Subgroups — #27155143

Order 12416.

1160 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261360	C₂	1	1	yes	maximal, characteristic, complemented
2	#20261334	C₂	1	1	yes	maximal, characteristic, complemented
3	#20261331	C₂	1	2	yes	maximal, complemented
4	#20261330	C₂	1	1	yes	maximal, characteristic, complemented
5	#20261328	C₂	1	2	yes	maximal, complemented
6	#20261321	C₂	1	2	yes	maximal, complemented
7	#20261320	C₂	1	2	yes	maximal, complemented
8	#20261317	C₂	1	2	yes	maximal, complemented
9	#20261295	C₂	1	2	yes	maximal, complemented
10	#20261293	C₂	1	1	yes	maximal, characteristic, complemented
11	#20261267	C₂	1	2	yes	maximal, complemented
12	#20261265	C₂	1	2	yes	maximal, complemented
13	#20261263	C₂	1	2	yes	maximal, complemented
14	#20261246	C₂	1	1	yes	maximal, characteristic, complemented
15	#20261244	C₂	1	2	yes	maximal, complemented
16	#20261242	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₉₇	C₂	1	2	yes	maximal, complemented
19	#525×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13095511	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₉₇	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₉₇	C₂²	1	2	yes	—
23	C₂²×C₄×D₉₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₉₇	C₂²	1	2	yes	complemented
25	#15690805	C₂²	1	2	yes	complemented
26	#15690805	C₂²	1	2	yes	complemented
27	#15690803	C₂²	1	2	yes	complemented
28	#15690803	C₂²	1	2	yes	complemented
29	#15690803	C₂²	1	2	yes	complemented
30	#15690803	C₂²	1	2	yes	complemented
31	#15690801	C₂²	1	2	yes	complemented
32	#15690800	C₂²	1	2	yes	complemented
33	#15690800	C₂²	1	2	yes	complemented
34	#15690797	C₂²	1	2	yes	complemented
35	#15690796	C₂²	1	2	yes	complemented
36	#15690796	C₂²	1	2	yes	complemented
37	#15690795	C₂²	1	2	yes	complemented
38	#15690795	C₂²	1	2	yes	complemented
39	#15690794	C₂²	1	2	yes	complemented
40	#15690793	C₂²	1	2	yes	complemented
41	#15690792	C₂²	1	2	yes	complemented
42	#15690792	C₂²	1	2	yes	complemented
43	#15690792	C₂²	1	2	yes	complemented
44	#15690792	C₂²	1	2	yes	complemented
45	#15690791	C₂²	1	2	yes	complemented
46	#15690791	C₂²	1	2	yes	complemented
47	#15690791	C₂²	1	2	yes	complemented
48	#15690790	C₂²	1	2	yes	complemented
49	#15690789	C₂²	1	1	yes	characteristic, complemented
50	#15690789	C₂²	1	1	yes	characteristic, complemented
51	#15690788	C₂²	1	2	yes	complemented
52	#15690788	C₂²	1	2	yes	complemented
53	#15690787	C₂²	1	2	yes	complemented
54	#15690787	C₂²	1	2	yes	complemented
55	#15690786	C₂²	1	2	yes	complemented
56	#15690786	C₂²	1	2	yes	complemented
57	#15690784	C₂²	1	1	yes	characteristic
58	#15690784	C₂²	1	1	yes	characteristic, complemented
59	#15690783	C₂²	1	2	yes	—
60	#15690783	C₂²	1	2	yes	—
61	#15690782	C₂²	1	2	yes	—
62	#15690782	C₂²	1	2	yes	complemented
63	#15690781	C₂²	1	2	yes	—
64	#15690781	C₂²	1	2	yes	—
65	#15690781	C₂²	1	2	yes	complemented
66	#15690780	C₂²	1	2	yes	complemented
67	#15690779	C₂²	1	2	yes	complemented
68	#15690778	C₂²	1	2	yes	complemented
69	#15690778	C₂²	1	2	yes	complemented
70	#15690778	C₂²	1	2	yes	complemented
71	C₄×Dic₁₉₄	C₂²	1	2	yes	complemented
72	C₄×D₃₈₈	C₂²	1	2	yes	complemented
73	D₄×Dic₉₇	C₂²	1	2	yes	complemented
74	#15690772	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
83	#15690770	C₂²	1	2	yes	complemented
84	#15690770	C₂²	1	2	yes	complemented
85	#15690769	C₂²	1	2	yes	complemented
86	#15690769	C₂²	1	1	yes	characteristic, complemented
87	#15690767	C₂²	1	2	yes	complemented
88	C₂×#13095490	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₉₇	C₂²	1	2	yes	complemented
90	C₂×C₂²⋊Dic₉₇	C₂²	1	1	yes	characteristic, complemented
91	C₂×#13095488	C₂²	1	1	yes	characteristic
92	C₂²⋊C₄×D₉₇	C₂²	1	2	yes	—
93	C₂²⋊C₄×D₉₇	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₉₇	C₂²	1	1	yes	characteristic, complemented
95	C₄²×D₉₇	C₂²	1	2	yes	complemented
96	C₂×#41×C₉₇	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₉₇	C₂²	1	1	yes	characteristic, complemented
98	#123×C₉₇	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₉₇	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₉₇	C₂²	1	1	yes	characteristic, complemented
101	#121×C₉₇	C₂²	1	1	yes	characteristic
102	#121×C₉₇	C₂²	1	1	yes	characteristic, complemented
103	#120×C₉₇	C₂²	1	2	yes	complemented
104	C₄×D₄×C₉₇	C₂²	1	2	yes	complemented
105	C₄×D₄×C₉₇	C₂²	1	2	yes	complemented
106	#117×C₉₇	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₉₇	C₂³	1	2	yes	—
108	C₂³×D₉₇	C₂³	1	1	yes	characteristic
109	#13095511	—	4	2	no	—
110	C₂×Dic₁₉₄	C₂³	1	2	yes	—
111	C₂×Dic₁₉₄	C₂³	1	1	yes	characteristic
112	C₂×D₃₈₈	C₂³	1	2	yes	—
113	C₂×D₃₈₈	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊D₉₇	—	2	4	no	—
115	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
122	D₄×D₉₇	—	2	8	no	—
123	C₂²×Dic₉₇	C₂³	1	1	yes	characteristic
124	C₂²×Dic₉₇	C₂³	1	1	yes	characteristic
125	C₂²×Dic₉₇	C₂³	1	1	yes	characteristic
126	C₂²×Dic₉₇	C₂³	1	2	yes	—
127	C₂×C₄×D₉₇	—	4	2	no	—
128	C₂×C₄×D₉₇	—	4	4	no	—
129	C₂×C₄×D₉₇	C₂³	1	2	yes	—
130	C₂×C₄×D₉₇	C₂³	1	2	yes	—
131	C₂×C₄×D₉₇	C₂³	1	2	yes	—
132	C₂×C₄×D₉₇	C₂³	1	2	yes	—
133	C₂×C₄×D₉₇	C₂³	1	2	yes	—
134	C₂×C₄×D₉₇	C₂³	1	2	yes	—
135	C₂×C₄×D₉₇	C₂³	1	2	yes	—
136	C₄⋊Dic₉₇	C₂³	1	2	yes	—
137	C₄⋊Dic₉₇	C₂³	1	2	yes	—
138	C₄⋊Dic₉₇	C₂³	1	2	yes	—
139	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₉₇	C₂³	1	2	yes	—
142	#13095490	C₂³	1	2	yes	—
143	#13095490	C₂³	1	2	yes	—
144	#13095490	C₂³	1	2	yes	—
145	#13095490	C₂³	1	2	yes	—
146	#13095490	C₂³	1	2	yes	—
147	#13095490	C₂³	1	2	yes	—
148	#13095490	C₂³	1	2	yes	—
149	#13095490	C₂³	1	2	yes	—
150	#13095490	C₂³	1	2	yes	—
151	#13095490	C₂³	1	2	yes	—
152	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
153	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
154	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
157	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
158	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
159	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
160	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
161	#13095488	C₂³	1	2	yes	—
162	#13095488	C₂³	1	2	yes	—
163	#13095488	C₂³	1	2	yes	—
164	#13095488	C₂³	1	2	yes	—
165	#13095488	C₂³	1	2	yes	—
166	#13095488	C₂³	1	2	yes	—
167	#13095488	C₂³	1	2	yes	—
168	#13095488	C₂³	1	2	yes	—
169	#13095488	C₂³	1	2	yes	—
170	#13095488	C₂³	1	2	yes	—
171	C₄×Dic₉₇	C₂³	1	2	yes	—
172	C₄×Dic₉₇	C₂³	1	2	yes	—
173	C₄×Dic₉₇	C₂³	1	2	yes	—
174	C₄×Dic₉₇	C₂³	1	2	yes	—
175	C₄×Dic₉₇	C₂³	1	2	yes	—
176	C₂⁴×C₉₇	C₂³	1	1	yes	characteristic
177	#41×C₉₇	—	4	2	no	—
178	C₂×Q₈×C₉₇	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₉₇	C₂³	1	2	yes	—
180	C₂×D₄×C₉₇	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₉₇	C₂³	1	2	yes	—
182	C₂×D₄×C₉₇	C₂³	1	2	yes	—
183	C₂²×C₄×C₉₇	—	4	2	no	—
184	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₉₇	C₂³	1	2	yes	—
186	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₉₇	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
192	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
194	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
200	C₄²×C₉₇	C₂³	1	2	yes	—
201	C₂³×C₉₇	—	2	2	no	—
202	C₂³×C₉₇	—	4	1	no	—
203	C₂³×C₉₇	—	4	1	no	—
204	C₂³×C₉₇	C₂⁴	1	1	yes	characteristic
205	C₂³×C₉₇	C₂⁴	1	1	yes	characteristic
206	C₂³×C₉₇	C₂⁴	1	2	yes	—
207	C₂³×C₉₇	C₂⁴	1	1	yes	characteristic
208	C₂²×D₉₇	—	2	4	no	—
209	C₂²×D₉₇	—	4	1	no	—
210	C₂²×D₉₇	—	4	2	no	—
211	C₂²×D₉₇	—	4	1	no	—
212	C₂²×D₉₇	—	4	2	no	—
213	C₂²×D₉₇	#41	1	4	yes	complemented
214	C₂²×D₉₇	C₂⁴	1	2	yes	—
215	C₂²×D₉₇	C₂⁴	1	2	yes	—
216	Q₈×C₉₇	—	4	1	no	—
217	D₄×C₉₇	—	2	4	no	—
218	D₄×C₉₇	—	4	2	no	—
219	D₄×C₉₇	—	4	2	no	—
220	D₄×C₉₇	—	4	1	no	—
221	C₂×C₄×C₉₇	—	2	2	no	—
222	C₂×C₄×C₉₇	—	2	2	no	—
223	C₂×C₄×C₉₇	—	2	2	no	—
224	C₂×C₄×C₉₇	—	2	4	no	—
225	C₂×C₄×C₉₇	—	4	1	no	—
226	C₂×C₄×C₉₇	—	4	1	no	—
227	C₂×C₄×C₉₇	—	4	1	no	—
228	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
229	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
230	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
233	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
235	C₂²⋊D₉₇	—	2	4	no	—
236	C₂²⋊D₉₇	—	2	4	no	—
237	C₂²⋊D₉₇	—	2	4	no	—
238	C₂²⋊D₉₇	—	2	4	no	—
239	C₂²⋊D₉₇	—	4	2	no	—
240	C₂²⋊D₉₇	—	4	2	no	—
241	C₂²⋊D₉₇	—	4	2	no	—
242	C₂×Dic₉₇	—	2	2	no	—
243	C₂×Dic₉₇	—	4	2	no	—
244	C₂×Dic₉₇	—	4	1	no	—
245	C₂×Dic₉₇	—	4	1	no	—
246	C₂×Dic₉₇	C₂⁴	1	2	yes	—
247	C₂×Dic₉₇	C₂⁴	1	2	yes	—
248	C₂×Dic₉₇	C₂⁴	1	2	yes	—
249	C₂×Dic₉₇	C₂⁴	1	2	yes	—
250	C₂×Dic₉₇	C₂⁴	1	2	yes	—
251	C₂×Dic₉₇	C₂⁴	1	2	yes	—
252	D₃₈₈	—	2	4	no	—
253	D₃₈₈	—	4	1	no	—
254	C₄×D₉₇	—	2	4	no	—
255	C₄×D₉₇	—	2	4	no	—
256	C₄×D₉₇	—	2	4	no	—
257	C₄×D₉₇	—	4	2	no	—
258	C₄×D₉₇	—	4	2	no	—
259	C₄×D₉₇	—	4	2	no	—
260	C₄×D₉₇	—	4	2	no	—
261	Dic₁₉₄	—	4	2	no	—
262	Dic₁₉₄	—	4	1	no	—
263	C₂²×C₉₇	—	2	1	no	—
264	C₂²×C₉₇	—	2	1	no	—
265	C₂²×C₉₇	—	2	1	no	—
266	C₂²×C₉₇	—	2	1	no	—
267	C₂²×C₉₇	—	2	2	no	—
268	C₂²×C₉₇	—	2	2	no	—
269	C₂²×C₉₇	—	2	1	no	—
270	C₂²×C₉₇	—	2	1	no	—
271	C₂²×C₉₇	—	2	1	no	—
272	C₂²×C₉₇	—	2	2	no	—
273	C₂²×C₉₇	—	2	1	no	—
274	C₂²×C₉₇	—	4	4	no	—
275	C₂²×C₉₇	C₂×#41	1	2	yes	—
276	C₂²×C₉₇	C₂⁵	1	1	yes	characteristic
277	C₂×D₉₇	—	2	2	no	—
278	C₂×D₉₇	—	2	2	no	—
279	C₂×D₉₇	—	2	2	no	—
280	C₂×D₉₇	—	2	2	no	—
281	C₂×D₉₇	—	2	2	no	—
282	C₂×D₉₇	—	4	4	no	—
283	C₂×D₉₇	—	4	8	no	—
284	C₂×D₉₇	C₂×#41	1	4	yes	—
285	C₄×C₉₇	—	2	2	no	—
286	C₄×C₉₇	—	2	1	no	—
287	C₄×C₉₇	—	2	1	no	—
288	C₄×C₉₇	—	2	2	no	—
289	C₄×C₉₇	—	2	1	no	—
290	C₄×C₉₇	—	2	2	no	—
291	C₄×C₉₇	H(5,𝔽₂)	1	2	yes	—
292	Dic₉₇	—	2	2	no	—
293	Dic₉₇	—	2	2	no	—
294	Dic₉₇	—	2	2	no	—
295	Dic₉₇	—	2	2	no	—
296	Dic₉₇	—	2	2	no	—
297	Dic₉₇	—	2	2	no	—
298	C₂×C₉₇	—	2	2	no	—
299	C₂×C₉₇	—	4	2	no	—
300	C₂×C₉₇	—	4	1	no	—
301	C₂×C₉₇	—	4	1	no	—
302	C₂×C₉₇	C₂²×#41	1	1	yes	characteristic
303	C₂×C₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₉₇	#585	1	1	yes	characteristic
305	D₉₇	—	2	4	no	—
306	D₉₇	—	4	2	no	—
307	#3459	—	97	1	no	maximal, Sylow
308	C₉₇	#3459	1	1	yes	characteristic, complemented, Sylow
309	#543	—	97	1	no	—
310	#539	—	97	2	no	—
311	#539	—	97	2	no	—
312	#539	—	97	1	no	—
313	#539	—	97	1	no	—
314	#538	—	97	2	no	—
315	#538	—	97	2	no	—
316	#538	—	97	2	no	—
317	#534	—	97	1	no	—
318	#534	—	97	2	no	—
319	#529	—	97	2	no	—
320	#529	—	97	2	no	—
321	#529	—	97	2	no	—
322	#525	—	97	2	no	—
323	#525	—	97	1	no	—
324	#525	—	97	2	no	—
325	#525	D₉₇	1	1	yes	characteristic, complemented
326	C₂×C₄×D₄	—	97	1	no	—
327	C₂×C₄×D₄	—	97	2	no	—
328	C₂×#41	—	97	1	no	—
329	C₂×#41	C₂×D₉₇	1	1	yes	characteristic, complemented
330	C₂²×D₄	—	97	1	no	—
331	C₂²×D₄	—	97	2	no	—
332	C₂³×C₄	—	97	1	no	—
333	C₂³×C₄	—	97	2	no	—
334	C₂³×C₄	C₂×D₉₇	1	1	yes	characteristic, complemented
335	#126	—	97	2	no	—
336	#126	—	97	2	no	—
337	#126	—	97	2	no	—
338	#126	—	97	2	no	—
339	#126	—	97	2	no	—
340	#126	—	97	2	no	—
341	#125	—	97	2	no	—
342	#125	—	97	2	no	—
343	#125	—	97	2	no	—
344	#124	—	97	2	no	—
345	#124	—	97	2	no	—
346	#124	—	97	2	no	—
347	#123	—	97	2	no	—
348	#123	—	97	2	no	—
349	#123	—	97	2	no	—
350	#123	—	97	2	no	—
351	#123	—	97	2	no	—
352	#123	—	97	2	no	—
353	#123	—	97	2	no	—
354	#123	—	97	2	no	—
355	#123	—	97	2	no	—
356	#123	—	97	2	no	—
357	#123	—	97	2	no	—
358	#123	C₂×D₉₇	1	2	yes	complemented
359	C₂²⋊Q₈	—	97	2	no	—
360	C₂²⋊Q₈	—	97	2	no	—
361	C₂²⋊Q₈	—	97	1	no	—
362	C₂²⋊Q₈	—	97	1	no	—
363	C₂²⋊Q₈	—	97	2	no	—
364	C₂²⋊Q₈	—	97	2	no	—
365	C₂²⋊Q₈	—	97	2	no	—
366	C₂²⋊Q₈	—	97	2	no	—
367	C₂²⋊Q₈	—	97	2	no	—
368	C₂²⋊Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
369	C₂²⋊Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
370	#121	—	97	2	no	—
371	#121	—	97	2	no	—
372	#121	—	97	2	no	—
373	#121	—	97	2	no	—
374	#121	—	97	2	no	—
375	#121	—	97	1	no	—
376	#121	—	97	1	no	—
377	#121	—	97	2	no	—
378	#121	—	97	2	no	—
379	#121	C₂×D₉₇	1	1	yes	characteristic
380	#121	C₂×D₉₇	1	1	yes	characteristic, complemented
381	#120	—	97	2	no	—
382	#120	—	97	2	no	—
383	#120	—	97	2	no	—
384	#120	—	97	2	no	—
385	#120	—	97	2	no	—
386	#120	C₂×D₉₇	1	2	yes	complemented
387	C₄×Q₈	—	97	2	no	—
388	C₄×D₄	—	97	2	no	—
389	C₄×D₄	—	97	2	no	—
390	C₄×D₄	—	97	2	no	—
391	C₄×D₄	—	97	2	no	—
392	C₄×D₄	—	97	2	no	—
393	C₄×D₄	—	97	2	no	—
394	C₄×D₄	—	97	2	no	—
395	C₄×D₄	—	97	2	no	—
396	C₄×D₄	—	97	2	no	—
397	C₄×D₄	—	97	2	no	—
398	C₄×D₄	—	97	2	no	—
399	C₄×D₄	—	97	2	no	—
400	C₄×D₄	—	97	2	no	—
401	C₄×D₄	C₂×D₉₇	1	2	yes	complemented
402	C₄×D₄	C₂×D₉₇	1	2	yes	complemented
403	#117	—	97	2	no	—
404	#117	—	97	1	no	—
405	#117	—	97	2	no	—
406	#117	C₂×D₉₇	1	1	yes	characteristic, complemented
407	C₂×C₄⋊C₄	—	97	1	no	—
408	C₂×C₄⋊C₄	—	97	2	no	—
409	C₂×C₂²⋊C₄	—	97	1	no	—
410	C₂×C₂²⋊C₄	—	97	1	no	—
411	C₂×C₂²⋊C₄	—	97	2	no	—
412	C₂×C₂²⋊C₄	—	97	2	no	—
413	C₂×C₄²	—	97	1	no	—
414	C₂×C₄²	—	97	2	no	—
415	C₂⁴	—	97	1	no	—
416	C₂⁴	—	97	2	no	—
417	C₂⁴	C₂²×D₉₇	1	1	yes	characteristic
418	#41	—	4	2	no	—
419	#41	—	388	2	no	—
420	C₂×Q₈	—	97	2	no	—
421	C₂×Q₈	—	97	1	no	—
422	C₂×Q₈	C₂²×D₉₇	1	1	yes	characteristic
423	C₂×D₄	—	97	2	no	—
424	C₂×D₄	—	97	2	no	—
425	C₂×D₄	—	97	2	no	—
426	C₂×D₄	—	97	2	no	—
427	C₂×D₄	—	97	2	no	—
428	C₂×D₄	—	97	2	no	—
429	C₂×D₄	—	97	2	no	—
430	C₂×D₄	—	97	1	no	—
431	C₂×D₄	—	97	2	no	—
432	C₂×D₄	—	194	8	no	—
433	C₂×D₄	—	194	4	no	—
434	C₂×D₄	C₂²×D₉₇	1	2	yes	—
435	C₂×D₄	C₂²×D₉₇	1	2	yes	—
436	C₂×D₄	C₂²×D₉₇	1	1	yes	characteristic
437	C₂×D₄	C₂²×D₉₇	1	2	yes	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	97	1	no	—
440	C₂²×C₄	—	97	1	no	—
441	C₂²×C₄	—	97	2	no	—
442	C₂²×C₄	—	97	1	no	—
443	C₂²×C₄	—	97	2	no	—
444	C₂²×C₄	—	97	2	no	—
445	C₂²×C₄	—	97	2	no	—
446	C₂²×C₄	—	97	2	no	—
447	C₂²×C₄	—	97	2	no	—
448	C₂²×C₄	—	97	2	no	—
449	C₂²×C₄	—	97	2	no	—
450	C₂²×C₄	—	388	2	no	—
451	C₂²×C₄	—	388	4	no	—
452	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₉₇	1	2	yes	—
454	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₉₇	1	1	yes	characteristic
459	C₄⋊C₄	—	97	2	no	—
460	C₄⋊C₄	—	97	2	no	—
461	C₄⋊C₄	—	97	2	no	—
462	C₄⋊C₄	—	97	2	no	—
463	C₄⋊C₄	—	97	2	no	—
464	C₄⋊C₄	—	97	2	no	—
465	C₄⋊C₄	—	97	2	no	—
466	C₄⋊C₄	—	97	2	no	—
467	C₄⋊C₄	—	97	2	no	—
468	C₄⋊C₄	—	97	2	no	—
469	C₄⋊C₄	—	97	2	no	—
470	C₄⋊C₄	—	97	2	no	—
471	C₄⋊C₄	—	97	1	no	—
472	C₄⋊C₄	—	97	2	no	—
473	C₄⋊C₄	—	97	1	no	—
474	C₄⋊C₄	—	97	2	no	—
475	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
476	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
479	C₂²⋊C₄	—	97	2	no	—
480	C₂²⋊C₄	—	97	2	no	—
481	C₂²⋊C₄	—	97	2	no	—
482	C₂²⋊C₄	—	97	2	no	—
483	C₂²⋊C₄	—	97	2	no	—
484	C₂²⋊C₄	—	97	2	no	—
485	C₂²⋊C₄	—	97	2	no	—
486	C₂²⋊C₄	—	97	2	no	—
487	C₂²⋊C₄	—	97	2	no	—
488	C₂²⋊C₄	—	97	2	no	—
489	C₂²⋊C₄	—	97	2	no	—
490	C₂²⋊C₄	—	97	2	no	—
491	C₂²⋊C₄	—	97	2	no	—
492	C₂²⋊C₄	—	97	2	no	—
493	C₂²⋊C₄	—	97	2	no	—
494	C₂²⋊C₄	—	97	2	no	—
495	C₂²⋊C₄	—	97	2	no	—
496	C₂²⋊C₄	—	97	2	no	—
497	C₂²⋊C₄	—	97	2	no	—
498	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
503	C₄²	—	97	2	no	—
504	C₄²	—	97	2	no	—
505	C₄²	—	97	2	no	—
506	C₄²	—	97	2	no	—
507	C₄²	—	97	2	no	—
508	C₄²	C₂²×D₉₇	1	2	yes	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	97	4	no	—
513	C₂³	—	97	2	no	—
514	C₂³	—	97	2	no	—
515	C₂³	—	388	1	no	—
516	C₂³	—	388	2	no	—
517	C₂³	—	388	1	no	—
518	C₂³	—	388	2	no	—
519	C₂³	—	194	4	no	—
520	C₂³	C₂³×D₉₇	1	2	yes	—
521	C₂³	C₂³×D₉₇	1	1	yes	characteristic
522	C₂³	C₂³×D₉₇	1	1	yes	characteristic
523	C₂³	C₂³×D₉₇	1	1	yes	characteristic
524	Q₈	—	4	1	no	—
525	Q₈	—	388	1	no	—
526	Q₈	—	388	2	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	388	1	no	—
532	D₄	—	388	2	no	—
533	D₄	—	388	2	no	—
534	D₄	—	388	2	no	—
535	D₄	—	194	4	no	—
536	D₄	—	194	4	no	—
537	D₄	—	194	4	no	—
538	D₄	—	194	4	no	—
539	D₄	—	194	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	97	2	no	—
548	C₂×C₄	—	97	2	no	—
549	C₂×C₄	—	97	2	no	—
550	C₂×C₄	—	97	2	no	—
551	C₂×C₄	—	97	2	no	—
552	C₂×C₄	—	97	2	no	—
553	C₂×C₄	—	388	2	no	—
554	C₂×C₄	—	388	2	no	—
555	C₂×C₄	—	388	2	no	—
556	C₂×C₄	—	388	2	no	—
557	C₂×C₄	—	388	1	no	—
558	C₂×C₄	—	388	2	no	—
559	C₂×C₄	—	388	1	no	—
560	C₂×C₄	—	194	4	no	—
561	C₂×C₄	—	194	2	no	—
562	C₂×C₄	—	194	4	no	—
563	C₂×C₄	—	194	4	no	—
564	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₉₇	1	2	yes	—
566	C₂×C₄	C₂³×D₉₇	1	2	yes	—
567	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₉₇	1	2	yes	—
569	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	97	4	no	—
584	C₂²	—	388	4	no	—
585	C₂²	—	388	8	no	—
586	C₂²	—	194	2	no	—
587	C₂²	—	194	2	no	—
588	C₂²	—	194	2	no	—
589	C₂²	—	194	2	no	—
590	C₂²	—	194	2	no	—
591	C₂²	#41×D₉₇	1	2	yes	—
592	C₂²	C₂⁴×D₉₇	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	194	2	no	—
600	C₄	—	194	2	no	—
601	C₄	—	194	2	no	—
602	C₄	—	194	2	no	—
603	C₄	—	194	2	no	—
604	C₄	—	194	2	no	—
605	C₄	#15690855	1	2	yes	—
606	C₂	—	2	2	no	—
607	C₂	—	4	1	no	—
608	C₂	—	4	1	no	—
609	C₂	—	4	2	no	—
610	C₂	—	388	2	no	—
611	C₂	—	194	4	no	—
612	C₂	C₂×#41×D₉₇	1	1	yes	characteristic
613	C₂	C₂×#15690855	1	1	yes	characteristic
614	C₂	#20261571	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₉₇
commutator, socle, cosocle	C₂²×C₉₇	C₂⁵
Frattini	C₂²	C₂⁴×D₉₇
Fitting	#525×C₉₇	C₂
hypercenter	#525	D₉₇
hypocenter	C₉₇	#3459
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #20261360	C₂	semidirect
2. #20261334	C₂	semidirect
3. #20261331	C₂	semidirect
4. #20261330	C₂	semidirect
5. #20261328	C₂	semidirect
6. #20261321	C₂	semidirect
7. #20261320	C₂	semidirect
8. #20261317	C₂	semidirect
9. #20261295	C₂	semidirect
10. #20261293	C₂	semidirect
11. #20261267	C₂	semidirect
12. #20261265	C₂	semidirect
13. #20261263	C₂	semidirect
14. #20261246	C₂	semidirect
15. #20261244	C₂	semidirect
16. #20261242	C₂	semidirect
17. C₂×C₄×C₂²⋊D₉₇	C₂	semidirect
18. C₄×D₄×D₉₇	C₂	semidirect
19. #525×C₉₇	C₂	semidirect
20. C₂×#13095511	C₂²	semidirect
24. C₂²×C₄×D₉₇	C₂²	semidirect
25. #15690805	C₂²	semidirect
26. #15690805	C₂²	semidirect
27. #15690803	C₂²	semidirect
28. #15690803	C₂²	semidirect
29. #15690803	C₂²	semidirect
30. #15690803	C₂²	semidirect
31. #15690801	C₂²	semidirect
32. #15690800	C₂²	semidirect
33. #15690800	C₂²	semidirect
34. #15690797	C₂²	semidirect
35. #15690796	C₂²	semidirect
36. #15690796	C₂²	semidirect
37. #15690795	C₂²	semidirect
38. #15690795	C₂²	semidirect
39. #15690794	C₂²	semidirect
40. #15690793	C₂²	semidirect
41. #15690792	C₂²	semidirect
42. #15690792	C₂²	semidirect
43. #15690792	C₂²	semidirect
44. #15690792	C₂²	semidirect
45. #15690791	C₂²	semidirect
46. #15690791	C₂²	semidirect
47. #15690791	C₂²	semidirect
48. #15690790	C₂²	semidirect
49. #15690789	C₂²	semidirect
50. #15690789	C₂²	semidirect
51. #15690788	C₂²	semidirect
52. #15690788	C₂²	semidirect
53. #15690787	C₂²	semidirect
54. #15690787	C₂²	semidirect
55. #15690786	C₂²	semidirect
56. #15690786	C₂²	semidirect
58. #15690784	C₂²	semidirect
62. #15690782	C₂²	semidirect
65. #15690781	C₂²	semidirect
66. #15690780	C₂²	semidirect
67. #15690779	C₂²	semidirect
68. #15690778	C₂²	semidirect
69. #15690778	C₂²	semidirect
70. #15690778	C₂²	semidirect
71. C₄×Dic₁₉₄	C₂²	semidirect
72. C₄×D₃₈₈	C₂²	semidirect
73. D₄×Dic₉₇	C₂²	semidirect
74. #15690772	C₂²	semidirect
75. C₄×C₂²⋊D₉₇	C₂²	semidirect
76. C₄×C₂²⋊D₉₇	C₂²	semidirect
77. C₄×C₂²⋊D₉₇	C₂²	semidirect
78. C₄×C₂²⋊D₉₇	C₂²	semidirect
79. C₄×C₂²⋊D₉₇	C₂²	semidirect
80. C₄×C₂²⋊D₉₇	C₂²	semidirect
81. C₄×C₂²⋊D₉₇	C₂²	semidirect
82. C₄×C₂²⋊D₉₇	C₂²	semidirect
83. #15690770	C₂²	semidirect
84. #15690770	C₂²	semidirect
85. #15690769	C₂²	semidirect
86. #15690769	C₂²	semidirect
87. #15690767	C₂²	semidirect
88. C₂×#13095490	C₂²	semidirect
89. C₄⋊C₄×D₉₇	C₂²	semidirect
90. C₂×C₂²⋊Dic₉₇	C₂²	semidirect
93. C₂²⋊C₄×D₉₇	C₂²	semidirect
94. C₂×C₄×Dic₉₇	C₂²	semidirect
95. C₄²×D₉₇	C₂²	semidirect
96. C₂×#41×C₉₇	C₂²	semidirect
97. C₂³×C₄×C₉₇	C₂²	semidirect
98. #123×C₉₇	C₂²	semidirect
99. C₂²⋊Q₈×C₉₇	C₂²	semidirect
100. C₂²⋊Q₈×C₉₇	C₂²	semidirect
102. #121×C₉₇	C₂²	semidirect
103. #120×C₉₇	C₂²	semidirect
104. C₄×D₄×C₉₇	C₂²	semidirect
105. C₄×D₄×C₉₇	C₂²	semidirect
106. #117×C₉₇	C₂²	semidirect
213. C₂²×D₉₇	#41	semidirect
308. C₉₇	#3459	semidirect
325. #525	D₉₇	semidirect
329. C₂×#41	C₂×D₉₇	semidirect
334. C₂³×C₄	C₂×D₉₇	semidirect
358. #123	C₂×D₉₇	semidirect
368. C₂²⋊Q₈	C₂×D₉₇	semidirect
369. C₂²⋊Q₈	C₂×D₉₇	semidirect
380. #121	C₂×D₉₇	semidirect
386. #120	C₂×D₉₇	semidirect
401. C₄×D₄	C₂×D₉₇	semidirect
402. C₄×D₄	C₂×D₉₇	semidirect
406. #117	C₂×D₉₇	semidirect

Maximal subgroups

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

subgroup	index
#20261360	2
#20261334	2
#20261331	2
#20261330	2
#20261328	2
#20261321	2
#20261320	2
#20261317	2
#20261295	2
#20261293	2
#20261267	2
#20261265	2
#20261263	2
#20261246	2
#20261244	2
#20261242	2
C₂×C₄×C₂²⋊D₉₇	2
C₄×D₄×D₉₇	2
#525×C₉₇	2
#3459	97