Subgroups — C₆₇×#59411 #30738662

Order 17152.

2584 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2701	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2544	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2447	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2445	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2432	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2427	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2425	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2422	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2349	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2339	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	#559×C₆₇	—	2	8	no	—
20	#550×C₆₇	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#127×C₆₇	C₂²	1	2	yes	—
23	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	C₂²	1	2	yes	—
27	C₂×#123×C₆₇	C₂²	1	4	yes	—
28	C₂×#123×C₆₇	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₂×#121×C₆₇	C₂²	1	4	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
42	#398×C₆₇	C₂²	1	4	yes	—
43	#397×C₆₇	C₂²	1	4	yes	—
44	#397×C₆₇	C₂²	1	4	yes	—
45	#396×C₆₇	C₂²	1	4	yes	—
46	#394×C₆₇	C₂²	1	4	yes	—
47	#394×C₆₇	C₂²	1	4	yes	—
48	#394×C₆₇	C₂²	1	4	yes	—
49	#394×C₆₇	C₂²	1	4	yes	—
50	#391×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	1	yes	characteristic
53	#391×C₆₇	C₂²	1	1	yes	characteristic
54	#391×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	2	yes	—
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#386×C₆₇	C₂²	1	4	yes	—
68	#386×C₆₇	C₂²	1	4	yes	—
69	#386×C₆₇	C₂²	1	4	yes	—
70	#385×C₆₇	C₂²	1	4	yes	—
71	#385×C₆₇	C₂²	1	4	yes	—
72	#385×C₆₇	C₂²	1	4	yes	—
73	#384×C₆₇	C₂²	1	1	yes	characteristic
74	#384×C₆₇	C₂²	1	1	yes	characteristic
75	#382×C₆₇	C₂²	1	1	yes	characteristic
76	#381×C₆₇	C₂²	1	4	yes	—
77	#380×C₆₇	C₂²	1	2	yes	—
78	#380×C₆₇	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
83	C₂×#95×C₆₇	C₂²	1	4	yes	—
84	C₄³×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₇	—	2	8	no	—
86	C₂×#41×C₆₇	—	2	8	no	—
87	C₂×#41×C₆₇	—	4	4	no	—
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
98	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
99	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
101	C₄⋊Q₈×C₆₇	—	2	4	no	—
102	#127×C₆₇	—	2	8	no	—
103	#127×C₆₇	D₄	1	8	yes	—
104	#124×C₆₇	—	2	8	no	—
105	#124×C₆₇	—	2	8	no	—
106	#124×C₆₇	—	2	4	no	—
107	#123×C₆₇	—	2	16	no	—
108	#123×C₆₇	—	4	8	no	—
109	C₂²⋊Q₈×C₆₇	—	4	4	no	—
110	#121×C₆₇	—	2	8	no	—
111	#121×C₆₇	—	2	16	no	—
112	C₄×Q₈×C₆₇	—	2	4	no	—
113	C₄×Q₈×C₆₇	—	2	4	no	—
114	C₄×Q₈×C₆₇	—	2	4	no	—
115	C₄×D₄×C₆₇	—	2	8	no	—
116	C₄×D₄×C₆₇	—	2	8	no	—
117	C₄×D₄×C₆₇	—	2	8	no	—
118	C₄×D₄×C₆₇	—	2	4	no	—
119	C₄×D₄×C₆₇	—	2	8	no	—
120	C₄×D₄×C₆₇	—	4	4	no	—
121	C₄×D₄×C₆₇	—	4	4	no	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	#95×C₆₇	C₂³	1	2	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	2	yes	—
169	#95×C₆₇	C₂³	1	2	yes	—
170	#95×C₆₇	C₂³	1	2	yes	—
171	#95×C₆₇	C₂³	1	2	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
175	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
176	#41×C₆₇	—	4	32	no	—
177	C₂×Q₈×C₆₇	—	2	2	no	—
178	C₂×Q₈×C₆₇	—	2	2	no	—
179	C₂×Q₈×C₆₇	—	2	2	no	—
180	C₂×Q₈×C₆₇	—	2	2	no	—
181	C₂×Q₈×C₆₇	—	2	2	no	—
182	C₂×Q₈×C₆₇	—	2	2	no	—
183	C₂×Q₈×C₆₇	—	2	2	no	—
184	C₂×Q₈×C₆₇	—	2	2	no	—
185	C₂×Q₈×C₆₇	#41	1	4	yes	—
186	C₂×D₄×C₆₇	—	2	8	no	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	2	2	no	—
189	C₂×D₄×C₆₇	—	2	4	no	—
190	C₂×D₄×C₆₇	—	2	4	no	—
191	C₂×D₄×C₆₇	—	2	2	no	—
192	C₂×D₄×C₆₇	—	2	8	no	—
193	C₂×D₄×C₆₇	—	2	4	no	—
194	C₂×D₄×C₆₇	—	2	4	no	—
195	C₂×D₄×C₆₇	—	2	2	no	—
196	C₂×D₄×C₆₇	—	4	2	no	—
197	C₂×D₄×C₆₇	—	4	2	no	—
198	C₂×D₄×C₆₇	—	4	4	no	—
199	C₂×D₄×C₆₇	—	4	4	no	—
200	C₂×D₄×C₆₇	—	4	4	no	—
201	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
202	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
203	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
204	C₂²×C₄×C₆₇	—	2	8	no	—
205	C₂²×C₄×C₆₇	—	2	8	no	—
206	C₂²×C₄×C₆₇	—	2	4	no	—
207	C₂²×C₄×C₆₇	—	2	8	no	—
208	C₂²×C₄×C₆₇	—	2	4	no	—
209	C₂²×C₄×C₆₇	—	2	4	no	—
210	C₂²×C₄×C₆₇	—	2	8	no	—
211	C₂²×C₄×C₆₇	—	4	4	no	—
212	C₂²×C₄×C₆₇	—	4	4	no	—
213	C₂²×C₄×C₆₇	—	4	4	no	—
214	C₂²×C₄×C₆₇	—	4	4	no	—
215	C₂²×C₄×C₆₇	—	4	4	no	—
216	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₆₇	—	2	2	no	—
232	C₄⋊C₄×C₆₇	—	2	2	no	—
233	C₄⋊C₄×C₆₇	—	2	2	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	4	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	4	2	no	—
244	C₄⋊C₄×C₆₇	—	4	2	no	—
245	C₄⋊C₄×C₆₇	—	4	4	no	—
246	C₄⋊C₄×C₆₇	—	4	4	no	—
247	C₂²⋊C₄×C₆₇	—	2	8	no	—
248	C₂²⋊C₄×C₆₇	—	2	8	no	—
249	C₂²⋊C₄×C₆₇	—	2	8	no	—
250	C₂²⋊C₄×C₆₇	—	2	8	no	—
251	C₂²⋊C₄×C₆₇	—	2	4	no	—
252	C₂²⋊C₄×C₆₇	—	2	8	no	—
253	C₂²⋊C₄×C₆₇	—	2	4	no	—
254	C₂²⋊C₄×C₆₇	—	2	4	no	—
255	C₂²⋊C₄×C₆₇	—	2	8	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	4	2	no	—
258	C₂²⋊C₄×C₆₇	—	4	4	no	—
259	C₂²⋊C₄×C₆₇	—	4	4	no	—
260	C₂²⋊C₄×C₆₇	—	4	4	no	—
261	C₄²×C₆₇	—	2	4	no	—
262	C₄²×C₆₇	—	2	4	no	—
263	C₄²×C₆₇	—	2	4	no	—
264	C₄²×C₆₇	—	2	2	no	—
265	C₄²×C₆₇	—	2	2	no	—
266	C₄²×C₆₇	—	2	2	no	—
267	C₄²×C₆₇	—	2	2	no	—
268	C₄²×C₆₇	—	4	1	no	—
269	C₄²×C₆₇	C₂×D₄	1	4	yes	—
270	C₄²×C₆₇	#41	1	4	yes	complemented
271	C₂³×C₆₇	—	2	4	no	—
272	C₂³×C₆₇	—	2	4	no	—
273	C₂³×C₆₇	—	2	4	no	—
274	C₂³×C₆₇	—	2	4	no	—
275	C₂³×C₆₇	—	2	4	no	—
276	C₂³×C₆₇	—	2	4	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	2	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	C₂²×D₄	1	8	yes	—
285	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
286	Q₈×C₆₇	—	2	8	no	—
287	Q₈×C₆₇	—	4	4	no	—
288	Q₈×C₆₇	—	4	4	no	—
289	D₄×C₆₇	—	2	16	no	—
290	D₄×C₆₇	—	2	16	no	—
291	D₄×C₆₇	—	4	8	no	—
292	D₄×C₆₇	—	4	16	no	—
293	D₄×C₆₇	—	4	4	no	—
294	D₄×C₆₇	—	8	8	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	1	no	—
300	C₂×C₄×C₆₇	—	2	1	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	4	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	1	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	1	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	4	16	no	—
330	C₂×C₄×C₆₇	—	4	8	no	—
331	C₂×C₄×C₆₇	—	8	8	no	—
332	C₂×C₄×C₆₇	—	8	8	no	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
337	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
338	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
339	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
340	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
341	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
342	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
344	C₂²×C₆₇	—	2	8	no	—
345	C₂²×C₆₇	—	2	8	no	—
346	C₂²×C₆₇	—	2	8	no	—
347	C₂²×C₆₇	—	4	4	no	—
348	C₂²×C₆₇	—	4	4	no	—
349	C₂²×C₆₇	—	4	4	no	—
350	C₂²×C₆₇	—	4	4	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	—	4	2	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
359	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
361	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	C₂²×C₆₇	#585	1	1	yes	characteristic
365	C₄×C₆₇	—	2	4	no	—
366	C₄×C₆₇	—	2	2	no	—
367	C₄×C₆₇	—	2	2	no	—
368	C₄×C₆₇	—	2	2	no	—
369	C₄×C₆₇	—	2	2	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	4	no	—
377	C₄×C₆₇	—	4	1	no	—
378	C₄×C₆₇	#546	1	4	yes	—
379	C₄×C₆₇	#547	1	4	yes	—
380	#59411	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₆₇	—	4	8	no	—
382	C₂×C₆₇	—	8	2	no	—
383	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
384	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
385	C₂×C₆₇	#3480	1	1	yes	characteristic
386	C₂×C₆₇	#3496	1	1	yes	characteristic
387	C₂×C₆₇	#3508	1	1	yes	characteristic
388	C₂×C₆₇	#3522	1	1	yes	characteristic
389	C₂×C₆₇	#3554	1	1	yes	characteristic
390	C₂×#559	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂×#550	C₂×C₆₇	1	1	yes	characteristic
392	#2701	C₂×C₆₇	1	4	yes	complemented
393	#2582	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#2544	C₂×C₆₇	1	2	yes	complemented
395	#2538	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#2447	C₂×C₆₇	1	2	yes	complemented
397	#2445	C₂×C₆₇	1	2	yes	complemented
398	#2432	C₂×C₆₇	1	2	yes	complemented
399	#2427	C₂×C₆₇	1	2	yes	complemented
400	#2425	C₂×C₆₇	1	4	yes	complemented
401	#2422	C₂×C₆₇	1	2	yes	complemented
402	#2349	C₂×C₆₇	1	2	yes	complemented
403	#2339	C₂×C₆₇	1	2	yes	complemented
404	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
405	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
406	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
407	C₆₇	#59411	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²×#41	C₂²×C₆₇	1	2	yes	—
409	#559	—	2	8	no	—
410	#550	—	2	8	no	—
411	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#127	C₂²×C₆₇	1	2	yes	—
413	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×#124	C₂²×C₆₇	1	2	yes	—
415	C₂×#124	C₂²×C₆₇	1	2	yes	—
416	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×#123	C₂²×C₆₇	1	4	yes	—
418	C₂×#123	C₂²×C₆₇	1	4	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
420	C₂×#121	C₂²×C₆₇	1	2	yes	—
421	C₂×#121	C₂²×C₆₇	1	4	yes	—
422	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
432	#398	C₂²×C₆₇	1	4	yes	—
433	#397	C₂²×C₆₇	1	4	yes	—
434	#397	C₂²×C₆₇	1	4	yes	—
435	#396	C₂²×C₆₇	1	4	yes	—
436	#394	C₂²×C₆₇	1	4	yes	—
437	#394	C₂²×C₆₇	1	4	yes	—
438	#394	C₂²×C₆₇	1	4	yes	—
439	#394	C₂²×C₆₇	1	4	yes	—
440	#391	C₂²×C₆₇	1	1	yes	characteristic
441	#391	C₂²×C₆₇	1	1	yes	characteristic
442	#391	C₂²×C₆₇	1	2	yes	—
443	#391	C₂²×C₆₇	1	2	yes	—
444	#391	C₂²×C₆₇	1	1	yes	characteristic
445	#390	C₂²×C₆₇	1	2	yes	—
446	#390	C₂²×C₆₇	1	2	yes	—
447	#390	C₂²×C₆₇	1	2	yes	—
448	#390	C₂²×C₆₇	1	1	yes	characteristic
449	#390	C₂²×C₆₇	1	2	yes	—
450	#389	C₂²×C₆₇	1	2	yes	—
451	#389	C₂²×C₆₇	1	2	yes	—
452	#389	C₂²×C₆₇	1	2	yes	—
453	#389	C₂²×C₆₇	1	2	yes	—
454	#389	C₂²×C₆₇	1	2	yes	—
455	#388	C₂²×C₆₇	1	2	yes	—
456	#388	C₂²×C₆₇	1	2	yes	—
457	#386	C₂²×C₆₇	1	4	yes	—
458	#386	C₂²×C₆₇	1	4	yes	—
459	#386	C₂²×C₆₇	1	4	yes	—
460	#385	C₂²×C₆₇	1	4	yes	—
461	#385	C₂²×C₆₇	1	4	yes	—
462	#385	C₂²×C₆₇	1	4	yes	—
463	#384	C₂²×C₆₇	1	1	yes	characteristic
464	#384	C₂²×C₆₇	1	1	yes	characteristic
465	#382	C₂²×C₆₇	1	1	yes	characteristic
466	#381	C₂²×C₆₇	1	4	yes	—
467	#380	C₂²×C₆₇	1	2	yes	—
468	#380	C₂²×C₆₇	1	4	yes	—
469	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
473	C₂×#95	C₂²×C₆₇	1	4	yes	—
474	C₄³	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×#41	—	2	8	no	—
476	C₂×#41	—	2	8	no	—
477	C₂×#41	—	4	4	no	—
478	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
483	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
484	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
485	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
486	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
487	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
488	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
489	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
490	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
491	C₄⋊Q₈	—	2	4	no	—
492	#127	—	2	8	no	—
493	#127	D₄×C₆₇	1	8	yes	—
494	#124	—	2	8	no	—
495	#124	—	2	8	no	—
496	#124	—	2	4	no	—
497	#123	—	2	16	no	—
498	#123	—	4	8	no	—
499	C₂²⋊Q₈	—	4	4	no	—
500	#121	—	2	8	no	—
501	#121	—	2	16	no	—
502	C₄×Q₈	—	2	4	no	—
503	C₄×Q₈	—	2	4	no	—
504	C₄×Q₈	—	2	4	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	8	no	—
510	C₄×D₄	—	4	4	no	—
511	C₄×D₄	—	4	4	no	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
552	#95	C₂³×C₆₇	1	2	yes	—
553	#95	C₂³×C₆₇	1	2	yes	—
554	#95	C₂³×C₆₇	1	4	yes	—
555	#95	C₂³×C₆₇	1	4	yes	—
556	#95	C₂³×C₆₇	1	2	yes	—
557	#95	C₂³×C₆₇	1	2	yes	—
558	#95	C₂³×C₆₇	1	2	yes	—
559	#95	C₂³×C₆₇	1	2	yes	—
560	#95	C₂³×C₆₇	1	2	yes	—
561	#95	C₂³×C₆₇	1	2	yes	—
562	#95	C₂³×C₆₇	1	4	yes	—
563	#95	C₂³×C₆₇	1	4	yes	—
564	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
565	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
566	#41	—	4	32	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	#41×C₆₇	1	4	yes	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	4	no	—
591	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
592	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
593	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	8	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	8	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	4	no	—
635	C₄⋊C₄	—	4	4	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	4	4	no	—
648	C₂²⋊C₄	—	4	4	no	—
649	C₂²⋊C₄	—	4	4	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	4	1	no	—
659	C₄²	C₂×D₄×C₆₇	1	4	yes	—
660	C₄²	#41×C₆₇	1	4	yes	complemented
661	C₂³	—	2	4	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	C₂²×D₄×C₆₇	1	8	yes	—
675	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
676	Q₈	—	2	8	no	—
677	Q₈	—	4	4	no	—
678	Q₈	—	4	4	no	—
679	D₄	—	2	16	no	—
680	D₄	—	2	16	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	16	no	—
683	D₄	—	4	4	no	—
684	D₄	—	8	8	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	16	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	8	8	no	—
722	C₂×C₄	—	8	8	no	—
723	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
724	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
726	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
727	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
728	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
729	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
730	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
731	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
732	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
733	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
734	C₂²	—	2	8	no	—
735	C₂²	—	2	8	no	—
736	C₂²	—	2	8	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
750	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
751	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
752	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
753	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
754	C₂²	#585×C₆₇	1	1	yes	characteristic
755	C₄	—	2	2	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	#546×C₆₇	1	4	yes	—
769	C₄	#547×C₆₇	1	4	yes	—
770	C₂	—	4	8	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
773	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
774	C₂	C₆₇×#3480	1	1	yes	characteristic
775	C₂	C₆₇×#3496	1	1	yes	characteristic
776	C₂	C₆₇×#3508	1	1	yes	characteristic
777	C₂	C₆₇×#3522	1	1	yes	characteristic
778	C₂	C₆₇×#3554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#550×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#559×C₆₇	C₂	semidirect
3. C₆₇×#2701	C₂	semidirect
4. C₆₇×#2582	C₂	semidirect
5. C₆₇×#2544	C₂	semidirect
6. C₆₇×#2538	C₂	semidirect
7. C₆₇×#2447	C₂	semidirect
8. C₆₇×#2445	C₂	semidirect
9. C₆₇×#2432	C₂	semidirect
10. C₆₇×#2427	C₂	semidirect
11. C₆₇×#2425	C₂	semidirect
12. C₆₇×#2422	C₂	semidirect
13. C₆₇×#2349	C₂	semidirect
14. C₆₇×#2339	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
16. C₄×#127×C₆₇	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
270. C₄²×C₆₇	#41	semidirect
380. #59411	C₆₇	direct (N × H)
390. C₂×#559	C₂×C₆₇	semidirect
392. #2701	C₂×C₆₇	semidirect
393. #2582	C₂×C₆₇	semidirect
394. #2544	C₂×C₆₇	semidirect
395. #2538	C₂×C₆₇	semidirect
396. #2447	C₂×C₆₇	semidirect
397. #2445	C₂×C₆₇	semidirect
398. #2432	C₂×C₆₇	semidirect
399. #2427	C₂×C₆₇	semidirect
400. #2425	C₂×C₆₇	semidirect
401. #2422	C₂×C₆₇	semidirect
402. #2349	C₂×C₆₇	semidirect
403. #2339	C₂×C₆₇	semidirect
404. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
405. C₄×#127	C₂×C₆₇	semidirect
406. C₄×#124	C₂×C₆₇	semidirect
407. C₆₇	#59411	direct (N × H)
660. C₄²	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₆₇	2
C₂×#550×C₆₇	2
C₆₇×#2701	2
C₆₇×#2582	2
C₆₇×#2544	2
C₆₇×#2538	2
C₆₇×#2447	2
C₆₇×#2445	2
C₆₇×#2432	2
C₆₇×#2427	2
C₆₇×#2425	2
C₆₇×#2422	2
C₆₇×#2349	2
C₆₇×#2339	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
#59411	67

Subgroups — C67×#59411 #30738662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59411 #30738662