Subgroups — D₄×C₂₉×#135 #20355948

Order 7424.

2822 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×#135	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₂₉	C₂	1	2	yes	maximal, complemented
3	C₂₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3285	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3284	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3282	C₂	1	4	yes	maximal, complemented
9	D₄×SD₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3280	C₂	1	2	yes	maximal, complemented
11	D₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3147	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3050	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3035	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3002	C₂	1	4	yes	maximal, complemented
16	C₄×C₂₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₈×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₉	C₂²	1	4	yes	complemented
19	C₂×C₂₉×#135	—	2	16	no	—
20	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#135	C₂²	1	4	yes	complemented
22	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
23	C₂×C₂₉×#135	C₂²	1	4	yes	complemented
24	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
25	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
26	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₂₉	C₂²	1	4	yes	complemented
29	C₂²×D₈×C₂₉	C₂²	1	2	yes	complemented
30	C₂³×C₈×C₂₉	C₂²	1	2	yes	complemented
31	C₂₉×#550	C₂²	1	2	yes	complemented
32	D₄×Q₈×C₂₉	C₂²	1	2	yes	—
33	C₂₉×#548	C₂²	1	4	yes	complemented
34	C₂₉×#547	—	2	2	no	—
35	C₂₉×#547	C₂²	1	2	yes	complemented
36	C₂₉×#546	—	2	4	no	—
37	C₂₉×#546	C₂²	1	4	yes	complemented
38	D₄²×C₂₉	—	2	2	no	—
39	D₄²×C₂₉	C₂²	1	2	yes	—
40	C₂₉×#532	—	2	2	no	—
41	C₂₉×#532	C₂²	1	2	yes	complemented
42	C₂₉×#525	—	2	4	no	—
43	C₂₉×#525	C₂²	1	4	yes	complemented
44	C₄×#41×C₂₉	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₂₉	—	2	2	no	—
46	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
47	C₂₉×#495	C₂²	1	2	yes	complemented
48	C₂₉×#495	C₂²	1	2	yes	complemented
49	C₂₉×#494	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#493	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×#492	C₂²	1	2	yes	complemented
52	C₂₉×#467	C₂²	1	2	yes	complemented
53	C₂₉×#467	C₂²	1	2	yes	complemented
54	C₂₉×#466	C₂²	1	2	yes	complemented
55	C₂₉×#466	C₂²	1	2	yes	complemented
56	C₂₉×#465	C₂²	1	4	yes	complemented
57	C₂₉×#465	C₂²	1	4	yes	complemented
58	C₂₉×#464	C₂²	1	4	yes	complemented
59	C₂₉×#463	C₂²	1	4	yes	complemented
60	C₂₉×#462	C₂²	1	2	yes	complemented
61	C₂₉×#461	C₂²	1	2	yes	complemented
62	C₂₉×#460	C₂²	1	2	yes	complemented
63	C₂₉×#459	C₂²	1	2	yes	complemented
64	C₂₉×#452	C₂²	1	4	yes	complemented
65	C₂₉×#452	C₂²	1	4	yes	complemented
66	C₂₉×#451	C₂²	1	4	yes	complemented
67	C₂₉×#450	C₂²	1	4	yes	complemented
68	C₂₉×#449	C₂²	1	4	yes	complemented
69	C₂₉×#449	C₂²	1	4	yes	complemented
70	C₂₉×#448	C₂²	1	4	yes	complemented
71	C₂₉×#447	C₂²	1	4	yes	complemented
72	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
73	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
74	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
76	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
78	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
81	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
82	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
83	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
84	C₂₉×#427	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	C₂₉×#416	C₂²	1	2	yes	complemented
87	C₂₉×#416	C₂²	1	4	yes	complemented
88	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
89	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
90	C₂×#41×C₂₉	—	2	4	no	—
91	C₂×#41×C₂₉	—	2	4	no	—
92	C₂×#41×C₂₉	—	2	16	no	—
93	C₂×#41×C₂₉	—	4	8	no	—
94	C₂×#41×C₂₉	C₂³	1	4	yes	—
95	C₂×#41×C₂₉	C₂³	1	4	yes	—
96	C₂×#41×C₂₉	C₂³	1	4	yes	—
97	C₂×#41×C₂₉	C₂³	1	2	yes	—
98	C₂²×Q₈×C₂₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₂₉	—	2	4	no	—
100	C₂²×D₄×C₂₉	—	2	2	no	—
101	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
103	C₂³×C₄×C₂₉	—	2	4	no	—
104	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
105	C₂₉×#135	—	2	16	no	—
106	C₂₉×#135	—	2	8	no	—
107	C₂₉×#135	—	2	16	no	—
108	C₂₉×#135	—	2	8	no	—
109	C₂₉×#135	—	2	8	no	—
110	C₂₉×#135	—	4	4	no	—
111	C₂₉×#135	D₄	1	8	yes	direct product factor
112	C₂×Q₁₆×C₂₉	—	2	8	no	—
113	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
115	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×SD₁₆×C₂₉	—	2	16	no	—
118	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
121	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
122	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
123	C₂×D₈×C₂₉	—	2	8	no	—
124	C₂×D₈×C₂₉	C₂³	1	4	yes	—
125	C₂×D₈×C₂₉	C₂³	1	2	yes	—
126	C₂×D₈×C₂₉	C₂³	1	2	yes	—
127	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₂₉	—	2	8	no	—
129	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
130	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
131	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
132	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
133	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
134	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
136	C₂₉×C₄⋊Q₈	—	2	2	no	—
137	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₉×#127	—	2	2	no	—
139	C₂₉×#127	C₂³	1	2	yes	—
140	C₂₉×#124	—	2	4	no	—
141	C₂₉×#124	C₂³	1	4	yes	—
142	C₂₉×#123	—	2	4	no	—
143	C₂₉×#123	—	2	4	no	—
144	C₂₉×#123	—	2	4	no	—
145	C₂₉×C₂²⋊Q₈	—	2	4	no	—
146	C₂₉×C₂²⋊Q₈	—	2	4	no	—
147	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₂₉×#121	—	2	4	no	—
150	C₂₉×#121	—	2	2	no	—
151	C₂₉×#121	—	2	2	no	—
152	C₂₉×#121	—	2	2	no	—
153	C₂₉×#121	—	2	2	no	—
154	C₂₉×#121	—	2	4	no	—
155	C₂₉×#121	—	2	4	no	—
156	C₂₉×#121	C₂³	1	4	yes	—
157	C₂₉×#121	C₂³	1	4	yes	—
158	C₂₉×#120	—	2	4	no	—
159	C₂₉×#120	—	2	4	no	—
160	C₂₉×#120	—	2	4	no	—
161	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
162	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
163	C₄×D₄×C₂₉	—	2	2	no	—
164	C₄×D₄×C₂₉	—	2	4	no	—
165	C₄×D₄×C₂₉	—	2	2	no	—
166	C₄×D₄×C₂₉	—	2	2	no	—
167	C₄×D₄×C₂₉	—	2	4	no	—
168	C₄×D₄×C₂₉	—	2	2	no	—
169	C₄×D₄×C₂₉	—	2	4	no	—
170	C₄×D₄×C₂₉	—	2	2	no	—
171	C₄×D₄×C₂₉	—	2	2	no	—
172	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
173	C₄×D₄×C₂₉	D₄	1	2	yes	—
174	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
175	C₄×D₄×C₂₉	C₂³	1	2	yes	—
176	C₄×D₄×C₂₉	C₂³	1	2	yes	—
177	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₉	C₂³	1	2	yes	—
179	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
180	C₂₉×#117	—	2	2	no	—
181	C₂₉×#117	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
183	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
185	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
186	C₂×C₄²×C₂₉	—	2	2	no	—
187	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
188	C₂₉×#107	C₂³	1	1	yes	characteristic
189	C₂₉×#107	C₂³	1	1	yes	characteristic
190	C₂₉×#106	C₂³	1	2	yes	—
191	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
194	C₂₉×#103	C₂³	1	2	yes	—
195	C₂₉×#103	C₂³	1	2	yes	—
196	C₂₉×#103	C₂³	1	4	yes	—
197	C₂₉×#103	C₂³	1	4	yes	—
198	C₂₉×#102	C₂³	1	2	yes	—
199	C₂₉×#102	C₂³	1	2	yes	—
200	C₂₉×#102	C₂³	1	4	yes	—
201	C₂₉×#102	C₂³	1	4	yes	—
202	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
203	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
204	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
205	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
206	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
210	C₂⁴×C₂₉	—	2	4	no	—
211	C₂⁴×C₂₉	C₂×D₄	1	2	yes	—
212	#41×C₂₉	—	2	4	no	—
213	#41×C₂₉	—	2	8	no	—
214	#41×C₂₉	—	2	8	no	—
215	#41×C₂₉	—	2	8	no	—
216	#41×C₂₉	—	2	8	no	—
217	#41×C₂₉	—	4	16	no	—
218	#41×C₂₉	—	4	4	no	—
219	#41×C₂₉	—	4	4	no	—
220	#41×C₂₉	—	4	16	no	—
221	#41×C₂₉	C₂×D₄	1	8	yes	complemented
222	C₂×Q₈×C₂₉	—	2	4	no	—
223	C₂×Q₈×C₂₉	—	2	8	no	—
224	C₂×Q₈×C₂₉	—	4	4	no	—
225	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
226	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
227	C₂×D₄×C₂₉	—	2	2	no	—
228	C₂×D₄×C₂₉	—	2	4	no	—
229	C₂×D₄×C₂₉	—	2	8	no	—
230	C₂×D₄×C₂₉	—	2	4	no	—
231	C₂×D₄×C₂₉	—	2	4	no	—
232	C₂×D₄×C₂₉	—	2	4	no	—
233	C₂×D₄×C₂₉	—	2	4	no	—
234	C₂×D₄×C₂₉	—	2	4	no	—
235	C₂×D₄×C₂₉	—	2	2	no	—
236	C₂×D₄×C₂₉	—	2	4	no	—
237	C₂×D₄×C₂₉	—	2	2	no	—
238	C₂×D₄×C₂₉	—	4	4	no	—
239	C₂×D₄×C₂₉	—	4	16	no	—
240	C₂×D₄×C₂₉	—	4	8	no	—
241	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
243	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
244	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
245	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₉	—	2	4	no	—
247	C₂²×C₄×C₂₉	—	2	2	no	—
248	C₂²×C₄×C₂₉	—	2	4	no	—
249	C₂²×C₄×C₂₉	—	2	4	no	—
250	C₂²×C₄×C₂₉	—	2	2	no	—
251	C₂²×C₄×C₂₉	—	2	4	no	—
252	C₂²×C₄×C₂₉	—	2	4	no	—
253	C₂²×C₄×C₂₉	—	2	4	no	—
254	C₂²×C₄×C₂₉	—	2	2	no	—
255	C₂²×C₄×C₂₉	—	4	16	no	—
256	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₂₉	—	2	8	no	—
265	Q₁₆×C₂₉	—	2	4	no	—
266	Q₁₆×C₂₉	—	4	2	no	—
267	Q₁₆×C₂₉	C₂×D₄	1	4	yes	complemented
268	SD₁₆×C₂₉	—	2	8	no	—
269	SD₁₆×C₂₉	—	2	8	no	—
270	SD₁₆×C₂₉	—	2	8	no	—
271	SD₁₆×C₂₉	—	4	4	no	—
272	SD₁₆×C₂₉	C₂×D₄	1	8	yes	complemented
273	D₈×C₂₉	—	2	8	no	—
274	D₈×C₂₉	—	2	4	no	—
275	D₈×C₂₉	—	4	2	no	—
276	D₈×C₂₉	C₂×D₄	1	4	yes	complemented
277	C₂×C₈×C₂₉	—	2	4	no	—
278	C₂×C₈×C₂₉	—	2	2	no	—
279	C₂×C₈×C₂₉	—	2	4	no	—
280	C₂×C₈×C₂₉	—	2	4	no	—
281	C₂×C₈×C₂₉	—	2	4	no	—
282	C₂×C₈×C₂₉	—	2	4	no	—
283	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	complemented
284	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
285	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
286	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
287	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
288	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
289	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₂₉	—	2	2	no	—
291	C₄⋊C₄×C₂₉	—	2	4	no	—
292	C₄⋊C₄×C₂₉	—	2	2	no	—
293	C₄⋊C₄×C₂₉	—	2	2	no	—
294	C₄⋊C₄×C₂₉	—	2	2	no	—
295	C₄⋊C₄×C₂₉	—	2	4	no	—
296	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
301	C₂²⋊C₄×C₂₉	—	2	4	no	—
302	C₂²⋊C₄×C₂₉	—	2	2	no	—
303	C₂²⋊C₄×C₂₉	—	2	4	no	—
304	C₂²⋊C₄×C₂₉	—	2	4	no	—
305	C₂²⋊C₄×C₂₉	—	2	4	no	—
306	C₂²⋊C₄×C₂₉	—	2	2	no	—
307	C₂²⋊C₄×C₂₉	—	2	2	no	—
308	C₂²⋊C₄×C₂₉	—	2	4	no	—
309	C₂²⋊C₄×C₂₉	—	2	4	no	—
310	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
312	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
314	C₄²×C₂₉	—	2	2	no	—
315	C₄²×C₂₉	—	2	2	no	—
316	C₄²×C₂₉	—	2	2	no	—
317	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
320	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
321	D₄×#135	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₂₉	—	2	4	no	—
323	C₂³×C₂₉	—	2	4	no	—
324	C₂³×C₂₉	—	2	2	no	—
325	C₂³×C₂₉	—	2	4	no	—
326	C₂³×C₂₉	—	4	2	no	—
327	C₂³×C₂₉	—	4	8	no	—
328	C₂³×C₂₉	—	4	8	no	—
329	C₂³×C₂₉	—	8	4	no	—
330	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
331	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
333	Q₈×C₂₉	—	2	2	no	—
334	Q₈×C₂₉	—	2	4	no	—
335	Q₈×C₂₉	—	2	4	no	—
336	Q₈×C₂₉	—	4	8	no	—
337	Q₈×C₂₉	C₂²×D₄	1	4	yes	—
338	D₄×C₂₉	—	2	8	no	—
339	D₄×C₂₉	—	2	4	no	—
340	D₄×C₂₉	—	2	2	no	—
341	D₄×C₂₉	—	2	4	no	—
342	D₄×C₂₉	—	2	2	no	—
343	D₄×C₂₉	—	2	4	no	—
344	D₄×C₂₉	—	4	8	no	—
345	D₄×C₂₉	—	4	8	no	—
346	D₄×C₂₉	—	4	8	no	—
347	D₄×C₂₉	—	4	8	no	—
348	D₄×C₂₉	—	4	8	no	—
349	D₄×C₂₉	—	4	4	no	—
350	D₄×C₂₉	—	8	2	no	—
351	D₄×C₂₉	—	8	4	no	—
352	D₄×C₂₉	#135	1	4	yes	direct product factor
353	D₄×C₂₉	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₂₉	—	2	4	no	—
355	C₂×C₄×C₂₉	—	2	2	no	—
356	C₂×C₄×C₂₉	—	2	4	no	—
357	C₂×C₄×C₂₉	—	2	4	no	—
358	C₂×C₄×C₂₉	—	2	8	no	—
359	C₂×C₄×C₂₉	—	2	2	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	—	2	4	no	—
367	C₂×C₄×C₂₉	—	4	1	no	—
368	C₂×C₄×C₂₉	—	4	8	no	—
369	C₂×C₄×C₂₉	—	4	8	no	—
370	C₂×C₄×C₂₉	—	4	8	no	—
371	C₂×C₄×C₂₉	—	4	8	no	—
372	C₂×C₄×C₂₉	—	4	4	no	—
373	C₂×C₄×C₂₉	—	8	2	no	—
374	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
384	C₈×C₂₉	—	2	2	no	—
385	C₈×C₂₉	—	2	2	no	—
386	C₈×C₂₉	—	2	1	no	—
387	C₈×C₂₉	—	2	1	no	—
388	C₈×C₂₉	C₂²×D₄	1	2	yes	—
389	C₈×C₂₉	C₂²×D₄	1	2	yes	—
390	C₂²×#135	C₂×C₂₉	1	2	yes	complemented
391	D₄×#41	C₂×C₂₉	1	2	yes	complemented
392	#3287	C₂×C₂₉	1	1	yes	characteristic, complemented
393	D₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
394	#3285	C₂×C₂₉	1	2	yes	complemented
395	#3284	C₂×C₂₉	1	2	yes	complemented
396	#3283	C₂×C₂₉	1	1	yes	characteristic, complemented
397	#3282	C₂×C₂₉	1	4	yes	complemented
398	D₄×SD₁₆	C₂×C₂₉	1	2	yes	complemented
399	#3280	C₂×C₂₉	1	2	yes	complemented
400	D₄×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
401	#3147	C₂×C₂₉	1	1	yes	characteristic, complemented
402	#3050	C₂×C₂₉	1	2	yes	complemented
403	#3035	C₂×C₂₉	1	2	yes	complemented
404	#3002	C₂×C₂₉	1	4	yes	complemented
405	C₄×#135	C₂×C₂₉	1	1	yes	characteristic, complemented
406	C₂×C₈×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
407	C₂²×C₂₉	—	2	1	no	—
408	C₂²×C₂₉	—	2	2	no	—
409	C₂²×C₂₉	—	2	2	no	—
410	C₂²×C₂₉	—	2	1	no	—
411	C₂²×C₂₉	—	2	2	no	—
412	C₂²×C₂₉	—	2	2	no	—
413	C₂²×C₂₉	—	2	4	no	—
414	C₂²×C₂₉	—	2	2	no	—
415	C₂²×C₂₉	—	4	8	no	—
416	C₂²×C₂₉	—	4	2	no	—
417	C₂²×C₂₉	—	4	2	no	—
418	C₂²×C₂₉	—	4	4	no	—
419	C₂²×C₂₉	—	4	4	no	—
420	C₂²×C₂₉	—	4	4	no	—
421	C₂²×C₂₉	—	8	16	no	—
422	C₂²×C₂₉	D₄²	1	2	yes	—
423	C₂²×C₂₉	C₂×#135	1	4	yes	complemented
424	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₂₉	—	2	1	no	—
426	C₄×C₂₉	—	2	1	no	—
427	C₄×C₂₉	—	2	2	no	—
428	C₄×C₂₉	—	2	2	no	—
429	C₄×C₂₉	—	2	4	no	—
430	C₄×C₂₉	—	2	1	no	—
431	C₄×C₂₉	—	4	2	no	—
432	C₄×C₂₉	—	4	4	no	—
433	C₄×C₂₉	—	4	2	no	—
434	C₄×C₂₉	D₄²	1	2	yes	—
435	C₄×C₂₉	C₂×#135	1	2	yes	complemented
436	C₄×C₂₉	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×#41	C₂²×C₂₉	1	4	yes	complemented
439	C₂×#135	—	2	16	no	—
440	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
441	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
442	C₂×#135	C₂²×C₂₉	1	4	yes	complemented
443	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
444	C₂×#135	C₂²×C₂₉	1	4	yes	complemented
445	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
446	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
447	C₂²×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
448	C₂²×SD₁₆	C₂²×C₂₉	1	4	yes	complemented
449	C₂²×D₈	C₂²×C₂₉	1	2	yes	complemented
450	C₂³×C₈	C₂²×C₂₉	1	2	yes	complemented
451	#550	C₂²×C₂₉	1	2	yes	complemented
452	D₄×Q₈	C₂²×C₂₉	1	2	yes	—
453	#548	C₂²×C₂₉	1	4	yes	complemented
454	#547	—	2	2	no	—
455	#547	C₂²×C₂₉	1	2	yes	complemented
456	#546	—	2	4	no	—
457	#546	C₂²×C₂₉	1	4	yes	complemented
458	D₄²	—	2	2	no	—
459	D₄²	C₂²×C₂₉	1	2	yes	—
460	#532	—	2	2	no	—
461	#532	C₂²×C₂₉	1	2	yes	complemented
462	#525	—	2	4	no	—
463	#525	C₂²×C₂₉	1	4	yes	complemented
464	C₄×#41	C₂²×C₂₉	1	2	yes	complemented
465	C₂×C₄×D₄	—	2	2	no	—
466	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
467	#495	C₂²×C₂₉	1	2	yes	complemented
468	#495	C₂²×C₂₉	1	2	yes	complemented
469	#494	C₂²×C₂₉	1	1	yes	characteristic, complemented
470	#493	C₂²×C₂₉	1	1	yes	characteristic, complemented
471	#492	C₂²×C₂₉	1	2	yes	complemented
472	#467	C₂²×C₂₉	1	2	yes	complemented
473	#467	C₂²×C₂₉	1	2	yes	complemented
474	#466	C₂²×C₂₉	1	2	yes	complemented
475	#466	C₂²×C₂₉	1	2	yes	complemented
476	#465	C₂²×C₂₉	1	4	yes	complemented
477	#465	C₂²×C₂₉	1	4	yes	complemented
478	#464	C₂²×C₂₉	1	4	yes	complemented
479	#463	C₂²×C₂₉	1	4	yes	complemented
480	#462	C₂²×C₂₉	1	2	yes	complemented
481	#461	C₂²×C₂₉	1	2	yes	complemented
482	#460	C₂²×C₂₉	1	2	yes	complemented
483	#459	C₂²×C₂₉	1	2	yes	complemented
484	#452	C₂²×C₂₉	1	4	yes	complemented
485	#452	C₂²×C₂₉	1	4	yes	complemented
486	#451	C₂²×C₂₉	1	4	yes	complemented
487	#450	C₂²×C₂₉	1	4	yes	complemented
488	#449	C₂²×C₂₉	1	4	yes	complemented
489	#449	C₂²×C₂₉	1	4	yes	complemented
490	#448	C₂²×C₂₉	1	4	yes	complemented
491	#447	C₂²×C₂₉	1	4	yes	complemented
492	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
493	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
494	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
495	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
496	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
497	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
498	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
499	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
500	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
501	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
502	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
503	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
504	#427	C₂²×C₂₉	1	1	yes	characteristic, complemented
505	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
506	#416	C₂²×C₂₉	1	2	yes	complemented
507	#416	C₂²×C₂₉	1	4	yes	complemented
508	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	complemented
509	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
510	C₂×C₂₉	—	2	2	no	—
511	C₂×C₂₉	—	2	4	no	—
512	C₂×C₂₉	—	4	2	no	—
513	C₂×C₂₉	—	4	4	no	—
514	C₂×C₂₉	—	8	4	no	—
515	C₂×C₂₉	C₂×D₄²	1	1	yes	characteristic
516	C₂×C₂₉	C₂²×#135	1	1	yes	characteristic
517	C₂×C₂₉	#3584	1	1	yes	characteristic
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	2	16	no	—
521	C₂×#41	—	4	8	no	—
522	C₂×#41	C₂³×C₂₉	1	4	yes	—
523	C₂×#41	C₂³×C₂₉	1	4	yes	—
524	C₂×#41	C₂³×C₂₉	1	4	yes	—
525	C₂×#41	C₂³×C₂₉	1	2	yes	—
526	C₂²×Q₈	C₂³×C₂₉	1	4	yes	—
527	C₂²×D₄	—	2	4	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
533	#135	—	2	16	no	—
534	#135	—	2	8	no	—
535	#135	—	2	16	no	—
536	#135	—	2	8	no	—
537	#135	—	2	8	no	—
538	#135	—	4	4	no	—
539	#135	D₄×C₂₉	1	8	yes	direct product factor
540	C₂×Q₁₆	—	2	8	no	—
541	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
542	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
543	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
544	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
545	C₂×SD₁₆	—	2	16	no	—
546	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
548	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
550	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
551	C₂×D₈	—	2	8	no	—
552	C₂×D₈	C₂³×C₂₉	1	4	yes	—
553	C₂×D₈	C₂³×C₂₉	1	2	yes	—
554	C₂×D₈	C₂³×C₂₉	1	2	yes	—
555	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
556	C₂²×C₈	—	2	8	no	—
557	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
558	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
559	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
560	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
561	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
562	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
564	C₄⋊Q₈	—	2	2	no	—
565	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
566	#127	—	2	2	no	—
567	#127	C₂³×C₂₉	1	2	yes	—
568	#124	—	2	4	no	—
569	#124	C₂³×C₂₉	1	4	yes	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	4	no	—
575	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
576	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
577	#121	—	2	4	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	4	no	—
583	#121	—	2	4	no	—
584	#121	C₂³×C₂₉	1	4	yes	—
585	#121	C₂³×C₂₉	1	4	yes	—
586	#120	—	2	4	no	—
587	#120	—	2	4	no	—
588	#120	—	2	4	no	—
589	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	4	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
601	C₄×D₄	D₄×C₂₉	1	2	yes	—
602	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₂₉	1	2	yes	—
604	C₄×D₄	C₂³×C₂₉	1	2	yes	—
605	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₂₉	1	2	yes	—
607	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
608	#117	—	2	2	no	—
609	#117	C₂³×C₂₉	1	2	yes	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	4	no	—
613	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
614	C₂×C₄²	—	2	2	no	—
615	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
616	#107	C₂³×C₂₉	1	1	yes	characteristic
617	#107	C₂³×C₂₉	1	1	yes	characteristic
618	#106	C₂³×C₂₉	1	2	yes	—
619	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
620	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
621	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
622	#103	C₂³×C₂₉	1	2	yes	—
623	#103	C₂³×C₂₉	1	2	yes	—
624	#103	C₂³×C₂₉	1	4	yes	—
625	#103	C₂³×C₂₉	1	4	yes	—
626	#102	C₂³×C₂₉	1	2	yes	—
627	#102	C₂³×C₂₉	1	2	yes	—
628	#102	C₂³×C₂₉	1	4	yes	—
629	#102	C₂³×C₂₉	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
631	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
632	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
633	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
634	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
635	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
636	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
637	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
638	C₂₉	D₄×#135	1	1	yes	characteristic, direct product factor, Sylow
639	C₂⁴	—	2	4	no	—
640	C₂⁴	C₂×D₄×C₂₉	1	2	yes	—
641	#41	—	2	4	no	—
642	#41	—	2	8	no	—
643	#41	—	2	8	no	—
644	#41	—	2	8	no	—
645	#41	—	2	8	no	—
646	#41	—	4	16	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	16	no	—
650	#41	C₂×D₄×C₂₉	1	8	yes	complemented
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	8	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
655	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	8	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	4	16	no	—
669	C₂×D₄	—	4	8	no	—
670	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
671	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
672	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
673	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
674	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	4	16	no	—
685	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
689	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
693	Q₁₆	—	2	8	no	—
694	Q₁₆	—	2	4	no	—
695	Q₁₆	—	4	2	no	—
696	Q₁₆	C₂×D₄×C₂₉	1	4	yes	complemented
697	SD₁₆	—	2	8	no	—
698	SD₁₆	—	2	8	no	—
699	SD₁₆	—	2	8	no	—
700	SD₁₆	—	4	4	no	—
701	SD₁₆	C₂×D₄×C₂₉	1	8	yes	complemented
702	D₈	—	2	8	no	—
703	D₈	—	2	4	no	—
704	D₈	—	4	2	no	—
705	D₈	C₂×D₄×C₂₉	1	4	yes	complemented
706	C₂×C₈	—	2	4	no	—
707	C₂×C₈	—	2	2	no	—
708	C₂×C₈	—	2	4	no	—
709	C₂×C₈	—	2	4	no	—
710	C₂×C₈	—	2	4	no	—
711	C₂×C₈	—	2	4	no	—
712	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	complemented
713	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
714	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
715	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
716	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
717	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
718	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
740	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
741	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
742	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
748	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
749	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
750	C₂³	—	2	4	no	—
751	C₂³	—	2	4	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	8	no	—
756	C₂³	—	4	8	no	—
757	C₂³	—	8	4	no	—
758	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
759	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
760	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	4	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	4	8	no	—
765	Q₈	C₂²×D₄×C₂₉	1	4	yes	—
766	D₄	—	2	8	no	—
767	D₄	—	2	4	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	4	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	4	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	8	no	—
777	D₄	—	4	4	no	—
778	D₄	—	8	2	no	—
779	D₄	—	8	4	no	—
780	D₄	C₂₉×#135	1	4	yes	direct product factor
781	D₄	C₂²×D₄×C₂₉	1	4	yes	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	8	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	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	4	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
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	C₂²×D₄×C₂₉	1	2	yes	—
809	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
810	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
811	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	1	no	—
815	C₈	—	2	1	no	—
816	C₈	C₂²×D₄×C₂₉	1	2	yes	—
817	C₈	C₂²×D₄×C₂₉	1	2	yes	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	4	8	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	8	16	no	—
833	C₂²	D₄²×C₂₉	1	2	yes	—
834	C₂²	C₂×C₂₉×#135	1	4	yes	complemented
835	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	4	4	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	D₄²×C₂₉	1	2	yes	—
846	C₄	C₂×C₂₉×#135	1	2	yes	complemented
847	C₄	C₂³×D₄×C₂₉	1	1	yes	characteristic
848	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂	—	2	2	no	—
850	C₂	—	2	4	no	—
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	8	4	no	—
854	C₂	C₂×D₄²×C₂₉	1	1	yes	characteristic
855	C₂	C₂²×C₂₉×#135	1	1	yes	characteristic
856	C₂	C₂₉×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₉×#135	C₂	semidirect
2. D₄×#41×C₂₉	C₂	semidirect
3. C₂₉×#3287	C₂	semidirect
4. D₄×Q₁₆×C₂₉	C₂	semidirect
5. C₂₉×#3285	C₂	semidirect
6. C₂₉×#3284	C₂	semidirect
7. C₂₉×#3283	C₂	semidirect
8. C₂₉×#3282	C₂	semidirect
9. D₄×SD₁₆×C₂₉	C₂	semidirect
10. C₂₉×#3280	C₂	semidirect
11. D₄×D₈×C₂₉	C₂	semidirect
12. C₂₉×#3147	C₂	semidirect
13. C₂₉×#3050	C₂	semidirect
14. C₂₉×#3035	C₂	semidirect
15. C₂₉×#3002	C₂	semidirect
16. C₄×C₂₉×#135	C₂	semidirect
17. C₂×C₈×D₄×C₂₉	C₂	semidirect
18. C₂²×#41×C₂₉	C₂²	semidirect
21. C₂×C₂₉×#135	C₂²	semidirect
22. C₂×C₂₉×#135	C₂²	semidirect
23. C₂×C₂₉×#135	C₂²	semidirect
24. C₂×C₂₉×#135	C₂²	semidirect
25. C₂×C₂₉×#135	C₂²	semidirect
26. C₂×C₂₉×#135	C₂²	semidirect
27. C₂²×Q₁₆×C₂₉	C₂²	semidirect
28. C₂²×SD₁₆×C₂₉	C₂²	semidirect
29. C₂²×D₈×C₂₉	C₂²	semidirect
30. C₂³×C₈×C₂₉	C₂²	semidirect
31. C₂₉×#550	C₂²	semidirect
33. C₂₉×#548	C₂²	semidirect
35. C₂₉×#547	C₂²	semidirect
37. C₂₉×#546	C₂²	semidirect
41. C₂₉×#532	C₂²	semidirect
43. C₂₉×#525	C₂²	semidirect
44. C₄×#41×C₂₉	C₂²	semidirect
47. C₂₉×#495	C₂²	semidirect
48. C₂₉×#495	C₂²	semidirect
49. C₂₉×#494	C₂²	semidirect
50. C₂₉×#493	C₂²	semidirect
51. C₂₉×#492	C₂²	semidirect
52. C₂₉×#467	C₂²	semidirect
53. C₂₉×#467	C₂²	semidirect
54. C₂₉×#466	C₂²	semidirect
55. C₂₉×#466	C₂²	semidirect
56. C₂₉×#465	C₂²	semidirect
57. C₂₉×#465	C₂²	semidirect
58. C₂₉×#464	C₂²	semidirect
59. C₂₉×#463	C₂²	semidirect
60. C₂₉×#462	C₂²	semidirect
61. C₂₉×#461	C₂²	semidirect
62. C₂₉×#460	C₂²	semidirect
63. C₂₉×#459	C₂²	semidirect
64. C₂₉×#452	C₂²	semidirect
65. C₂₉×#452	C₂²	semidirect
66. C₂₉×#451	C₂²	semidirect
67. C₂₉×#450	C₂²	semidirect
68. C₂₉×#449	C₂²	semidirect
69. C₂₉×#449	C₂²	semidirect
70. C₂₉×#448	C₂²	semidirect
71. C₂₉×#447	C₂²	semidirect
72. C₄×Q₁₆×C₂₉	C₂²	semidirect
73. C₄×Q₁₆×C₂₉	C₂²	semidirect
74. C₄×SD₁₆×C₂₉	C₂²	semidirect
75. C₄×SD₁₆×C₂₉	C₂²	semidirect
76. C₄×D₈×C₂₉	C₂²	semidirect
77. C₄×D₈×C₂₉	C₂²	semidirect
80. C₈×D₄×C₂₉	C₂²	semidirect
81. C₈×D₄×C₂₉	C₂²	semidirect
82. C₈×D₄×C₂₉	C₂²	semidirect
83. C₈×D₄×C₂₉	C₂²	semidirect
84. C₂₉×#427	C₂²	semidirect
85. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
86. C₂₉×#416	C₂²	semidirect
87. C₂₉×#416	C₂²	semidirect
88. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
89. C₂×C₄×C₈×C₂₉	C₂²	semidirect
111. C₂₉×#135	D₄	direct (N × H)
221. #41×C₂₉	C₂×D₄	semidirect
267. Q₁₆×C₂₉	C₂×D₄	semidirect
272. SD₁₆×C₂₉	C₂×D₄	semidirect
276. D₈×C₂₉	C₂×D₄	semidirect
283. C₂×C₈×C₂₉	C₂×D₄	semidirect
321. D₄×#135	C₂₉	direct (N × H)
352. D₄×C₂₉	#135	direct (N × H)
390. C₂²×#135	C₂×C₂₉	semidirect
391. D₄×#41	C₂×C₂₉	semidirect
392. #3287	C₂×C₂₉	semidirect
393. D₄×Q₁₆	C₂×C₂₉	semidirect
394. #3285	C₂×C₂₉	semidirect
395. #3284	C₂×C₂₉	semidirect
396. #3283	C₂×C₂₉	semidirect
397. #3282	C₂×C₂₉	semidirect
398. D₄×SD₁₆	C₂×C₂₉	semidirect
399. #3280	C₂×C₂₉	semidirect
400. D₄×D₈	C₂×C₂₉	semidirect
401. #3147	C₂×C₂₉	semidirect
402. #3050	C₂×C₂₉	semidirect
403. #3035	C₂×C₂₉	semidirect
404. #3002	C₂×C₂₉	semidirect
405. C₄×#135	C₂×C₂₉	semidirect
406. C₂×C₈×D₄	C₂×C₂₉	semidirect
423. C₂²×C₂₉	C₂×#135	semidirect
435. C₄×C₂₉	C₂×#135	semidirect
438. C₂²×#41	C₂²×C₂₉	semidirect
441. C₂×#135	C₂²×C₂₉	semidirect
442. C₂×#135	C₂²×C₂₉	semidirect
443. C₂×#135	C₂²×C₂₉	semidirect
444. C₂×#135	C₂²×C₂₉	semidirect
445. C₂×#135	C₂²×C₂₉	semidirect
446. C₂×#135	C₂²×C₂₉	semidirect
447. C₂²×Q₁₆	C₂²×C₂₉	semidirect
448. C₂²×SD₁₆	C₂²×C₂₉	semidirect
449. C₂²×D₈	C₂²×C₂₉	semidirect
450. C₂³×C₈	C₂²×C₂₉	semidirect
451. #550	C₂²×C₂₉	semidirect
453. #548	C₂²×C₂₉	semidirect
455. #547	C₂²×C₂₉	semidirect
457. #546	C₂²×C₂₉	semidirect
461. #532	C₂²×C₂₉	semidirect
463. #525	C₂²×C₂₉	semidirect
464. C₄×#41	C₂²×C₂₉	semidirect
467. #495	C₂²×C₂₉	semidirect
468. #495	C₂²×C₂₉	semidirect
469. #494	C₂²×C₂₉	semidirect
470. #493	C₂²×C₂₉	semidirect
471. #492	C₂²×C₂₉	semidirect
472. #467	C₂²×C₂₉	semidirect
473. #467	C₂²×C₂₉	semidirect
474. #466	C₂²×C₂₉	semidirect
475. #466	C₂²×C₂₉	semidirect
476. #465	C₂²×C₂₉	semidirect
477. #465	C₂²×C₂₉	semidirect
478. #464	C₂²×C₂₉	semidirect
479. #463	C₂²×C₂₉	semidirect
480. #462	C₂²×C₂₉	semidirect
481. #461	C₂²×C₂₉	semidirect
482. #460	C₂²×C₂₉	semidirect
483. #459	C₂²×C₂₉	semidirect
484. #452	C₂²×C₂₉	semidirect
485. #452	C₂²×C₂₉	semidirect
486. #451	C₂²×C₂₉	semidirect
487. #450	C₂²×C₂₉	semidirect
488. #449	C₂²×C₂₉	semidirect
489. #449	C₂²×C₂₉	semidirect
490. #448	C₂²×C₂₉	semidirect
491. #447	C₂²×C₂₉	semidirect
492. C₄×Q₁₆	C₂²×C₂₉	semidirect
493. C₄×Q₁₆	C₂²×C₂₉	semidirect
494. C₄×SD₁₆	C₂²×C₂₉	semidirect
495. C₄×SD₁₆	C₂²×C₂₉	semidirect
496. C₄×D₈	C₂²×C₂₉	semidirect
497. C₄×D₈	C₂²×C₂₉	semidirect
500. C₈×D₄	C₂²×C₂₉	semidirect
501. C₈×D₄	C₂²×C₂₉	semidirect
502. C₈×D₄	C₂²×C₂₉	semidirect
503. C₈×D₄	C₂²×C₂₉	semidirect
504. #427	C₂²×C₂₉	semidirect
505. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
506. #416	C₂²×C₂₉	semidirect
507. #416	C₂²×C₂₉	semidirect
508. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
509. C₂×C₄×C₈	C₂²×C₂₉	semidirect
539. #135	D₄×C₂₉	direct (N × H)
638. C₂₉	D₄×#135	direct (N × H)
650. #41	C₂×D₄×C₂₉	semidirect
696. Q₁₆	C₂×D₄×C₂₉	semidirect
701. SD₁₆	C₂×D₄×C₂₉	semidirect
705. D₈	C₂×D₄×C₂₉	semidirect
712. C₂×C₈	C₂×D₄×C₂₉	semidirect
780. D₄	C₂₉×#135	direct (N × H)
834. C₂²	C₂×C₂₉×#135	semidirect
846. C₄	C₂×C₂₉×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂₉×#135	2
D₄×#41×C₂₉	2
C₂₉×#3287	2
D₄×Q₁₆×C₂₉	2
C₂₉×#3285	2
C₂₉×#3284	2
C₂₉×#3283	2
C₂₉×#3282	2
D₄×SD₁₆×C₂₉	2
C₂₉×#3280	2
D₄×D₈×C₂₉	2
C₂₉×#3147	2
C₂₉×#3050	2
C₂₉×#3035	2
C₂₉×#3002	2
C₄×C₂₉×#135	2
C₂×C₈×D₄×C₂₉	2
D₄×#135	29

Subgroups — D4×C29×#135 #20355948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₂₉×#135 #20355948