Subgroups — #16833559

Order 3712.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271886	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271873	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271864	C₂	1	2	yes	maximal, complemented
4	#14271863	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271854	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271849	C₂	1	2	yes	maximal, complemented
7	#14271840	C₂	1	2	yes	maximal, complemented
8	#14271837	C₂	1	2	yes	maximal, complemented
9	#14271816	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271806	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271806	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271782	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271774	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271759	C₂	1	2	yes	maximal, complemented
15	#14271752	C₂	1	2	yes	maximal, complemented
16	#14271700	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271692	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271691	C₂	1	2	yes	maximal, complemented
19	#126×D₂₉	C₂	1	2	yes	maximal, complemented
20	#14271645	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271635	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#90809	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#90809	C₂²	1	1	yes	characteristic
25	C₂×#90809	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂₉×#126	C₂²	1	2	yes	complemented
29	C₂₉×#126	C₂²	1	2	yes	complemented
30	C₂₉×#124	C₂²	1	1	yes	characteristic
31	C₂₉×#124	C₂²	1	1	yes	characteristic
32	C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
34	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#117	C₂²	1	2	yes	complemented
38	#11745309	C₂²	1	1	yes	characteristic
39	#11745308	C₂²	1	1	yes	characteristic
40	#11745308	C₂²	1	1	yes	characteristic
41	#11745308	C₂²	1	1	yes	characteristic, complemented
42	#11745308	C₂²	1	2	yes	complemented
43	#11745308	C₂²	1	1	yes	characteristic, complemented
44	#11745308	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
47	#11745300	C₂²	1	1	yes	characteristic
48	#11745300	C₂²	1	1	yes	characteristic
49	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
50	#11745291	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	complemented
53	C₂×#90781	C₂²	1	2	yes	—
54	#11745260	C₂²	1	2	yes	—
55	#11745260	C₂²	1	2	yes	—
56	#11745260	C₂²	1	2	yes	—
57	#11745260	C₂²	1	1	yes	characteristic
58	#11745260	C₂²	1	2	yes	complemented
59	#11745260	C₂²	1	1	yes	characteristic, complemented
60	#11745258	C₂²	1	2	yes	complemented
61	#11745258	C₂²	1	2	yes	complemented
62	#11745257	C₂²	1	1	yes	characteristic
63	#11745257	C₂²	1	2	yes	complemented
64	#11745256	C₂²	1	2	yes	—
65	#11745256	C₂²	1	1	yes	characteristic
66	#11745256	C₂²	1	2	yes	complemented
67	#11745256	C₂²	1	2	yes	complemented
68	#11745256	C₂²	1	1	yes	characteristic, complemented
69	#11745255	C₂²	1	1	yes	characteristic
70	#11745255	C₂²	1	2	yes	complemented
71	#11745255	C₂²	1	2	yes	complemented
72	#11745254	C₂²	1	1	yes	characteristic
73	#11745254	C₂²	1	2	yes	complemented
74	#11745254	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊C₄×D₂₉	C₂²	1	2	yes	complemented
76	C₄⋊C₄×D₂₉	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
78	C₄⋊C₄×D₂₉	C₂²	1	2	yes	complemented
79	#11745252	C₂²	1	1	yes	characteristic, complemented
80	#11745251	C₂²	1	2	yes	complemented
81	#11745251	C₂²	1	2	yes	complemented
82	#11745251	C₂²	1	2	yes	complemented
83	#11745248	C₂²	1	2	yes	complemented
84	#11745247	C₂²	1	2	yes	complemented
85	#11745246	C₂²	1	2	yes	—
86	#11745246	C₂²	1	2	yes	—
87	#11745246	C₂²	1	2	yes	complemented
88	#11745245	C₂²	1	2	yes	—
89	#11745245	C₂²	1	2	yes	—
90	#11745245	C₂²	1	2	yes	complemented
91	#11745244	C₂²	1	2	yes	—
92	#11745244	C₂²	1	2	yes	—
93	#11745243	C₂²	1	2	yes	—
94	#11745243	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₂₉	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₂₉	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₂₉	C₂²	1	2	yes	—
98	#11745241	C₂²	1	2	yes	complemented
99	#11745241	C₂²	1	2	yes	complemented
100	#11745241	C₂²	1	2	yes	complemented
101	#11745240	C₂²	1	2	yes	complemented
102	#11745239	C₂²	1	2	yes	complemented
103	#11745238	C₂²	1	2	yes	—
104	#11745237	C₂²	1	2	yes	—
105	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
106	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
107	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
108	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
109	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
110	C₄×D₁₁₆	C₂²	1	2	yes	complemented
111	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₁₁₆	C₂²	1	2	yes	complemented
113	#11745234	C₂²	1	1	yes	characteristic
114	#11745234	C₂²	1	1	yes	characteristic, complemented
115	#11745234	C₂²	1	2	yes	complemented
116	#11745234	C₂²	1	2	yes	complemented
117	C₄²×D₂₉	C₂²	1	2	yes	complemented
118	C₄²×D₂₉	C₂²	1	1	yes	characteristic, complemented
119	#11745232	C₂²	1	1	yes	characteristic, complemented
120	#11745232	C₂²	1	1	yes	characteristic, complemented
121	#11745231	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₅₈	C₂²	1	2	yes	complemented
123	C₂³×D₂₉	C₂³	1	2	yes	—
124	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
132	C₂²×Dic₂₉	C₂³	1	2	yes	—
133	#90809	—	2	4	no	—
134	#90809	—	2	4	no	—
135	D₄×D₂₉	—	2	4	no	—
136	C₂×D₁₁₆	C₂³	1	2	yes	—
137	C₂×D₁₁₆	C₂³	1	2	yes	—
138	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
139	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
140	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
141	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₂₉	C₂³	1	2	yes	—
146	C₂×C₄×D₂₉	C₂³	1	2	yes	—
147	C₂×C₄×D₂₉	C₂³	1	2	yes	—
148	C₂×C₄×D₂₉	C₂³	1	2	yes	—
149	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₉	C₂³	1	2	yes	—
151	C₂×C₄×D₂₉	C₂³	1	2	yes	—
152	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₂₉	C₂³	1	2	yes	—
154	C₂×Dic₅₈	C₂³	1	2	yes	—
155	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
159	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
160	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
168	C₄²×C₂₉	C₂³	1	2	yes	—
169	C₄²×C₂₉	C₂³	1	2	yes	—
170	C₄²×C₂₉	C₂³	1	1	yes	characteristic
171	C₄²×C₂₉	C₂³	1	1	yes	characteristic
172	C₄²×C₂₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
176	#90781	C₂³	1	1	yes	characteristic
177	#90781	C₂³	1	2	yes	—
178	#90781	C₂³	1	2	yes	—
179	#90781	C₂³	1	2	yes	—
180	#90781	C₂³	1	1	yes	characteristic
181	#90781	C₂³	1	1	yes	characteristic
182	#90781	C₂³	1	2	yes	—
183	#90781	C₂³	1	2	yes	—
184	#90781	C₂³	1	2	yes	—
185	#90781	C₂³	1	2	yes	—
186	#90781	C₂³	1	2	yes	—
187	#90781	C₂³	1	1	yes	characteristic
188	#90781	C₂³	1	2	yes	—
189	#90781	C₂³	1	1	yes	characteristic
190	#90781	C₂³	1	1	yes	characteristic
191	#90781	C₂³	1	1	yes	characteristic
192	#90781	C₂³	1	1	yes	characteristic
193	#90781	C₂³	1	2	yes	—
194	#90781	C₂³	1	1	yes	characteristic
195	#90781	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₂₉	C₂³	1	2	yes	—
200	C₄⋊Dic₂₉	C₂³	1	2	yes	—
201	C₄⋊Dic₂₉	C₂³	1	2	yes	—
202	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
205	#90779	C₂³	1	1	yes	characteristic
206	#90779	C₂³	1	2	yes	—
207	#90779	C₂³	1	2	yes	—
208	#90779	C₂³	1	2	yes	—
209	#90779	C₂³	1	2	yes	—
210	#90779	C₂³	1	2	yes	—
211	#90779	C₂³	1	2	yes	—
212	#90779	C₂³	1	1	yes	characteristic
213	#90779	C₂³	1	2	yes	—
214	#90779	C₂³	1	2	yes	—
215	#90779	C₂³	1	2	yes	—
216	#90779	C₂³	1	1	yes	characteristic
217	#90779	C₂³	1	1	yes	characteristic
218	C₄×Dic₂₉	C₂³	1	2	yes	—
219	C₄×Dic₂₉	C₂³	1	2	yes	—
220	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₂₉	C₂³	1	2	yes	—
222	C₄×Dic₂₉	C₂³	1	2	yes	—
223	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
225	C₂³×C₂₉	C₂⁴	1	2	yes	—
226	C₂²×D₂₉	—	2	4	no	—
227	C₂²×D₂₉	—	4	2	no	—
228	C₂²×D₂₉	—	4	2	no	—
229	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₂₉	C₂⁴	1	2	yes	—
233	Q₈×C₂₉	—	2	2	no	—
234	Q₈×C₂₉	—	2	2	no	—
235	Q₈×C₂₉	—	4	1	no	—
236	D₄×C₂₉	—	2	2	no	—
237	C₂×C₄×C₂₉	—	4	2	no	—
238	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
239	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₂₉	—	2	4	no	—
249	C₂²⋊D₂₉	—	4	2	no	—
250	C₂²⋊D₂₉	—	4	2	no	—
251	C₂×Dic₂₉	—	4	2	no	—
252	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₂₉	C₂⁴	1	2	yes	—
257	C₂×Dic₂₉	C₂⁴	1	2	yes	—
258	C₂×Dic₂₉	C₂⁴	1	2	yes	—
259	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
260	D₁₁₆	—	2	4	no	—
261	D₁₁₆	—	2	4	no	—
262	D₁₁₆	—	4	1	no	—
263	D₁₁₆	—	4	1	no	—
264	D₁₁₆	—	4	1	no	—
265	D₁₁₆	#41	1	4	yes	—
266	C₄×D₂₉	—	2	4	no	—
267	C₄×D₂₉	—	2	4	no	—
268	C₄×D₂₉	—	2	2	no	—
269	C₄×D₂₉	—	2	2	no	—
270	C₄×D₂₉	—	2	2	no	—
271	C₄×D₂₉	—	4	2	no	—
272	C₄×D₂₉	—	4	2	no	—
273	C₄×D₂₉	—	4	2	no	—
274	C₄×D₂₉	—	4	1	no	—
275	C₄×D₂₉	—	4	2	no	—
276	C₄×D₂₉	—	4	2	no	—
277	C₄×D₂₉	—	4	1	no	—
278	Dic₅₈	—	4	2	no	—
279	#3521	—	29	1	no	maximal, Sylow
280	C₂²×C₂₉	—	2	2	no	—
281	C₂²×C₂₉	—	2	2	no	—
282	C₂²×C₂₉	—	2	2	no	—
283	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
284	C₂×D₂₉	—	2	2	no	—
285	C₂×D₂₉	—	2	2	no	—
286	C₂×D₂₉	—	2	1	no	—
287	C₂×D₂₉	—	2	1	no	—
288	C₂×D₂₉	—	2	1	no	—
289	C₂×D₂₉	—	2	1	no	—
290	C₂×D₂₉	—	2	1	no	—
291	C₂×D₂₉	—	2	1	no	—
292	C₂×D₂₉	—	2	1	no	—
293	C₂×D₂₉	—	2	1	no	—
294	C₂×D₂₉	—	2	1	no	—
295	C₂×D₂₉	—	8	4	no	—
296	C₂×D₂₉	C₂×#41	1	4	yes	—
297	C₄×C₂₉	—	2	2	no	—
298	C₄×C₂₉	—	2	2	no	—
299	C₄×C₂₉	—	2	1	no	—
300	C₄×C₂₉	—	2	1	no	—
301	C₄×C₂₉	—	2	1	no	—
302	C₄×C₂₉	—	2	2	no	—
303	C₄×C₂₉	—	2	1	no	—
304	C₄×C₂₉	—	2	1	no	—
305	C₄×C₂₉	—	2	1	no	—
306	C₄×C₂₉	C₂×#41	1	2	yes	—
307	Dic₂₉	—	2	1	no	—
308	Dic₂₉	—	2	1	no	—
309	Dic₂₉	—	2	1	no	—
310	Dic₂₉	—	2	2	no	—
311	Dic₂₉	—	2	2	no	—
312	Dic₂₉	—	2	1	no	—
313	Dic₂₉	—	2	2	no	—
314	Dic₂₉	—	2	1	no	—
315	#556	—	29	1	no	—
316	#556	D₂₉	1	1	yes	characteristic, complemented
317	#554	—	29	1	no	—
318	#553	—	29	2	no	—
319	#553	—	29	1	no	—
320	#552	—	29	2	no	—
321	#552	—	29	1	no	—
322	#551	—	29	2	no	—
323	#551	—	29	2	no	—
324	#547	—	29	1	no	—
325	#546	—	29	1	no	—
326	#546	—	29	1	no	—
327	#542	—	29	1	no	—
328	#541	—	29	1	no	—
329	#539	—	29	2	no	—
330	#538	—	29	2	no	—
331	#529	—	29	1	no	—
332	#529	—	29	1	no	—
333	#529	—	29	2	no	—
334	C₂×#126	—	29	2	no	—
335	#520	—	29	1	no	—
336	#518	—	29	1	no	—
337	C₄×#41	—	29	1	no	—
338	C₂×C₂₉	—	4	2	no	—
339	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
340	C₂×C₂₉	#585	1	1	yes	characteristic
341	C₂×C₂₉	#585	1	1	yes	characteristic
342	D₂₉	—	2	4	no	—
343	D₂₉	—	4	1	no	—
344	D₂₉	—	4	1	no	—
345	D₂₉	—	4	1	no	—
346	C₂×#41	—	29	1	no	—
347	C₂×#41	—	29	1	no	—
348	C₂²×D₄	—	29	1	no	—
349	C₄⋊Q₈	—	29	1	no	—
350	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
351	#126	—	29	1	no	—
352	#126	—	29	2	no	—
353	#126	—	29	2	no	—
354	#126	—	29	1	no	—
355	#126	—	29	2	no	—
356	#126	—	29	2	no	—
357	#126	—	29	2	no	—
358	#126	—	29	2	no	—
359	#126	—	29	2	no	—
360	#126	—	29	2	no	—
361	#126	C₂×D₂₉	1	2	yes	complemented
362	#126	C₂×D₂₉	1	2	yes	complemented
363	#125	—	29	2	no	—
364	#125	—	29	1	no	—
365	#125	—	29	2	no	—
366	#125	—	29	2	no	—
367	#125	—	29	1	no	—
368	#125	—	29	1	no	—
369	#124	—	29	1	no	—
370	#124	—	29	2	no	—
371	#124	—	29	2	no	—
372	#124	C₂×D₂₉	1	1	yes	characteristic
373	#124	C₂×D₂₉	1	1	yes	characteristic
374	#123	—	29	2	no	—
375	#123	—	29	2	no	—
376	#123	—	29	1	no	—
377	#123	—	29	1	no	—
378	#123	—	29	2	no	—
379	#123	—	29	2	no	—
380	#123	—	29	2	no	—
381	#123	—	29	2	no	—
382	#123	—	29	2	no	—
383	#123	—	29	2	no	—
384	C₂²⋊Q₈	—	29	1	no	—
385	C₂²⋊Q₈	—	29	1	no	—
386	C₂²⋊Q₈	—	29	2	no	—
387	C₂²⋊Q₈	—	29	1	no	—
388	C₂²⋊Q₈	—	29	1	no	—
389	C₂²⋊Q₈	—	29	1	no	—
390	C₂²⋊Q₈	—	29	2	no	—
391	C₂²⋊Q₈	—	29	2	no	—
392	C₂²⋊Q₈	—	29	2	no	—
393	C₂²⋊Q₈	C₂×D₂₉	1	2	yes	complemented
394	#121	—	29	1	no	—
395	#121	—	29	1	no	—
396	#121	—	29	1	no	—
397	#121	—	29	2	no	—
398	#121	—	29	2	no	—
399	#121	—	29	2	no	—
400	#121	—	29	2	no	—
401	#120	—	29	2	no	—
402	#120	—	29	2	no	—
403	C₄×Q₈	—	29	1	no	—
404	C₄×Q₈	—	29	1	no	—
405	C₄×Q₈	—	29	2	no	—
406	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
407	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
408	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
409	C₄×D₄	—	29	1	no	—
410	C₄×D₄	—	29	2	no	—
411	C₄×D₄	—	29	2	no	—
412	C₄×D₄	—	29	1	no	—
413	C₄×D₄	—	29	2	no	—
414	C₄×D₄	—	29	2	no	—
415	C₄×D₄	—	29	2	no	—
416	C₄×D₄	—	29	2	no	—
417	C₄×D₄	—	29	1	no	—
418	C₄×D₄	—	29	2	no	—
419	C₄×D₄	—	29	1	no	—
420	C₄×D₄	—	29	2	no	—
421	C₄×D₄	—	29	1	no	—
422	C₄×D₄	—	29	1	no	—
423	C₄×D₄	—	29	1	no	—
424	C₄×D₄	—	29	1	no	—
425	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
426	#117	—	29	2	no	—
427	#117	—	29	1	no	—
428	#117	—	29	1	no	—
429	#117	—	29	2	no	—
430	#117	—	29	1	no	—
431	#117	—	29	1	no	—
432	#117	—	29	2	no	—
433	#117	—	29	2	no	—
434	#117	C₂×D₂₉	1	2	yes	complemented
435	C₂×C₄⋊C₄	—	29	2	no	—
436	C₂×C₄⋊C₄	—	29	1	no	—
437	C₂×C₄⋊C₄	—	29	2	no	—
438	C₂×C₄⋊C₄	—	29	2	no	—
439	C₂×C₂²⋊C₄	—	29	2	no	—
440	C₂×C₂²⋊C₄	—	29	2	no	—
441	C₂×C₂²⋊C₄	—	29	2	no	—
442	C₂×C₂²⋊C₄	—	29	2	no	—
443	C₂×C₄²	—	29	2	no	—
444	C₂×C₄²	—	29	1	no	—
445	C₂₉	#3521	1	1	yes	characteristic, complemented, Sylow
446	C₂⁴	—	29	2	no	—
447	#41	—	58	4	no	—
448	#41	—	58	4	no	—
449	C₂×Q₈	—	29	2	no	—
450	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
451	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
453	C₂×D₄	—	29	2	no	—
454	C₂×D₄	—	29	2	no	—
455	C₂×D₄	—	29	2	no	—
456	C₂×D₄	—	29	1	no	—
457	C₂×D₄	—	29	2	no	—
458	C₂×D₄	—	29	2	no	—
459	C₂×D₄	—	29	1	no	—
460	C₂×D₄	—	29	1	no	—
461	C₂×D₄	—	29	1	no	—
462	C₂×D₄	—	58	4	no	—
463	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
464	C₂²×C₄	—	29	2	no	—
465	C₂²×C₄	—	29	2	no	—
466	C₂²×C₄	—	29	1	no	—
467	C₂²×C₄	—	29	2	no	—
468	C₂²×C₄	—	29	1	no	—
469	C₂²×C₄	—	29	1	no	—
470	C₂²×C₄	—	29	2	no	—
471	C₂²×C₄	—	29	2	no	—
472	C₂²×C₄	—	29	1	no	—
473	C₂²×C₄	—	29	1	no	—
474	C₂²×C₄	—	29	2	no	—
475	C₂²×C₄	—	29	2	no	—
476	C₂²×C₄	—	29	2	no	—
477	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
478	C₄⋊C₄	—	29	1	no	—
479	C₄⋊C₄	—	29	2	no	—
480	C₄⋊C₄	—	29	1	no	—
481	C₄⋊C₄	—	29	2	no	—
482	C₄⋊C₄	—	29	2	no	—
483	C₄⋊C₄	—	29	1	no	—
484	C₄⋊C₄	—	29	2	no	—
485	C₄⋊C₄	—	29	2	no	—
486	C₄⋊C₄	—	29	2	no	—
487	C₄⋊C₄	—	29	2	no	—
488	C₄⋊C₄	—	29	1	no	—
489	C₄⋊C₄	—	29	1	no	—
490	C₄⋊C₄	—	29	1	no	—
491	C₄⋊C₄	—	29	1	no	—
492	C₄⋊C₄	—	29	1	no	—
493	C₄⋊C₄	—	29	2	no	—
494	C₄⋊C₄	—	29	2	no	—
495	C₄⋊C₄	—	29	2	no	—
496	C₄⋊C₄	—	29	1	no	—
497	C₄⋊C₄	—	29	2	no	—
498	C₄⋊C₄	—	29	1	no	—
499	C₄⋊C₄	—	29	2	no	—
500	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
505	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	29	2	no	—
509	C₂²⋊C₄	—	29	2	no	—
510	C₂²⋊C₄	—	29	2	no	—
511	C₂²⋊C₄	—	29	1	no	—
512	C₂²⋊C₄	—	29	1	no	—
513	C₂²⋊C₄	—	29	2	no	—
514	C₂²⋊C₄	—	29	1	no	—
515	C₂²⋊C₄	—	29	1	no	—
516	C₂²⋊C₄	—	29	2	no	—
517	C₂²⋊C₄	—	29	2	no	—
518	C₂²⋊C₄	—	29	2	no	—
519	C₂²⋊C₄	—	29	2	no	—
520	C₂²⋊C₄	—	29	1	no	—
521	C₂²⋊C₄	—	29	2	no	—
522	C₂²⋊C₄	—	29	2	no	—
523	C₂²⋊C₄	—	29	2	no	—
524	C₂²⋊C₄	—	29	1	no	—
525	C₂²⋊C₄	—	29	1	no	—
526	C₂²⋊C₄	—	29	2	no	—
527	C₂²⋊C₄	—	29	1	no	—
528	C₂²⋊C₄	—	29	1	no	—
529	C₂²⋊C₄	—	29	2	no	—
530	C₂²⋊C₄	—	29	1	no	—
531	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
536	C₄²	—	29	1	no	—
537	C₄²	—	29	1	no	—
538	C₄²	—	29	1	no	—
539	C₄²	—	29	2	no	—
540	C₄²	—	29	2	no	—
541	C₄²	—	29	2	no	—
542	C₄²	—	29	2	no	—
543	C₄²	C₂²×D₂₉	1	2	yes	—
544	C₄²	C₂²×D₂₉	1	1	yes	characteristic
545	C₄²	C₂²×D₂₉	1	2	yes	—
546	C₄²	C₂²×D₂₉	1	1	yes	characteristic
547	C₄²	C₂²×D₂₉	1	1	yes	characteristic
548	C₂³	—	29	2	no	—
549	C₂³	—	29	1	no	—
550	C₂³	—	29	1	no	—
551	C₂³	—	29	1	no	—
552	C₂³	—	58	4	no	—
553	C₂³	—	116	2	no	—
554	C₂³	—	116	2	no	—
555	C₂³	C₂³×D₂₉	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	116	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	29	4	no	—
562	D₄	—	58	4	no	—
563	D₄	—	58	4	no	—
564	D₄	—	58	4	no	—
565	D₄	—	116	1	no	—
566	D₄	—	116	1	no	—
567	D₄	—	116	1	no	—
568	D₄	—	116	2	no	—
569	D₄	—	116	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	29	1	no	—
572	C₂×C₄	—	29	1	no	—
573	C₂×C₄	—	29	1	no	—
574	C₂×C₄	—	29	2	no	—
575	C₂×C₄	—	29	1	no	—
576	C₂×C₄	—	29	2	no	—
577	C₂×C₄	—	29	2	no	—
578	C₂×C₄	—	29	1	no	—
579	C₂×C₄	—	58	4	no	—
580	C₂×C₄	—	58	4	no	—
581	C₂×C₄	—	58	2	no	—
582	C₂×C₄	—	58	2	no	—
583	C₂×C₄	—	58	2	no	—
584	C₂×C₄	—	116	1	no	—
585	C₂×C₄	—	116	2	no	—
586	C₂×C₄	—	116	2	no	—
587	C₂×C₄	—	116	2	no	—
588	C₂×C₄	—	116	2	no	—
589	C₂×C₄	—	116	2	no	—
590	C₂×C₄	—	116	1	no	—
591	C₂×C₄	—	116	2	no	—
592	C₂×C₄	C₂³×D₂₉	1	2	yes	—
593	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₂₉	1	2	yes	—
595	C₂×C₄	C₂³×D₂₉	1	2	yes	—
596	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	29	4	no	—
606	C₂²	—	58	2	no	—
607	C₂²	—	58	2	no	—
608	C₂²	—	58	1	no	—
609	C₂²	—	58	1	no	—
610	C₂²	—	58	1	no	—
611	C₂²	—	58	1	no	—
612	C₂²	—	58	1	no	—
613	C₂²	—	58	1	no	—
614	C₂²	—	58	1	no	—
615	C₂²	—	58	1	no	—
616	C₂²	—	58	1	no	—
617	C₂²	—	232	4	no	—
618	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	58	1	no	—
629	C₄	—	58	2	no	—
630	C₄	—	58	2	no	—
631	C₄	—	58	1	no	—
632	C₄	—	58	1	no	—
633	C₄	—	58	1	no	—
634	C₄	—	58	1	no	—
635	C₄	—	58	2	no	—
636	C₄	#41×D₂₉	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	58	4	no	—
639	C₂	—	116	1	no	—
640	C₂	—	116	1	no	—
641	C₂	—	116	1	no	—
642	C₂	C₂×#41×D₂₉	1	1	yes	characteristic
643	C₂	#14271999	1	1	yes	characteristic
644	C₂	#14272000	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#556	C₂
hypercenter	#556	D₂₉
hypocenter	C₂₉	#3521
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #14271886	C₂	semidirect
2. #14271873	C₂	semidirect
3. #14271864	C₂	semidirect
4. #14271863	C₂	semidirect
5. #14271854	C₂	semidirect
6. #14271849	C₂	semidirect
7. #14271840	C₂	semidirect
8. #14271837	C₂	semidirect
9. #14271816	C₂	semidirect
10. #14271806	C₂	semidirect
11. #14271806	C₂	semidirect
12. #14271782	C₂	semidirect
13. #14271774	C₂	semidirect
14. #14271759	C₂	semidirect
15. #14271752	C₂	semidirect
16. #14271700	C₂	semidirect
17. #14271692	C₂	semidirect
18. #14271691	C₂	semidirect
19. #126×D₂₉	C₂	semidirect
20. #14271645	C₂	semidirect
21. #14271635	C₂	semidirect
22. C₄×#90809	C₂	semidirect
23. C₂₉×#556	C₂	semidirect
27. C₂₉×C₄⋊Q₈	C₂²	semidirect
28. C₂₉×#126	C₂²	semidirect
29. C₂₉×#126	C₂²	semidirect
32. C₂₉×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₂₉	C₂²	semidirect
34. C₄×Q₈×C₂₉	C₂²	semidirect
35. C₄×Q₈×C₂₉	C₂²	semidirect
37. C₂₉×#117	C₂²	semidirect
41. #11745308	C₂²	semidirect
42. #11745308	C₂²	semidirect
43. #11745308	C₂²	semidirect
44. #11745308	C₂²	semidirect
45. Q₈×Dic₂₉	C₂²	semidirect
46. Q₈×Dic₂₉	C₂²	semidirect
50. #11745291	C₂²	semidirect
52. C₄×C₂²⋊D₂₉	C₂²	semidirect
58. #11745260	C₂²	semidirect
59. #11745260	C₂²	semidirect
60. #11745258	C₂²	semidirect
61. #11745258	C₂²	semidirect
63. #11745257	C₂²	semidirect
66. #11745256	C₂²	semidirect
67. #11745256	C₂²	semidirect
68. #11745256	C₂²	semidirect
70. #11745255	C₂²	semidirect
71. #11745255	C₂²	semidirect
73. #11745254	C₂²	semidirect
74. #11745254	C₂²	semidirect
75. C₄⋊C₄×D₂₉	C₂²	semidirect
76. C₄⋊C₄×D₂₉	C₂²	semidirect
77. C₄⋊C₄×D₂₉	C₂²	semidirect
78. C₄⋊C₄×D₂₉	C₂²	semidirect
79. #11745252	C₂²	semidirect
80. #11745251	C₂²	semidirect
81. #11745251	C₂²	semidirect
82. #11745251	C₂²	semidirect
83. #11745248	C₂²	semidirect
84. #11745247	C₂²	semidirect
87. #11745246	C₂²	semidirect
90. #11745245	C₂²	semidirect
94. #11745243	C₂²	semidirect
98. #11745241	C₂²	semidirect
99. #11745241	C₂²	semidirect
100. #11745241	C₂²	semidirect
101. #11745240	C₂²	semidirect
102. #11745239	C₂²	semidirect
110. C₄×D₁₁₆	C₂²	semidirect
111. C₄×D₁₁₆	C₂²	semidirect
112. C₄×D₁₁₆	C₂²	semidirect
114. #11745234	C₂²	semidirect
115. #11745234	C₂²	semidirect
116. #11745234	C₂²	semidirect
117. C₄²×D₂₉	C₂²	semidirect
118. C₄²×D₂₉	C₂²	semidirect
119. #11745232	C₂²	semidirect
120. #11745232	C₂²	semidirect
121. #11745231	C₂²	semidirect
122. C₄×Dic₅₈	C₂²	semidirect
316. #556	D₂₉	semidirect
350. C₄⋊Q₈	C₂×D₂₉	semidirect
361. #126	C₂×D₂₉	semidirect
362. #126	C₂×D₂₉	semidirect
393. C₂²⋊Q₈	C₂×D₂₉	semidirect
406. C₄×Q₈	C₂×D₂₉	semidirect
407. C₄×Q₈	C₂×D₂₉	semidirect
408. C₄×Q₈	C₂×D₂₉	semidirect
434. #117	C₂×D₂₉	semidirect
445. C₂₉	#3521	semidirect

Maximal subgroups

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

subgroup	index
#14271886	2
#14271873	2
#14271864	2
#14271863	2
#14271854	2
#14271849	2
#14271840	2
#14271837	2
#14271816	2
#14271806	2
#14271782	2
#14271774	2
#14271759	2
#14271752	2
#14271700	2
#14271692	2
#14271691	2
#126×D₂₉	2
#14271645	2
#14271635	2
C₄×#90809	2
C₂₉×#556	2
#3521	29