Subgroups — #34058404

Order 19072.

1040 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750348	C₂	1	2	yes	maximal, complemented
2	#23750343	C₂	1	2	yes	maximal, complemented
3	#23750340	C₂	1	2	yes	maximal, complemented
4	#23750338	C₂	1	2	yes	maximal, complemented
5	#23750325	C₂	1	2	yes	maximal, complemented
6	#23750323	C₂	1	2	yes	maximal, complemented
7	#23750316	C₂	1	2	yes	maximal, complemented
8	#23750310	C₂	1	2	yes	maximal, complemented
9	#23750253	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750208	C₂	1	4	yes	maximal, complemented
11	#23750203	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750155	C₂	1	4	yes	maximal, complemented
13	#23750137	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750132	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#18011869	C₂	1	1	yes	maximal, characteristic, complemented
17	#520×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558736	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
20	#18011911	C₂²	1	2	yes	complemented
21	#18011910	C₂²	1	2	yes	complemented
22	#18011906	C₂²	1	4	yes	—
23	#18011906	C₂²	1	4	yes	complemented
24	#18011905	C₂²	1	4	yes	—
25	#18011904	C₂²	1	4	yes	complemented
26	#18011903	C₂²	1	2	yes	complemented
27	#18011902	C₂²	1	2	yes	complemented
28	#18011901	C₂²	1	4	yes	complemented
29	#18011899	C₂²	1	4	yes	—
30	#18011897	C₂²	1	4	yes	—
31	#18011897	C₂²	1	4	yes	complemented
32	#18011896	C₂²	1	4	yes	—
33	#18011895	C₂²	1	2	yes	—
34	#18011894	C₂²	1	4	yes	—
35	#18011892	C₂²	1	2	yes	—
36	#18011891	C₂²	1	1	yes	characteristic
37	#18011891	C₂²	1	1	yes	characteristic
38	#18011890	C₂²	1	2	yes	complemented
39	#18011888	C₂²	1	4	yes	—
40	#18011887	C₂²	1	1	yes	characteristic
41	#18011887	C₂²	1	1	yes	characteristic
42	#18011887	C₂²	1	2	yes	complemented
43	#18011886	C₂²	1	1	yes	characteristic
44	#18011886	C₂²	1	1	yes	characteristic
45	#18011885	C₂²	1	4	yes	—
46	#18011885	C₂²	1	2	yes	complemented
47	#18011884	C₂²	1	4	yes	—
48	#18011883	C₂²	1	4	yes	—
49	#18011882	C₂²	1	1	yes	characteristic
50	#18011882	C₂²	1	1	yes	characteristic
51	#18011882	C₂²	1	2	yes	complemented
52	#18011881	C₂²	1	2	yes	—
53	#18011879	C₂²	1	2	yes	—
54	C₄×Dic₂₉₈	C₂²	1	4	yes	complemented
55	#18011876	C₂²	1	2	yes	complemented
56	C₄×D₅₉₆	C₂²	1	2	yes	—
57	C₄×D₅₉₆	C₂²	1	2	yes	—
58	#18011873	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
63	#18011870	C₂²	1	1	yes	characteristic
64	#18011870	C₂²	1	4	yes	complemented
65	#18011869	C₂²	1	2	yes	—
66	#18011869	C₂²	1	2	yes	—
67	#18011869	C₂²	1	2	yes	—
68	#18011869	C₂²	1	2	yes	—
69	#18011869	C₂²	1	2	yes	complemented
70	#18011868	C₂²	1	4	yes	complemented
71	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
73	C₂×#14558713	C₂²	1	2	yes	—
74	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
75	C₂×#41×C₁₄₉	C₂²	1	1	yes	characteristic
76	C₄×Q₈×C₁₄₉	C₂²	1	2	yes	complemented
77	C₄×D₄×C₁₄₉	C₂²	1	4	yes	—
78	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
79	#117×C₁₄₉	C₂²	1	1	yes	characteristic
80	#117×C₁₄₉	C₂²	1	2	yes	complemented
81	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
84	#14558736	—	2	4	no	—
85	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₉₈	C₂³	1	4	yes	—
87	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
88	C₂×D₅₉₆	C₂³	1	2	yes	—
89	C₂×D₅₉₆	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
94	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
96	C₂×C₄×D₁₄₉	—	2	4	no	—
97	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
102	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
103	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
104	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
105	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
106	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
108	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
110	#14558715	C₂³	1	4	yes	—
111	#14558715	C₂³	1	4	yes	—
112	#14558715	C₂³	1	4	yes	—
113	#14558715	C₂³	1	2	yes	—
114	#14558715	C₂³	1	2	yes	—
115	#14558715	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
120	#14558713	C₂³	1	2	yes	—
121	#14558713	C₂³	1	2	yes	—
122	#14558713	C₂³	1	4	yes	—
123	#14558713	C₂³	1	2	yes	—
124	#14558713	C₂³	1	2	yes	—
125	#14558713	C₂³	1	4	yes	—
126	#14558713	C₂³	1	2	yes	—
127	#14558713	C₂³	1	4	yes	—
128	#14558713	C₂³	1	4	yes	—
129	#14558713	C₂³	1	2	yes	—
130	C₄×Dic₁₄₉	C₂³	1	4	yes	—
131	C₄×Dic₁₄₉	C₂³	1	4	yes	—
132	C₄×Dic₁₄₉	C₂³	1	2	yes	—
133	C₄×Dic₁₄₉	C₂³	1	4	yes	—
134	#41×C₁₄₉	—	2	4	no	—
135	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
137	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
141	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
148	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
149	C₄²×C₁₄₉	C₂³	1	4	yes	—
150	C₄²×C₁₄₉	C₂³	1	2	yes	—
151	C₂²×D₁₄₉	—	2	2	no	—
152	C₂²×D₁₄₉	—	4	1	no	—
153	C₂²×D₁₄₉	—	4	1	no	—
154	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
155	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
156	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
157	Dic₂₉₈	—	2	2	no	—
158	Dic₂₉₈	—	4	4	no	—
159	D₅₉₆	—	2	2	no	—
160	D₅₉₆	—	4	2	no	—
161	D₅₉₆	—	4	2	no	—
162	C₂²⋊D₁₄₉	—	2	4	no	—
163	C₂²⋊D₁₄₉	—	4	2	no	—
164	C₂²⋊D₁₄₉	—	4	4	no	—
165	C₂²⋊D₁₄₉	—	4	2	no	—
166	C₂×Dic₁₄₉	—	2	2	no	—
167	C₂×Dic₁₄₉	—	4	2	no	—
168	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
169	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
170	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
171	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
172	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
173	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
174	C₄×D₁₄₉	—	2	2	no	—
175	C₄×D₁₄₉	—	2	2	no	—
176	C₄×D₁₄₉	—	2	2	no	—
177	C₄×D₁₄₉	—	2	2	no	—
178	C₄×D₁₄₉	—	2	4	no	—
179	C₄×D₁₄₉	—	4	4	no	—
180	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
181	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
182	Q₈×C₁₄₉	—	2	2	no	—
183	D₄×C₁₄₉	—	2	4	no	—
184	D₄×C₁₄₉	—	2	2	no	—
185	C₂×C₄×C₁₄₉	—	2	4	no	—
186	C₂×C₄×C₁₄₉	—	4	2	no	—
187	C₂×C₄×C₁₄₉	—	4	4	no	—
188	C₂×C₄×C₁₄₉	#41	1	4	yes	—
189	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
190	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
191	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
192	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
193	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
195	C₂²×C₁₄₉	—	2	1	no	—
196	C₂²×C₁₄₉	—	2	1	no	—
197	C₂²×C₁₄₉	—	2	2	no	—
198	C₂²×C₁₄₉	—	2	2	no	—
199	C₂²×C₁₄₉	—	2	2	no	—
200	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
201	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₄₉	—	2	1	no	—
203	C₂×D₁₄₉	—	2	1	no	—
204	C₂×D₁₄₉	—	2	2	no	—
205	C₂×D₁₄₉	—	2	2	no	—
206	C₂×D₁₄₉	—	2	2	no	—
207	C₂×D₁₄₉	—	2	1	no	—
208	C₂×D₁₄₉	—	2	1	no	—
209	C₂×D₁₄₉	—	2	1	no	—
210	C₂×D₁₄₉	—	2	1	no	—
211	C₂×D₁₄₉	—	4	4	no	—
212	C₄×C₁₄₉	—	2	2	no	—
213	C₄×C₁₄₉	—	2	4	no	—
214	C₄×C₁₄₉	—	2	2	no	—
215	C₄×C₁₄₉	—	2	2	no	—
216	C₄×C₁₄₉	C₂×#41	1	2	yes	—
217	C₄×C₁₄₉	C₂×#41	1	2	yes	—
218	Dic₁₄₉	—	2	1	no	—
219	Dic₁₄₉	—	2	1	no	—
220	Dic₁₄₉	—	2	2	no	—
221	Dic₁₄₉	—	2	2	no	—
222	Dic₁₄₉	—	2	4	no	—
223	Dic₁₄₉	—	2	2	no	—
224	C₂×C₁₄₉	—	2	2	no	—
225	C₂×C₁₄₉	—	4	2	no	—
226	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
227	C₂×C₁₄₉	#585	1	1	yes	characteristic
228	C₂×C₁₄₉	#585	1	1	yes	characteristic
229	D₁₄₉	—	4	2	no	—
230	D₁₄₉	—	4	1	no	—
231	D₁₄₉	—	4	1	no	—
232	C₁₄₉	#3493	1	1	yes	characteristic, complemented, Sylow
233	#3493	—	149	1	no	maximal, Sylow
234	#556	—	149	2	no	—
235	#556	—	149	2	no	—
236	#555	—	149	2	no	—
237	#555	—	149	2	no	—
238	#553	—	149	2	no	—
239	#553	—	149	2	no	—
240	#552	—	149	2	no	—
241	#552	—	149	2	no	—
242	#544	—	149	1	no	—
243	#538	—	149	4	no	—
244	#537	—	149	1	no	—
245	#529	—	149	4	no	—
246	#525	—	149	1	no	—
247	#525	—	149	1	no	—
248	#520	—	149	1	no	—
249	#520	D₁₄₉	1	1	yes	characteristic, complemented
250	C₂×#117	—	149	1	no	—
251	C₂×#41	—	149	1	no	—
252	C₂×#41	C₂×D₁₄₉	1	1	yes	characteristic
253	C₂³×C₄	—	149	1	no	—
254	C₄⋊Q₈	—	149	2	no	—
255	C₄⋊Q₈	—	149	2	no	—
256	#126	—	149	4	no	—
257	#126	—	149	4	no	—
258	#126	—	149	4	no	—
259	#126	—	149	4	no	—
260	#125	—	149	4	no	—
261	#125	—	149	2	no	—
262	#125	—	149	2	no	—
263	#124	—	149	4	no	—
264	#124	—	149	4	no	—
265	#124	—	149	4	no	—
266	#123	—	149	2	no	—
267	#123	—	149	4	no	—
268	#123	—	149	4	no	—
269	#123	—	149	2	no	—
270	C₂²⋊Q₈	—	149	1	no	—
271	C₂²⋊Q₈	—	149	1	no	—
272	C₂²⋊Q₈	—	149	2	no	—
273	C₂²⋊Q₈	—	149	2	no	—
274	C₂²⋊Q₈	—	149	1	no	—
275	C₂²⋊Q₈	—	149	1	no	—
276	C₂²⋊Q₈	—	149	4	no	—
277	#121	—	149	1	no	—
278	#121	—	149	1	no	—
279	#121	—	149	4	no	—
280	#121	—	149	2	no	—
281	#121	—	149	2	no	—
282	#121	—	149	4	no	—
283	#121	—	149	1	no	—
284	#121	—	149	1	no	—
285	#121	—	149	4	no	—
286	#120	—	149	2	no	—
287	#120	—	149	2	no	—
288	C₄×Q₈	—	149	2	no	—
289	C₄×Q₈	—	149	4	no	—
290	C₄×Q₈	C₂×D₁₄₉	1	2	yes	complemented
291	C₄×D₄	—	149	4	no	—
292	C₄×D₄	—	149	2	no	—
293	C₄×D₄	—	149	2	no	—
294	C₄×D₄	—	149	4	no	—
295	C₄×D₄	—	149	2	no	—
296	C₄×D₄	—	149	2	no	—
297	C₄×D₄	—	149	2	no	—
298	C₄×D₄	C₂×D₁₄₉	1	4	yes	—
299	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
300	#117	—	149	1	no	—
301	#117	—	149	4	no	—
302	#117	—	149	2	no	—
303	#117	—	149	2	no	—
304	#117	—	149	2	no	—
305	#117	—	149	2	no	—
306	#117	—	149	2	no	—
307	#117	—	149	4	no	—
308	#117	C₂×D₁₄₉	1	1	yes	characteristic
309	#117	C₂×D₁₄₉	1	2	yes	complemented
310	C₂×C₄⋊C₄	—	149	1	no	—
311	C₂×C₄⋊C₄	—	149	2	no	—
312	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
314	C₂×C₂²⋊C₄	—	149	2	no	—
315	C₂×C₄²	—	149	2	no	—
316	C₂⁴	—	149	1	no	—
317	#41	—	2	4	no	—
318	#41	—	298	4	no	—
319	C₂×Q₈	—	149	1	no	—
320	C₂×Q₈	—	149	4	no	—
321	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
322	C₂×D₄	—	149	2	no	—
323	C₂×D₄	—	149	2	no	—
324	C₂×D₄	—	149	2	no	—
325	C₂×D₄	—	149	4	no	—
326	C₂×D₄	—	149	1	no	—
327	C₂×D₄	—	149	2	no	—
328	C₂×D₄	—	149	2	no	—
329	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
330	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
331	C₂²×C₄	—	298	4	no	—
332	C₂²×C₄	—	149	1	no	—
333	C₂²×C₄	—	149	2	no	—
334	C₂²×C₄	—	149	1	no	—
335	C₂²×C₄	—	149	1	no	—
336	C₂²×C₄	—	149	1	no	—
337	C₂²×C₄	—	149	1	no	—
338	C₂²×C₄	—	149	2	no	—
339	C₂²×C₄	—	149	4	no	—
340	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
341	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
342	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
343	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
344	C₄⋊C₄	—	149	1	no	—
345	C₄⋊C₄	—	149	2	no	—
346	C₄⋊C₄	—	149	2	no	—
347	C₄⋊C₄	—	149	4	no	—
348	C₄⋊C₄	—	149	1	no	—
349	C₄⋊C₄	—	149	2	no	—
350	C₄⋊C₄	—	149	2	no	—
351	C₄⋊C₄	—	149	4	no	—
352	C₄⋊C₄	—	149	4	no	—
353	C₄⋊C₄	—	149	2	no	—
354	C₄⋊C₄	—	149	2	no	—
355	C₄⋊C₄	—	149	4	no	—
356	C₄⋊C₄	—	149	4	no	—
357	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
359	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
361	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
362	C₂²⋊C₄	—	149	2	no	—
363	C₂²⋊C₄	—	149	2	no	—
364	C₂²⋊C₄	—	149	4	no	—
365	C₂²⋊C₄	—	149	2	no	—
366	C₂²⋊C₄	—	149	4	no	—
367	C₂²⋊C₄	—	149	4	no	—
368	C₂²⋊C₄	—	149	2	no	—
369	C₂²⋊C₄	—	149	4	no	—
370	C₂²⋊C₄	—	149	4	no	—
371	C₂²⋊C₄	—	149	2	no	—
372	C₂²⋊C₄	—	149	2	no	—
373	C₂²⋊C₄	—	149	2	no	—
374	C₂²⋊C₄	—	149	2	no	—
375	C₂²⋊C₄	—	149	2	no	—
376	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
378	C₄²	—	149	4	no	—
379	C₄²	—	149	4	no	—
380	C₄²	—	149	4	no	—
381	C₄²	—	149	2	no	—
382	C₄²	C₂²×D₁₄₉	1	4	yes	—
383	C₄²	C₂²×D₁₄₉	1	2	yes	—
384	C₂³	—	298	2	no	—
385	C₂³	—	596	1	no	—
386	C₂³	—	596	1	no	—
387	C₂³	—	149	1	no	—
388	C₂³	—	149	1	no	—
389	C₂³	—	149	2	no	—
390	C₂³	C₂³×D₁₄₉	1	2	yes	—
391	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	298	2	no	—
394	Q₈	—	596	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	298	4	no	—
398	D₄	—	298	2	no	—
399	D₄	—	596	2	no	—
400	D₄	—	596	2	no	—
401	D₄	—	596	2	no	—
402	D₄	—	596	4	no	—
403	D₄	—	596	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	298	2	no	—
408	C₂×C₄	—	298	2	no	—
409	C₂×C₄	—	298	2	no	—
410	C₂×C₄	—	298	2	no	—
411	C₂×C₄	—	298	2	no	—
412	C₂×C₄	—	298	4	no	—
413	C₂×C₄	—	596	4	no	—
414	C₂×C₄	—	596	2	no	—
415	C₂×C₄	—	149	1	no	—
416	C₂×C₄	—	149	1	no	—
417	C₂×C₄	—	149	2	no	—
418	C₂×C₄	—	149	2	no	—
419	C₂×C₄	—	149	4	no	—
420	C₂×C₄	—	149	2	no	—
421	C₂×C₄	#14558736	1	4	yes	—
422	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
423	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
424	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
425	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
426	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	298	1	no	—
434	C₂²	—	298	1	no	—
435	C₂²	—	298	2	no	—
436	C₂²	—	298	2	no	—
437	C₂²	—	298	1	no	—
438	C₂²	—	298	1	no	—
439	C₂²	—	298	2	no	—
440	C₂²	—	298	1	no	—
441	C₂²	—	298	1	no	—
442	C₂²	—	596	4	no	—
443	C₂²	C₂×#14558736	1	2	yes	—
444	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	298	1	no	—
450	C₄	—	298	1	no	—
451	C₄	—	298	2	no	—
452	C₄	—	298	2	no	—
453	C₄	—	298	4	no	—
454	C₄	—	298	2	no	—
455	C₄	C₂×#14558736	1	2	yes	—
456	C₄	C₂×#14558736	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	596	1	no	—
460	C₂	—	596	1	no	—
461	C₂	—	596	2	no	—
462	C₂	C₂²×#14558736	1	1	yes	characteristic
463	C₂	#23750460	1	1	yes	characteristic
464	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#520×C₁₄₉	C₂
hypercenter	#520	D₁₄₉
hypocenter	C₁₄₉	#3493
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #23750348	C₂	semidirect
2. #23750343	C₂	semidirect
3. #23750340	C₂	semidirect
4. #23750338	C₂	semidirect
5. #23750325	C₂	semidirect
6. #23750323	C₂	semidirect
7. #23750316	C₂	semidirect
8. #23750310	C₂	semidirect
9. #23750253	C₂	semidirect
10. #23750208	C₂	semidirect
11. #23750203	C₂	semidirect
12. #23750155	C₂	semidirect
13. #23750137	C₂	semidirect
14. #23750132	C₂	semidirect
15. #23750106	C₂	semidirect
16. C₂×#18011869	C₂	semidirect
17. #520×C₁₄₉	C₂	semidirect
20. #18011911	C₂²	semidirect
21. #18011910	C₂²	semidirect
23. #18011906	C₂²	semidirect
25. #18011904	C₂²	semidirect
26. #18011903	C₂²	semidirect
27. #18011902	C₂²	semidirect
28. #18011901	C₂²	semidirect
31. #18011897	C₂²	semidirect
38. #18011890	C₂²	semidirect
42. #18011887	C₂²	semidirect
46. #18011885	C₂²	semidirect
51. #18011882	C₂²	semidirect
54. C₄×Dic₂₉₈	C₂²	semidirect
55. #18011876	C₂²	semidirect
58. #18011873	C₂²	semidirect
62. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
64. #18011870	C₂²	semidirect
69. #18011869	C₂²	semidirect
70. #18011868	C₂²	semidirect
72. C₄⋊C₄×D₁₄₉	C₂²	semidirect
76. C₄×Q₈×C₁₄₉	C₂²	semidirect
78. C₄×D₄×C₁₄₉	C₂²	semidirect
80. #117×C₁₄₉	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
232. C₁₄₉	#3493	semidirect
249. #520	D₁₄₉	semidirect
290. C₄×Q₈	C₂×D₁₄₉	semidirect
299. C₄×D₄	C₂×D₁₄₉	semidirect
309. #117	C₂×D₁₄₉	semidirect
313. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750348	2
#23750343	2
#23750340	2
#23750338	2
#23750325	2
#23750323	2
#23750316	2
#23750310	2
#23750253	2
#23750208	2
#23750203	2
#23750155	2
#23750137	2
#23750132	2
#23750106	2
C₂×#18011869	2
#520×C₁₄₉	2
#3493	149