₉×#102	C₂²	semidirect
72. C₂×C₂₉×#102	C₂²	semidirect
75. C₂×C₂₉×#97	C₂²	semidirect
76. C₂×C₄×C₈×C₂₉	C₂²	semidirect
104. C₂×Q₁₆×C₂₉	C₂³	semidirect
111. C₂×SD₁₆×C₂₉	C₂³	semidirect
112. C₂×SD₁₆×C₂₉	C₂³	semidirect
118. C₂×D₈×C₂₉	C₂³	semidirect
124. C₂₉×C₄⋊Q₈	C₂³	semidirect
136. C₂₉×#124	C₂³	semidirect
148. C₄×Q₈×C₂₉	C₂³	semidirect
150. C₄×D₄×C₂₉	C₂³	semidirect
174. C₂₉×C₄⋊C₈	C₂³	semidirect
175. C₂₉×C₄⋊C₈	C₂³	semidirect
176. C₂₉×#103	C₂³	semidirect
177. C₂₉×#103	C₂³	semidirect
182. C₂₉×#102	C₂³	semidirect
183. C₂₉×#102	C₂³	semidirect
186. C₂₉×#97	C₂³	semidirect
187. C₄×C₈×C₂₉	C₂³	semidirect
302. C₂×#3224	C₂₉	direct (N × H)
385. C₂×#542	C₂×C₂₉	semidirect
386. C₂×#535	C₂×C₂₉	semidirect
387. #3224	C₂×C₂₉	direct (N × H)
388. C₂×#496	C₂×C₂₉	semidirect
389. C₂×#495	C₂×C₂₉	semidirect
390. C₂×#489	C₂×C₂₉	semidirect
391. C₂×#486	C₂×C₂₉	semidirect
392. C₂×#464	C₂×C₂₉	semidirect
393. C₂×#460	C₂×C₂₉	semidirect
394. C₂×#463	C₂×C₂₉	semidirect
395. C₂×#459	C₂×C₂₉	semidirect
396. C₂×#452	C₂×C₂₉	semidirect
397. C₂×#449	C₂×C₂₉	semidirect
398. C₂×#450	C₂×C₂₉	semidirect
399. C₂×#447	C₂×C₂₉	semidirect
400. C₂×#433	C₂×C₂₉	semidirect
440. C₂²×Q₁₆	C₂²×C₂₉	semidirect
443. C₂²×SD₁₆	C₂²×C₂₉	semidirect
444. C₂²×SD₁₆	C₂²×C₂₉	semidirect
447. C₂²×D₈	C₂²×C₂₉	semidirect
449. #542	C₂²×C₂₉	semidirect
451. #535	C₂²×C₂₉	semidirect
452. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
459. C₂×#124	C₂²×C₂₉	semidirect
468. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
469. C₂×C₄×D₄	C₂²×C₂₉	semidirect
471. #496	C₂²×C₂₉	semidirect
472. #495	C₂²×C₂₉	semidirect
473. #489	C₂²×C₂₉	semidirect
474. #486	C₂²×C₂₉	semidirect
475. #464	C₂²×C₂₉	semidirect
476. #463	C₂²×C₂₉	semidirect
477. #460	C₂²×C₂₉	semidirect
478. #459	C₂²×C₂₉	semidirect
479. #452	C₂²×C₂₉	semidirect
480. #450	C₂²×C₂₉	semidirect
481. #449	C₂²×C₂₉	semidirect
482. #447	C₂²×C₂₉	semidirect
483. #433	C₂²×C₂₉	semidirect
484. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
485. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
486. C₂×#103	C₂²×C₂₉	semidirect
487. C₂×#103	C₂²×C₂₉	semidirect
492. C₂×#102	C₂²×C₂₉	semidirect
493. C₂×#102	C₂²×C₂₉	semidirect
496. C₂×#97	C₂²×C₂₉	semidirect
497. C₂×C₄×C₈	C₂²×C₂₉	semidirect
503. C₂×C₂₉	#3224	direct (N × H)
534. C₂×Q₁₆	C₂³×C₂₉	semidirect
541. C₂×SD₁₆	C₂³×C₂₉	semidirect
542. C₂×SD₁₆	C₂³×C₂₉	semidirect
548. C₂×D₈	C₂³×C₂₉	semidirect
554. C₄⋊Q₈	C₂³×C₂₉	semidirect
566. #124	C₂³×C₂₉	semidirect
578. C₄×Q₈	C₂³×C₂₉	semidirect
580. C₄×D₄	C₂³×C₂₉	semidirect
604. C₄⋊C₈	C₂³×C₂₉	semidirect
605. C₄⋊C₈	C₂³×C₂₉	semidirect
606. #103	C₂³×C₂₉	semidirect
607. #103	C₂³×C₂₉	semidirect
612. #102	C₂³×C₂₉	semidirect
613. #102	C₂³×C₂₉	semidirect
616. #97	C₂³×C₂₉	semidirect
617. C₄×C₈	C₂³×C₂₉	semidirect
618. C₂₉	C₂×#3224	direct (N × H)
857. C₂	C₂₉×#3224	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×#542	2
C₂×C₂₉×#535	2
C₂₉×#3224	2
C₂×C₂₉×#496	2
C₂×C₂₉×#495	2
C₂×C₂₉×#489	2
C₂×C₂₉×#486	2
C₂×C₂₉×#464	2
C₂×C₂₉×#460	2
C₂×C₂₉×#463	2
C₂×C₂₉×#459	2
C₂×C₂₉×#452	2
C₂×C₂₉×#449	2
C₂×C₂₉×#450	2
C₂×C₂₉×#447	2
C₂×C₂₉×#433	2
C₂×#3224	29

Subgroups — C2×C29×#3224 #20355693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3224 #20355693